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Damage identification in spent nuclear fuel canisters using dynamic modal analysis and machine learning

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Damage identification in spent nuclear fuel canisters using dynamic modal analysis and machine learning

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Content Copyright 2025 Anna Arcaro
Damage Identification in Spent Nuclear Fuel Canisters using Dynamic
Modal Analysis and Machine Learning
by
Anna Arcaro
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CIVIL ENGINEERING)
May 2025

ii
Dedication
To my parents, Joe and Lisa Arcaro, and my brothers, Anthony and Jimmy:
I could not have done this without your support.
And to my late grandfather, James Sprague, who inspired me to become an engineer.

iii
Acknowledgements
I would first like to extend my sincerest gratitude to my Ph.D. advisor, Dr. Bora Gencturk,
for his unwavering guidance throughout this journey. The advice I received from him will remain
with me throughout my career. Whenever I needed an extra push, motivation, or reassurance, I
could always rely on him to bring out the best in me as a researcher. I am profoundly grateful for
his mentorship.
I would also like to express my thanks to my co-advisor, Dr. Roger Ghanem. Our
discussions shaped the way I approach research questions and challenged me to think more
critically and deeply about my work. Additionally, I am deeply grateful to the members of my
Ph.D. screening and qualifying exam committees: Dr. Assad Oberai, Dr. Erik Johnson, Dr. Sami
Masri, and Dr. Lucio Soibelman. Your insights and feedback undoubtedly enhanced the quality of
my research and helped me grow as a scholar.
This work would not have been possible without the funding provided by the United States
Nuclear Regulatory Commission. I am also grateful for the financial support from other sources,
including the Annenberg Endowed Fellowship from the USC Graduate School and the Viterbi
Graduate Fellowship. I would like to also extend my thanks to the Das Family for their support
through the Das Family Travel Award. Additionally, I appreciate the National Science Foundation
(NSF) for providing travel funding for the PREEMPTIVE ASI in New Zealand.
My Ph.D. experience would not have been complete without the incredible lab mates and
friends I made along the way. I am deeply grateful for the travels and experiences shared with my
friend, Bozhou Zhuang. Our conversations about our work provided significant inspiration along

iv
the way. I also want to express my heartfelt thanks to Mehrdad Aghagholizadeh, whose mentorship
when I first arrived at USC was invaluable. I appreciated our discussions and time together in the
lab, as well as the advice that helped ease my transition to graduate school. Special thanks are also
owed to Mr. Fidel Hurtado and Mr. Juan Tuchan for their assistance in the lab. I would also like
to acknowledge Xiaoying, Xiaoshu, Huanpeng, Ethan, Audie, and Botong for their support. My
Ph.D. experience at USC would not have been complete without my dear friends Nick and Patrick
whose friendship brought so much joy to this chapter of my life.
Finally, I could not have done this without the support of my parents, Joe and Lisa Arcaro.
From the very beginning of my academic journey, you instilled in me the confidence to pursue my
dreams and gave me the support to overcome any challenge. Your belief in me, your
encouragement, and your love have been the foundation of my success, and I am forever grateful.
I also want to acknowledge my brothers, Anthony and Jimmy, who kept me laughing the whole
way.

v
Table of Contents
Dedication....................................................................................................................................... ii
Acknowledgements........................................................................................................................iii
List of Tables ............................................................................................................................... viii
List of Figures................................................................................................................................ ix
Abstract....................................................................................................................................... xvii
Chapter 1: Introduction ................................................................................................................... 1
1.1. Problem Statement.......................................................................................................... 1
1.2. Research Gap .................................................................................................................. 4
1.3. Research Novelty............................................................................................................ 6
1.4. Dissertation Overview .................................................................................................... 7
Chapter 2: Numerical Damage Identification Methodology........................................................... 9
2.1. Introduction..................................................................................................................... 9
2.2. Configuration of the High-fidelity Finite Element Model (FEM)................................ 10
2.3. Nested Craig-Bampton (CB) Method ........................................................................... 11
2.4. Numerical Frequency Response Functions (FRF)........................................................ 15
2.5. Results and Analysis..................................................................................................... 17
2.6. Conclusions................................................................................................................... 21
Chapter 3: Experimental Damage Identification Methodology.................................................... 23
3.1. Introduction................................................................................................................... 23
3.2. Configuration of the Experimental Mock-up Canister ................................................. 23
3.3. Experimental Setup....................................................................................................... 24
3.4. Experimental FRF Calculation ..................................................................................... 25

vi
3.5. Results and Analysis..................................................................................................... 27
3.6. Conclusions................................................................................................................... 35
Chapter 4: Autoregressive Moving Average (ARMA)-based Damage Detection........................ 37
4.1. Introduction................................................................................................................... 37
4.2. ARMA Modeling.......................................................................................................... 38
4.3. ARMA Modeling for Experimental Time Series Data ................................................. 39
4.4. Damage Sensitive Features (DSF)................................................................................ 42
4.5. Results and Analysis..................................................................................................... 44
4.6. Conclusions................................................................................................................... 46
Chapter 5: ML-Aided Damage Identification Method.................................................................. 48
5.1. Introduction................................................................................................................... 48
5.2. Damage Detection Problem.......................................................................................... 48
5.3. Multi-task Damage Detection and Localization Problem............................................. 81
5.4. Conclusions................................................................................................................. 110
Chapter 6: Effect of Experimental Noise on Internal Damage Identification............................. 114
6.1. Introduction................................................................................................................. 114
6.2. Dataset Preparation ..................................................................................................... 115
6.3. Experimental Noise Modeling .................................................................................... 122
6.4. Multi-task Extreme Gradient Boosting (XGBoost).................................................... 132
6.5. Results and Analysis................................................................................................... 136
6.6. Conclusions................................................................................................................. 144
Chapter 7: Conclusions, Limitations, and Recommendations for Future Work......................... 146
7.1. Conclusions................................................................................................................. 146

vii
7.2. Limitations.................................................................................................................. 147
7.3. Recommendations for Future Work............................................................................ 148
References................................................................................................................................... 150

viii
List of Tables
Table 1. Extracted features from truncated FRF differences........................................................ 56
Table 2. Predictions for every measurement in all test cases from RF......................................... 73
Table 3. Predictions for every measurement in all test cases from ANN. .................................... 73
Table 4. Predictions for every measurement in all test cases from GNB. .................................... 74
Table 5. Detailed damage identification predictions from all accelerometers for testing
cases using the k-NN: (a) damage detection, and (b) localization. ......................... 98
Table 6. Detailed damage identification predictions from all accelerometers for all
testing cases using the CNN: (a) damage detection, and (b) localization. ............ 104
Table 7. Summary of nine WGAN models................................................................................. 127
Table 8. Summary of hyperparameters for nine WGAN models. .............................................. 128

ix
List of Figures
Figure 1-1. Components and contents of SNF canister: (a) canister shell and basket, and
(b) FA. ....................................................................................................................... 3
Figure 2-1. Components and dimensions of the FEM developed in LS-DYNA: (a)
canister-basket model, and (b) simplified FA model. ............................................. 11
Figure 2-2. Nested CB substructures for: (a) inner CB, and (b) outer CB. .................................. 15
Figure 2-3. Numerical FRF computed with nested CB: (a) observation node locations
on bottom plate, and (b) numerical FRF. ................................................................ 17
Figure 2-4. Numerical FRF from FLCB and canister with four missing FA: (a)-(g)
observation nodes 1-7, and (h) location of the observation nodes and
removed FA............................................................................................................. 19
Figure 2-5. RMSE of FRF from FEM analysis of FLCB and canister with missing FA:
(a) two missing FA, (b) three missing FA, (c) four missing FA, (d) two
nonadjacent missing FA. ......................................................................................... 21
Figure 3-1. Experimental setup for SNF canister mock-up. ......................................................... 25
Figure 3-2. Experimental FRF calculations from measured time series data: (a)
simultaneously recorded force and acceleration time series signals, (b)
equations used to compute experimental FRF in decibels, and (c) resulting
experimental FRF.................................................................................................... 27

x
Figure 3-3. Experimentally obtained FRF from FLCB and canister with four missing
FA: (a) S1, (b) S2, (c) S3, (d) S4, (e) S5, (f) S6, (g) S7, and (h) locations
of sensors and missing FA. ..................................................................................... 28
Figure 3-4. RMSE of FRF obtained from experiments of FLCB and canister-basket
with: (a) two missing FA, and (b)-(d) four missing FA. ......................................... 30
Figure 3-5. Histograms of FRF difference between FLCB and canister with two missing
FA: (a) S1, (b) S2, (c) S3, (d) S4, (e) S5, (f) S6, (g) S7, and (h) locations
of sensors and missing FA. ..................................................................................... 32
Figure 3-6. Experimentally obtained FRF from FLCB and canister with one missing
FA: (a) S1, (b) S2, (c) S3, (d) S4, (e) S5, (f) S6, (g) S7, (h) S8, (i) S9, (j)
S10, (k) S11, (l) S12, (m) S13, (n) S14, and (o) locations of sensors and
missing FA. ............................................................................................................. 34
Figure 3-7. RMSE of FRF obtained from experiments of FLCB and canister with one
missing FA. ............................................................................................................. 35
Figure 4-1. Example of time series measurement: (a) force, and (b) acceleration
responses from sensors attached to FLCB. ............................................................. 40
Figure 4-2. AIC for different q-values with p-value of 100. ........................................................ 41
Figure 4-3. Portion of measured and estimated acceleration time series measurements.............. 42
Figure 4-4. DSF for FLCB and canister with missing FA: (a) S1, (b) S2, (c) S3, (d) S4,
(e) S5, (f) S6, (g) S7, and (h) sensor locations on canister bottom plate. ............... 43
Figure 4-5. Difference in average DSF......................................................................................... 44

xi
Figure 4-6. Damage localization based on t-test results. .............................................................. 46
Figure 5-1. Examples of FA damage levels simulated with the physical canister mockup: (a) no damage represented by the FLCB, (b) moderate damage
represented by one missing FA, (c) severe damage represented by four
missing FA, and slight damage cases represented by (d) missing spacer
grids, (e) missing casing, and (f) three missing fuel rods. ...................................... 50
Figure 5-2. Dataset preparation workflow. ................................................................................... 51
Figure 5-3. Truncated FRF of four damage classes...................................................................... 52
Figure 5-4. Accelerometer and damage locations for experiments in training dataset................. 54
Figure 5-5. Accelerometer and damage locations for experiments in testing dataset: (a)
no damage, (b) first slight damage, (c) second slight damage, (d) third
slight damage, (e) first moderate damage, (f) second moderate damage,
and (g) severe damage............................................................................................. 55
Figure 5-6. Standardized feature distribution. .............................................................................. 58
Figure 5-7. Correlation matrix of features. ................................................................................... 60
Figure 5-8. Schematic of RF......................................................................................................... 62
Figure 5-9. ANN architecture. ...................................................................................................... 65
Figure 5-10. MCE loss and accuracy history of the ANN............................................................ 66
Figure 5-11. Confusion matrix resulting from evaluating testing dataset with RF. ..................... 70
Figure 5-12. Confusion matrix resulting from evaluating testing dataset with ANN................... 71
Figure 5-13. Confusion matrix resulting from evaluating testing dataset with GNB................... 71

xii
Figure 5-14. Comparison of recall and precision among three ML models for testing
dataset...................................................................................................................... 75
Figure 5-15. Comparison of macro-F1 score and accuracy among three ML models for
testing dataset. ......................................................................................................... 76
Figure 5-16. Confidence analysis of ANN on testing set: (a) no damage, (b) slight
damage, (c) moderate damage, and (d) severe damage........................................... 77
Figure 5-17. Feature importance of trained RF model. ................................................................ 79
Figure 5-18. Damage identification of different accelerometers using RF for each test
case: (a) no damage, (b) first slight damage, (c) second slight damage, (d)
third slight damage, (e) first moderate damage, (f) second moderate
damage, and (g) severe damage. ............................................................................. 81
Figure 5-19. Flowchart of data preparation for multi-task k-NN and CNN classifiers. ............... 83
Figure 5-20. Examples of truncated and filtered FRF differences: (a) no damage, (b)
slight damage, (c) moderate damage, and (d) severe damage................................. 84
Figure 5-21. Accelerometer layout for experiments in training dataset for multi-task
models. .................................................................................................................... 86
Figure 5-22. Sensor layouts for experiments in testing dataset for multi-task models: (a)
no damage, (b) slight damage, (c) first moderate damage, (d) second
moderate damage, and (e) severe damage test cases............................................... 87
Figure 5-23. Accuracy of k-NN for damage and location classification tasks: (a)
different values of k, and (b) different number of PC. ............................................ 90

xiii
Figure 5-24. Schematic of CNN architecture. .............................................................................. 93
Figure 5-25. Training and testing losses versus epoch for CNN: (a) damage
classification task, and (b) location classification task............................................ 96
Figure 5-26. Confusion matrices calculated on testing set for multi-task k-NN model:
(a) damage classification task, and (b) location classification task.
“Outside” refers to sensors predicted to be outside of damage quarter, and
“inside” refers to sensors predicted to be inside damage quarter............................ 97
Figure 5-27. Majority vote damage and location predictions from multi-task k-NN for
each test case: (a) no damage, (b) slight damage, (c) first moderate
damage, (d) second moderate damage, and (e) severe damage............................... 99
Figure 5-28. Visualization of first and second PC: (a) damage severity classes in training
dataset, (b) localization classes in training dataset, (c) damage severity
classes in testing dataset, and (d) localization classes in testing dataset............... 100
Figure 5-29. Classifying one measurement from S6 in severe damage test experiment
with k-NN: (a) damage classification, and (b) location classification. ................. 101
Figure 5-30. Confusion matrices calculated on testing set for multi-task CNN model:
(a) damage classification task, and (b) location classification task.
“Outside” refers to sensors predicted to be outside of damage quarter, and
“inside” refers to sensors predicted to be inside damage quarter.......................... 102
Figure 5-31. Majority vote damage and location predictions from multi-task CNN for
each test case: (a) no damage, (b) slight damage, (c) first moderate
damage, (d) second moderate damage, and (e) severe damage............................. 105

xiv
Figure 5-32. Average probability that damage is located inside the sensor’s quarter: (a)
no damage, (b) slight damage, (c) first moderate damage, (d) second
moderate damage, (e) severe damage test cases, and (f) schematic of
extracted SoftMax probability values. .................................................................. 107
Figure 5-33. Violin plots of 10,000 probabilities predicted by CNN that sensors were
inside the damage quarter: (a) no damage, (b) slight damage, (c) first
moderate damage, (d) second moderate damage, and (e) severe damage
test experiments..................................................................................................... 109
Figure 6-1. Flowchart of FRF difference calculation. ................................................................ 116
Figure 6-2. Sensor layout for experiments in experimental testing dataset: (a) no damage
test case, (b) slight damage test case representing three missing fuel rods,
(c) moderate damage test case, and (d) severe damage test case. ......................... 117
Figure 6-3. Accelerometer and damage locations for scenarios in experimental training
dataset.................................................................................................................... 118
Figure 6-4. Flowchart for FEM dataset pre-processing.............................................................. 120
Figure 6-5. Locations of damage for simulations in FEM training dataset (a) FA location
labels, and (b) damage locations in each simulated damage scenario.
Parentheses indicate FA missing together in a group............................................ 121
Figure 6-6. One standard deviation of noise samples for damage modes in each damage
class: (a) no damage, (b) slight damage, (c) moderate damage, and (d)
severe damage. ...................................................................................................... 123
Figure 6-7. WGAN architecture. ................................................................................................ 125

xv
Figure 6-8. Critic and generator losses for each WGAN model: (a) no damage (W1),
(b) missing casing (W2), (c) missing spacer grids (W3), (d) missing fuel
rods (W4), (e) all slight damage data (W5), (f) moderate damage (W6),
(g) two missing FA (W7), (h) three missing FA (W8), and (i) four missing
FA (W9). ............................................................................................................... 129
Figure 6-9. t-stochastic neighbor embedding plot for real noise and synthetic noise
signals: (a) no damage (W1), (b) missing casing (W2), (c) missing spacer
grids (W3), (d) missing fuel rods (W4), (e) all slight damage data (W5),
(f) one missing FA (W6), (g) two missing FA (W7), (h) three missing FA
(W8), and (i) four missing FA (W9). .................................................................... 131
Figure 6-10. FRF difference with and without added WGAN-generated noise: (a) no
damage, (b) slight damage, (c) moderate damage, and (d) severe damage........... 132
Figure 6-11. XGBoost training process. ..................................................................................... 135
Figure 6-12. Damage detection and localization testing accuracy for XGBoost using
different numbers of trees. .................................................................................... 136
Figure 6-13. Macro-F1 scores of the testing datasets after training XGBoost with three
different training datasets. ..................................................................................... 137
Figure 6-14. Confusion matrices for noisy FEM testing dataset: (a) damage detection
task, and (b) localization task................................................................................ 138
Figure 6-15. Confusion matrices for experimental testing dataset: (a) damage detection
task, and (b) localization task................................................................................ 139

xvi
Figure 6-16. Majority vote damage and location predictions from the XGBoost for each
experimental test case: (a) no damage, (b) slight damage, (c) moderate
damage, (d) severe damage. .................................................................................. 142
Figure 6-17. Damage and location predictions from the XGBoost for each FEM test
case: (a) no damage, (b) missing casing, (c) missing interior spacer grids,
(d) one missing fuel rod, (e) one fractured fuel rod, (f) two fractured fuel
rods, (g) one missing FA, (h) two missing FA, (i) three missing FA, and
(j) four missing FA................................................................................................ 143

xvii
Abstract
Nuclear fuel assemblies (FA) become high-level radioactive waste known as spent nuclear
fuel (SNF) after several years of operation in nuclear reactors. The FA are placed in stainless-steel
canisters during interim storage periods to provide an inter environment. The canisters are
backfilled with helium and either welded or bolted shut. In the United States and other countries
around the world, currently, the FA are stored in these canisters for periods exceeding those
initially intended for interim storage due to a lack of a permanent storage solution. Accidental
damage to these canisters may occur during handling or transportation events. If such events occur,
it is necessary to assess the integrity of FA before long-term storage. Additionally, degradation of
the contents could occur over prolonged storage times. Since the canisters are sealed shut and can
only be opened in special handling facilities, non-destructive evaluation (NDE) is critical for
detecting the FA damage from the canister’s exterior.
This study introduces a NDE method that utilizes frequency response functions (FRF)
collected from the external surface of sealed SNF canisters to detect abnormalities to their contents.
The variation in the FRF as an indication of probable damage is introduced. First, a high-fidelity
finite element model (FEM) of a 2/3-scale experimental mock-up SNF canister is introduced. The
FRF were obtained from the FEM using a previously developed efficient nested Craig-Bampton
(CB) method for dimensionality reduction. Next, experimental modal analysis (EMA) was
conducted on the experimental mock-up canister to obtain a dataset of experimental FRF.
Accelerometers were mounted on the exterior surface of the canister and dynamic excitation was
applied. The location of hypothetical cases of multiple missing FA was accurately determined by
comparing the root mean square error (RMSE) between the FRF of the healthy fully loaded

xviii
canister-basket (FLCB) structure and that of the canister with missing FA as obtained using either
computational or experimental models. Additionally, acceleration time series measurements were
analyzed with autoregressive moving average (ARMA) models to extract damage-sensitive
features (DSF) for localizing missing FA.
To detect damage modes smaller than multiple missing FA, a novel machine learning
(ML)-aided method was developed. Three ML classifiers: random forest (RF), artificial neural
network (ANN), and Gaussian Naïve Bayes (GNB), were trained and tested using features
extracted from the FRF difference between the FLCB and the canister with internal FA damage.
Among these, the RF model achieved the highest performance and predicted the damage levels
regardless of sensor (accelerometer) locations. Subsequently, multi-task classifiers, including a
convolutional neural network (CNN) and k-nearest neighbors (k-NN), were developed to
simultaneously detect the level of FA damage and localize the damage within the canister. The kNN outperformed the CNN, achieving correct damage and location predictions for all sensors in
the testing dataset. In contrast, the CNN incorrectly localized two sensors for one experiment in
the testing dataset.
While the studies mentioned above primarily focused on training ML models on
experimental data, certain damage modes, such as fractured fuel rods, are not easy to simulate
experimentally. To address this, the high-fidelity FEM was employed to simulate the fractured fuel
rods. Wasserstein generative adversarial networks (WGAN) were developed to learn and generate
the experimental noise, which was then added to the numerical FRF to bridge the gap between
experimental and numerical domains. A multi-task extreme gradient boosting (XGBoost) model
analyzed the noisy computational data and experimental data to identify the damage level and
location. The XGBoost achieved macro-F1 scores of 0.998 and 0.900 for damage detection and

xix
localization in the FEM dataset and perfect scores of 1.0 in the experimental dataset. The results
demonstrated that the ML-aided NDE method was successful in identifying various damage modes
within SNF canisters even in the presence of noise levels observed in actual large-scale
experiments.
In summary, this study explored the use of FRF collected from the external surface of
numerical and experimental SNF canisters to characterize internal FA damage. For the first time,
this research employed ML algorithms that analyzed FRF data to identify both the level of FA
damage and its location within sealed SNF canisters. By developing an experimental noise
modeling technique, this framework enabling the detection of multiple FA damage modes while
reducing reliance on labor-intensive experiments. This research has real-life implications for
nuclear waste management as it addresses the limitations of visual inspection and provides a
practical, non-invasive solution for assessing FA integrity during dry storage.

1
Chapter 1: Introduction
1.1. Problem Statement
Nuclear energy is produced by using heat from uranium-based fuel pellets to boil water
coolant into steam, which drives the turbines to generate electricity [1]. The fuel pellets are stacked
in long tubes named fuel rods, and the fuel rods are bundled to form the fuel assemblies (FA). The
FA are used in the nuclear reactors for 4-6 years until they are no longer efficient for power
generation and are considered spent nuclear fuel (SNF). To contain the decay heat from the FA
and shield the radioactivity, the FA are first placed inside spent fuel pools (SFP) [2]. As the SFP
reached their capacities in the 1970s and 1980s, dry cask storage systems (DCSS) became a
popular temporary storage solution in the United States of America (USA). The FA are transferred
from the SFP into the stainless-steel canisters. The canisters are vacuum dried, backfilled with
helium, and then welded or bolted shut before being placed inside a vertical overpack or a
horizontal concrete module to shield the residual radiation and contain the decay heat [3][4]. The
components of the mock-up SNF canister structure used in this study are displayed in Figure 1-1
(a). The canister includes the shell, bottom plate, fuel basket, and the lid. Furthermore, the
components of the FA are shown in Figure 1-1 (b). Each FA includes the fuel rods, spacer grids,
casing, and top and bottom nozzles. In this study, the SNF canister with all FA properly housed
within the basket is referred to as the fully loaded canister-basket (FLCB) structure. By 2018,
nearly 30,000 metric tons of SNF were stored in about 3,000 DCSS across 75 storage sites in the
USA [5][6][7]. It is estimated that nearly 136,000 metric tons of SNF will be housed in around
10,000 DCSS by 2067 [6].

2
Currently, the FA are being stored in these canisters for durations that exceed the initially
intended interim storage periods due to a lack of a permanent storage solution. Consequently, there
is a potential for damage or failure of FA during long-term storage. Over time, the internal pressure
in the fuel rods, coupled with the effects of vacuum drying and temperature fluctuations during the
transition from wet to dry storage, induce stresses leading to cladding degradation mechanisms
such as creep and hydride reorientation [8][9]. Additionally, the FA may be accidentally damaged
during handling or transportation of canisters. Human errors during canister loading may result in
incorrect placement or complete absence of FA within the canisters. Mishandling incidents, such
as dropping or tipping of canisters, can lead to FA breakage or collapse [10][11][12].
Transportation accidents further pose risks to the structural integrity of the FA [13]. The dynamic
impacts, collisions, or vibrations can compromise the integrity of the FA components. Because the
canisters are sealed, direct visual inspection to identify the internal FA damage is challenging.
Therefore, it is critical to develop non-destructive evaluation (NDE) techniques that can assess the
condition of the FA through measurements on the exterior surface of the canisters.
This study aims to develop a method for accurately identifying FA damage modes that can
develop inside sealed dry storage canisters. Given that the canisters are sealed after FA loading,
the proposed approach relies exclusively on structural dynamics measurements taken from the
exterior surface of an experimental canister mock-up and its representative numerical model.
Machine learning (ML) algorithms were employed to automate the identification of internal FA
damage using these measurements. By eliminating the need to unseal the canister, this approach
advances research on the safety of nuclear waste management.

3
Figure 1-1. Components and contents of SNF canister: (a) canister shell and basket, and (b) FA.
Bottom
plate
Lid
1092
3137
2972
1194
Canister
basket
Canister
shell
10 @ 101
ELEVATION
A A
A-A
FLCB
Canister
a)
Canister
89
Detailed FA
101
5 @ 11.4
Simplified FA
19
38
Bottom
nose
Casing
Fuel
rods
Spacer
grids
101
b)

4
1.2. Research Gap
1.2.1. Non-destructive evaluation (NDE) techniques
Researchers have developed different NDE techniques for detecting damage in SNF canisters
[14]. For instance, robotic vehicle systems have been employed to inspect the surfaces of SNF
canisters. In [15], a vehicle with NDE sensors entered the gap between the overpack and the
canister surface to measure the temperature and radiation dose on the canister surface.
Additionally, the use of ultrasonic guided waves (UGW) for surface inspection has been widely
studied. Electromagnetic acoustic transducers (EMAT) were developed by Choi et al. [16] to
generate shear horizontal (SH) waves that detected perpendicular cracks on a laboratory-scale
mock-up canister. Other studies include the detection of water in a Transnuclear TN-32 DCSS
mock-up and crack detection of resistance seam welding (RSW) joints on SNF canisters [17][18].
Furthermore, stress corrosion cracking (SCC) on the surface of SNF canisters has been evaluated
with the use of acoustic emission (AE) techniques [19][20][21] and laser-based approaches
[22][23]. Additionally, the detection of chloride deposits on canisters has been proven successful
with laser-induced breakdown spectroscopy (LIBS) [24]. Eddy current testing (ECT) is a noncontact method that uses electromagnetism to detect surface and near-surface flaws in metallic
structures like SNF canisters [25]. Foster et al. [26] used a robotic arm with ECT sensors and Cscan ultrasonic testing to detect and localize 16 simulated SCC cracks on a stainless-steel canister.
Furthermore, the use of cosmic ray muon tomography has been extensively investigated. These
methods generate images of the internal contents to SNF canisters without direct contact from the
use of muons. Fully loaded and partially loaded canister loading scenarios have been detected with
this method [27][28][29][30][31][32][33][34][35][36]. However, the time to identify the internal
configuration of the canisters with this technique can take several hours to days [14]. Other NDE

5
methods for canister inspections outlined in the literature implement neutron imaging, gamma ray
detection, fiber optical sensors, vibrothermography, through-wall communications, among others
[14]. However, despite these advancements, the majority of NDE approaches prioritize the
detection and characterization of SCC on the canister surface. Methods capable of detecting the
internal configuration, such as cosmic ray muon tomography, often require significant time to
produce results. Consequently, there is a clear research gap in efficiently identifying potential
interior FA damage modes. This highlights the need for NDE methodologies specifically designed
to target internal FA damage.
1.2.2. Machine learning (ML)-aided damage detection techniques
Machine learning algorithms leverage large datasets to identify patterns and generalize them
for test applications. Recently, ML has been applied to detect abnormalities in FA. Papamarkou et
al. [37] trained a residual neural network (ResNet) on images of a SNF canister to identify SCC.
A convolutional neural network (CNN) was developed and trained on images in [38] to classify
scratches on fuel pellets. Furthermore, Dong et al. [39][40] developed neural networks (NN) using
fission product measurements from coolant as input to successfully classifying degrees of FA
damage during reactor operations. Guo et al. [41] employed a deep NN with a faster region-based
convolutional neural network (R-CNN) to identify FA scratches in digital images, achieving high
precision and recall. Ai et al. developed numerous ML models for source localization of AE signals
on steel plates that mimic the canister surface [42][43][44]. From these studies, ML-based methods
have demonstrated potential in detecting surface defects and characterizing FA damage. However,
these methods have not yet been applied to efficiently identify and localize internal FA damage
within sealed SNF canisters. These limitations highlight the need for innovative approaches that
combine NDE and ML methodologies to address this challenge.

6
1.3. Research Novelty
Direct imaging or visual inspection of FA inside sealed canisters is not feasible in field
applications. To the best of the author’s knowledge, no existing studies propose an ML-aided
methodology for identifying FA damage in dry storage canisters. This research introduces a novel
integrated methodology that combines ML and NDE techniques to assess FA integrity using data
collected exclusively from the canister's exterior surface. In this study, an experimental mock-up
SNF canister was fabricated, and a high-fidelity finite element model (FEM) of the mock-up was
developed as its digital twin. For both the numerical and experimental analyses, the frequency
response functions (FRF) were obtained from the external surface of the healthy canister and
canister with internal FA damage. Signal processing algorithms and feature extraction techniques
were employed to identify differences in FRF between the healthy and damaged states.
Subsequently, ML algorithms analyzed the FRF features to classify the FA damage into levels and
localized its position within the canister.
The contributions of this study are the following. (1) The use of a high-fidelity FEM for the
identification of FA damage using FRF obtained from the exterior surface of the model. (2) The
development of an experimental modal analysis (EMA) methodology to obtain FRF from the
bottom plate of a SNF canister mock-up, enabling the characterization of multiple missing FA
within the canister. Additionally, time series analysis was implemented on the collected
measurements as an alternative damage detection approach. (3) The creation of an integrated NDEML methodology capable of detecting and localizing four levels of FA damage inside the
experimental mock-up canister. (4) The development of an experimental noise modeling technique
to bridge the gap between computational and experimental data. This enabled the identification of
minor internal damage (e.g., fractured fuel rods) within sealed SNF canisters.

7
1.4. Dissertation Overview
As shown in Figure 1-1 (a)-(b), a 2/3-scale physical mock-up boiling water reactor (BWR)
canister with 68 mock-up FA was built at the University of Southern California (USC) Structures
and Materials Research Laboratory (SMRL) [45][46][47][48]. Additionally, a high-fidelity FEM
of the mock-up canister and FA was developed in LS-DYNA [49]. To expedite the modal analysis
of the FEM, a novel model reduction technique developed by Ezvan et al. [50][51] was adopted to
enable efficient computation of numerical FRF for detecting multiple missing FA. This procedure
is outlined in Chapter 2.
Next, experimental validation was performed using the physical mock-up canister in Figure
1-1 (a)-(b) and is detailed in Chapter 3. Experimental modal analysis was performed to obtain FRF
for both healthy and damaged canister conditions, confirming that external measurements could
reliably detect two or more missing FA [45]. Time series data were further analyzed using
autoregressive moving average (ARMA) models to extract damage-sensitive features (DSF) for
localizing the missing FA, as discussed in Chapter 4.
To address challenges in detecting smaller FA damage modes, ML techniques were
implemented as outlined in Chapter 5. Three ML classifiers: random forest (RF), artificial neural
network (ANN), and Gaussian Naïve Bayes (GNB) were trained to predict four FA damage levels
using features from the experimental FRF [46]. Multi-task CNN and k-nearest neighbors (k-NN)
models were then developed to (1) identify the FA damage level, and (2) localize the damage to a
specific canister quarter [47].
For minor FA damage difficult to simulate experimentally, the FEM was modified to include
these scenarios. Wasserstein generative adversarial networks (WGAN) were employed to generate

8
experimental noise, which was added to numerical FRF to bridge the experimental and numerical
domains. A multi-task XGBoost model then analyzed the noisy FEM and experimental FRF to
predict FA damage levels and locations as detailed in Chapter 6 [48]. The major conclusions,
limitations, and recommendations for future work are summarized in Chapter 7.

9
Chapter 2: Numerical Damage Identification Methodology
2.1. Introduction
High-fidelity FEM modeling has become increasingly feasible with modern computational
tools. However, these detailed analyses remain resource-intensive, particularly when dynamic
characteristics such as eigenvalues, eigenmodes, and FRF are of interest. To address these
challenges, component mode synthesis (CMS) methods are often employed to reduce
computational demands [52]. The CMS method, introduced by Hurty [53][54] and Gladwell [55]
in the early 1960s, has undergone extensive research with notable contributions from figures like
Craig and Bampton [56], MacNeal [57], and others [58][59][60][61][62][63]. These methods aim
to reduce the degrees of freedom (DOF) in a model, resulting in a significant reduction in
computational costs. The process involves three primary steps: (1) partitioning the structure into
components, (2) defining sets of component modes, and (3) developing a reduced-order model
using these component modes [64].
This modular reduction process enables efficient analysis of complex systems and supports
methods like Craig-Bampton (CB) in structural dynamics, which simplifies models without
sacrificing accuracy [65]. By leveraging fixed-interface modes and boundary constraints, it
produces reduced matrices that are computationally efficient to analyze [56]. This makes this
method ideal for the dynamic analysis of complex systems with applications ranging from tall
buildings [66], frames [67], satellites [68][69], and fairground attractions [70].
In this study, the pseudo-periodicity of the SNF canister and multiple identical FA (i.e., the
FLCB package) makes the calculation of eigenpairs using the CB method particularly
advantageous. Therefore, the eigenpairs of the entire system were determined through a multilevel

10
nested CB method as introduced in the work of Ezvan et al. [50][51]. Subsequently, the FRF of
the FLCB and the canister with multiple missing FA were computed and compared with the root
mean square error (RMSE) as a damage detection metric. The RSME values were then mapped
onto the bottom plate of the canister to identify the locations of the missing FA inside the canister.
These analyses demonstrate the potential of using dynamic vibration measurements to detect
multiple missing FA in SNF canisters.
2.2. Configuration of the High-fidelity Finite Element Model (FEM)
A high-fidelity FEM of the physical canister mock-up was developed in LS-DYNA [49] as
shown in Figure 2-1 (a)-(b) [45]. The canister-basket structure shown in Figure 2-1 (a) was
modeled with 91,034 Belytschko-Tsay shell elements that utilized quadratic shape functions with
two through-thickness Gaussian points of integration. This configuration included 85,219 nodes
and had a total of 501,309 DOF. The bottom nodes of the basket and canister shell were fully
connected to the bottom plate. The bottom plate was modeled with solid elements that implement
single-point integration with linear shape functions. In the simplified FA model shown in Figure
2-1 (b), the casing, spacer grids, and bottom nose were modeled with Belytschko-Tsay shell
elements, and the fuel rods were modeled with tubular Hughes-Liu beam elements. The beam
elements employed 2×2 Gauss quadrature integration. Furthermore, discrete springs with a
translational stiffness of 1.75 × 106 kN·mm and a rotational stiffness of 1.13 × 109 kN·mm/rad
were used to mimic the connections between the spacer grids and the casing. Additionally, discrete
springs with the same translational and rotational stiffnesses mentioned above were used to model
the interactions between the casing and the basket structure. High stiffness values were selected to
reflect the tight fit of the FA that prevents translational and rotational movement within the basket
cells of the experimental mock-up. The rotational DOF were fixed at the contact points between

11
each FA and bottom plate. Furthermore, connections between model parts were considered fully
fixed wherever nodes were shared. This ensured that no relative translation or rotation occurred at
the shared points. One FA model had 7,800 elements, 7,872 nodes, and a total of 47,181 DOF.
For all components of the FLCB system, a linear elastic steel material was defined with a modulus
of elasticity of 207 GPa and a density of 7.83 × 10-6 kg/mm3
. The FLCB model with all 68 FA
inside the basket structure had nearly 3.7 million DOF. The parallel multi-frontal sparse solver
was used for stable solution processing in the implicit solver configuration in LS-DYNA to obtain
the mass and stiffness matrices of the canister-basket structure and FA, which were then processed
in MATLAB to obtain the FRF as discussed in the next section.
Figure 2-1. Components and dimensions of the FEM developed in LS-DYNA: (a) canister-basket model, and (b) simplified FA
model.
2.3. Nested Craig-Bampton (CB) Method
A novel nested CB substructuring method was developed by Ezvan et al. [50][51] that
expedited the modal analysis of the high-fidelity FEM. This method was used in this study to
Canister shell
Basket
Bottom plate
Casing
Fuel
rods
a) b)
Bottom
nose
Springs connecting
casing and spacer
grids
Springs connecting
casing and basket
z
x
z
x
Spacer
grids

12
obtain the FRF at observation nodes on the bottom plate [45]. To find the eigenvalues, λ, and
eigenmodes, φ, of the numerical FLCB, the generalized eigenvalue problem needed to be solved
and is written as
[ ][ ] [ ][ ][ ]   Φ= Φ Λ (1)
where [ ]  is the stiffness matrix, [ ]  is the mass matrix, [ ] Λ is the diagonal matrix of
eigenvalues, and [ ] Φ is a matrix with columns as the corresponding eigenmodes. An approximate
solution of Eq. (1) was sought due to the high computational cost associated with 3.7 million DOF
in the FLCB model. Therefore, the CB method was used to reduce the dimensionality of the model
via substructuring.
The CB method partitions the main substructure into smaller substructures and solves for
the eigenpairs of each substructure individually assuming the boundary nodes between them are
fixed. The partitioned [ ]  and [ ]  are written as
[ ] SS SB
BS BB
  =    
 

  (2)
[ ] SS SB
BS BB
  =    
 

  (3)
where the first subscript S indicates the DOF of the internal substructures and the second subscript
B indicates the boundary DOF. The generalized eigenvalue problem can be rewritten for a given
eigenmode as
SS SB S S SS SB
BS BB B B BS BB
φ φ λ
φ φ
            =         
 
  (4)

13
The physical coordinates of the model were reduced with a set of generalized coordinates, qs, and
physical coordinates, φb. Therefore, any eigenvector can be projected onto this reduced set of
coordinates with the CB transformation matrix expressed as
[ ] 0
S SB
B
t
I
  Φ
Ψ =     (5)
where [ ] SB t is a matrix of static constraint modes written as
[ ] [ ] [ ] 1
SB SS SB t −
= −   (6)
and [ ] ΦS is the eigenvector that satisfies the equation written as
[ ][ ] [ ][ ][ ]   SS S SS S S Φ= Φ Λ (7)
where [ ] SS and [ ] ΛS are both block diagonal. Therefore, for each substructure j, the generalized
eigenvalue equation can be written as
jj j jj j j    Φ = ΦΛ      (8)
where j is the j-th substructure up to the total number of substructures, NS, and Λj and Φ j contain
the first nj eigenvalues and eigenmodes of each substructure, respectively. The CB mass and
stiffness matrices, [ ] M and [ ] K , were then computed as
[ ] SS SB
BS BB
M M
M
M M
  =     (9)
[ ] SS SB
BS BB
K K
K
K K
  =     (10)

14
where the submatrices in [ ] K and [ ] M were defined as
[ ] [ ] M I SS S = (11)
[ ] [ ] [ ] [ ] ( )[ ] T
M t BS =+ Φ   BS SB SS S (12)
[ ] [ ] [ ][ ] [ ][ ] ( ) [ ] [ ][ ] T T
MBB BB BS SB BS SB SB SS SB =+ + +    t tt t (13)
[ ] [ ] KSS S = Λ (14)
[ ] [ ] [ ] 0 K K SB BS = = (15)
[ ] [ ] [ ][ ] [ ] 1
KBB BB BS SS SB
−
= −    (16)
The reduced-order numerical FLCB model is defined by the number of boundary DOF and
eigenmodes up to a cutoff frequency. In this study, a cutoff frequency of 21 kHz was used and it
was selected based on previous studies [50][51]. The canister-basket substructure had 82,827
eigenmodes, and the FA model had 3,298 eigenmodes, totaling 307,091 eigenmodes up to the
cutoff frequency for the 68 FA. With 2,076 boundary DOF, the total DOF in the reduced-order
FLCB was 309,167. This is nearly a 12-fold reduction from the original physical-coordinate
model.
The FEM of the FLCB was partitioned into two levels of substructures: one level for the
FA model, and another level for the canister-basket with the 68 FA as substructures. Therefore, a
nested CB approach was used containing two CB steps. The first step was the inner CB that
computed the eigenpairs for one FA that included the casing, spacer grids, and four fuel rods as
shown in Figure 2-2 (a). Second, the outer CB treated the canister-basket structure as the main
structure and the 68 FA as the substructures as shown in Figure 2-2 (b). The FA were connected

15
to the basket with linear springs at 17 locations at the top, middle, and bottom of the FA, with
another spring at the bottom nose. The springs were used to restrain the FA against rotation within
the basket. This resulted in 692 boundary nodes in the outer CB step, and the outputs were the
eigenpairs of the FLCB. The eigenpairs of each substructure were computed with a shift-inverseLanczos method as detailed in [71][72]. The limited number of boundary nodes and the identical
nature of the FA significantly reduced the computational cost of calculating the eigenpairs of the
FLCB using the nested CB approach [45].
Figure 2-2. Nested CB substructures for: (a) inner CB, and (b) outer CB.
2.4. Numerical Frequency Response Functions (FRF)
To perform the nested CB in MATLAB, the mass and stiffness matrices of the FA and
canister-basket model were obtained from LS-DYNA. To address the fact that actual SNF canisters
are sealed in field applications, the nodes on the exterior surface of the bottom plate were selected
b)
z
x
Casing
Four fuel rods
a)
Bottom spacer grid
Springs connecting
casing and spacer grids
z
x
Three interior spacer grids
17 linear springs
Top spacer grid

16
to obtain FRF. The limited observation nodes, illustrated as gray circles in Figure 2-3 (a), further
reduced the computational costs by decreasing the size of the mass and stiffness matrices. After
completing the outer CB, the numerical FRF were calculated as
[ ] [ ] [ ] [ ][ ] [ ] ( ) [ ] 1 2 ( ) 2 T
UOE O ne E ω ωω I i −
=Φ − + Ξ Ω+Λ Φ (17)
where [ ] ( ) UOE ω is the FRF matrix for the observation nodes, ω is the frequency range of interest,
[ ] ΦO is the modal matrix for the observation nodes, [ ] ne I is the identity matrix with the dimension
as the number of system eigenmodes, ne, [ ] Ξ is the diagonal matrix of modal damping ratios, [ ] Λ
is the diagonal matrix of ne eigenvalues, [ ] Ω is the square root of the [ ] Λ (i.e., the modal
frequencies) in rad/sec, and [ ] ΦE is the modal matrix at the excitation DOF (i.e., at the center
node of the bottom plate) [45]. The accelerance FRF was computed with Eq. (18) and Eq. (19)
written as
[ ] 2 ( ) FRF U ω ω OE = (18)
FRFdB = 20log10 ( ) FRF (19)
where FRFdB is the FRF matrix in dB units.
An example of a numerical FRF for the FLCB and the canister with one FA removed from
the damage location in the red square of Figure 2-3 (a) is shown in Figure 2-3 (b). The black FRF
corresponds to the center node of the damage location from the FLCB, and the gray FRF represents
the same node with one missing FA. It is observed that both FRF are clean and noise-free. There
is a difference in the frequency varying amplitude of the two internal configurations of the canister.

17
Figure 2-3. Numerical FRF computed with nested CB: (a) observation node locations on bottom plate, and (b) numerical FRF.
2.5. Results and Analysis
This section explores the use of FRF from the high-fidelity FEM to detect abnormalities
associated with potential misload scenarios in sealed canister packages. The damage condition was
represented by multiple missing FA. The FRF of the FEM were calculated for the frequency range
of (0-2] kHz. Figure 2-4 (a)-(g) shows the resulting FRF from the FEM analysis using Eq. (17)-
(19). The black FRF is from the FLCB model while the gray FRF is from the canister with four
missing FA. The locations of the missing FA are shown in Figure 2-4 (h). To obtain the FRF, the
excitation was applied in the middle node of the bottom plate along the height of the canister. The
responses were obtained in the same direction at each observation node.
The locations of the selected observation nodes for the FRF shown in Figure 2-4 (a)-(g) are
indicated in Figure 2-4 (h). Seven locations on the bottom plate were selected, with the center node
of each respective FA cell used for demonstration. The FRF for the healthy and damaged canister
conditions for nodes located near the missing FA positions (i.e., S1, S2, S3, and S4) exhibit visually
distinct differences within the frequency range excited in the FEM. In contrast, the differences are
a) b)

18
less noticeable at observation locations with unchanged contents (i.e., S5, S6, and S7). This
suggests that variations in FRF across multiple observation nodes can indicate the internal FA
damage location(s).

19
Figure 2-4. Numerical FRF from FLCB and canister with four missing FA: (a)-(g) observation nodes 1-7, and (h) location of the
observation nodes and removed FA.
a) b)
c) d)
e) f)
g)
h)

20
To locate the missing FA in the canister, a scalar metric to define the variations in the FRF
between canister conditions implemented. The RMSE was chosen and is written as
2
1
() ()
N
FLCB i damaged i
i
FRF FRF
RMSE
N
ω ω =
  −   =
∑ (20)
where FRFFLCB is the FRF of the FLCB, FRFdamaged is the FRF from the canister with missing
FA, ωi are the discrete frequencies, and N is the number of data points in the FRF (i.e., the length
of the frequency band).
Figure 2-5 (a)-(d) presents the RMSE calculation results from the FEM analysis. Each dot
in the color plot corresponds to the location of an observation node, and the missing FA locations
are highlighted in red squares at the top right of each subplot. Figure 2-5 (a)-(d) illustrates various
misload scenarios: (a) two missing FA, (b) three missing FA, (c) four missing FA, and (d) two
nonadjacent missing FA. In each case, the RMSE values at the observation nodes corresponding
to the missing FA are distinctly higher than those at unaffected locations. For instance, in Figure
2-5 (a), the RMSE values at the two missing FA exceed five dB, whereas the unaffected locations
exhibit RMSE values ranging from 0.5 to 1.5 dB. A similar pattern is observed in Figure 2-5 (b)-
(d). Therefore, variations in RMSE at different observation nodes demonstrate its effectiveness as
a metric for identifying two or more missing FA within a sealed SNF canister.

21
Figure 2-5. RMSE of FRF from FEM analysis of FLCB and canister with missing FA: (a) two missing FA, (b) three missing FA,
(c) four missing FA, (d) two nonadjacent missing FA.
2.6. Conclusions
This chapter investigated the damage detection of multiple missing FA in a high-fidelity FEM
of a mock-up SNF canister. A nested CB technique was introduced to efficiently calculate the FRF
of the exterior surface of the FEM. Then, the FRF were obtained for the healthy FLCB and canister
with various scenarios of missing FA. The RMSE metric was used to compare the FRF from the
undamaged and damaged cases and localize the missing FA. The results led to the following
conclusions:
1 2 3 4 5 6 7
RMSE (dB)
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
RMSE (dB)
1 2 3 4 5 6 7
RMSE (dB)
a)
c)
b)
d)
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
RMSE (dB)

22
• The study confirmed the computational efficiency of the nested CB method in leveraging the
pseudo-periodicity of the FLCB structure for effective model reduction and eigenpair
computation.
• The location of multiple missing FA from hypothetical misloading scenarios was accurately
spotted in the FEM with only observation nodes located on the exterior surface of the canister
bottom plate.
• The study concludes that the use of dynamic vibration measurements on the outside shell of a
sealed canister can provide valuable information to detect physical internal abnormalities.

23
Chapter 3: Experimental Damage Identification Methodology
3.1. Introduction
Experimental modal analysis is a NDE technique commonly used in structural health
monitoring (SHM) and damage detection studies to estimate dynamic properties such as natural
frequencies, mode shapes, and damping ratios [73]. This method involves exciting a structure
using an input force, typically using a modal shaker or impact hammer, and measuring the resulting
vibration responses with accelerometers. The collected time-series data are processed to compute
FRF or other dynamic properties of the structure [74]. Studies have demonstrated that variations
in modal parameters, such as frequency shifts or mode shape distortions, can reliably indicate
structural damage [73][75][76].
In this chapter, EMA is employed to validate the numerical damage detection methodology
presented in Chapter 2. Furthermore, this experimental approach aims to demonstrate the
feasibility of using NDE techniques to detect multiple missing FA based solely on exterior
measurements [45]. A modal shaker was used to excite the bottom plate of the canister, and
accelerometers were used to record the resulting acceleration responses. Subsequently, FRF were
obtained on the FLCB and the canister with multiple missing FA. The RMSE between these FRF
was computed and mapped onto the bottom plate of the canister to identify the locations of the
missing FA. These analyses highlight the potential of non-destructive vibration measurements for
detecting and localizing interior FA damage in sealed SNF canisters.
3.2. Configuration of the Experimental Mock-up Canister
A 2/3-scale physical mock-up SNF canister with 68 mock-up FA were previously fabricated
at the SMRL at the USC [45][46][47][48]. The mock-up was based on a BWR canister

24
configuration whose dimensions are shown in Figure 1-1 (a). To lower the cost, all components
were made with ASTM A36 carbon steel [77], as the type of steel does not influence the results of
the experiments conducted in the linear range of the materials. The mock-up had a canister shell
and a honeycomb shaped basket that housed the 68 mock-up FA. The canister shell was 3,137 mm
in height, 1,194 mm in diameter, and had a wall thickness of 12.7 mm. The bottom plate had a
thickness of 44.5 mm. Additionally, the honeycomb-shaped basket was fabricated by welding steel
tubes that had heights of 2,972 mm, wall thicknesses of 4.76 mm, and side lengths of 101 mm.
Five of the mock-up FA had had a detailed configuration while the remaining 63 FA had a
simplified configuration as shown in Figure 1-1 (b). For the detailed FA, 36 solid steel bars with
a length of 2,840 mm and a diameter of 6.45 mm were used to replicate the fuel rods. The
simplified FA had 4 solid steel bars with a length of 2,840 mm and a diameter of 19 mm. In all
FA, the casing was represented by steel square tubes with a length of 2,870 mm and a wall
thickness of 3.05 mm. The spacer grids were represented with solid steel plates placed along the
height of the FA at a spacing of 700 mm. The bottom nose was fabricated by welding half-circle
shaped steel plates and were connected to the lower-most spacer grid.
3.3. Experimental Setup
The setup to perform EMA on the mock-up SNF canister is shown in Figure 3-1. The structure
rested on a support frame. Underneath, at the center of the canister bottom plate was a Sentek
Dynamics MS-100 modal shaker with a maximum frequency of 2 kHz and a maximum force of 1
kN. The shaker excited the canister bottom plate in the vertical z-direction as shown in Figure 3-1.
The force from the shaker was recorded with a PCB Piezotronics 208C04 force sensor with a
measurement range of ±4.45 kN that was attached to the shaker stinger. Multiple PCB 355B04
accelerometers with a measurement range of ±5g and a sensitivity of 1,000 mV/g were attached to

25
the bottom plate to record the structural responses from the applied excitation. A custom data
acquisition system (DAQ) was built using a National Instruments (NI) cDAQ-9188 chassis. The
chassis housed four NI-9234 vibration input modules that were used to record the input force and
output acceleration responses simultaneously. A single NI-9260 voltage output module was used
to generate the excitation. A Dell XPS laptop with a custom LabVIEW [78] software was used to
control the excitation signal and record the acceleration measurements. The excitation signal was
generated using the “Analog Output Generator” application in MATLAB [79] in the form of a
Gaussian white noise in (0-2] kHz range for 60 s. A sampling rate of 5.12 kHz was used. The
excitation signal was sent to the modal shaker with a Sentek Dynamics LA1500 power amplifier.
Figure 3-1. Experimental setup for SNF canister mock-up.
3.4. Experimental FRF Calculation
Frequency response functions are the ratio of an output response to an applied force in the
frequency domain [75][80]. In the experiments, the applied force, x, and resulting acceleration
response, y, were recorded as time series signals simultaneously and were used to compute the
Canister
Support frame
Modal shaker .
.
DAQ
Accelerometers z
x
Canister
DAQ Amplifier
Computer
Accelerometers Force sensor
Support frame
Force sensor
Modal shaker
Bottom Plate

26
FRF. First, Welch’s method [81] was used to compute the auto-spectral density of x, Sxx, the autospectral density of y, Syy, and the cross-spectral density of x and y, Sxy. With Welch’s method, the
signals were divided into overlapping windows. For each window, the Fast Fourier Transform
(FFT) was computed, and Sxx and Syy were obtained by averaging the squared magnitude of the
FFT of the respective signals over all windows. The cross-spectral density, Sxy, was obtained by
multiplying the FFT of x with the complex conjugate of the FFT of y for each window. The results
were then averaged over all windows [75]. The experimental accelerance FRF was computed as
xy
xx
S
H
S = (21)
where H is the complex-valued experimental FRF. The amplitude of the FRF in decibels was
obtained as
H H dB = 20log10 ( ) (22)
An example of the time series signals x and y and the resulting experimental FRF are provided
in Figure 3-2 (a)-(c). The upper plot in Figure 3-2 (a) is an example of a force time series
measurement. The lower plot in Figure 3-2 (a) shows two examples of time series acceleration
measurements. The dark gray line is the signal obtained from the FLCB (i.e., the healthy status of
the canister), and the light gray line is that of the same sensor when one FA was removed from the
FA (i.e., the canister with an internal abnormality). The time series signals were subject to the
computations in Eq. (21) and Eq. (22) as demonstrated with Figure 3-2 (b). The results of Eq. (22)
for the two acceleration responses are shown in Figure 3-2 (c). A Hanning window with a window
length of 0.6 s was applied to reduce the leakage in the FRF. Based on the figure, there were clear
differences between the FRF that represent different internal conditions of the mock-up canister.

27
Therefore, the difference between the healthy and damaged FRF was the damage detection input
of this study.
Figure 3-2. Experimental FRF calculations from measured time series data: (a) simultaneously recorded force and acceleration
time series signals, (b) equations used to compute experimental FRF in decibels, and (c) resulting experimental FRF.
3.5. Results and Analysis
The experimentally obtained FRF are displayed in Figure 3-3 (a)-(g) for the case of four
missing FA. The FRF for the FLCB are shown in black, while the FRF for the canister with four
missing FA are shown in gray. The missing FA were located at S1, S2, S3, and S4 as highlighted
with red squares in Figure 3-3 (h). The 95% confidence intervals, representing variability in the
repeated FRF measurements obtained for each case, are shaded in red for the FLCB and blue for
the canister with missing FA. For S1-S4, corresponding to the missing FA locations, a noticeable
difference in FRF is observed between the FLCB and the canister with missing FA, as shown in
Figure 3-3 (a)-(d). At the unchanged locations (i.e. S5-S7) shown in Figure 3-3 (e)-(g), the FRF
differences are less pronounced and are particularly evident in the [1.0, 1.3] kHz range. This
demonstrates that changes in the internal contents of the canister result in alterations to the dynamic
signature of its external surface.
a)
b)
c)

28
Figure 3-3. Experimentally obtained FRF from FLCB and canister with four missing FA: (a) S1, (b) S2, (c) S3, (d) S4, (e) S5, (f)
S6, (g) S7, and (h) locations of sensors and missing FA.
a) b)
c) d)
e) f)
g)
h)

29
To quantify the difference in FRF between internal canister conditions, the RMSE between
the FRF from the FLCB and from the canister with missing FA was calculated. The RMSE results
for scenarios of missing FA are shown in Figure 3-4 (a)-(d) and were computed using Eq. (20). In
these plots, the circles represent the accelerometer locations, and the sensor labels are displayed in
gray font above the circles. The locations of the missing FA are highlighted with red squares in
each subplot.
As shown in the plots, sensors positioned at the missing FA locations exhibited higher
RMSE values compared to those at unchanged FA locations. For example, in Figure 3-4 (a), S1
and S5, located directly at missing FA positions, had RMSE values of 2.80 dB and 2.75 dB,
respectively. In contrast, an unchanged location (S6) had an RMSE value of 1.23 dB. Similarly, in
the experiment with four missing FA shown in Figure 3-4 (b), sensors S1, S2, S3, and S4 were
positioned at the missing FA locations and had RMSE values of 3.65 dB, 4.89 dB, 3.57 dB, and
4.83 dB, respectively. Sensors at the unchanged locations (i.e., S5, S6, and S7) recorded lower
RMSE values of 1.61 dB, 1.35 dB, and 1.50 dB, respectively. The trend of higher RMSE values
at missing FA locations compared to unchanged locations is consistent across all experiments as
illustrated in Figure 3-4 (a)-(d). These results demonstrate that changes in the internal contents of
the sealed canister are reflected in observable differences in RMSE between the FRF. This
confirms that experimental observations align with the results obtained from computer simulations
in Chapter 2, and the RMSE is a reasonable metric to localize multiple missing FA [45].

30
Figure 3-4. RMSE of FRF obtained from experiments of FLCB and canister-basket with: (a) two missing FA, and (b)-(d) four
missing FA.
As an additional damage metric, distributions of the difference in FRF between the FLCB
and the canister with damage was used [45]. The difference between the FRF from the FLCB and
the FRF from the canister with missing FA was computed at every frequency point in the (0, 2]
kHz frequency range and is written as
a) b)
c) d)
RMSE (dB) RMSE (dB)
RMSE (dB) RMSE (dB)

31
() () FRF FRF FLCB i damaged i δω ω = − (23)
where δ is the FRF difference.
The experiment from the two missing FA damage scenario in Figure 3-4 (a) was used for
this analysis. After using Eq. (23) to compute δ at every frequency, histograms of the values are
provided in Figure 3-5 (a)-(g) for S1-S7, respectively. The locations of the missing FA and the
sensor locations are in Figure 3-5 (h). From visual inspection, the histograms indicate a Gaussian
shape. Therefore, Gaussian distributions were fit to the data for each sensor. The mean value, μ,
was determined from the properties of the fitted normal distributions. These values are in dB units
and are indicated in black font next to the histograms in each subplot.
At the locations of the missing FA (i.e., S1 and S5), the magnitude of μ is noticeably higher
compared to the unchanged locations (i.e., S2, S3, S4, S6, and S7), where μ values remain close to
zero. Specifically, the μ values at the missing FA locations shift from zero, with magnitudes
ranging from 1.54 to 1.58 dB, as shown in Figure 3-5 (a) and Figure 3-5 (e). By visualizing the
distributions of the FRF difference between the FLCB and the canister with missing FA, the
locations of the missing FA can be identified based on the shifts in the mean of the distribution.
This provides a reasonable damage detection metric that compliments the results of the RMSE
method.

32
Figure 3-5. Histograms of FRF difference between FLCB and canister with two missing FA: (a) S1, (b) S2, (c) S3, (d) S4, (e) S5,
(f) S6, (g) S7, and (h) locations of sensors and missing FA.
a) b)
c) d)
e) f)
g)
h)
μ = -1.54 μ = -0.495
μ = -0.657 μ = -0.537
μ = -1.58 μ = -0.045
μ = -0.366

33
Furthermore, experiments were conducted with only one missing FA inside the canister.
were conducted with smaller FA damage modes inside the canister. Figure 3-6 (a)-(n)
demonstrates the results of this damage scenario. A graphic of the bottom plate of the canister with
labeled sensor locations is in Figure 3-6 (o), and the missing FA was located at S5 as outlined in
the red square. The black FRF is from the FLCB and the gray FRF is from the canister with the
missing FA. The difference in the black and gray FRF in Figure 3-6 (a)-(n) are not visually
detectable in comparison to the case of four missing FA in Figure 3-3. Furthermore, this infers
there was minimal variation in RMSE between the FRF at every sensor. This is shown with the
RMSE values plotted on the canister bottom plate in Figure 3-7. Since the RMSE method was
unsuccessful in detecting one missing FA, other damage detection methods needed to be
implemented. Therefore, ML algorithms were developed to detect one missing FA and other FA
damage modes and are discussed further in Chapter 5.

34
Figure 3-6. Experimentally obtained FRF from FLCB and canister with one missing FA: (a) S1, (b) S2, (c) S3, (d) S4, (e) S5, (f)
S6, (g) S7, (h) S8, (i) S9, (j) S10, (k) S11, (l) S12, (m) S13, (n) S14, and (o) locations of sensors and missing FA.
a) b)
d) e)
g) h)
j)
c)
f)
i)
k) l)
m) n)
o)

35
Figure 3-7. RMSE of FRF obtained from experiments of FLCB and canister with one missing FA.
3.6. Conclusions
In this section, the detection of multiple missing FA from the experimental mock-up SNF
canister was investigated. The method included the EMA of the physical mock-up shown in Figure
1-1 (a)-(b). Since the canisters are sealed in real-world applications, the accelerometers were
mounted on the exterior surface of the bottom plate. The center of the bottom plate was excited
with Gaussian white noise excitation using a modal shaker. The resulting FRF were computed for
the FLCB and for the canister with missing FA in various configurations. To identify the locations
of the missing FA, the RMSE between the FRF from the two canister configurations was computed
for each sensor in each experiment. Additionally, an alternative damage detection metric was RMSE (dB)

36
developed by analyzing the distribution of the difference in FRF between canister configurations.
The results led to the following conclusions:
• Experimental results confirmed the FEM analysis findings from Chapter 2. The results
showed that FRF from observation nodes beneath the bottom plate differ when compared
to an undamaged FLCB package in the presence of missing FA.
• The location of two or more missing FA inside the experimental mock-up canister was
accurately identified using RMSE as a metric. This was computed with measurements
collected solely from the exterior surface of the bottom plate.
• Dynamic vibration measurements on the exterior surface of SNF canisters provide critical
information for detecting internal physical abnormalities. This is useful since the canisters
are sealed in field applications.
• The RMSE metric was unsuccessful in detecting the location of only one missing FA from
the canister mock-up.

37
Chapter 4: Autoregressive Moving Average (ARMA)-based Damage Detection
4.1. Introduction
Time series analysis is a statistical framework for examining sequential data points collected
over time for the identification of patterns and temporal dependencies in dynamic systems
[82][83]. In SHM, time series methods have been implemented to analyze vibration responses to
detect and localize damage [84][85][86][87]. Models such as autoregressive (AR), ARMA, and
related variants are commonly used to capture the dynamic behavior of structures by leveraging
temporal correlations in acceleration or displacement data [82]. These models are valuable for
predicting system behavior in an undamaged state and detecting anomalies through deviations in
model parameters or residual errors [83]. By identifying these deviations, time series models
provide DSF that can detect structural abnormalities [84].
This chapter explores the application of ARMA modeling for identifying missing FA within
the SNF canister mock-up used in this study. The experiment used for this analysis is the case of
four missing FA as illustrated in Figure 3-4 (b). Like the previous chapter, the healthy state of the
canister is represented by the FLCB, while the damaged state is represented by the canister with
missing FA. Autoregressive moving average models were fitted to acceleration data collected from
both the FLCB and the canister with missing FA, and the resulting AR coefficients at each sensor
location were used to compute DSF. After calculating the DSF for multiple acceleration time series
recordings, the average DSF values were obtained for both the FLCB and the canister with missing
FA. Differences in the average DSF at each accelerometer location were used to identify the
missing FA locations. Additionally, a t-test was conducted on the DSF data to assess the statistical

38
significance of these differences at each sensor location. The results of the t-test provided
probabilistic confirmation of the missing FA locations.
4.2. ARMA Modeling
Acceleration and force time series data collected during the experiments described in Chapter
3 are inherently high-dimensional. Autoregressive moving average modeling provides a method
to extract DSF by representing the time series using its past values and model coefficients. The
ARMA model includes an AR component, based on past time series values, and a moving average
(MA) component, which accounts for residual errors. The general form of an ARMA model is
expressed as
1 1
() ( ) ( ) ()
p q
ij k ij k ij ij
k k
xt xt k t k t α βε ε = =
= −+ −+ ∑ ∑ (24)
where ( ) ij x t is the acceleration signal for the i-th accelerometer and the j-th measurement, αk are
the AR coefficients, βk are the MA coefficients, 𝑝𝑝 is the model order of the AR process, 𝑞𝑞 is the
model order of the MA process, and ( ) ij ε t are the residuals [84].
Nair et al. [84] demonstrated the use of ARMA modeling for SHM by extracting DSF from
the AR coefficients of acceleration time series data. The method was applied to the American
Society of Civil Engineers (ASCE) benchmark structure under healthy and damaged conditions,
using the first three AR coefficients to calculate a DSF. The DSF was defined as
1
222
1 23
DSF α
ααα = + +
(25)

39
where α1 , α2 , and α3 are the first three AR coefficients estimated by the model. The results
showed that differences in average DSF between healthy and damaged states could reliably
identify damage locations. Therefore, the same DSF metric was used in this study for the
identification of multiple missing FA in the experimental mock-up canister.
4.3. ARMA Modeling for Experimental Time Series Data
The acceleration and force time series data collected during the experiment with four missing
FA, as shown in Figure 3-4 (b), serve as the basis for the ARMA modeling process. Rather than
analyzing the entire time series signals, which contain approximately 220,000 data points per
measurement, a smaller portion of the full 60-second time series recording was chosen for analysis.
Figure 4-1 (a) displays the applied force over time in the range of [6, 10] seconds, while Figure
4-1 (b) illustrates the corresponding acceleration responses recorded by all seven sensors for the
FLCB configuration. This time interval was randomly selected from the full time series recording.
The segmentation approach ensured that the ARMA models captured the dynamic characteristics
of the system during active excitation while reducing the computational burden.

40
Figure 4-1. Example of time series measurement: (a) force, and (b) acceleration responses from sensors attached to FLCB.
To determine the optimal model orders, p and q, for fitting the ARMA models, the Akaike
Information Criterion (AIC) was employed. The AIC provides a measure of model quality by
balancing the goodness of fit via residual sum of squares (RSS) against model complexity. It is
defined as:
ln( ) 2 d AIC RSS
t
  = −    
(26)
where RSS is the residual sum of squares of the model fit, d is the total number of model parameters
(p + q), and n is the number of data points in the time series segment. The model order with the
minimum AIC value is considered the best fit for the time series data as it minimized information
loss while avoiding overfitting.
6 6.5 7 7.5 8 8.5 9 9.5 10
Time (s)
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Acceleration (g)
Sensor 1 Sensor 2 Sensor 3 Sensor 4 Sensor 5 Sensor 6 Sensor 7
6 6.5 7 7.5 8 8.5 9 9.5 10
-15
-10
-5
0
5
10
15
Force (lb)
a)
b)

41
The acceleration response of S1, shown in Figure 4-1 (b), was used as an example for
determining the ARMA model orders. A range of values for 𝑝𝑝 and 𝑞𝑞 was tested, and the AIC was
used to identify the optimal combination. The model order, 𝑝𝑝, of 100 minimized the AIC across
all tested values, and the corresponding optimal value of 𝑞𝑞 was found to be 30, as shown in Figure
4-2. These selected model orders were then used for fitting ARMA models to the time series data.
Figure 4-2. AIC for different q-values with p-value of 100.
Using the chosen model orders, ARMA models were fit to the 30 segments of acceleration
time series data for both the FLCB case and the case with missing FA at all seven sensor locations.
This resulted in a total of 420 ARMA models. Figure 4-3 illustrates an example of an ARMA
model prediction for one of the measured acceleration time series segments from S1. The figure
demonstrates that the chosen model orders adequately captured the dynamic response of the system
as the residuals were low.

42
Figure 4-3. Portion of measured and estimated acceleration time series measurements.
4.4. Damage Sensitive Features (DSF)
For each time series segment, the ARMA model generated 100 AR coefficients, of which the
first three were extracted for use in the computation of DSF using Eq. (25). Since each time series
measurement was divided into 30 segments, this resulted in 30 DSF values for each sensor. These
values were averaged to obtain the mean DSF for each sensor location in the FLCB case. The same
procedure was applied to the data set for the case with missing FA.
Figure 4-4 (a)-(g) shows the DSF values for each time series segment at all sensor locations.
The black dots represent the DSF for the FLCB case, while red dots represent the DSF for the
missing FA case. The dashed lines indicate the average DSF for each case to highlight the
differences between the two configurations. Figure 4-4 (h) displays the sensor layout on the bottom
plate of the canister for this experiment. Significant differences in average DSF are observed at
S1-S4, suggesting changes in the canister contents at these locations. Conversely, minimal
differences are seen at S5-S7, indicating no changes in canister contents. This aligns with the
results of the RMSE method in Figure 3-4 (b).

43
Figure 4-4. DSF for FLCB and canister with missing FA: (a) S1, (b) S2, (c) S3, (d) S4, (e) S5, (f) S6, (g) S7, and (h) sensor
locations on canister bottom plate.
a) b)
c) d)
e) f)
g)
h)

44
4.5. Results and Analysis
To localize the missing FA within the canister, the differences in average DSF between the
FLCB case and the missing FA case were analyzed for each sensor location. The difference in
average DSF for all sensors is shown in Figure 4-5. In the figure, the circles represent the
accelerometer locations, the sensor labels are in gray font above the dots, and the red squares
indicate the location of the missing FA. The DSF difference values are in black font below each
circle. The sensors corresponding to the locations of the missing FA (i.e., S1, S2, S3 and S4),
exhibited significantly larger differences compared to the unchanged FA locations (i.e., S5, S6,
and S7). However, the difference at S1, a missing FA location, was only slightly greater than that
at S6, a location with no change. This suggested that a statistical approach was needed to confirm
whether the observed differences at each sensor location were significant.
Figure 4-5. Difference in average DSF.

45
To evaluate the statistical significance of the differences in DSF between the FLCB case and
the missing FA case, a two-sample t-test was conducted for each sensor location. The null, H0 ,
and alternative, H1 , hypotheses are defined as
0 ,
1 ,
:
:
i i
i i
DSF FLCB DSF,damaged
DSF FLCB DSF,damaged
H
H
µ µ
µ µ
=
≠
(27)
where , DSF FLCBi µ is the mean DSF in the FLCB case, and DSF,damaged i µ represents the mean DSF
for the missing FA case at sensor location i. Statistical t-tests were performed for all sensor
locations using the DSF computed for both cases. A significance level, α, of 0.05 was chosen,
meaning that differences were considered statistically significant if the p-value was below 0.05.
This threshold represents a 5% probability of incorrectly rejecting the null hypothesis (i.e., type I
error).
The results of the t-test for all sensor locations are shown in Figure 4-6. The sensor labels
are in gray font at the top left corner of the FA cell, and the p-values are in black font on the FA
cell. For S1-S4, which correspond to the locations of the missing FA, all p-values are below the
significance level of 0.05. This leads to the rejection of the null hypothesis, indicating statistically
significant differences in DSF at these locations. Conversely, for S5- S7, the p-values exceed 0.05,
resulting in the acceptance of the null hypothesis. This indicates that no statistically significant
differences exist in the DSF at these locations and supports the conclusion that there were no
missing FA at these sensor locations. These findings align closely with the RMSE results
illustrated with Figure 3-4 (b). Furthermore, the results confirm the ability of the DSF-based
method to identify missing FA with a high degree of confidence.

46
Figure 4-6. Damage localization based on t-test results.
4.6. Conclusions
In this chapter, a damage detection methodology for the canister mock-up based on ARMA
modeling of measured acceleration time series data was developed. The methodology followed the
framework outlined by Nair et al. [84]. In this study, the differences in average DSF at each sensor
location between the FLCB case and the missing FA case were used to infer a damage decision.
To validate these findings, a statistical analysis was performed using a t-test. This confirmed the
significance of the DSF differences at sensor locations corresponding to missing FA. The results
led to the following conclusions:

47
• The ARMA-based modeling approach effectively modeled the collected acceleration time
series data and identified DSF that captured changes in the canister's dynamic behavior
between damage states.
• The location of missing FA was successfully identified using differences in average DSF,
even for cases where the observed differences were small, such as at S1.
• The t-test results demonstrated that statistically significant differences in DSF reliably
confirmed the presence of missing FA, despite similarities in average DSF values at some
sensor locations (e.g., S1 and S6). The t-test results also emphasize the robustness of this
method even with experimental noise and other uncertainties present.
• The results serve as a secondary confirmation of the RMSE damage detection metric
presented in Chapter 3.

48
Chapter 5: ML-Aided Damage Identification Method
5.1. Introduction
Detecting and localizing smaller damage modes, such as one missing FA, posed significant
challenges using traditional experimental methods, as described in Chapter 3. To overcome these
limitations, ML models were introduced to analyze the FRF datasets for identification of patterns
indicative of internal FA damage. Machine learning algorithms are particularly well-suited for this
task because they can learn from data during training and generalize their findings to test cases
[46]. In this study, features derived from the subtraction between the FRF of the healthy FLCB
system and the damaged canister were used to represent four internal FA damage levels. The
damage severity levels were defined based on the configuration of the simulated damage modes
within the experimental mock-up.
To classify the FRF differences into damage levels, three ML algorithms: ANN, RF, and GNB,
were developed [46]. However, these models were limited to damage detection and could not
localize the damage within the canister. To address this gap, a multi-task k-NN and CNN were
used to simultaneously detect and localize internal FA damage. For localization, the canister was
divided into four quarters, and the damage was pinpointed to one of them [47]. This chapter first
outlines the models used solely for damage detection, followed by the development of multi-task
classifiers used for damage detection and localization.
5.2. Damage Detection Problem
For the damage detection task, the three ML algorithms used in this study (i.e., ANN, RF, and
GNB) were implemented [46]. The ANN is a powerful function approximator that is trained using
mini-batch stochastic gradient descent to optimize their parameters and minimize classification

49
error. The RF algorithm is an ensemble learning method that aggregates predictions from multiple
decision trees. Each tree is trained to partition input features by minimizing entropy or Gini
impurity. The GNB model is a probabilistic algorithm that applies Bayes’ theorem with the
assumption of feature independence to model the likelihood of features using a Gaussian
distribution. The hyperparameters of each model were fine-tuned to achieve optimal balance of
performance between the training and testing datasets. Once trained, the testing dataset was used
as input to obtain damage class predictions.
5.2.1. Experimental internal damage simulation and dataset preparation
Four levels of damage were feasible to simulate physically with the mock-up canister [46][47].
The damage levels included: no damage, slight damage, moderate damage, and severe damage.
Different components of the FA within the canister were altered or removed completely to simulate
these damage levels as shown in Figure 5-1 (a)-(f). The no damage case was represented by the
FLCB system. The slight damage case had one simplified FA with either a missing casing, missing
interior spacer grids, or three missing fuel rods. Moderate damage was represented by one missing
FA, and severe damage was defined as two or more missing FA. The location of the simulated
damage was arbitrarily selected for each experiment.

50
Figure 5-1. Examples of FA damage levels simulated with the physical canister mock-up: (a) no damage represented by the
FLCB, (b) moderate damage represented by one missing FA, (c) severe damage represented by four missing FA, and slight
damage cases represented by (d) missing spacer grids, (e) missing casing, and (f) three missing fuel rods.
The experimental FRF were pre-processed with the procedure outlined in Figure 5-2. First,
FRF measurements were collected from the FLCB and the canister with simulated damage. The
FRF had dimension, D, of 1,126. Then, to improve model performance, the FRF were subtracted
and bandlimited to [0.5, 1.5] kHz, which reduced the dimension to 439. This frequency range was
selected as a suitable hyperparameter for the study as it demonstrated improved model accuracy
compared to cases where smaller or larger frequency ranges were included. Furthermore, this
reduction resulted in a frequency increment of 2.28 × 10-3
kHz per data point. In this study, a
sample is defined as a row vector containing the dB values of the FRF difference across the
bandlimited frequency range. Each sample corresponds to the subtraction of an FRF measurement
FLCB
a)
One Missing FA
b)
Four Missing FAs
c)
Missing Spacer Grids Missing Casing Missing Fuel Rods d) e) f)

51
from the FLCB and a corresponding measurement from the canister with FA damage recorded at
the same sensor location.
Figure 5-2. Dataset preparation workflow.
FRF of FLCB
(D = 1,126)
FRF of
Damaged Canister
(D = 1,126)
FRF Difference
(D = 1,126)
FRF Truncation
(D = 439)
Subtraction
Feature Extraction
(D = 439)
Standardization
(D = 11)
Data Preprocessing
RF
Damage Prediction
Classifier Training and Testing
ANN GNB

52
The truncated FRF differences are visualized in Figure 5-3. Each line in the figure illustrates
an example of an FRF difference sample from each damage class. From the figure, it was observed
that higher damage levels corresponded to larger differences between the FRF of the FLCB system
and the damaged canister. This is shown with higher oscillations in the FRF difference samples
with an increase in damage severity. However, some samples exhibited overlapping characteristics
between damage levels, making it difficult to distinguish between the four classes through direct
visual inspection alone. This necessitated the use of ML algorithms as they can detect features in
datasets that are not directly observable with visual inspection or traditional statistics.
Figure 5-3. Truncated FRF of four damage classes.

53
The FRF difference dataset contained 2,098 differential FRF samples. The training set included
samples across four damage classes: 410 samples for no damage, 410 for slight damage, 328 for
moderate damage, and 350 for severe damage. Similarly, the testing set contained 130 samples for
no damage, 270 for slight damage, 165 for moderate damage, and 105 for severe damage. Figure
5-4 and Figure 5-5 (a)-(g) illustrate the sensor placements and damage configurations used for
constructing the training and testing datasets, respectively. In Figure 5-5 (a)-(g), the sensor
numbers are in black font, and the damage location(s) are in the red square(s). Specifically, the
first, second, and third slight damage test cases corresponded to a missing casing, three missing
fuel rods, and missing spacer grids, respectively. The first and second moderate damage test cases
each had one missing FA at different locations. The severe damage test case had four missing FA.

54
Figure 5-4. Accelerometer and damage locations for experiments in training dataset.
Measurements = 10 Measurements = 10 Measurements = 7
No Damage
Measurements = 3 Measurements = 10 Measurements = 12 Measurements = 3
Moderate Damage
Damage Location
Measurements = 15 Measurements = 20 Measurements = 15
Severe Damage
Measurements = 10
(Casing)
Measurements = 10
(Spacer grids)
Slight Damage
Measurements = 10
(Three fuel rods)
Accelerometer

55
Figure 5-5. Accelerometer and damage locations for experiments in testing dataset: (a) no damage, (b) first slight damage, (c)
second slight damage, (d) third slight damage, (e) first moderate damage, (f) second moderate damage, and (g) severe damage.
The next pre-processing step included the manual extraction of 11 features from the truncated
FRF differences. The features with descriptions are listed in Table 1. These features included the
mean, standard deviation, L2-norm square, peak-to-peak amplitude, maximum and minimum
amplitudes, peak frequency, median, means of the first and second derivatives, and zero crossing
count. This feature extraction approach was adapted from techniques commonly used in timea) b) c)
d) e) f)
g)
= Actual Damage Location

56
series analysis [44]. By selecting these features, the feature dimension was reduced from 439 to
11. This ensured computational efficiency while preserving the information necessary to
distinguish between the different damage levels.
Table 1. Extracted features from truncated FRF differences.
Number Feature Description
1 Mean (dB) Mean of the FRF difference
2 Standard deviation (dB) Standard deviation of the FRF difference
3 L2-norm square (dB2) Square of the L2-norm of the FRF difference
4 Peak-to-peak amplitude (dB) The peak-to-peak amplitude of the FRF difference
5 Maximum amplitude (dB) The maximum amplitude of the FRF difference
6 Minimum amplitude (dB) The minimum amplitude of the FRF difference
7 Peak frequency (Hz) The frequency at which the maximum amplitude occurs
8 Median (dB) Median of the FRF difference
9 Mean of first derivative (dB/Hz) The mean of the first derivative of the FRF difference
10 Mean of second derivative (dB/Hz2) The mean of the second derivative of the FRF difference
11 Zero crossing The total count of the zero crossings of the FRF difference
In the next step, the extracted features were standardized to ensure they were on the same
scale. The standardization process was defined as
nd d
nd
d
x
z µ
σ
− = (28)
where nd x and nd z are the d-th feature value of the n-th sample before and after standardization,
respectively, and µd and σ d are the mean and standard deviation of the d-th feature vector in
the training dataset. These were computed as
1
0
1 Ntrain
d nd
train n
x
N µ
−
=
= ∑ (29)

57
( )
1
2
0
1 Ntrain
d nd d
train n
x
N σ µ
−
=
= ∑ − (30)
where Ntrain is the number of datapoints in the training set. This was also done to the testing set
using the parameters (i.e., µd and σ d ) derived from the training set to ensure consistency. After
standardization, each feature vector had a mean of zero and a standard deviation of one. For
classification, the true class labels were assigned to each sample with integers: 0 for no damage, 1
for slight damage, 2 for moderate damage, and 3 for severe damage. The standardized training and
testing datasets were then input into the ANN, RF, and GNB models for to obtain damage class
predictions for each input sample.
An exploratory data analysis (EDA) was performed to examine the distributions and
correlations of the extracted features. Violin plots were used to illustrate the feature distribution
among the four damage classes and are shown in Figure 5-6. In these plots, the dots indicate the
medians, while the top and bottom edges of the boxes represent the third and first quartiles,
respectively. The symmetric shape of the violins illustrates the density of the feature distributions.
Among the damage class, features including mean, standard deviation, L2-norm square, peakto-peak amplitude, maximum amplitude, and minimum amplitude were visually distinguishable
with the violin plots. Conversely, the mean of the first derivative and the mean of the second
derivative displayed similar medians and quartile ranges across all classes which indicated limited
variation. It was observed that as the damage level increased, the mean, standard deviation, L2-
norm square, peak-to-peak amplitude, maximum amplitude, and median generally increased, while
the minimum amplitude and zero-crossing features tended to decrease. Furthermore, the mean and
standard deviation showed clear separation between the no damage and severe damage classes. In

58
contrast, significant overlap was observed in the distributions for slight and moderate damage
levels, particularly for the peak frequency and mean of the derivatives, suggesting these features
may have limited utility in differentiating adjacent damage classes.
Figure 5-6. Standardized feature distribution.
The correlation matrix for the 11 extracted features is presented in Figure 5-7. This matrix
provides the correlation coefficients between different feature pairs with values ranging from -1.0

59
to 1.0. A positive value indicates a direct correlation, while a negative value denotes an inverse
relationship. The correlation matrix highlights significant positive relationships among features
including the mean, standard deviation, L2-norm square, peak-to-peak amplitude, and maximum
amplitude. This is consistent with the expectation that larger differences in the FRF between the
FLCB and the damaged canister amplify the differences in these specific features. In contrast, the
minimum amplitude exhibits a strong negative correlation with the peak-to-peak amplitude,
aligning with the idea that larger differences reduce the minimum amplitude of the FRF difference.
A notable positive correlation between the mean and median suggests a degree of uniformity
within the dataset. Conversely, the mean of the first derivative shows a negative correlation with
the mean, median, standard deviation, and other related features. Lastly, the zero-crossing feature
displays a mild negative correlation with several features, which suggests that higher frequencies
of zero crossings are associated with lower values for the mean, standard deviation, and L2-norm.

60
Figure 5-7. Correlation matrix of features.
5.2.2. ML algorithms
5.2.2.1. Random Forest (RF) classifier
A RF classifier was employed to classify a dataset of differential FRF into the damage severity
classes [46]. The RF classifier is a powerful and versatile ML algorithm that excels in both
classification and regression tasks [88]. It is particularly well-suited for handling high-

61
dimensional, noisy, and imbalanced datasets. By combining the predictions of multiple decision
trees, RF reduces the risk of overfitting and enhances generalization [88]. This makes it a popular
choice in SHM and damage detection studies [89][90][91][92]. This ensemble-based approach
leverages the idea that aggregating multiple weaker models can produce a stronger overall
prediction.
The RF classifier used in this study is illustrated in Figure 5-8. To train the RF, bootstrapping
is used, where the training data is sampled with replacement to create subsets for each decision
tree. Each tree in the forest is trained independently on one of these subsets. At each decision node
within a tree, the RF considers a random selection of features to determine the best split point. This
feature randomness ensures that individual trees focus on different aspects of the data to promote
diversity within the ensemble and to reduce correlations between trees.
During training, the trees are constructed by recursively splitting the data based on feature
thresholds that minimize the Gini impurity [93], expressed as
( )
1
2
0
1
C
c
c
Gini p
−
=
= −∑ (31)
where C is the number of classes, and pc is the proportion of samples in class c at a particular node.
The tree-building process continues until each tree reaches a maximum depth of five, or a leaf
node contains at least one sample. In this study, the RF model had nine decision trees. After
training, the RF combines predictions by taking the majority vote from all individual trees to
generate the final damage prediction.

62
Figure 5-8. Schematic of RF.
5.2.2.2. Artificial Neural Network (ANN)
Artificial neural networks are a class of ML algorithms inspired by the structure and the
information processing operations of the human brain. They consist of layers of interconnected
nodes (i.e., neurons) that transform inputs into outputs through weighted linear combinations
followed by non-linear activation functions [94]. These networks typically include an input layer
to receive data, hidden layers to extract hierarchical features, and an output layer to generate output
predictions. By iteratively adjusting the connection weights using optimization techniques, ANN
learn to model complex relationships in the input data. Artificial neural networks have found
widespread application in fields such as: pattern recognition [95], classification tasks [96], image
analysis [97], natural language processing [98], anomaly detection [99], and data mining [100].
Bootstrapping
Majority Vote
Final Damage
Prediction
…
Prediction Prediction Prediction Prediction
Tree 1 Tree 2 Tree 3 Tree 9
Training Data

63
In this study, an ANN with a single hidden layer was utilized to classify the differential FRF
into damage levels [46]. The designed architecture of the ANN is illustrated in Figure 5-9. The
network consisted of three layers: an input layer, a hidden layer, and an output layer. The
architecture was determined based on a commonly used heuristic that suggests the number of
training samples should be approximately 3 to 10 times the number of trainable parameters. In this
study, there were 1,498 training samples, and the network contained 132 trainable parameters. The
input layer contained 11 neurons, and each neuron received one of the 11 standardized features of
each input sample. The transformation from the input layer to the hidden layer for an input sample
can be expressed as
( ) (1) (1) (0) (1) z Wz b = ReLU + (32)
where (0) z is the input feature vector, (0) 11 1 z × ∈ , and (1) W and (1) b are the weight matrix and the
bias vector between the input and the hidden layer, respectively. There were eight neurons in the
hidden layer size, therefore (1) 8 11 W × ∈ and (1) 8 1 b × ∈ . The rectified linear unit (ReLU) activation
function was applied in the hidden layer. This activation function was chosen as it is effective in
introducing non-linearity while being computationally efficient and mitigating the vanishing
gradient problem. Next, the mapping between the hidden layer and output layer is defined as
 (2) (1) (2) yWz b = + (33)
where (2) 4 8 W × ∈ , (2) 4 1 b × ∈ , and  4 1
y × ∈ is the direct output from the ANN. The multi-class
cross-entropy (MCE) loss defined in PyTorch [101] was employed in this study. The MCE loss
has two steps. First, the raw output scores, 
y , are converted to a probability vector, p , with the
SoftMax activation function. The SoftMax activation operation is defined as

64
 
1
2
3
4
1 SoftMax( ) j
y
y
y y
j y
e
e
p y
e e
e
 
 
  = =  
 
 
∑ (34)
where y0, y1, y2 and y3 are individual entries in the raw output vector 
y , representing the raw scores
(i.e., logits) assigned by the ANN to each of the four classes. Next, the MCE loss is computed
between the probability vector p and the one-hot encoded true label p. One-hot encoding
represents categorical labels as binary vectors, where the vector for each class contains a single
integer 1 indicating the true class and integer 0 elsewhere. Since the true label vector p is one-hot
encoded, the MCE loss can be written as
 ( )  , (1)log( ) MCE p p p = − true (35)
where true p is the predicted probability of the true class from the ANN.
The training process of the ANN involves optimizing its parameters to minimize the
discrepancy between predicted outputs and true labels. Using backpropagation, the network
calculates the gradient of the loss function with respect to each parameter and updates them via
the mini-batch gradient descent algorithm [94][102]. The ANN used in this study was designed
with only 132 trainable parameters, making it computationally efficient while retaining sufficient
complexity for the classification problem.
A mini-batch size of 32 was chosen in this study to ensure computational efficiency while
maintaining a representative sample for gradient estimation. The Adam optimizer [103], a widely
used adaptive learning algorithm, was employed for parameter updates. Adam combines

65
momentum, which smooths gradients, with adaptive learning rates that dynamically adjust step
sizes for each parameter. For this study, the learning rate was set to 1 × 10-4, and a weight decay
regularization term of 1 × 10-3 was applied to penalize large parameter value and reduce overfitting.
All other Adam hyperparameters were set to their default values [103]. After training, the predicted
damage class was determined by selecting the class with the highest probability in p using the
Argmax operation.
Figure 5-9. ANN architecture.
The performance of the ANN during training was evaluated by tracking the MCE loss and
accuracy on both the training and testing datasets after each epoch. Figure 5-10 shows the
progression of the MCE loss and accuracy over 400 training epochs. Throughout the training
Damage Class
Prediction
z(0)
Inpu
t
Feature 1
Feature 4
Feature 5
Feature 6
Feature 7
Feature 8
Feature 9
Feature 10
Feature 11
Feature 2
Feature 3
z(1)
Argmax
SoftMax

66
process, the MCE loss decreased while the accuracy consistently improved. Both the training and
testing accuracy displayed improvement until 150 epochs and converged by 400 epochs. The
consistency between the training and testing performance suggested that the model was
sufficiently trained under the chosen hyperparameters.
Figure 5-10. MCE loss and accuracy history of the ANN.
5.2.2.3. Gaussian Naïve Bayes (GNB)
The GNB classifier is a simple probabilistic ML model that is widely used in various
classification tasks, including damage detection applications [104][105]. The algorithm is based
on Bayes' theorem, which calculates the posterior probability of a class given the observed data.
The term "naïve" reflects the assumption that all features are conditionally independent of each
other given the class label.

67
The GNB algorithm is particularly well-suited for datasets where features are continuous
variables as it assumes that the likelihood of each feature follows a Gaussian distribution [106].
This assumption allows the algorithm to efficiently model the probability of a given feature vector
belonging to a specific class. Due to its simplicity, GNB has found applications in multiple
research areas including text classification [107] and medical diagnostics [108][109].
In this study, the GNB algorithm calculates the conditional probability of the class label y
being equal to a specific class c (e.g., 0, 1, 2, or 3) given a feature vector x. Based on Bayes’
theorem, this is expressed as:
( ) ( ) ( )
( )
| | Pxy cPy c Py cx P x
= = = = (36)
where Px y c (| ) = is the likelihood function, Py c ( ) = is the prior probability of class c,
Py cx ( ) = | is the posterior probability, and P x( ) is the probability of the feature vector, which
is the same across all classes. Since P x( ) does not affect the relative class probabilities, it can be
ignored when determining the most likely class. The prior probabilities, Py c ( ) = , are estimated
as the relative frequencies of each class in the training data, leaving the likelihood function,
Px y c (| ) = , to be computed. The GNB algorithm assumes that the features are conditionally
independent given the class label which simplifies the likelihood calculation. Using this
assumption, the likelihood can be written as
( ) ( )
1
0
| |
D
d
d
Pxy c Px y c
−
=
= =∏ = (37)

68
where D is the number of features, and d x is the value of the d-th feature. Each conditional
probability is modeled as a Gaussian distribution.
Finally, the predicted class label for a given sample x is determined by selecting the class
with the highest posterior probability. This decision rule is expressed as
 ( ) ( ) ( )
1
2
0
argmax | argmax , ,
D
c c d cd cd
d
y Py cx Py c Nx µ σ
−
=
= = = = ∏ (38)
where µcd and σ cd are the mean and standard deviations of the d-th feature in the training set,
respectively, whose label is c.
5.2.3. Results and analysis
5.2.3.1. Evaluation metrics
To assess the performance of the ML models in classifying the FRF differences, multiple
metrics were used. The confusion matrix is a visual summary of the model predictions as they are
categorized into true positives (TP), true negatives (TN), false positives (FP), and false negatives
(FN). Since there were four classes in this problem, the confusion matrix for damage classification
had a dimension of 4 x 4. Furthermore, the accuracy of the model for each task is defined as the
ratio of correct predictions to the total predictions made by the model. This gives an overall
assessment of its performance. Recall (i.e., sensitivity) evaluates the model’s ability to identify
positive instances. The recall is calculated as
TP Recall
TP FN = + (39)

69
The precision assesses the proportion of correct positive predictions among all predicted positives
and is calculated as
TP Precision
TP FP = + (40)
Furthermore, the F1 score was computed as the harmonic average of recall and precision for each
class demonstrated as
2× Precision× Recall F1=
Precision+ Recall (41)
The macro-F1 score is therefore the average of the F1 scores for each class in each task, written as
1
0
C
c
c=
1 Macro - F1= F1
C
−
∑ (42)
where F1c is the F1 score for class c, and C is the number of classes (i.e., four) in the task.
Figure 5-11, Figure 5-12, and Figure 5-13 show the confusion matrices from the testing set
obtained from RF, ANN and GNB models, respectively. The RF demonstrated the best
performance in classifying the differential FRF in the testing dataset into damage classes as shown
in Figure 5-11. Most of the samples were positively identified as shown in the diagonal of the
matrix. It also achieved the highest recall and precision rates for most classes among the three
models. In contrast, the ANN misclassified 84 samples in the slight damage class, 40 samples in
the moderate damage class, and 11 samples in the severe damage class as shown in Figure 5-12.
Furthermore, the GNB had an inferior performance to the ANN model as shown with the matrix
in Figure 5-13. The GNB misclassified 98 samples in slight damage, 70 samples in moderate
damage, and 13 samples in severe damage. The low recall rates produced by the GNB highlights

70
the limitation of the model in handling subtle variations in features. The misclassifications from
both the ANN and GNB models, particularly their high false negative rates, may raise potential
safety concerns.
Figure 5-11. Confusion matrix resulting from evaluating testing dataset with RF.

71
Figure 5-12. Confusion matrix resulting from evaluating testing dataset with ANN.
Figure 5-13. Confusion matrix resulting from evaluating testing dataset with GNB.

72
In addition to the confusion matrices, Table 2, Table 3, and Table 4 provide a detailed
breakdown of the predictions made by the RF, ANN, and GNB models, respectively, for the
multiple measurements recorded by each sensor in the testing dataset. In the tables, the columns
are the sensors, and the rows are the test cases. In these tables, the denominator indicates the total
number of predictions (measurements), while the numerator represents the number of correctly
classified predictions. These tables highlight sensor-specific variability in predicting FA damage
levels and compliment the confusion matrices by demonstrating localized trends not evident in the
aggregate metrics.
From the RF model in Table 2, it is evident that this model achieved high accuracy across
most sensors in each test case. For example, in the no damage test case, the RF model misclassified
only one measurement each for sensors S1, S2, S3, and S7, reliably identifying the baseline FLCB
condition. However, in the third slight damage case corresponding to missing spacer grids, S11
produced entirely incorrect predictions and was located far from the damage location as shown in
Figure 5-5 (b). This suggests that sensor location influenced the RF model's classification
performance in this slight damage scenario. The results from the ANN model in Table 3
demonstrated strong performance in no damage and severe damage scenarios but struggled in
distinguishing the slight and moderate damage test cases. For instance, in the third slight damage
test case, S6, S7, S8, S9, S11, and S12 had a large proportion of misclassified measurements.
Furthermore, the GNB model in Table 4, while the weakest performer overall, showed accurate
results in the severe damage test case. However, its performance declined in the slight and
moderate damage classes, as most sensors had measurements with mostly incorrect predictions.
This indicated that the performance was weak at sensor locations near and far the damage location
for the GNB model.

73
Table 2. Predictions for every measurement in all test cases from RF.
Test Case S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14
No
Damage 9/10 9/10 9/10 10/10 10/10 10/10 9/10 10/10 10/10 10/10 10/10 10/10 10/10 N/A
Slight
Damage #1 9/10 10/10 10/10 10/10 9/10 10/10 10/10 10/10 10/10 10/10 8/10 10/10 7/10 8/10
Slight
Damage #2 5/5 5/5 5/5 5/5 4/5 5/5 5/5 3/5 5/5 5/5 5/5 5/5 5/5 N/A
Slight
Damage #3 5/5 5/5 4/5 5/5 5/5 5/5 4/5 4/5 5/5 5/5 0/5 4/5 5/5 N/A
Moderate
Damage #1 10/12 12/12 12/12 11/12 11/12 11/12 12/12 8/12 8/12 10/12 12/12 N/A N/A N/A
Moderate
Damage #2 3/3 3/3 3/3 3/3 2/3 2/3 3/3 2/3 2/3 2/3 3/3 N/A N/A N/A
Severe
Damage 14/15 13/15 13/15 13/15 14/15 14/15 13/15 N/A N/A N/A N/A N/A N/A N/A
Table 3. Predictions for every measurement in all test cases from ANN.
Test Case S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14
No
Damage 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 N/A
Slight
Damage #1 10/10 9/10 10/10 10/10 9/10 10/10 10/10 10/10 10/10 7/10 2/10 10/10 4/10 10/10
Slight
Damage #2 5/5 4/5 4/5 2/5 3/5 0/5 4/5 0/5 0/5 5/5 0/5 0/5 5/5 N/A
Slight
Damage #3 5/5 5/5 2/5 5/5 5/5 0/5 0/5 0/5 1/5 5/5 0/5 0/5 5/5 N/A
Moderate
Damage #1 12/12 12/12 11/12 10/12 10/12 8/12 10/12 4/12 4/12 6/12 10/12 N/A N/A N/A
Moderate
Damage #2 3/3 3/3 3/3 3/3 2/3 2/3 3/3 2/3 2/3 2/3 3/3 N/A N/A N/A
Severe
Damage 13/15 13/15 14/15 14/15 14/15 13/15 13/15 N/A N/A N/A N/A N/A N/A N/A

74
Table 4. Predictions for every measurement in all test cases from GNB.
Test Case S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14
No
Damage 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 N/A
Slight
Damage #1 10/10 10/10 10/10 10/10 9/10 10/10 10/10 10/10 5/10 0/10 3/10 10/10 0/10 8/10
Slight
Damage #2 5/5 5/5 5/5 4/5 5/5 0/5 0/5 0/5 0/5 5/5 0/5 0/5 5/5 N/A
Slight
Damage #3 5/5 5/5 2/5 5/5 5/5 0/5 0/5 0/5 1/5 5/5 0/5 0/5 5/5 N/A
Moderate
Damage #1 7/12 9/12 9/12 6/12 6/12 6/12 6/12 4/12 4/12 4/12 7/12 N/A N/A N/A
Moderate
Damage #2 3/3 3/3 3/3 2/3 2/3 2/3 3/3 2/3 2/3 2/3 3/3 N/A N/A N/A
Severe
Damage 13/15 14/15 13/15 13/15 14/15 13/15 12/15 N/A N/A N/A N/A N/A N/A N/A
A summary of the recall and precision values for each class among the three models is
illustrated in Figure 5-14. The upper plot shows the recall values, and the lower plot shows the
precision values. Furthermore, a summary of the macro-F1 scores and accuracies for each model
is shown in Figure 5-15. The RF produced recall rates of 0.969, 0.922, 0.879 and 0.895, and
precisions of 0.947, 0.889, 0.924, and 0.940 for the no damage, slight damage, moderate damage,
and severe damage levels, respectively, as shown in Figure 5-14. Furthermore, from visual
inspection of Figure 5-15, the RF model demonstrated the highest performance of the three models
on the testing dataset as it achieved a macro-F1 score of 0. 920 and a testing accuracy of 0.916.
The ANN achieved an accuracy of 0.800 and a macro-F1 score of 0.803. The GNB had the weakest
performance on the testing dataset among the three models as it produced an accuracy of 0.730
and a macro-F1 score of 0.736.

75
Figure 5-14. Comparison of recall and precision among three ML models for testing dataset.

76
Figure 5-15. Comparison of macro-F1 score and accuracy among three ML models for testing dataset.
Further analysis was conducted with the ANN to assess its performance. The output
probability vector for each test sample was obtained after applying the SoftMax activation function
in the ANN. This offered a quantifiable measure of the predictive confidence of the model. Figure
5-16 illustrates the confidence levels for correctly classifying test samples across the four damage
classes. The ANN displayed strong confidence when predicting the no damage and severe damage
classes, with average probabilities of 0.925 and 0.857, respectively. Interestingly, the model
achieved nearly perfect confidence in classifying the severe damage class after the 6th
measurement (i.e., sample index 42), as indicated with the spike in probability values to 1.0. This
heightened confidence is likely due to reduced contact linearity between the sensors and the
canister during sequential tests. This was evidenced with more pronounced oscillations in the FRF
differences observed in the severe damage test case after index 42.

77
However, the model exhibited significantly lower confidence for the slight damage and
moderate damage classes, with mean probabilities of 0.557 and 0.717, respectively. Additionally,
these classes showed greater variability in prediction confidence, as evidenced by standard
deviations of 0.240 for slight damage and 0.312 for moderate damage. These results indicate that
the ANN struggled to reliably distinguish between intermediate damage levels. This could have
stemmed from overlapping feature distributions or higher noise levels in the FRF differences.
Figure 5-16. Confidence analysis of ANN on testing set: (a) no damage, (b) slight damage, (c) moderate damage, and (d) severe
damage.
a) b)
c) d)
0.925 ± 0.093 0.557 ± 0.240
0.717 ± 0.312 0.857 ± 0.254

78
5.2.3.2. Detailed results with RF
Given the superior performance of the RF model on the testing dataset compared to the
other models, it was selected for final classification predictions and was subjected to an in-depth
analysis of its results. Figure 5-17 highlights the feature importance derived from the trained RF
model, where each feature's contribution was measured by its average reduction in Gini impurity
across all decision trees. The analysis revealed that the standard deviation was the most influential
feature and accounted for approximately 30% of the total importance. This indicates that variations
in the standard deviations of the FRF differences were highly effective in distinguishing damage
levels. Furthermore, the second most important feature was the L2-norm square as it contributed
around 14.5% of the feature importance. This indicates that the overall magnitude of the FRF
differences in identifying damage severity was significant. Other notable features include the mean
and peak-to-peak amplitude, each contributing approximately 9.1%. These features further
highlight the importance of amplitude-related metrics in classifying the damage levels.
Conversely, features like maximum amplitude and the means of the first and second derivatives
had smaller contributions and therefore had minor significance in the classification task.
The alignment between feature importance rankings and the EDA results in Figure 5-6
suggests consistency in the importance of specific features, such as the standard deviation, which
showed clear class separability in the EDA. This reinforces its role in the classification task and
demonstrates the decision-making process of the RF model.

79
Figure 5-17. Feature importance of trained RF model.
The final damage predictions for each sensor in the testing experiments are visualized in
Figure 5-18 (a)-(g). The final predictions were obtained by taking the majority vote prediction
from multiple measurements recorded by the respective sensor. In Figure 5-18 (a)-(g), the sensor
numbers are in black font, while the corresponding final damage predictions are in red font. The
actual damage location(s) are outlined in red square(s).
The final damage class predictions for most sensors in each testing experiment were
correct. For example, all sensors had correct final predictions in the no damage case as shown in
Figure 5-18 (a). Similarly, accurate final predictions were obtained for the first and second slight
damage cases, as shown in Figure 5-18 (b) and Figure 5-18 (c); the first and second moderate
damage cases, depicted in Figure 5-18 (e) and Figure 5-18 (f); and the severe damage case, shown
in Figure 5-18 (g). However, one misclassified sensor was found in the entire testing dataset at
S11 in the third slight damage test case (i.e., missing spacer grids), as shown in Figure 5-18 (d). It

80
was predicted to be no damage. This misclassification likely occurred due to the smaller structural
changes from removing spacer grids compared to other slight damage modes such as missing
casing or fuel rods. Despite the misclassified sensor, the final damage predictions across all sensors
in each testing case indicate that the RF model achieved high accuracy in classifying the FRF
differences into internal FA damage levels.

81
Figure 5-18. Damage identification of different accelerometers using RF for each test case: (a) no damage, (b) first slight damage,
(c) second slight damage, (d) third slight damage, (e) first moderate damage, (f) second moderate damage, and (g) severe
damage.
5.3. Multi-task Damage Detection and Localization Problem
Although the ML models in Chapter 5.2 successfully classified the damage severity level
within the mock-up canister, they did not provide information on the location of the damage. To
address this limitation, multi-task ML classifiers were developed in this section to simultaneously
identify both the damage severity level and its location within the canister mock-up. The damage
a) b) c)
d) e) f)
g)
N = No Damage
SL = Slight Damage
M = Moderate Damage
SV = Severe Damage
= Actual Damage Location

82
detection problem had the same multi-class structure as outlined in Chapter 5.2. The damage
location was identified to be within one of the four quarters of the symmetric canister layout.
Therefore, the localization task was defined as a binary classification problem: for a given sensor,
either the damage was located outside or inside the quarter where the sensor was placed.
The multi-task damage detection and localization problem required models capable of
addressing both tasks simultaneously. Therefore, a multi-task k-NN and CNN were chosen based
on their suitability for multi-task learning and their applications in literature. The k-NN is a nonparametric algorithm, and it makes predictions based on the similarity of new (testing) data points
to the training data. Conversely, the CNN is a deep-learning algorithm that requires the
optimization of trainable parameters. Utilizing two models with largely different learning
algorithms allowed for a robust comparison of accuracy in the damage identification and
localization tasks.
5.3.1. Dataset preparation
The data pre-processing procedure for the multi-task k-NN and CNN classifiers is displayed
Figure 5-19. First, the FRF obtained on the canister with damage was subtracted from the FRF
obtained from the FLCB system. The FRF differences had a dimension, D, of 1,126. Then, to
remove the experimental noise in the low and high frequency ranges, the FRF differences were
truncated to a range of [0.5, 1.5] kHz. This truncation reduced the dimension of the samples to
439. The samples therefore had a frequency increment of 2.28 × 10-3
kHz per data point. A median
filter with a window length of three datapoints was used to further denoise the FRF differences,
examples of which are shown in Figure 5-20. For each damage case, the filtered FRF difference
reduced the large peaks without sacrificing information from the unfiltered FRF differences.

83
Figure 5-19. Flowchart of data preparation for multi-task k-NN and CNN classifiers.
FRF of FLCB
(Dimension = 1,126)
FRF of Damaged
Canister
(Dimension = 1,126)
FRF Differences
(Dimension = 1,126)
FRF Truncation and
Filtering
(Dimension = 439)
PCA
(Dimension = 15)
Multi-task k-NN
Location Class
Prediction
Damage Class
Prediction
Subtraction
k-NN
Training
and
Testing
Multi-task CNN
CNN
Training
and
Testing
Location Class
Prediction
Damage Class
Prediction

84
Figure 5-20. Examples of truncated and filtered FRF differences: (a) no damage, (b) slight damage, (c) moderate damage, and (d)
severe damage.

85
After the truncation and filtering, the samples were then given their true class labels as integer
values. Each sample had two labels, one for damage identification and the another for localization.
The integers: 0, 1, 2, and 3 were assigned for no damage, slight damage, moderate damage, and
severe damage, respectively. For the localization task, 0 denoted the sensor being positioned
outside of the damage quarter, and 1 denoted the sensor being positioned inside the damage
quarter.
The experimental dataset in Chapter 5.2 was used in this study with the addition of new
experimental data. A uniform accelerometer layout across the four canister quarters was employed
in the new experiments since the location of internal FA damage is unknown in real canisters. The
pre-processed dataset for the multi-task models was split into a training set and a testing set. The
split was based on a common rule-of-thumb to utilize approximately 80% of the data for training
and about 20% for testing. In the training dataset, there were 648 samples for no damage, 550
samples for slight damage, 1,053 samples for moderate damage, and 1,265 samples for severe
damage. The sensor layouts in the training dataset are provided in Figure 5-21. The testing dataset
contained 140 samples for no damage, 130 samples for slight damage, 280 samples for moderate
damage, and 140 samples for severe damage. The sensor layout with sensor numbers for the
experiments in the testing dataset are shown in Figure 5-22 (a)-(e). The testing cases were selected
from those experiments with uniform sensor layouts except for the slight damage case.

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Figure 5-21. Accelerometer layout for experiments in training dataset for multi-task models.
Measurements = 10 Measurements = 10 Measurements = 7 Measurements = 10 Measurements = 10
No Damage
Measurements = 10
(Casing)
Measurements = 10
(Casing)
Measurements = 10
(Spacer grids)
Measurements = 5
(Spacer grids)
Measurements = 10
(Three fuel rods)
Slight Damage
Measurements = 3 Measurements = 3 Measurements = 12 Measurements = 12 Measurements = 3
Measurements = 10 Measurements = 10 Measurements = 10 Measurements = 20 Measurements = 10
Moderate Damage
Measurements = 15 Measurements = 20 Measurements = 15 Measurements = 15
Measurements = 10 Measurements = 10 Measurements = 10 Measurements = 10
Measurements = 10
Measurements = 10
Severe Damage
Accelerometer Damage Location

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Figure 5-22. Sensor layouts for experiments in testing dataset for multi-task models: (a) no damage, (b) slight damage, (c) first
moderate damage, (d) second moderate damage, and (e) severe damage test cases.
5.3.2. ML classifiers
5.3.2.1. Multi-task k-nearest neighbors (k-NN)
The k-NN algorithm is an instance-based ML algorithm widely employed for both
classification and regression tasks. It operates on the principle of proximity of data points in a
feature space. When a new data point is introduced to that feature space, the algorithm assigns a
class label to it by considering the majority class label of its k-nearest neighbors [110][111]. The
number of nearest neighbors, k, is a hyperparameter of the model. Here, the Euclidean distance
was used to compute the distance between the new data and the data in the training set. k-NNs are
non-parametric and efficient, which makes the algorithm suitable for applications in fields such as
image recognition and anomaly detection [112][113][114].
c)
d) e)
a) b)
Damage Location

88
To enhance the efficiency of the k-NN in this study, principal component analysis (PCA)
was applied as a feature reduction tool. Principal component analysis is widely employed for noise
reduction, feature extraction, and damage identification tasks [115][116]. It operates by
transforming the original high-dimensional feature space into a new orthogonal coordinate system
defined by the data’s principal components (PC). The PC are calculated to lie in the directions of
maximum variance in the dataset. By projecting the dataset onto the PC, it is represented in a
significantly lower feature space without compromising important information [117].
First, each feature in the training and testing datasets was standardized to have a mean of
zero and a standard deviation of one. Then, the covariance matrix for each dataset was calculated
as
1
1 ( )( ) 1
n T
i i
i
Cov X X X X
n =
= −− − ∑ (43)
where Xi is the i-th FRF difference of length 439, X is a vector of length 439 containing the
average values of each feature, n is the number of FRF differences in the dataset, and T indicates
the matrix transpose operation. The covariance matrices are therefore square and symmetric with
dimensions of 439 x 439. Next, to uncover the PC of the covariance matrices, the eigenpairs were
calculated. The resulting PC (i.e., the eigenvectors) were uncorrelated linear combinations of the
initial features that were ordered by decreasing variance. Then, the resulting eigenvectors
corresponding to each eigenvalue were computed as
( )0 Cov I v λi i − = (44)

89
where i v is the eigenvector associated with the eigenvalue λi , and I indicates the identity matrix.
In this study, the number of PC (i.e., the number of eigenpairs) was chosen as 15 as shown in
Figure 5-23 (b). Finally, the original dataset was projected onto PC according to
X XV PCA std j , = ⋅ (45)
where XPCA is a matrix of dimension 15 containing the projection of the original dataset onto the
PC, Xstd, j is the standardized value of feature X j , and V is a matrix with the columns containing
the PC. It is important to note that PCA was conducted on the training set and applied directly to
the testing set using the same transformation.
After dimensionality reduction with PCA, the k-NN classifier was applied to classify each
testing sample into (1) a damage class and (2) a location class. The reduced dimension training
dataset after PCA with class labels was considered as the feature space for classifying test points.
For each testing point, the k-NN classifier calculated the Euclidean distance between the testing
point and each training datapoint. The Euclidean distance metric was used in this study due to its
simplicity and its effectiveness in a PCA-transformed, lower-dimensional feature space. In these
spaces, Euclidean distance generally performs well because it is less prone to overfitting compared
to more complex distance metrics. Then, the calculated distances were sorted in descending order
and the samples with the k (i.e., three) shortest distances were selected as the nearest neighbors
[118]. The majority class of the k nearest neighbors was chosen as the predicted class label for the
testing datapoint. This was completed for each classification task.
The k and number of PC were fine-tunned for an optimal model performance and to prevent
overfitting. Figure 5-23 (a) demonstrates the model accuracy for varying values of k on the testing

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set, and Figure 5-23 (b) demonstrates the same for varying numbers of PC. The accuracy reached
its peak for both tasks when k was three. Additionally, the accuracy peaked for both tasks when
the number of PC was 15. Therefore, these hyperparameter values were selected.
Figure 5-23. Accuracy of k-NN for damage and location classification tasks: (a) different values of k, and (b) different number of
PC.
5.3.2.2. Multi-task Convolutional Neural Network (CNN)
Convolutional neural networks are a specialized type of ANN tailored for the processing of
visual data, such as images, videos, and one-dimensional signals [119]. They use convolutional
layers that employ filters (i.e., kernels) to analyze localized portions of an input image or signal.
The kernels contain trainable weights that enable the network to learn and extract features of the
input at varying levels of complexity [119]. This automatic feature extraction capability of CNN
renders them effective for damage detection tasks, as the distinctions between undamaged and
damaged structural states often depend on subtle features that traditional statistical approaches
may not detect [120][121][122]. Additionally, CNN incorporate max-pooling or average-pooling
layers that reduce the dimensional complexity of the feature maps [123]. Following the
convolution layers are fully connected (i.e., linear) layers that perform the multi-task classification.
a) b)

91
The neurons are connected between layers through trainable weights and biases that are optimized
via the mini-batch gradient descent algorithm during the backpropagation of the network [102].
The final fully connected layers (i.e., the output layers) contain the same number of neurons as
there are classes in each respective task. The output values of this layer provide the final class
predictions for each task.
The CNN architecture utilized in this study is shown in Figure 5-24. It was developed from a
previously trialed ANN whose performance will be discussed briefly in Chapter 5.3.3.2. The CNN
had an input layer that was fed with the FRF difference of length 439. This input was passed to the
first convolution layer. The kernel in the convolution layer carried out the one-dimensional
convolution operation between the filter and the localized sections of the input data. The kernel
moved along the input (or feature maps) to perform the operations at a stride s. The convolution
operation can be written as
1 ( )
,
[ , ] (( [ , ] [ , ]) ) l l
k k
m c
x j k ReLU g m c x j s m c b + = ∑ ×+ + (46)
where 1
[, ] l x jk + is the output of the j-th node in the k-th output channel, 𝑔𝑔𝑘𝑘 is the kernel, 𝑚𝑚 is the
kernel size, 𝑐𝑐 is the input channel index, 𝑥𝑥(𝑙𝑙) are the inputs, and 𝑏𝑏𝑘𝑘 is the bias term of the k-th
output channel [94][124]. This operation is conducted in both convolution layers, and 𝑚𝑚 and 𝑠𝑠 are
equal to three in both layers. The results of all convolutions in 𝑐𝑐 were summed and 𝑏𝑏𝑘𝑘 was added
to it. Then, the ReLU activation function was applied to introduce nonlinearity to the model [120].
The choice of activation function was a hyperparameter of the model.
Additionally, a max-pooling layer was applied after the convolutions to reduce the
dimension of the output feature maps. The kernel length and stride were both two for the max-

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pooling layers. After the data was fed through the two convolution layers with max-pooling, the
output data was flattened into a vector of length 192. This feature vector was used as the input into
the fully connected layers that processed the learned features. The first fully connected layer had
64 neurons, and the second had 16 neurons. Both layers had ReLU activation. The mapping
operation performed in the l-th linear layer can be written as
( ) ( ) ( 1) ( ) ReLU( ) l ll l z Wz b − = + (47)
where ( )l W and ( )l b are respectively the weight matrix and the bias vector. The flattened input
feature vector was (0) 192 1x z ∈ . Since there were 64 neurons in the first linear layer, (1) 64 192 W × ∈
and (1) 64 1 b × ∈ . The second linear layer contained 16 neurons thus (2) 16 64 W × ∈ and (2) 16 1 b × ∈ .
The output feature vectors resulting from this layer were then fed into two independent output
layers that separately predicted the damage severity class and the location class. ReLU activation
was not considered for the two output layers. The dimension of the output layer corresponding to
the damage classification task was four, thus (3) 4 16 Wdamage
× ∈ and (3) 4 1
damage b × ∈ . The output of each
neuron after this layer was stored in the vector ˆdamage y . The output layer responsible for the
localization task had a dimension of two, thus (3) 2 16 Wlocation
× ∈ and (3) 2 1
location b × ∈ , and the outputs
were stored in the vector ˆlocation y .
To obtain the damage class probabilities, the SoftMax function was applied to both
classifier outputs to convert the raw output scores to its corresponding probability vectors. This
step is expressed as

93
1
2
3
4
1 ˆ ˆ SoftMax( )
d
d
d j d
d
y
y
damage damage y y
j y
e
e
p y
e e
e
 
 
  = =  
 
   
∑ (48)
where 1 d y , 2 d y , 3 d y and 4 d y are the individual values in vector ˆdamage y . SoftMax was also applied
to ˆlocation y obtain the location class probabilities. These probabilities are defined as
1
2
1 ˆ ˆ SoftMax( )
l
l j l
y
location location y y
j
e
p y
e e
  = =  
  ∑   (49)
where 1
l y and 2l y are entries in vector ˆlocation y .
Figure 5-24. Schematic of CNN architecture.
Input
(439x1)
Kernel
(3xc)
Stride = 3
(146x8)
(73x8)
(24x16)
(12x16)
Damage
class
prediction
Location
class
prediction
Fully-connected layers = Convolution
= Max-pooling
= Flattening
= SoftMax Activation
…
…
(192x1)
(64)
(16)
(4)
(2)
Dropout
(p = 0.1)
Dropout
(p = 0.1)
Input

94
To introduce uncertainty into the CNN, dropout was applied to both hidden layers as shown in
Figure 5-24. Dropout randomly removes a fraction of neurons from each layer by a selected
probability value. Therefore, with each training iteration, different neurons are deactivated from
the network. This leads to the training of different subnetworks in each iteration, as different
combinations of neurons are dropped out. This stochasticity in neuron activations creates a form
of ensemble learning within a single model which prevents overfitting [125][126]. More
importantly, the dropout operation can be used as a means of approximating Bayesian inference
for a neural network [127].
The dropout operation can be described as utilizing random samples of a Bernoulli distribution
to determine the activation status of a neuron, j, in a fully connected layer, l [128]. The samples
can be expressed as
Bernoulli( ) dropout ε = p (50)
where ε are the samples from the Bernoulli distribution based on the probability hyperparameter
in the dropout layers, dropout p . Furthermore, the output of the j-th neuron in the l-th fully connected
layer after applying dropout can be expressed as
( ) ( ) l l
j j z z = ε   (51)
where  indicates element-wise multiplication, and ( )l
j z represents the output of the j-th neuron
in the l-th fully connected layer.
In this study, minimizing the individual MCE losses (i.e., between the class true labels and the
predicted probabilities) for both tasks was the goal of the training process. The MCE loss defined

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in PyTorch [101] was employed. The losses from the damage classification task and the location
classification task were computed individually then summed together as a total loss for the
backpropagation of the CNN. For hyperparameter selection, a trial-and-error method was used to
tailor the CNN to solve the multi-task problem. The hyperparameter values were adjusted by
observing their impact on minimizing the individual task losses during training. The final
hyperparameter values were determined based on their ability to minimize task losses while
ensuring that the model was able to converge, thus making accurate predictions regarding damage
and location. A batch size of 32 was employed, and Adam [103] was chosen as the mini-batch
stochastic gradient descent algorithm with a learning rate of 1 × 10-4
. To mitigate overfitting, a
weight decay of 1 × 10-5 was implemented. Additionally, a dropout probability of 0.1 was
implemented in the dropout layers. This value was selected based on a trade-off between the
robustness of the network and model uncertainty. The CNN was trained for 200 epochs. Once the
CNN finished training, the class with the highest probability in both 𝑝𝑝̂
𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 and 𝑝𝑝̂
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 was
selected as the predicted damage and location class of the input sample, respectively.
The losses for the damage classification and location classification tasks are shown in Figure
5-25 (a) and Figure 5-25 (b), respectively. It is noted that the losses for the two classification tasks
both converged by 200 epochs.

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Figure 5-25. Training and testing losses versus epoch for CNN: (a) damage classification task, and (b) location classification task.
5.3.3. Results and analysis
5.3.3.1. Multi-task k-NN
For the multi-task models, the evaluation metrics were computed once for each classification
task. The confusion matrices for the damage and localization classification tasks from the k-NN
are shown in Figure 5-26 (a) and Figure 5-26 (b), respectively. The k-NN performed with a perfect
macro-F1 score of 1.00 for the damage detection task and a macro-F1 score of 0.996 for the
localization task. Specifically, in the localization task, the k-NN achieved recall rates of 1.00 and
0.990, and precisions of 0.996 and 1.00 for the sensors being outside the damage quarter and for
the sensors being inside the damage quarter, respectively.
a) b)

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Figure 5-26. Confusion matrices calculated on testing set for multi-task k-NN model: (a) damage classification task, and (b)
location classification task. “Outside” refers to sensors predicted to be outside of damage quarter, and “inside” refers to sensors
predicted to be inside damage quarter.
Table 5 (a)-(b) provides a summary of the number of correct predictions out of the ten total
predictions for each test case as reference. In Table 5 (a), the k-NN performed with perfect
accuracy in damage detection for all test cases. However, as indicated in Table 5 (b), the k-NN had
incorrect localization predictions for some measurements in the slight and severe damage test
cases. For instance, in the slight damage case, S6 had one misclassified prediction, and in the
severe damage case, S11 had one incorrect prediction. These results suggest that the k-NN model
performed well overall in the multi-task classification problem.
a)) b))

98
Table 5. Detailed damage identification predictions from all accelerometers for testing cases using the k-NN: (a) damage
detection, and (b) localization.
a)
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14
No Damage 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10
Slight
Damage 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 N/A
Moderate
Damage #1 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10
Moderate
Damage #2 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10
Severe
Damage 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10
b)
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14
No Damage 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10
Slight
Damage 10/10 10/10 10/10 10/10 10/10 9/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 N/A
Moderate
Damage #1 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10
Moderate
Damage #2 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10
Severe
Damage 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 9/10 10/10 10/10 10/10
Figure 5-27 (a)-(e) display the final damage detection and localization predictions obtained
from specific accelerometers in each testing case. In the figures, the sensor numbers are in black
font, and the actual damage location is marked with a heavy red square around the FA cell. The
final damage class labels are in red font. The FA cell was filled with red shading if the k-NN
predicted the damage was inside of the respective sensor’s quarter. Each testing case represented
one experiment, and each experiment contained ten measurements. The final class predictions
were determined by taking the majority vote prediction of the ten measurements for each sensor
in the testing case. As shown in Figure 5-27 (a), the k-NN made correct damage and location class
predictions at all the accelerometer locations for the no damage case. This is also true for the slight

99
damage test case in Figure 5-27 (b) in which three fuel rods were removed from the FA located in
the red square. The moderate damage test cases had a missing FA at the locations of the red squares
as indicated in Figure 5-27 (c) and Figure 5-27 (d). The k-NN made correct damage and location
predictions for every sensor in these cases. In the severe damage test case, the k-NN made the
correct damage and location predictions for all sensors as indicated in Figure 5-27 (e). It is
noteworthy that the k-NN demonstrated perfect performance in detecting and localizing the
damage quarter in each experiment.
Figure 5-27. Majority vote damage and location predictions from multi-task k-NN for each test case: (a) no damage, (b) slight
damage, (c) first moderate damage, (d) second moderate damage, and (e) severe damage.
The first and second PC of the training and testing set are visualized in Figure 5-28 (a)-(d).
The first and second PC accounted for 48.6% and 10.2% of the variance in the dataset, respectively.
Each point in the scatter plots represents a sample of the FRF difference, and its position is
N = No damage
SL = Slight damage
M = Moderate damage
SV = Severe damage
= Inside damage quarter
a) b)
d) e)
c)

100
determined by their scalar values of the first and second PC. The plots on the diagonal show the
kernel density estimation (KDE) of the first and second PC values. As shown in Figure 5-28 (a),
there is visual clustering of the data points among the four damage classes. The shapes and
locations of the KDE plots for each PC also demonstrate some separation among the damage
classes. The clustering of the two localization classes is more difficult to differentiate as
demonstrated in Figure 5-28 (b) yet has a clearer distinction in the testing dataset as shown in
Figure 5-28 (d).
Figure 5-28. Visualization of first and second PC: (a) damage severity classes in training dataset, (b) localization classes in
training dataset, (c) damage severity classes in testing dataset, and (d) localization classes in testing dataset.
a) b)
c) d)
a) b)
c) d)

101
Figure 5-29 (a)-(b) displays an example of how the k-NN algorithm operates within the
PCA feature space for both damage and location classification. For demonstration purposes, only
the first two of the 15 PC are illustrated. It should be noted that the algorithm considers all 15 PC
when testing the model. In Figure 5-29 (a), the test data point in the black star represents one
measurement for S6 in the severe damage testing case in Figure 5-27 (e). When making predictions
for this sample in the training space, the k-NN calculated the Euclidean distance from this sample
to all training samples and selected its three closest neighbors. The closest neighbors are filled
with their respective ground truth class label colors. Since all the three closest neighbors were
severe damage, as indicated by the red fill in Figure 5-29 (a), the testing datapoint was also
assigned the severe damage class. The same procedure was applied for the location classification
in Figure 5-29 (b). Since the three closest neighbors to the test point were labeled as being outside
the damage quarter, the test datapoint was also assigned as the damage being outside the quarter,
which is the correct prediction.
Figure 5-29. Classifying one measurement from S6 in severe damage test experiment with k-NN: (a) damage classification, and
(b) location classification.
a) b)

102
5.3.3.2. Multi-task CNN
For the multi-task CNN, the evaluation metrics were computed once for each classification
task. The confusion matrices from the CNN classifier for the damage detection and localization
classification tasks are illustrated in Figure 5-30 (a) and Figure 5-30 (b), respectively. The CNN
had high macro-F1 scores of 0.991 and 0.964 for the damage detection and localization tasks,
respectively. The multi-task CNN outperformed the trialed ANN as the macro-F1 scores were only
0.826 for the damage detection task and 0.691 for the localization task. As shown in Figure 5-30
(a), the CNN achieved recall rates of 1.00, 1.00, 0.993, and 0.964 and precisions of 0.993, 1.00,
0.982, and 0.993 for the no damage, slight damage, moderate damage, and severe damage classes,
respectively. Additionally, it achieved recall rates of 0.990 and 0.925, and precisions of 0.970 and
0.974 for the sensors being outside the damage quarter and for the sensors being inside the damage
quarter, respectively.
Figure 5-30. Confusion matrices calculated on testing set for multi-task CNN model: (a) damage classification task, and (b)
location classification task. “Outside” refers to sensors predicted to be outside of damage quarter, and “inside” refers to sensors
predicted to be inside damage quarter.
a) b)

103
Table 6 (a)-(b) provides a summary of the number of correct predictions out of the ten total
predictions for each test case as reference. In Table 6 (a), the CNN model demonstrates high
accuracy for damage detection in most test cases. For the no damage, slight damage, and moderate
damage cases, nearly all sensors had correct predictions. In the severe damage case, however,
minor misclassifications were observed. For instance, S1 had one incorrect prediction, S9 had two
incorrect predictions, S10 had one incorrect prediction, and S13 had one incorrect prediction.
Table 6 (b) shows the localization predictions from the CNN. The model achieved strong
performance for the no damage, slight damage, and moderate damage cases, as most sensors had
correct location predictions. However, misclassifications were more pronounced in the severe
damage case. For example, S1, S9, S10, and S11 had two, three, six, and six misclassifications,
respectively. This suggests that while the CNN effectively identified damage levels, localizing
severe damage accurately posed a greater challenge. This occurred at sensor locations that were
near the defined canister quarter boundaries.

104
Table 6. Detailed damage identification predictions from all accelerometers for all testing cases using the CNN: (a) damage
detection, and (b) localization.
a)
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14
No Damage 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10
Slight
Damage 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 N/A
Moderate
Damage #1 10/10 10/10 10/10 10/10 10/10 10/10 10/10 9/10 10/10 10/10 10/10 10/10 10/10 10/10
Moderate
Damage #2 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 9/10 10/10 10/10
Severe
Damage 9/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 8/10 9/10 10/10 10/10 9/10 10/10
b)
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14
No Damage 10/10 10/10 10/10 10/10 10/10 10/10 10/10 9/10 10/10 10/10 10/10 10/10 10/10 10/10
Slight
Damage 10/10 10/10 10/10 10/10 10/10 9/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 N/A
Moderate
Damage #1 10/10 10/10 10/10 10/10 10/10 9/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10
Moderate
Damage #2 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10
Severe
Damage 8/10 10/10 10/10 10/10 10/10 10/10 10/10 10/10 7/10 4/10 4/10 10/10 10/10 9/10
Figure 5-31 (a)-(e) displays the final damage and location predictions obtained from specific
accelerometers in each testing case. Figure 5-31 (a)-(e) shows that the CNN made correct damage
and location class predictions at all the accelerometer locations for the no damage, slight damage,
and moderate damage test cases. Furthermore, the CNN model made the correct damage
predictions for the severe damage case in Figure 5-31 (e). However, the CNN misclassified the
location for two sensors, S10 and S11. It is still noteworthy that the CNN demonstrated accurate
localization by considering the results from all four quarters.

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Figure 5-31. Majority vote damage and location predictions from multi-task CNN for each test case: (a) no damage, (b) slight
damage, (c) first moderate damage, (d) second moderate damage, and (e) severe damage.
5.3.4. Probabilistic analysis
The probabilities of the neurons corresponding to the localization task were extracted after
SoftMax activation with the CNN. The first neuron had the probability that the sensor was outside
the damage quarter, 𝑝𝑝̂𝑙𝑙1, while the second neuron contained the probability that the sensor was
inside the damage quarter, 𝑝𝑝̂𝑙𝑙2. For each test case, the ten probabilities (one from each measurement
in one experiment) for each sensor in 𝑝𝑝̂𝑙𝑙2 were averaged. These average probability values are
plotted on the canister bottom plate as shown in Figure 5-32 (a)-(e). The shaded circles are the
locations of the accelerometers, and the average probability values are shown in black font. The
damage locations are highlighted by the red squares. The extracted probability values were from
the red highlighted neuron in Figure 5-32 (f). For a correct localization, the average probability
N = No damage
SL = Slight damage
M = Moderate damage
SV = Severe damage
= Inside damage quarter
a) b)
d) e)
c)

106
values for the sensors located inside the damage quarter should be closer to one among all the
sensors on the bottom plate.
For the no damage test case, the average probability for each sensor was close to zero, as
shown in Figure 5-32 (a). This indicates that when the canister is in its healthy FLCB status, the
probability that there is damage located in any quarter of the canister is almost zero. The average
probability values for the slight damage test experiment are shown in Figure 5-32 (b). The values
for the sensors outside of the damage quarter were much lower than those of the sensors that were
inside the damage quarter. This probability difference confirmed that the CNN can localize the
slight damage with high confidence. The same trends apply for both moderate damage experiments
in Figure 5-32 (c)-(d). Furthermore, the probability values for S10 and S11 in Figure 5-32 (e) were
only 0.40 and 0.24, respectively. This is the reason that these two sensors were incorrectly
localized as shown in Figure 5-31 (e). Conversely, the sensors directly located at the damage
locations had average probabilities of 0.998 and 0.999. Therefore, it can be concluded that the
CNN exhibits good performance in accurately predicting both the damage severity level and the
quarter in which the damage occurs within a sealed SNF canister using measurements only
obtained from the canister's external surface. This holds true for sensors positioned either near or
far from the damage position.

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Figure 5-32. Average probability that damage is located inside the sensor’s quarter: (a) no damage, (b) slight damage, (c) first
moderate damage, (d) second moderate damage, (e) severe damage test cases, and (f) schematic of extracted SoftMax probability
values.
An additional probabilistic analysis was conducted on the testing dataset using the trained
CNN. For all testing samples, dropout was still activated. Consequently, the predicted probabilities
of each sample (i.e., each FRF difference) for both tasks varied each time the testing data was
inputted. This variability arose from the activation of dropout in the fully connected layers, leading
to the deactivation of different neurons in each test iteration. As a result, different output
probabilities were produced for each sample in the testing dataset with every testing iteration.
To create a distribution of the varying outputs with each test of the CNN, the entire testing
dataset was analyzed by the trained model 1,000 times. A violin plot was generated for each sensor
c)
d) e)
a) b)
SoftMax
f) 𝑦𝑙𝑜𝑐𝑐𝑎𝑡𝑖𝑜𝑛 𝑝𝑝𝑙𝑜𝑐𝑐𝑎𝑡𝑖𝑜𝑛
𝑦𝑙1
𝑦𝑙2
𝑝𝑝𝑙1
𝑝𝑝𝑙2

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in the experiment as shown in Figure 5-33 (a)-(e). The width of each violin plot represents the
KDE that was fit to the data with Gaussian kernels. The locations of the sensors for each
experiment can be found in Figure 5-22, and the “inside" and “outside” labels below the plots
indicate the ground truth location class for each sensor. Values beyond the (0, 1] range were
disregarded in the plots.
For the no damage test experiment shown in Figure 5-33 (a), all sensors had probability
densities around zero. This suggests a high level of confidence from the CNN that there is
negligible probability that these sensors were inside the damage quarter (i.e., no damage in the
canister). Next, in the slight damage case in Figure 5-33 (b), the sensors situated inside the same
quarter as the damage had distributions that were dense around the probability value of one,
indicating that those sensors were most likely positioned inside the damage quarter. On the
contrary, sensors outside of the damage quarter had probability densities that were around zero.
The two moderate damage experiments shown in Figure 5-33 (c)-(d) had distributions with similar
patterns as the slight damage experiment. For the severe damage case in Figure 5-33 (e), S1 and
S2 were placed under the actual damage position and showed high probability densities around
one. Other sensors inside the damage quarter (i.e., S10 and S11) showed a flat distribution along
the probability range. This insinuates the CNN was not confident when making the localization
predictions for those sensors. However, all the other sensors had strong probability densities below
0.5, indicating that the sensors were outside of the damage quarter. Despite the minimal number
of misclassified sensors, the results offer probabilistic interpretation of the CNN’s accuracy in
localizing the damage into the correct quarter for experiments in all damage levels.

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Figure 5-33. Violin plots of 10,000 probabilities predicted by CNN that sensors were inside the damage quarter: (a) no damage,
(b) slight damage, (c) first moderate damage, (d) second moderate damage, and (e) severe damage test experiments.
a) b)
c) d)
e)

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5.4. Conclusions
This study demonstrated the successful application of ML algorithms for detecting internal
damage modes in a sealed SNF canister using only measurements obtained from its external
surface. Experimental modal analysis was conducted on a 2/3-scaled canister mock-up. The
differences in FRF between the intact FLCB and the canister with four levels of FA damage were
computed. Then, the ANN, RF, and GNB models were trained using features extracted from the
differential FRF. These models were tasked with classifying the FRF differences into damage
severity classes. Based on the results and analyses, the following conclusions were made:
• The RF model exhibited high performance on the testing dataset as it produced a testing
accuracy of 0.916 and a macro-F1 score of 0.920. However, it was noted that the model
error increased when the spacer grids were removed in the slight damage class. This was
due to the minimal structural changes introduced by the removal of the spacer grids as
compared to other damage conditions in this class. In comparison, the ANN achieved a
lower testing accuracy of 0.800 with a macro-F1 score of 0.803, while the GNB model
performed the worst of the three models, with a testing accuracy of 0.730 and a macro-F1
score of 0.736.
• The GNB’s reduced performance was largely attributed to its difficulty in managing
correlated features and deviations from the assumed Gaussian distribution, as highlighted
by the EDA of the experimental dataset [106].
• The feature importance analysis revealed key characteristics of the trained RF model.
Notably, the standard deviation emerged as the most influential feature, accounting for
approximately 30% of the model’s importance. The overall magnitude of the FRF

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difference, represented by the L2-norm square, also played a critical role, contributing
around 14.5%. Additional features, including the mean and peak-to-peak amplitude,
provided important contributions to the model’s classification performance.
• The RF model’s success stemmed from its ability to manage correlated features and avoid
making assumptions about the underlying data distribution, unlike the GNB. This
flexibility allowed it to utilize critical features, such as the standard deviation and L2-norm
square, which were important in identifying FA damage levels. The RF’s adaptability to
diverse data characteristics and its robustness in handling feature interactions contributed
to its performance in detecting FA damage levels.
• The RF model demonstrated the ability to accurately predict FA damage levels inside a
sealed SNF canister using external canister surface measurements. Notably, it could
reliably classify damage severity even at accelerometers located far from the damaged area.
This capability suggests that the RF model can effectively identify damage levels
regardless of accelerometer placement on the bottom plate. This potentially reduces the
number of sensors required for inspections in field applications.
• The experimental approach and ML models developed in this study can be directly applied
to real SNF canisters. Identifying damage within the internal FA requires only a series of
measurements taken at the canister’s bottom plate. For example, measurements conducted
before and after transportation events can effectively detect potential FA damage. This
method avoids the need for visual inspections that require unsealing the canisters. This is
a key challenge in current inspection practices.

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However, since the location of the damage within the canister was still unknown, a multi-task
k-NN and CNN were trained to simultaneously classify each FRF difference into a damage severity
class and a localization class. The following conclusions were made from the multi-task classifiers:
• By taking measurements solely on the exterior surface of the canister, the interior damage
level was accurately identified, and the damage was localized to specific quarter of the
canister in all test cases. The multi-task k-NN and CNN models exhibited a similar
performance for the damage detection task with testing macro-F1 scores of 1.000 and
0.991, respectively. The macro-F1 scores for the localization task were 0.982 and 0.964 for
the multi-task k-NN and CNN, respectively.
• The PCA effectively reduced the dimension of the FRF difference from 439 to 15. The
reduced-dimension dataset carried sufficient information on the original dataset and
enabled the k-NN to classify the testing samples into their respective damage and
localization classes.
• The CNN required the tuning of multiple hyperparameters to balance the performance of
the two classification tasks. Therefore, optimizing the 13,926 trainable parameters to
minimize the combined loss function was challenging. However, the CNN’s high macroF1 scores can be attributed to the inclusion of a high number (i.e., 192) of automatically
detected features that were used as input into the fully connected layers of the network.
• The multi-task CNN classified all sensors in the testing set into their correct damage classes
by their majority vote predictions. However, in the severe damage test experiment, the
CNN misclassified the location of damage at two sensors inside the damage quarter. Most

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sensors still made correct predictions for the localization thus the model was accurate in
this multi-task classification problem.
• The probabilistic analysis performed by testing the CNN with dropout layers 1,000 times
confirmed the accuracy of the CNN model in localizing the sensors inside the damage
quarter in the testing dataset. The probability densities of the 10,000 output probabilities
that each sensor was inside the damage quarter aligned with the ground truth class labels
for each sensor, making the network reliable even with uncertainty introduced.

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Chapter 6: Effect of Experimental Noise on Internal Damage Identification
6.1. Introduction
The studies briefly reviewed above thus far have addressed training ML models on pure
experimental data for internal FA damage detection. However, conducting physical experiments
on canisters is both time-consuming and costly, and the types of damage that can be simulated are
limited. Therefore, a high-fidelity FEM developed in [45] was largely modified in this study to
serve as the digital twin of the physical mock-up and simulate fractured fuel rods. A nested CB
substructuring method that was originally developed by Ezvan et al. [50][51] was used to reduce
the dimensionality of the numerical model for efficient calculation of the numerical FRF. The FEM
only provided deterministic outputs. To bridge the gap between the numerical and experimental
data for a more realistic simulation, WGAN were trained to generate measurement noise and
uncertainties that mimic experimental conditions. The difference between the FRF of the FLCB
and the damaged canister was computed to determine different damage levels and damage
locations. A multi-task XGBoost classifier was trained to classify each FRF difference into a
damage severity class and a location class. The model was trained with three different datasets: (1)
pure FEM data, (2) noisy FEM data, and (3) a combination of noisy FEM and experimental data,
to evaluate the model’s performance on the experimental testing dataset. As such, to the knowledge
of the author, this study constitutes the very first study on identification of very minor internal
damage states and their locations in sealed SNF canisters.
The contributions of this study include the following: (1) The development of WGAN to learn
and extract experimental measurement noise into the computational domain. This approach serves
as a domain adaptation method to bridge the gap between computational and experimental

115
domains. (2) The application of mixed training, which trains ML models on the dataset with mostly
computational data and a small amount of experimental data. These two methodologies enabled
ML models in this study trained primarily on computational data to still have high accuracy when
making predictions on experimental data. (3) Additionally, this is the first study on identification
and localization of minor internal damage (e.g., a single fractured fuel rod) within sealed SNF
canisters using measurements collected only externally; thereby, further advancing the research on
safety of nuclear fuel cycle.
6.2. Dataset Preparation
6.2.1. Experimental dataset
The experimental FRF were pre-processed with the procedure outlined in Figure 6-1. First,
FRF measurements were collected from the FLCB and the canister with simulated damage. The
FRF had dimension, D, of 1,126. Then, the FRF were subtracted and bandlimited to [0.5, 1.5] kHz,
which reduced the dimension to 439. This reduction resulted in a frequency increment of 2.28 ×
10-3
kHz per data point. In this study, a sample is defined as a row vector containing the dB values
of the FRF difference across the bandlimited frequency range. Each sample corresponds to the
subtraction of an FRF measurement from the FLCB and a corresponding measurement from the
canister with FA damage recorded at the same sensor location. An example of an experimental
FRF difference sample for each damage class in the experimental dataset is provided in Figure
5-3. A clear difference in FRF amplitude between the FLCB (i.e., the healthy canister) and
damaged canister is seen. Therefore, the difference in FRF between the FLCB and the canister
with an internal abnormality was used as the damage metric in this study.

116
Figure 6-1. Flowchart of FRF difference calculation.
After pre-processing, the experimental dataset was appended with two ground truth class
labels (i.e., one for damage detection and one for localization). For the damage detection labels,
the integers: 0, 1, 2, and 3 were given for no damage, slight damage, moderate damage, and severe
damage, respectively. The localization labels were a binary choice: 0 was given for the sensors
that were positioned on an undamaged location (i.e., “negative” damage location) and 1 was given
sensors directly located on the damage position (i.e., “positive” damage location). Then, the dataset
was split into training and testing. The experimental training dataset had 648 samples for no
damage, 615 samples for slight damage, 1,193 samples for moderate damage, and 1,265 samples
for severe damage. In the testing dataset, there were 140 samples for no damage, 65 samples for
slight damage, 140 samples for moderate damage, and 130 samples for severe damage. The sensor
locations for the experiments in the testing dataset are illustrated in Figure 6-2 (a)-(d). In the figure,
the black labels are the sensor numbers, and the red square(s) represent the damage location(s).
The sensor locations for the experiments in the training dataset are provided in Figure 6-3.
FRF of FLCB
(D = 1,126)
FRF of
Damaged Canister
(D = 1,126)
FRF Difference
(D = 1,126)
FRF Truncation
(D = 439)
Subtraction

117
Figure 6-2. Sensor layout for experiments in experimental testing dataset: (a) no damage test case, (b) slight damage test case
representing three missing fuel rods, (c) moderate damage test case, and (d) severe damage test case.
Damage Location
a) b)
c) d)

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Figure 6-3. Accelerometer and damage locations for scenarios in experimental training dataset.
Measurements = 10 Measurements = 10 Measurements = 7 Measurements = 10 Measurements = 10
No Damage
Measurements = 10
(Casing)
Measurements = 10
(Casing)
Measurements = 10
(Spacer grids)
Measurements = 5
(Spacer grids)
Measurements = 10
(Three fuel rods)
Slight Damage
Accelerometer Damage Location
Measurements = 3 Measurements = 3 Measurements = 12 Measurements = 12 Measurements = 3
Measurements = 10 Measurements = 10 Measurements = 10 Measurements = 20 Measurements = 10
Moderate Damage
Measurements = 15 Measurements = 20 Measurements = 15 Measurements = 15
Measurements = 10 Measurements = 10 Measurements = 10 Measurements = 10
Measurements = 10
Measurements = 10
Severe Damage

119
6.2.2. FEM dataset
With the high-fidelity FEM, the finer damage modes were simulated by modifying
components of the FA. The no damage case was simulated with the FLCB. The slight damage
included scenarios such as missing casing, missing spacer grids, missing fuel rods, and one or two
fractured fuel rods. To model a missing casing, the stiffness of the springs connecting the casing
to the basket was reduced from 1.13 × 109 kN·mm/rad to 1 kN·mm/rad. The same reduction was
performed for the springs connecting the spacer grids to the casing to simulate missing spacer
grids. To simulate missing fuel rods, the Young’s modulus of the rod material was reduced to 2.07
GPa (i.e., to 1% of its original value). The Young’s modulus of fractured fuel rods was reduced to
50% of the original value (i.e., to 103 GPa). The parameter reductions were used to simulate
damage rather than deleting the components from the model to avoid numerical instabilities in the
nested CB calculation. Furthermore, like the experiments, the moderate damage case had one
missing FA, and the severe damage case had two or more missing FA. After simulating damage
with the FA model, the nested CB was performed to compute the numerical FRF.
The pre-processing procedure for the FEM dataset is shown in Figure 6-4. The numerical FRF
were collected at 1,169 observation nodes located at the bottom plate of the canister. First, the FRF
were obtained from the FLCB, and another set of FRF was obtained from the canister with
simulated FA damage. The numerical frequencies were interpolated to match those of the
experiments; therefore, the frequency increment was 2.28 × 10-3
kHz per data point. Then, the
FRF were bandlimited to [0.5, 1.5] kHz. To make the numerical FRF more representative of the
physical mock-up canister, experimental noise generated with WGAN models was added to the
numerical FRF. This will be discussed in the next section. To obtain the FRF differences between
canister configurations, the two noisy FRF (for FLCB and damaged canister) were subtracted. In

120
this study, a sample in the FEM dataset is defined as a row vector containing the dB values of the
noisy FRF difference across the bandlimited frequency range. Each sample represents the
subtraction of an FRF measurement at each frequency point from the FLCB and a corresponding
measurement from the damaged canister, both taken at the same observation node on the bottom
plate. After pre-processing, the noisy FRF difference samples in the FEM dataset were appended
with their ground truth damage and location class labels. Then, the training and testing datasets
were created. In training, there were 3,507 samples for no damage, 12,859 samples for slight
damage, 3,507 samples for moderate damage, and 3,507 samples for severe damage. The testing
dataset contained 1,169 samples for no damage, 5,845 samples for slight damage, 1,169 samples
for moderate damage, and 3,507 samples for severe damage. Note that all these numbers are
multiples of 1,169, which are the number of observation nodes as mentioned earlier. The locations
damage for simulations in the training dataset are provided in Figure 6-5.
Figure 6-4. Flowchart for FEM dataset pre-processing.
Truncated FRF
(D = 439)
WGAN-Generated
Experimental Noise
(D = 439)
Pre-processed Noisy
FRF Dataset
(D = 439)
FEM Domain Experimental Domain
Noisy FEM Domain
Noisy Truncated
FRF of FLCB
(D = 439)
Noisy Truncated FRF
from Damaged Canister
(D = 439)
Noisy FRF
Difference
(D = 439)
Subtraction
Noisy FEM Domain

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b)
Damage Class Damage Mode Damage Location(s)
Slight Damage
Missing Casing FA6, FA24, FA35, FA40, FA48
Missing Spacer Grids FA14, FA40
Missing Fuel Rods FA27, FA46
One Fractured Fuel Rod FA50
Two Fractured Fuel Rods FA45
Moderate Damage One Missing FA FA14, FA17, FA54
Severe Damage
Two Missing FA (FA48, FA49)
Three Missing FA (FA13, FA14, FA15)
Four Missing FA (FA31, FA32, FA41, FA42)
Figure 6-5. Locations of damage for simulations in FEM training dataset (a) FA location labels, and (b) damage locations in each
simulated damage scenario. Parentheses indicate FA missing together in a group.
FA1 FA2
FA3 FA4 FA5 FA6 FA7 FA8
FA9 FA10 FA11 FA12 FA13 FA14 FA15 FA16
FA17 FA18 FA19 FA20 FA21 FA22 FA23 FA24
FA25 FA26 FA27 FA28 FA29 FA30 FA31 FA32 FA33 FA34
FA35 FA36 FA37 FA38 FA39 FA40 FA41 FA42 FA43 FA44
FA45 FA46 FA47 FA48 FA49 FA50 FA51 FA52
FA53 FA54 FA55 FA56 FA57 FA58 FA59 FA60
FA61 FA62 FA63 FA64 FA65 FA66
FA67 FA68
a)

122
6.3. Experimental Noise Modeling
The goal of this study was to detect damage modes that could not be easily simulated
experimentally using the high-fidelity FEM. However, the numerical FRF were noise-free,
whereas the experimental FRF contain significant noise, marked by oscillations in FRF amplitude
as shown in Figure 3-2 (c). To realistically model real-world conditions, experimental noise was
injected into the numerical FRF. The experimental noise in this study refers to the measurement
uncertainties (including errors) between repeated measurements of nominally identical conditions.
A generative model was chosen for this task since they are effective at learning the distribution of
high-dimensional data [129]. By learning noise distributions directly from experimental data, the
generative model ensured that the noise closely matched the real noise observed in the
experiments.
6.3.1. Experimental noise extraction
During experimentation, repeated measurements were recorded by each accelerometer. The
number of measurements from a sensor was defined as m. The variation among m FRF was defined
as the experimental noise. To center the datasets, the m FRF were averaged, and the average was
removed from each FRF sample for each sensor. The centered FRF are referred to as the
experimental noise signals in this study.
Figure 6-6 (a)-(d) shows a plot of ± one standard deviation oscillating around zero mean for
the noise samples for each damage mode. Each subplot represents a damage class, and each color
corresponds to a damage mode within the damage class. It is observed that the variation of noise
generally increased with damage severity, with a few exceptions including missing casing, missing
fuel rods, and three missing FA. Since each damage mode exhibited a different noise level, a

123
separate model was used for each mode to ensure the noise added to the numerical FRF was
representative of the noise in the corresponding experiments.
Figure 6-6. One standard deviation of noise samples for damage modes in each damage class: (a) no damage, (b) slight damage,
(c) moderate damage, and (d) severe damage.
6.3.2. Generative ML models
Generative adversarial networks (GAN) are ML models designed to learn the distribution of
a dataset and thus generate new samples. They consist of two neural networks: a generator tasked
with creating the synthetic data, and a discriminator tasked with distinguishing between the real
and synthetic data [129]. The two networks are trained simultaneously to minimize the crossentropy loss and improve the generator’s ability to replicate the real data distribution.
6.3.3. Wasserstein generative adversarial network (WGAN)
Traditional GAN may be susceptible to training instability caused by vanishing gradients,
which occurs when the discriminator becomes overly confident in distinguishing real data from
a) b)
c) d)

124
synthetic data [130][131]. This leads to mode collapse as the generator produces a limited range
of samples [130]. To address this, WGAN were introduced by Arjovsky et al. [132]. Wasserstein
generative adversarial networks reduce sensitivity to vanishing gradients by optimizing the
Wasserstein distance between the real and synthetic data distributions in the discriminator network
(called the “critic” in WGAN) [132][133][134][135]. This loss function provides smoother
gradients and leads to greater stability during training. Additionally, WGAN employ a gradient
penalty to regularize the critic’s gradients. This regularization ensures a more stable optimization
process when updating the generator and critic simultaneously [132]. As a result, WGAN generate
samples that better capture the complexity of the entire real data distribution.
The WGAN architecture used in this study is shown in Figure 6-7. The input to the
generator network was a random noise signal with a length of 439 generated by sampling a
standard Gaussian distribution. The generator consisted of two fully connected hidden layers and
an output layer. The first and second hidden layers had 200 and 400 neurons, respectively, and
both employed ReLU activation and dropout with a specified probability, p. For the generator, the
affine transformation in the l-th fully connected layer is calculated as
( ) ( ) ( 1) ( ) ReLU( ) l ll l z Wz b − = + (52)
where ( )l W is the weight matrix of layer l and ( )l b is the bias vector of layer l [94]. The random noise
signal used as input had (0) 439 1x z ∈ , therefore (1) 200 439 Wg
× ∈ and (1) 200 1
g b × ∈ , where the
subscript g indicates the generator. The second fully connected layer had (2) 400 200 Wg
× ∈ and
(2) 400 1
g b × ∈ . The dimension of the output layer in the generator representing the synthetic
experimental noise signal was 439, therefore (3) 439 400 Wg
× ∈ and (3) 439 1
g b × ∈ .

125
The critic then processed the syntethic noise signals from the generator and the real noise
signals. The first hidden layer had (1) 350 439 Wc
× ∈ and (1) 350 1
c b × ∈ , where the subscript c indicates
the critic network. The second hidden layer in the critic had (2) 150 350 Wc
× ∈ and (2) 150 1
c b × ∈ . The
output layer of the critic provided a scalar score for the synthetic and real input signals, thus the
output layer had (3) 1 150 Wc
× ∈ and (3) 1 1
c b × ∈ .
Figure 6-7. WGAN architecture.
The training process for the WGAN models involved alternating updates to the critic and
generator networks. During training, batches of real and synthetic noise signals were fed to the
critic network. The total loss, representing the approximate Wasserstein distance, was computed
as the difference between the critic’s average score for real samples and its average score for
synthetic samples, written as
  ( , ) [ ( )] [ ( )] r s
WPP fx fx r s xP x P ≈ −     (53)
…
…
…
…
…
Random Noise
Generator Critic
Synthetic
Loss
Real
Loss
Synthetic Signal Real Signal
Total Loss
(Wasserstein
Distance)
Gradient
Penalty
(200) -1
(400)
(439)
(350)
…
(150)
(1)
(439)
(439x1) (439x1)
Input (439x1)

126
where f is the critic network, f x( ) is the critic’s scalar score for the real noise sample x , and
 f x( ) is the scalar score for the synthetic sample 
x . Furthermore, Pr is the distribution of real
noise samples, and Ps is the distribution of synthetic noise samples. The expected value
[ ( )]
r x P f x   is the average critic score for the real noise signals, and  [ ( )]
s x P f x   is the average
critic score for the synthetic noise signals.
A gradient penalty was then added to the loss function to satisfy the Lipschitz constraint
on the critic’s loss. The gradient penalty is written as
   ( )
2
2
() 1 x GP x P x GP λ f x   = ∇−    

  (54)
where λGP is the gradient penalty coefficient, 
x is the interpolated sample between x and 
x ,
 f x( ) is the critic’s score for 
x , and   2
( ) x ∇ f x is the L2 norm of the gradient of the critic’s output
with respect to 
x [133][134].
The training process for the WGAN is outlined in Figure 6-7. The alternating updating
process between the generator and critic continued until the synthetic samples closely matched the
distribution of the real samples. The total critic loss (i.e., the addition of the real and synthetic data
losses) was used for the backpropagation of the critic, while only the negative of the synthetic loss
was used for the backpropagation of the generator.
In this study, nine WGAN models were trained, and each corresponded to a specific
damage mode in the experiments. Table 7 provides a summary of the damage modes used to train

127
each WGAN. Each damage mode had its own model, except one or two fractured fuel rods, which
were only simulated numerically. For these simulations, a single WGAN (W5) was trained using
data from all slight damage modes (i.e., missing casing, missing spacer grids, and missing fuel
rods).
Table 7. Summary of nine WGAN models.
Damage Class Internal Damage Mode
Numerical
Data
Label
WGAN Noisy Data
No Damage No Damage D1 W1 D1+W1
Slight Damage
Missing Casing D2 W2
W5
D2+W2
Missing Spacer Grids D3 W3 D3+W3
Missing Fuel Rods D4 W4 D4+W4
One Fractured Fuel Rod D5 - D5+W5
Two Fractured Fuel Rods D6 - D6+W5
Moderate
Damage One Missing FA D7 W6 D7+W6
Severe
Damage
Two Missing FA D8 W7 D8+W7
Three Missing FA D9 W8 D9+W8
Four Missing FA D10 W9 D10+W9
Each WGAN model was considered trained when two objectives were met: convergence
of the generator and critic losses, and alignment of real and synthetic noise in the t-stochastic
neighbor embedding (t-SNE) plots [133]. The hyperparameters of the nine WGAN models,
including the number of epochs, batch size, gradient penalty coefficient, weight decay, learning
rate, and dropout probability, are summarized in Table 8. The same dropout probability was
applied across all layers of the critic and generator networks. Additionally, the Adam optimizer
[103] was selected as the mini-batch stochastic gradient descent algorithm for both networks with
identical weight decay and learning rate values provided in Table 8.

128
Table 8. Summary of hyperparameters for nine WGAN models.
WGAN Epochs Batch Size λGP Weight Decay Learning Rate Dropout Probability
W1 600 128 1 1.00 × 10-5 5.00 × 10-4 0.5
W2 600 32 1 1.00 × 10-3 5.00 × 10-4 0.2
W3 1,600 128 2 1.00 × 10-5 5.00 × 10-4 0.5
W4 800 32 3 1.00 × 10-5 5.00 × 10-4 0.2
W5 600 128 1 1.00 × 10-5 5.00 × 10-4 0.5
W6 800 128 1 1.00 × 10-5 5.00 × 10-4 0.5
W7 1,000 128 5 1.00 × 10-5 5.00 × 10-4 0.2
W8 600 32 3 1.00 × 10-4 5.00 × 10-4 0.2
W9 600 128 1 1.00 × 10-4 5.00 × 10-4 0.5
The critic and generator losses for each WGAN model are shown in Figure 6-8 (a)-(i). The
scales of each subfigure in Figure 6-8 vary due to differences in hyperparameters. The black line
represents the critic loss, and the gray line represents the generator loss. In each plot, the generator
loss shows maximization since it represents the negative of the synthetic data loss. It was
concluded that the losses for both networks in each WGAN model converged by the number of
epochs specified in Table 8.

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Figure 6-8. Critic and generator losses for each WGAN model: (a) no damage (W1), (b) missing casing (W2), (c) missing spacer
grids (W3), (d) missing fuel rods (W4), (e) all slight damage data (W5), (f) moderate damage (W6), (g) two missing FA (W7),
(h) three missing FA (W8), and (i) four missing FA (W9).
After training, the generator was used to produce experimental noise samples equal to the
number of FRF difference samples for each damage mode. Then, t-SNE plots were created to
visualize the alignment between the real and WGAN-generated signals [133]. t-stochastic neighbor
embedding is a dimensionality reduction technique that projects the noise signals to a twodimensional space [136]. For both the real noise and synthetic noise signals, the algorithm
calculated the pairwise similarities between samples in the high-dimensional space using a
Gaussian distribution. Then, the samples were projected into two dimensions using a t-distribution.
a) b) c)
e) f)
h) i)
d)
g)

130
The optimal projection was found by minimizing the Kullback-Leibler (KL) divergence between
the high and low dimensional spaces [136].
Figure 6-9 (a)-(i) shows the t-SNE plots for each WGAN model. In all cases besides two
missing FA in Figure 6-9 (g), the t-SNE plots show clear overlap between the samples in the real
and synthetic datasets, indicating that the WGAN-generated noise was representative of the real
noise distributions. However, despite some overlap in the central region, the WGAN for two
missing FA produced synthetic signals that had less overlap. This was attributed to the higher noise
levels in this dataset with amplitudes nearing 8 dB as shown in Figure 6-6 (d). As expected,
modeling the complexity of the noise signals for this damage case was a more challenging task for
the WGAN. To further evaluate the performance, the mean absolute error (MAE) between the real
and generated signals was calculated at each frequency point in dB and averaged across all
samples. The MAE between the real and generated signals for the WGAN for two missing FA was
2.94 dB, which was considered reasonable given the noise variability for this damage mode. The
MAE values for each WGAN are provided on the respective subplots in Figure 6-9 (a)-(i), and all
were considered reasonable compared to the noise variation in each of the damage modes as shown
in Figure 6-6 (a)-(d).

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Figure 6-9. t-stochastic neighbor embedding plot for real noise and synthetic noise signals: (a) no damage (W1), (b) missing
casing (W2), (c) missing spacer grids (W3), (d) missing fuel rods (W4), (e) all slight damage data (W5), (f) one missing FA
(W6), (g) two missing FA (W7), (h) three missing FA (W8), and (i) four missing FA (W9).
After training, the generator in each WGAN was used to generate synthetic noise signals
which were then added to the numerical FRF according to Table 8. Figure 6-10 (a)-(d) shows FRF
difference samples with and without noise for the FEM dataset. The y-axes are scaled differently
to visualize the differences in signal for each damage class. In all cases, the FRF difference without
noise is smoother compared to the noisy FRF differences as shown with increased oscillations.
These oscillations are like those present in experimental FRF differences in Figure 5-3. This
confirmed that the WGAN-generated noise successfully incorporated experimental variations into
the numerical simulations.
a) b) c)
d) e) f)
g) h) i)
MAE = 0.984 dB MAE = 0.215 dB MAE = 0.952 dB
MAE = 0.101 dB MAE = 0.481 dB MAE = 0.921 dB
MAE = 2.94 dB MAE = 0.095 dB MAE = 1.74 dB

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Figure 6-10. FRF difference with and without added WGAN-generated noise: (a) no damage, (b) slight damage, (c) moderate
damage, and (d) severe damage.
6.4. Multi-task Extreme Gradient Boosting (XGBoost)
The goal of this study was to classify each FRF difference sample into (1) a damage severity
class and (2) a localization class. Therefore, a multi-task XGBoost model was selected over a kNN, RF, and support vector machine (SVM) due to its strong predictive accuracy and reduced risk
of overfitting [137][138][139]. The XGBoost algorithm is an ensemble ML model that employs
gradient boosting to build a strong learner from a sequence of weak learners (i.e., decision trees)
[137]. Each tree is trained to correct the errors of the previous ones by minimizing the gradients of
a loss function. Once the errors are minimized, the final prediction is obtained by calculating the
weighted sum of the outputs from all trees.
a) b)
c) d)

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The training process for the XGBoost is shown in Figure 6-11. Each tree was trained to
minimize the objective function defined as
J L () () () θθθ = +Ω ∑ ∑ (55)
where L is the SoftMax cross-entropy loss between the tree predictions and true labels, and Ω is
the regularization function [137]. The regularization function is defined as
1 2
( ) 2
Ω=+ θ γ λω T (56)
where T is the number of leaf nodes in the tree, ω is the score in each leaf node, and γ and λ
are the regularization parameters that penalize trees with large numbers of leaves or leaf weights
to reduce overfitting. A second-order Taylor expansion is used to approximate the objective
function to allow efficient optimization according to

( 1) ( ) 2
1
1 (, ) () () () 2
n t t
i i it i i t i t
i
J L y y gf x hf x f −
=
 
≈ + + + Ω     ∑ (57)
where i g is the first-order derivative and i h is the second-order derivative of the loss function
[137]. During training, the tree starts from a single leaf and adds branches greedily [137][140].
Therefore, at every tree split, the gain is computed as
2 2 2
1
2
L R
L R
i i i
i I i I i I
i ii
i I i I i I
g g g
Gain
hhh γ λλλ
∈ ∈ ∈
∈∈ ∈
                  = +− −
+++
 
∑ ∑ ∑
∑∑∑ (58)

134
where L I and RI are the sets of instances in the left and right nodes after the split, respectively,
and L R II I = ∪ . The tree stops growing if the gain value is smaller than γ . The output of the
trained XGBoost is the sum of the predictions from the individual trees calculated as

1
( ),
K
i ki k
k
y fx f F =
= ∑ ∈ (59)
where 
i y is the predicted output for the i-th sample, ( ) k i f x is the output of the k-th tree for input
i x , and F is the set of all possible trees [137]. With each iteration t, a new tree is trained to
minimize the residuals (i.e., the difference in the true and predicted values) made by the previous
trees. Therefore, the predicted outputs are updated by adding the contributions of the new tree to
the previous prediction, written as
  ( ) ( 1)
( ) t t
i i t i y y fx η −
= + (60)
where  ( 1) t
i y −
is the output of the previous tree, η is the learning rate, and ( ) t i f x is the output of
the new tree.
Once the trees have been trained, the XGBoost aggregates the output raw class scores from
each tree and applies SoftMax activation for conversion to class probabilities. Since the XGBoost
is a multi-task model, there is one set of predictions for each task, namely, 
damage y for damage
detection and 
location y for localization. The final class probabilities for damage detection and
localization are determined after the SoftMax operation is performed on 
damage y and 
location y using

135
Eq. (48) and Eq. (49), respectively. For each task, the class with the highest probability was the
predicted class of the sample.
Figure 6-11. XGBoost training process.
In this study, the XGBoost was trained on three different training datasets: (1) FEM data,
(2) noisy FEM data, and (3) noisy FEM data plus experimental data. The XGBoost library in
Python was used [141]. Several hyperparameters were evaluated to optimize the model’s
performance. For instance, a range of values for the number of estimators was tested. For the
training dataset containing noisy FEM data and experimental data, the results in Figure 6-12 show
that 800 trees provided a balance of computational efficiency and high accuracy for damage
detection and localization. Additionally, based on trial-and-error, a learning rate of 0.1 was
selected, and the maximum tree depth was chosen to be six.
FRF Difference
Sum
Final Prediction
…
Residuals Residuals Residuals Residuals
Tree 1 Tree 2 Tree 3 Tree 800
SoftMax Activation

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Figure 6-12. Damage detection and localization testing accuracy for XGBoost using different numbers of trees.
6.5. Results and Analysis
6.5.1. Effect of the noise in training
Three training datasets were used to assess the impact of noise on the testing performance.
The first training dataset consisted of pure FEM data, the second included noisy FEM, and the
third combined noisy FEM data with additional experimental samples (i.e., 13.7% of the training
dataset was experimental data). After training the XGBoost model on each dataset, the model was
evaluated on both the noisy FEM and the experimental testing datasets. The macro-F1 scores of
each testing dataset are shown in Figure 6-13. The horizontal axis shows the training datasets.
White bars represent the experimental testing dataset, while gray bars represent the noisy FEM
testing dataset. Solid bars indicate damage level predictions, and hatched bars represent damage

137
location predictions. The macro-F1 scores for the noisy FEM testing dataset showed negligible
differences across the three training datasets. However, the effect of training dataset on the
experimental testing dataset was significant. Adding noise to the FEM data alone increased the
macro-F1 scores of the experimental testing dataset from 0.060 to 0.594 for the damage detection
and from 0.645 to 0.926 for localization. These constitute major improvements with the proposed
approach. Furthermore, adding 3,721 experimental samples to training further improved the
macro-F1 scores for both the damage detection and the localization tasks. Therefore, it was
concluded that using noisy FEM plus experimental data for XGBoost training significantly
improved the damage identification performance for the physical mock-up canister. The following
sections present detailed damage identification results using the combined noisy FEM and
experimental training dataset.
Figure 6-13. Macro-F1 scores of the testing datasets after training XGBoost with three different training datasets.

138
6.5.2. Confusion matrices
The confusion matrices for the damage detection and localization tasks are provided in Figure
6-14 (a)-(b) and Figure 6-15 (a)-(b) for the noisy FEM and experimental testing datasets,
respectively. For the FEM dataset, the XGBoost achieved a macro-F1 score of 0.998 for damage
detection and 0.890 for localization. In the damage detection task, the no damage, slight damage,
moderate damage, and severe damage classes had recall rates of 0.991, 1.00, 0.998, and 1.00, and
precisions of 1.00, 0.998, 0.999, and 0.999, respectively. For localization, the negative and positive
location classes had recall rates of 0.997 and 0.716, and precisions of 0.991 and 0.871, respectively.
As shown with Figure 6-15 (a)-(b), all samples were correctly classified for both tasks in the
experimental testing dataset thus achieving perfect macro-F1 scores of 1.00.
Figure 6-14. Confusion matrices for noisy FEM testing dataset: (a) damage detection task, and (b) localization task.
a) b)

139
Figure 6-15. Confusion matrices for experimental testing dataset: (a) damage detection task, and (b) localization task.
6.5.3. Detailed damage and localization predictions
During experimentation, since there were multiple measurements recorded for each
accelerometer, the XGBoost produced multiple predictions per sensor. Therefore, the majority
vote damage prediction for each sensor was calculated as the final prediction for that sensor. The
majority vote predictions for damage detection and localization in each experimental test case are
provided in Figure 6-16 (a)-(d). In the figures, the sensor numbers are in black, the majority vote
damage predictions are in red, and the actual damage location(s) are highlighted by red squares. If
the majority vote prediction for localization was positive, the corresponding FA cell was shaded
in pink. For all test cases, the damage and localization predictions were perfect, meaning every
prediction for each sensor was correct. This demonstrates the XGBoost model’s ability to
accurately detect the internal damage level and specific damage location within the physical mockup canister. This is a significant improvement from [47] as the damage location was narrowed
from a canister quarter to an exact FA cell.
a) b)

140
The damage detection and localization predictions for the damage simulations in the FEM
testing dataset are shown in Figure 6-17 (a)-(j). There is one test case per damage mode. Each
circle on the bottom plate represents one of the 1,169 observation nodes. The nodes were colorcoded based on their predicted damage level from the XGBoost: gray for no damage, green for
slight damage, blue for moderate damage, and orange for severe damage. Additionally, if the
location prediction was positive, the node was outlined in black. For each test case, the majority
of nodes were correctly classified, with only two misclassifications each for no damage in Figure
6-17 (a), one fractured fuel rod in Figure 6-17 (e), and one missing FA in Figure 6-17 (g). Given
the minimal number of misclassified nodes in these test cases compared to the total 1,169
observation nodes, it was concluded that the XGBoost was capable of accurately identifying the
level of damage within the numerical canister, even with experimental noise introduced to the
samples.
Additionally, the XGBoost correctly predicted most of the damage locations for each test
case with only a few errors. The no damage test case in Figure 6-17 (a) had all negative location
predictions. Furthermore, in the cases of missing spacer grids, two fractured fuel rods, one missing
FA, two missing FA, three missing FA, and four missing FA in Figure 6-17 (c), Figure 6-17 (d),
Figure 6-17 (f), Figure 6-17 (g), Figure 6-17 (h), Figure 6-17 (i), and Figure 6-17 (j), respectively,
nearly all nodes within the actual damage location(s) had positive location predictions. Only a few
nodes inside and outside the actual damage location were misclassified. The missing casing and
one fractured fuel rod test cases in Figure 6-17 (b) and Figure 6-17 (e) had only one positive
location prediction each. However, importantly, the node with the positive location prediction was
inside the actual damage location for each case. Considering the localization results from all the
observation nodes in each test case, it was concluded that the XGBoost demonstrated accurate

141
damage localization for the FEM data with added experimental noise. Notably, the XGBoost
accurately identified the cases of one and two fractured fuel rods, which were not experimented
with the physical mock-up canister.
These results demonstrate the feasibility of using FEM data in combination with limited
experimental information to simulate damage modes that are not feasible to replicate
experimentally. These findings suggest that in real-world canister inspections, collecting a small
set of experimental data and combining it with a large set of numerical data can provide a solution
for accurate damage identification. Furthermore, the experimentally collected data does not
necessarily need to match the numerically simulated damage modes. The experimental data can
even be collected on the healthy FLCB to improve the predictive ability of the computational
models. This approach minimizes the need for time-consuming physical experiments while
enabling the detection of a broader range of damage modes in sealed SNF canisters. Consequently,
it enhances the overall efficiency of the internal FA damage identification methodology.

142
Figure 6-16. Majority vote damage and location predictions from the XGBoost for each experimental test case: (a) no damage,
(b) slight damage, (c) moderate damage, (d) severe damage.
a) b)
c) d)
N = No Damage
SL = Slight Damage
M = Moderate Damage
SV = Severe Damage
= Predicted Damage Location
= Actual Damage Location

143
Figure 6-17. Damage and location predictions from the XGBoost for each FEM test case: (a) no damage, (b) missing casing, (c)
missing interior spacer grids, (d) one missing fuel rod, (e) one fractured fuel rod, (f) two fractured fuel rods, (g) one missing FA,
(h) two missing FA, (i) three missing FA, and (j) four missing FA.
a) b) c)
d) e) f)
g) h) i)
j)

144
6.6. Conclusions
In this study, a multi-task XGBoost was used to detect and localize damage in a 2/3-scale
experimental mock-up canister and its corresponding high-fidelity FEM. The FEM was employed
to simulate damage modes that could not be physically considered by the mock-up (i.e., fractured
fuel rods). Since the damage location is unknown in real canisters, accelerometers were positioned
at arbitrary locations on the exterior surface of the mock-up’s bottom plate. The observation nodes
for numerical data collection were similarly restricted to the bottom plate. To address the absence
of noise in the numerical FRF, nine WGAN models were trained to generate experimental noise
signals. The generated noise signals were added to the numerical computed FRF to replicate
experimental conditions. The difference in FRF between the FLCB and the canister with internal
damage for both the noisy FEM and experimental datasets were used as input to test the XGBoost.
The XGBoost successfully classified the FRF differences into damage severity and localization
classes. The macro-F1 scores for the FEM testing dataset were 0.998 and 0.890 for damage
detection and localization, and the macro-F1 scores were 1.00 for the experimental testing dataset.
The following conclusions were made from this work:
• Measurements from accelerometers mounted solely on the bottom of the canister offered
accurate detection and localization of internal FA damage within a mock-up SNF canister.
The multi-task XGBoost successfully identified the damage level and exact FA cell
position of the damage(s) as all predictions were perfect for each experimental test case.
• The multi-task XGBoost model successfully generalized across both experimental and
noisy numerical datasets. It accurately detected damage modes, including fractured fuel
rods, that were not physically simulated in the experimental mock-up, alongside those that
were simulated experimentally. While some FEM test cases had incorrect localization at

145
certain observation nodes, accurate overall localization was achieved by considering results
from all nodes.
• The nested CB method significantly reduced the computational cost of calculating the
numerical FRF while maintaining accuracy. By limiting the observation nodes to the
bottom plate of the canister, the model mirrored practical constraints in real-world canister
measurements and further contributed to dimensionality reduction of the model.
• The trained WGAN successfully generated noise signals that accurately represented the
distribution of experimental noise for each damage mode. This method retained the
characteristics of each damage mode to ensure proper modification of the numerical data
represented the appropriate experimental conditions.
• Despite the introduction of experimental noise to the numerical simulations, the XGBoost
was still capable of detecting damage modes that were unseen in experiments. This
demonstrates the potential of using FEM simulations combined with noise modeling
techniques to detect more complex damage modes.
• By incorporating noisy FEM data with experimental samples into the training dataset, the
performance on the experimental testing dataset significantly improved. A low percentage
(i.e., 13.7%) of experimental data was needed in training for accurate damage identification
of the canister mock-up, reducing the time and cost of conducting experiments. This
highlights the effectiveness of combining numerical and experimental datasets to enhance
the real-world internal inspections of SNF canisters.

146
Chapter 7: Conclusions, Limitations, and Recommendations for Future Work
7.1. Conclusions
This study investigated the use of dynamic modal analysis and ML to identify internal FA
damage within sealed SNF canisters. Specifically, the use of FRF measured on the exterior surface
of sealed SNF canisters to detect and localize internal FA damage was studied. By combining highfidelity FEM, EMA of the physical canister mock-up, and ML techniques, this research introduced
a novel integrated NDE-ML framework for identifying FA damage without the need to open sealed
canisters. This work therefore provides advancements in the safety and efficiency of real-world
SNF canister inspections.
A key contribution of this study was the development of a high-fidelity FEM of a mock-up
SNF canister and the application of a previously developed nested CB method to reduce
computational demands for modal analysis. The FEM results were validated through EMA tests,
where FRF were obtained on the bottom plate of the canister mock-up. For both the numerical and
experimental method, the FRF were calculated for the healthy FLCB and for the canister with
missing FA. Both approaches successfully localized multiple missing FA using the RMSE between
the FRF from different canister conditions. As an additional method, ARMA models were fit to
the collected time series data, and the AR coefficient were used as DSF. The difference in average
DSF between the FLCB and the canister with missing FA correctly identified the location of the
missing FA, and this was validated by a statistical t-test. This highlighted the potential of vibrationbased internal damage assessments for sealed SNF canisters.
To address the limitations of RMSE-based damage detection in detecting finer damage modes
such as one missing FA and missing FA components, ML algorithms were employed. Multiple

147
ML classifiers, including RF, ANN, and GNB, were tasked with analyzing the FRF difference data
to detect four internal FA damage levels. This was extended to a multi-task problem where a kNN and CNN were trained to (1) detect damage levels and (2) localize the FA damage to a specific
quarter of the canister. To the author’s knowledge, this represented the first successful application
of ML to classify and localize internal FA damage within sealed SNF canisters. Furthermore, a
WGAN-based experimental noise modeling technique was developed to generate noise samples,
which were then added to the numerical FRF data. This approach helped align the numerical and
experimental domains. A multi-task XGBoost model was employed to analyze the combined noisy
FEM and experimental datasets. The XGBoost could identify fractured fuel rods; this was a
damage mode that is difficult to simulate experimentally. This experimental noise modeling
minimizes the need for time-consuming physical experiments and enables the detection of a larger
range of damage modes in sealed SNF canisters.
The contributions of this research are significant for advancing non-invasive inspection
methods for SNF canisters. By leveraging ML to analyze exterior surface measurements, this
framework reduces the reliance on labor-intensive canister openings and provides an efficient
solution for monitoring internal FA damage. Combined with numerical modeling, the ML-aided
NDE approach provides a practical solution for the internal inspection of sealed SNF canisters in
field applications, thereby, increasing the safe operation of nuclear waste and reducing the
potential exposure risk of the public.
7.2. Limitations
Although this study advanced the identification of internal FA damage from sealed SNF
canisters, several limitations were identified. These limitations include:

148
• Limited FA damage modes. The experimental and numerical analyses were limited to
missing FA, missing FA components, and fractured fuel rods as the primary damage
scenarios. More complex or subtle damage types, such as total FA collapse or fuel rod
deformation, were not explored and may require additional analyses.
• Environmental effects. This study does not consider the effects of radiation, high
temperatures, or long-term aging on the dynamic response of the canister. The investigation
of these conditions in SMRL was not feasible to simulate in this study.
7.3. Recommendations for Future Work
Several areas for future work have been identified to further advance the detection of internal
FA damage in real-world canister inspections. These include:
• Model updating of the high-fidelity FEM. Future work should focus on refining the FEM
through model updating techniques, including Bayesian inference, to improve alignment
with experimental results. Discrepancies due to assumptions about material properties,
boundary conditions, and environmental factors can be addressed by integrating modal
parameters from EMA. Bayesian inference offers a probabilistic approach to iteratively
refine uncertain parameters while quantifying uncertainties. Enhanced FEM accuracy
would enable more reliable damage detection and localization, particularly for complex or
subtle scenarios, and potentially advance canister inspections by reducing experimental
demands.
• Optimization of sensor placement. Enhancing sensor placement strategies using
optimization-based approaches could improve the resolution and accuracy of damage
localization in SNF canisters. Optimized networks can ensure reliable detection of internal

149
damage, even in hard-to-access areas, while reducing the number of sensors required.
Refined configurations would increase the efficiency and cost-effectiveness of real-world
canister inspections to support more practical and accurate monitoring of internal FA
damage modes.
• Incorporating risk assessment and decision-making. Risk assessment methods can evaluate
the likelihood and consequences of FA damage in SNF canisters under specific stressors.
Approaches such as probabilistic risk assessment (PRA), Bayesian networks, or Monte
Carlo simulations can quantify risks and provide insights into canister vulnerability. These
tools could help prioritize inspections and facilitate effective decision-making to enhance
the safety and efficiency of SNF canister inspections.

150
References
[1] United States Nuclear Regulatory Commission. (2023). Transportation of spent nuclear fuel.
https://www.nrc.gov/waste/spent-fuel-transp.html. (Accessed February 20, 2024).
[2] von Hippel, F. N., & Schoeppner, M. (2017). Economic Losses From a Fire in a Dense-Packed
U.S. Spent Fuel Pool. Science & Global Security, 25(2), 80-92.
https://doi.org/10.1080/08929882.2017.1318561.
[3] United States Nuclear Regulatory Commission. (2023). Storage of spent nuclear fuel.
https://www.nrc.gov/waste/spent-fuel-storage.html. (Accessed February 20, 2024).
[4] Raiko, H. (2005). Disposal Canister for Spent Nuclear Fuel-Design Report, POSIVA 2005-02,
Finland.
https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=405fd6cb5f80297762a
2f205754cf4c3ea497d7b.
[5] Rothwell, G. (2021). Spent nuclear fuel storage: What are the relationships between size and
cost of the alternatives? Energy Policy, 150. https://doi.org/10.1016/j.enpol.2020.112126.
[6] Bonano, E. J., Kalinina, E. A., & Swift, P. N. (2018). The Need for Integrating the Back End
of the Nuclear Fuel Cycle in the United States of America. MRS Advances, 3(19), 991-
1003. https://doi.org/10.1557/adv.2018.231.
[7] United States Department of Energy. (2019). Spent nuclear fuel and high-level radioactive
waste inventory report (Report No. FCRD-NFST-2013-000263, Rev. 6). Office of Spent
Fuel and Waste Disposition. https://doi.org/10.2172/1570351.
[8] Kim, J.-S., Hong, J.-D., Yang, Y.-S., & Kook, D.-H. (2017). Rod internal pressure of spent
nuclear fuel and its effects on cladding degradation during dry storage. Journal of Nuclear
Materials, 492, 253-259. https://doi.org/10.1016/j.jnucmat.2017.05.047.
[9] Duan, Z., Yang, H., Satoh, Y., Murakami, K., Kano, S., Zhao, Z., Shen, J., & Abe, H. (2017).
Current status of materials development of nuclear fuel cladding tubes for light water
reactors. Nuclear Engineering and Design, 316, 131-150.
https://doi.org/10.1016/j.nucengdes.2017.02.031.
[10] Hanifehzadeh, M., Gencturk, B., & Willam, K. (2017). Dynamic structural response of
reinforced concrete dry storage casks subjected to impact considering material degradation.
Nuclear Engineering and Design, 325, 192-204.
https://doi.org/10.1016/j.nucengdes.2017.10.001.

151
[11] Lin, C.-Y., Wu, T.-Y., & Huang, C.-C. (2015). Nonlinear dynamic impact analysis for
installing a dry storage canister into a vertical concrete cask. International Journal of
Pressure Vessels and Piping, 131, 22-35. https://doi.org/10.1016/j.ijpvp.2015.04.006.
[12] Lin, M., Wang, J., Wu, B., & Li, Y. (2021). Dynamic analysis of dry storage canister and the
spent fuels inside under vertical drop in HTR-PM. Annals of Nuclear Energy, 154.
https://doi.org/10.1016/j.anucene.2020.108030.
[13] United States Nuclear Regulatory Commission (U.S. NRC). (2014). Spent fuel transportation
risk assessment (NUREG-2125). Washington, DC, United States.
https://www.nrc.gov/docs/ML1403/ML14031A323.pdf.
[14] Zhuang B., Arcaro, A., Gencturk, B., Meyer, R., Oberai, A., Sinkov, A., & Good, M. (2025).
Non-destructive Evaluation and Machine Learning Methods for Inspection of Spent
Nuclear Fuel Canisters: a State-of-the-Art Review. Progress in Nuclear Energy, 185,
105697. https://doi.org/10.1016/j.pnucene.2025.105697.
[15] The Electric Power Research Institute (EPRI). (2019). Dry storage system inspection: Visual,
thermal, and radiation dose measurements (Report No. 3002016034). Palo Alto, CA,
United States. https://www.epri.com/research/products/000000003002016034.
[16] Choi, S., Cho, H., & Lissenden, C. J. (2018). Nondestructive inspection of spent nuclear fuel
storage canisters using shear horizontal guided waves. Nuclear Engineering and
Technology, 50(6), 890-898. https://doi.org/10.1016/j.net.2018.04.011.
[17] Meyer, R. M., Good, M. S., Suter, J. D., Luzi, F., Glass, B., & Hutchinson, C. (2019). Liquid
water sensing in dry cask storage systems by guided waves. Proceedings of the 46th Annual
Review of Progress in Quantitative Nondestructive Evaluation (QNDE2019), Portland,
OR, USA.
[18] Foster, E. A., Bernard, R., Bolton, G., Jackson-Camargo, J. C., Gachagan, A., Mohseni, E.,
& MacLeod, C. N. (2022). Inspection of nuclear assets with limited access using Feature
Guided Waves. NDT & E International, 131.
https://doi.org/10.1016/j.ndteint.2022.102695.
[19] Soltangharaei, V., Hill, J. W., Ai, L., Anay, R., Greer, B., Bayat, M., & Ziehl, P. (2020).
Acoustic emission technique to identify stress corrosion cracking damage. Structural
Engineering and Mechanics, 75(6), 723-736.
https://doi.org/https://doi.org/10.12989/sem.2020.75.6.723.
[20] Ai, L., Soltangharaei, V., Bayat, M., Greer, B., & Ziehl, P. (2021). Source localization on
large-scale canisters for used nuclear fuel storage using optimal number of acoustic

152
emission sensors. Nuclear Engineering and Design, 375.
https://doi.org/10.1016/j.nucengdes.2021.111097.
[21] Hwang, W., Bae, S., Kim, J., Kang, S., Kwag, N., & Lee, B. (2015). Acoustic emission
characteristics of stress corrosion cracks in a type 304 stainless steel tube. Nuclear
Engineering and Technology, 47(4), 454-460. https://doi.org/10.1016/j.net.2015.04.001.
[22] Hasanian, M., Choi, S., & Lissenden, C. (2019). Laser ultrasonics toward remote detection of
stress corrosion cracking. Materials Evaluation, 77(9), 1089-1098.
[23] Xiao, W., & Yu, L. (2020). Nondestructive evaluation of nuclear spent fuel dry cask structures
using non-contact ACT-SLDV Lamb wave method. Proceedings of SPIE 11382, Smart
Structures and NDE for Industry 4.0, Smart Cities, and Energy Systems, 113820D.
https://doi.org/10.1117/12.2558303.
[24] Fobar, D. G., Xiao, X., Burger, M., Le Berre, S., Motta, A. T., & Jovanovic, I. (2018). Robotic
delivery of laser-induced breakdown spectroscopy for sensitive chlorine measurement in
dry cask storage systems. Progress in Nuclear Energy, 109, 188-194.
https://doi.org/10.1016/j.pnucene.2018.08.001.
[25] Bakhtiari, S., Elmer, T. W., Koehl, E., Wang, K., Raptis, P., Kunerth, D. C., & Birk, S. M.
(2012). Dry cask storage inspection and monitoring: Interim report. Argonne National
Laboratory. https://publications.anl.gov/anlpubs/2014/03/77579.pdf.
[26] Foster, E. A., Bolton, G., Bernard, R., McInnes, M., McKnight, S., Nicolson, E., Loukas, C.,
Vasilev, M., Lines, D., Mohseni, E., Gachagan, A., Pierce, G., & Macleod, C. N. (2022).
Automated Real-Time Eddy Current Array Inspection of Nuclear Assets. Sensors, 22(16).
https://doi.org/10.3390/s22166036.
[27] Chatzidakis, S. (2017). Exploring the use of muon momentum for detection of nuclear
material within shielded spent nuclear fuel dry casks. Transactions of the American
Nuclear Society, 116, 190–193.
[28] Chatzidakis, S., Alamaniotis, M., & Tsoukalas, L. H. (2014). A Bayesian approach to
monitoring spent fuel using cosmic ray muons. Transactions of the American Nuclear
Society, 111(1), 369–370. https://www.ans.org/pubs/transactions/article-36379.
[29] Chatzidakis, S., Forsberg, P. T., Sims, B. T., & Tsoukalas, L. H. (2015). Monte Carlo
simulations of cosmic ray muons for dry cask monitoring. Transactions of the American
Nuclear Society, 112, 534–536.
https://www.researchgate.net/publication/312888752_Montecarlo_simulations_of_cosmic_ray_muons_for_dry_cask_monitoring.

153
[30] Chatzidakis, S., Forsberg, P. T., Sims, B. T., & Tsoukalas, L. H. (2016). Investigation of
imaging spent nuclear fuel dry casks using cosmic ray muons. Transactions of the
American Nuclear Society, 114(1), 152–155. https://www.osti.gov/biblio/22991850.
[31] Chatzidakis, S., Choi, C. K., & Tsoukalas, L. H. (2016). Interaction of cosmic ray muons with
spent nuclear fuel dry casks and determination of lower detection limit. Nuclear
Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment, 828, 37-45.
https://doi.org/10.1016/j.nima.2016.03.084.
[32] Chatzidakis, S., Choi, C. K., & Tsoukalas, L. H. (2016). Analysis of spent nuclear fuel
imaging using multiple Coulomb scattering of cosmic muons. IEEE Transactions on
Nuclear Science, 63(6), 2866–2874. https://doi.org/10.1109/TNS.2016.2618009.
[33] Chatzidakis, S., Hausladen, P. A., Croft, S., Chapman, J. A., Jarrell, J. J., Scaglione, J. M.,
Choi, C. K., & Tsoukalas, L. H. (2017). Classification and imaging of spent nuclear fuel
dry casks using cosmic ray muons. Nuclear Plant Instrumentation, Control, and HumanMachine Interface Technologies, 237–245. http://npic-hmit2017.org/wpcontent/data/pdfs/132-22923.pdf.
[34] Liu, Z., Chatzidakis, S., Scaglione, J. M., Liao, C., Yang, H., & Hayward, J. P. (2018). Muoncomputed tomography using PoCA trajectory for imaging spent nuclear fuel in dry storage
casks. Proceedings of the International Congress on Advances in Nuclear Power Plants
(ICAPP 2018), 701–705. https://www.osti.gov/servlets/purl/1486966.
[35] Jonkmans, G., Anghel, V. N. P., Jewett, C., & Thompson, M. (2013). Nuclear waste imaging
and spent fuel verification by muon tomography. Annals of Nuclear Energy, 53, 267-273.
https://doi.org/10.1016/j.anucene.2012.09.011.
[36] Poulson, D., Durham, J. M., Guardincerri, E., Morris, C. L., Bacon, J. D., Plaud-Ramos, K.,
Morley, D., & Hecht, A. A. (2017). Cosmic ray muon computed tomography of spent
nuclear fuel in dry storage casks. Nuclear Instruments and Methods in Physics Research
Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 842, 48-53.
https://doi.org/10.1016/j.nima.2016.10.040.
[37] Papamarkou, T., Guy, H., Kroencke, B., Miller, J., Robinette, P., Schultz, D., Hinkle, J.,
Pullum, L., Schuman, C., Renshaw, J., & Chatzidakis, S. (2021). Automated detection of
corrosion in used nuclear fuel dry storage canisters using residual neural networks. Nuclear
Engineering and Technology, 53(2), 657-665. https://doi.org/10.1016/j.net.2020.07.020.
[38] Zhang, B., Miao, Y., Tian, Y., Zhang, W., Wu, G., Wang, X., & Zhang, C. (2021).
Implementation of surface crack detection method for nuclear fuel pellets guided by

154
convolution neural network. Journal of Nuclear Science and Technology, 58(7), 787-796.
https://doi.org/10.1080/00223131.2020.1869622.
[39] Dong, B., Yang, K., Zhang, W., Yin, J., & Wang, D. (2022). An Improved Method for PWR
Fuel Failure Detection Using Cascade-forward Neural Network With Decision Tree.
Frontiers in Energy Research, 10. https://doi.org/10.3389/fenrg.2022.851848.
[40] Dong, B., Xiao, W., Yin, J., & Wang, D. (2020). Detection of fuel failure in pressurized water
reactor with artificial neural network. Annals of Nuclear Energy, 140.
https://doi.org/10.1016/j.anucene.2019.107104.
[41] Guo, Z., Wu, Z., Liu, S., Ma, X., Wang, C., Yan, D., & Niu, F. (2020). Defect detection of
nuclear fuel assembly based on deep neural network. Annals of Nuclear Energy, 137.
https://doi.org/10.1016/j.anucene.2019.107078.
[42] Ai, L., Soltangharaei, V., Bayat, M., Greer, B., & Ziehl, P. (2021). Source localization on
large-scale canisters for used nuclear fuel storage using optimal number of acoustic
emission sensors. Nuclear Engineering and Design, 375.
https://doi.org/10.1016/j.nucengdes.2021.111097.
[43] Ai, L., Zhang, B., & Ziehl, P. (2023). A transfer learning approach for acoustic emission zonal
localization on steel plate-like structure using numerical simulation and unsupervised
domain adaptation. Mechanical Systems and Signal Processing, 192.
https://doi.org/10.1016/j.ymssp.2023.110216.
[44] Ai, L., Bayat, M., & Ziehl, P. (2023). Localizing damage on stainless steel structures using
acoustic emission signals and weighted ensemble regression-based convolutional neural
network. Measurement, 211. https://doi.org/10.1016/j.measurement.2023.112659.
[45] Aghagholizadeh, M., Gencturk, B., Ghanem, R., & Arcaro, A. (2023). Damage detection of
spent nuclear fuel canisters using frequency response functions. Annals of Nuclear Energy,
185. https://doi.org/10.1016/j.anucene.2023.109707.
[46] Zhuang, B., Arcaro, A., Gencturk, B., & Ghanem, R. (2024). Machine learning-aided damage
identification of mock-up spent nuclear fuel assemblies in a sealed dry storage canister.
Engineering Applications of Artificial Intelligence, 128.
https://doi.org/10.1016/j.engappai.2023.107484.
[47] Arcaro, A., Zhuang, B., Gencturk, B., & Ghanem, R. (2024). Damage detection and
localization in sealed spent nuclear fuel dry storage canisters using multi-task machine
learning classifiers. Reliability Engineering & System Safety, 252.
https://doi.org/10.1016/j.ress.2024.110446.

155
[48] Arcaro, A., Gencturk, B., Ghanem, R & Zhuang, B. (2025). Effect of experimental noise on
internal damage detection of sealed spent nuclear fuel canisters. Engineering with
Computers. (Submitted for review).
[49] LS-DYNA. ANSYS, http://www.lstc.com/ 2021.
[50] Ezvan, O., Zeng, X., Ghanem, R., & Gencturk, B. (2020). Multiscale modal analysis of fullyloaded spent nuclear fuel canisters. Computer Methods in Applied Mechanics and
Engineering, 367. https://doi.org/10.1016/j.cma.2020.113072.
[51] Ezvan, O., Zeng, X., Ghanem, R., & Gencturk, B. (2020). Dominant substructural vibration
modes for fully-loaded spent nuclear fuel canisters. Computational Mechanics, 67(1), 365-
384. https://doi.org/10.1007/s00466-020-01937-8.
[52] Farhat, C., & Geradin, M. (1994). On a component mode synthesis method and its application
to incompatible substructures. Computers & Structures, 51(5), 459-473.
https://doi.org/10.1016/0045-7949(94)90053-1.
[53] Hurty, W. C. (1960). Vibrations of structural systems by component mode synthesis. Journal
of the Engineering Mechanics Division, 86, 51–69.
[54] Hurty, W. C. (1965). Dynamic analysis of structural systems using component modes. AIAA
Journal, 3(4), 678-685. https://doi.org/10.2514/3.2947.
[55] Gladwell, G. M. L. (1964). Branch mode analysis of vibrating systems. Journal of Sound and
Vibration, 1(1), 41-59. https://doi.org/10.1016/0022-460x(64)90006-9.
[56] Craig, R. R., & Bampton, M. C. C. (1968). Coupling of substructures for dynamic analyses.
AIAA Journal, 6(7), 1313-1319. https://doi.org/10.2514/3.4741.
[57] MacNeal, R. H. (1971). A hybrid method of component mode synthesis. Computers &
Structures, 1(4), 581-601. https://doi.org/10.1016/0045-7949(71)90031-9.
[58] Rubin, S. (1974). An improved component-mode representation. In Proceedings of the 15th
Structural Dynamics and Materials Conference. https://doi.org/10.2514/6.1974-386.
[59] Craig, R. R., & Hale, A. L. (1988). Block-Krylov component synthesis method for structural
model reduction. Journal of Guidance, Control, and Dynamics, 11(6), 562-570.
https://doi.org/10.2514/3.20353.
[60] Hintz, R. M. (1975). Analytical Methods in Component Modal Synthesis. AIAA Journal,
13(8), 1007-1016. https://doi.org/10.2514/3.60498.

156
[61] Rubin, S. (1977). Improved component-mode representation for structural dynamic analysis.
In Proceedings of the 18th Structures, Structural Dynamics, and Materials Conference.
https://doi.org/10.2514/6.1977-405.
[62] Rixen, D. J. (2004). A dual Craig–Bampton method for dynamic substructuring. Journal of
Computational and Applied Mathematics, 168(1-2), 383-391.
https://doi.org/10.1016/j.cam.2003.12.014.
[63] Markovic, D., Park, K. C., & Ibrahimbegovic, A. (2006). Reduction of substructural interface
degrees of freedom in flexibility‐based component mode synthesis. International Journal
for Numerical Methods in Engineering, 70(2), 163-180. https://doi.org/10.1002/nme.1878.
[64] Craig, R., Jr. (2000). Coupling of substructures for dynamic analyses: An overview. 41st
Structures, Structural Dynamics, and Materials Conference and Exhibit.
https://doi.org/10.2514/6.2000-1573.
[65] de Klerk, D., Rixen, D. J., & Voormeeren, S. N. (2008). General Framework for Dynamic
Substructuring: History, Review and Classification of Techniques. AIAA Journal, 46(5),
1169-1181. https://doi.org/10.2514/1.33274.
[66] Fang, M., Wang, J., & Li, H. (2017). An adaptive numerical scheme based on the Craig–
Bampton method for the dynamic analysis of tall buildings. The Structural Design of Tall
and Special Buildings, 27(1). https://doi.org/10.1002/tal.1410.
[67] Mapa, L., das Neves, F., & Guimarães, G. P. (2020). Dynamic Substructuring by the Craig–
Bampton Method Applied to Frames. Journal of Vibration Engineering & Technologies,
9(2), 257-266. https://doi.org/10.1007/s42417-020-00223-4.
[68] Lim, J. H., Hwang, D.-S., Kim, K.-W., Lee, G. H., & Kim, J.-G. (2017). A coupled dynamic
loads analysis of satellites with an enhanced Craig–Bampton approach. Aerospace Science
and Technology, 69, 114-122. https://doi.org/10.1016/j.ast.2017.06.023.
[69] De Lellis, S., Stabile, A., Aglietti, G. S., & Richardson, G. (2020). Structural uncertainty
estimation through a Craig-Bampton Stochastic Method optimisation in satellites
structures. Journal of Sound and Vibration, 469.
https://doi.org/10.1016/j.jsv.2019.115123.
[70] Blaauw, J. B., & Schilder, J. P. (2022). Structural analysis of a swinging fairground attraction
using a novel implementation of reduced order modeling in multibody dynamics.
Engineering Structures, 253. https://doi.org/10.1016/j.engstruct.2021.113742.
[71] Ericsson, T., & Ruhe, A. (1980). The spectral transformation Lánczos method for the
numerical solution of large sparse generalized symmetric eigenvalue problems.

157
Mathematics of Computation, 35(152), 1251-1268. https://doi.org/10.1090/s0025-5718-
1980-0583502-2.
[72] Grimes, R. G., Lewis, J. G., & Simon, H. D. (1994). A Shifted Block Lanczos Algorithm for
Solving Sparse Symmetric Generalized Eigenproblems. SIAM Journal on Matrix Analysis
and Applications, 15(1), 228-272. https://doi.org/10.1137/s0895479888151111.
[73] Hearn, G. & Testa, R. B. (1991). Modal Analysis for Damage Detection in Structures. Journal
of Structural Engineering, 117(10), 3042-3063.
[74] Eiras, J. N., Payan, C., Rakotonarivo, S., & Garnier, V. (2018). Experimental modal analysis
and finite element model updating for structural health monitoring of reinforced concrete
radioactive waste packages. Construction and Building Materials, 180, 531-543.
https://doi.org/10.1016/j.conbuildmat.2018.06.004.
[75] Avitabile, P. (2017). Modal Testing: A Practitioner's Guide.
https://doi.org/10.1002/9781119222989.
[76] Cunha, Á., & Caetano, E. (2006). Experimental modal analysis of civil engineering structures.
Sound and Vibration, 40(6), 12–20.
[77] American Society for Testing and Materials (ASTM). (2019). ASTM Standard A36/A36M:
Standard specification for carbon structural steel. ASTM International, West
Conshohocken, PA.
[78] National Instruments. (2023). LabVIEW documentation. https://www.ni.com/docs/enUS/bundle/labview/page/lvhelp/labview_help.html. (Accessed June 2, 2023).
[79] MathWorks, Inc. (2022). Signal Processing Toolbox documentation.
https://www.mathworks.com/help/signal/index.html?s_tid=CRUX_lftnav. (Accessed June
2, 2023).
[80] Jalali, M. H., & Rideout, D. G. (2022). Substructural damage detection using frequency
response function based inverse dynamic substructuring. Mechanical Systems and Signal
Processing, 163. https://doi.org/10.1016/j.ymssp.2021.108166.
[81] Welch, P. (1967). The use of fast Fourier transform for the estimation of power spectra: A
method based on time averaging over short, modified periodograms. IEEE Transactions
on Audio and Electroacoustics, 15(2), 70–73. https://doi.org/10.1109/TAU.1967.1161901.

158
[82] Entezami, A., Sarmadi, H., Behkamal, B., & Mariani, S. (2020). Big Data Analytics and
Structural Health Monitoring: A Statistical Pattern Recognition-Based Approach. Sensors,
20(8). https://doi.org/10.3390/s20082328.
[83] Tee, K. F. (2018). Time series analysis for vibration-based structural health monitoring: A
review. Structural Durability & Health Monitoring, 12(3), 129–147.
https://doi.org/10.3970/sdhm.2018.04316.
[84] Nair, K. K., Kiremidjian, A. S., & Law, K. H. (2006). Time series-based damage detection
and localization algorithm with application to the ASCE benchmark structure. Journal of
Sound and Vibration, 291(1-2), 349-368. https://doi.org/10.1016/j.jsv.2005.06.016.
[85] Carden, E. P., & Brownjohn, J. M. W. (2008). ARMA modelled time-series classification for
structural health monitoring of civil infrastructure. Mechanical Systems and Signal
Processing, 22(2), 295-314. https://doi.org/10.1016/j.ymssp.2007.07.003.
[86] Gul, M., & Catbas, F. N. (2011). Structural health monitoring and damage assessment using
a novel time series analysis methodology with sensor clustering. Journal of Sound and
Vibration, 330(6), 1196-1210. https://doi.org/10.1016/j.jsv.2010.09.024.
[87] Chen, J., Jiang, X., Yan, Y., Lang, Q., Wang, H., & Ai, Q. (2022). Dynamic Warning Method
for Structural Health Monitoring Data Based on ARIMA: Case Study of Hong KongZhuhai-Macao Bridge Immersed Tunnel. Sensors, 22(16).
https://doi.org/10.3390/s22166185.
[88] Breiman, L. (2001). Machine Learning, 45(1), 5-32.
https://doi.org/10.1023/a:1010933404324.
[89] Zhou, Q., Zhou, H., Zhou, Q., Yang, F., & Luo, L. (2014). Structure damage detection based
on random forest recursive feature elimination. Mechanical Systems and Signal
Processing, 46(1), 82-90. https://doi.org/10.1016/j.ymssp.2013.12.013.
[90] Bergmayr, T., Höll, S., Kralovec, C., & Schagerl, M. (2023). Local residual random forest
classifier for strain-based damage detection and localization in aerospace sandwich
structures. Composite Structures, 304. https://doi.org/10.1016/j.compstruct.2022.116331.
[91] Ghiasi, R., Ghasemi, M. R., & Noori, M. (2018). Comparative studies of metamodeling and
AI-Based techniques in damage detection of structures. Advances in Engineering Software,
125, 101-112. https://doi.org/10.1016/j.advengsoft.2018.02.006.
[92] Zhou, Q., Ning, Y., Zhou, Q., Luo, L., & Lei, J. (2012). Structural damage detection method
based on random forests and data fusion. Structural Health Monitoring, 12(1), 48-58.
https://doi.org/10.1177/1475921712464572.

159
[93] Asjodi, A. H., & Dolatshahi, K. M. (2023). Extended fragility surfaces for unreinforced
masonry walls using vision-derived damage parameters. Engineering Structures, 278.
https://doi.org/10.1016/j.engstruct.2022.115467.
[94] Deep, R., Orazio, P., & Oberai, A. (2023). Deep learning and computational physics (Lecture
notes). arXiv preprint, arXiv:2301.00942. https://doi.org/10.48550/arXiv.2301.00942.
[95] Salehi, H., Biswas, S., & Burgueño, R. (2019). Data interpretation framework integrating
machine learning and pattern recognition for self-powered data-driven damage
identification with harvested energy variations. Engineering Applications of Artificial
Intelligence, 86, 136-153. https://doi.org/10.1016/j.engappai.2019.08.004.
[96] Fontes, C. H., & Embiruçu, M. (2021). An approach combining a new weight initialization
method and constructive algorithm to configure a single Feedforward Neural Network for
multi-class classification. Engineering Applications of Artificial Intelligence, 106.
https://doi.org/10.1016/j.engappai.2021.104495.
[97] Lee, B. Y., Kim, Y. Y., Yi, S.-T., & Kim, J.-K. (2013). Automated image processing
technique for detecting and analysing concrete surface cracks. Structure and Infrastructure
Engineering, 9(6), 567-577. https://doi.org/10.1080/15732479.2011.593891.
[98] Khan, W., Daud, A., Khan, K., Muhammad, S., & Haq, R. (2023). Exploring the frontiers of
deep learning and natural language processing: A comprehensive overview of key
challenges and emerging trends. Natural Language Processing Journal, 4.
https://doi.org/10.1016/j.nlp.2023.100026.
[99] Ziaja, D., & Nazarko, P. (2021). SHM system for anomaly detection of bolted joints in
engineering structures. Structures, 33, 3877-3884.
https://doi.org/10.1016/j.istruc.2021.06.086.
[100] Tayyebi, A., & Pijanowski, B. C. (2014). Modeling multiple land use changes using ANN,
CART and MARS: Comparing tradeoffs in goodness of fit and explanatory power of data
mining tools. International Journal of Applied Earth Observation and Geoinformation, 28,
102-116. https://doi.org/10.1016/j.jag.2013.11.008.
[101] PyTorch. (2023). Cross-entropy loss.
https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html. (Accessed
July 17, 2023).
[102] Jenkins, K. (2023). Summary of gradient descent algorithms (EE559 Lecture Notes).
University of Southern California, Los Angeles, CA, United States.

160
[103] Kingma, D. P., & Ba, J. (2014). Adam: A method for stochastic optimization. arXiv preprint,
arXiv:1412.6980. https://doi.org/10.48550/arXiv.1412.6980.
[104] Mousavi, M., & Gandomi, A. H. (2021). Wood hole-damage detection and classification via
contact ultrasonic testing. Construction and Building Materials, 307.
https://doi.org/10.1016/j.conbuildmat.2021.124999.
[105] Sarmadi, H., & Entezami, A. (2020). Application of supervised learning to validation of
damage detection. Archive of Applied Mechanics, 91(1), 393-410.
https://doi.org/10.1007/s00419-020-01779-z.
[106] Buckley, T., Ghosh, B., & Pakrashi, V. (2022). A Feature Extraction & Selection Benchmark
for Structural Health Monitoring. Structural Health Monitoring, 22(3), 2082-2127.
https://doi.org/10.1177/14759217221111141.
[107] Bhavani, A., & Kumar, B. S. (2021). A review of state-of-the-art text classification
algorithms. In Proceedings of the 2021 5th International Conference on Computing
Methodologies and Communication (ICCMC) (pp. 1484–1490). Erode, India.
https://doi.org/10.1109/ICCMC51019.2021.9418262.
[108] Kamel, H., Abdulah, D., & Al-Tuwaijari, J. M. (2019). Cancer classification using Gaussian
Naive Bayes algorithm. In Proceedings of the 2019 International Engineering Conference
(IEC) (pp. 165–170). Erbil, Iraq. https://doi.org/10.1109/IEC47844.2019.8950650.
[109] Ali, L., Khan, S. U., Golilarz, N. A., Yakubu, I., Qasim, I., Noor, A., & Nour, R. (2019). A
Feature-Driven Decision Support System for Heart Failure Prediction Based on χ2
Statistical Model and Gaussian Naive Bayes. Computational and Mathematical Methods
in Medicine, 2019, 6314328. https://doi.org/10.1155/2019/6314328.
[110] Wang, Z., & Cha, Y. J. (2022). Unsupervised machine and deep learning methods for
structural damage detection: A comparative study. Engineering Reports.
https://doi.org/10.1002/eng2.12551.
[111] Gong, L., Wang, C., Wu, F., Zhang, J., Zhang, H., & Li, Q. (2016). Earthquake-Induced
Building Damage Detection with Post-Event Sub-Meter VHR TerraSAR-X Staring
Spotlight Imagery. Remote Sensing, 8(11). https://doi.org/10.3390/rs8110887.
[112] Salehi, H., Das, S., Chakrabartty, S., Biswas, S., & Burgueño, R. (2018). Damage
identification in aircraft structures with self‐powered sensing technology: A machine
learning approach. Structural Control and Health Monitoring, 25(12).
https://doi.org/10.1002/stc.2262.

161
[113] Walsh, S. B., Borello, D. J., Guldur, B., & Hajjar, J. F. (2013). Data Processing of Point
Clouds for Object Detection for Structural Engineering Applications. Computer-Aided
Civil and Infrastructure Engineering, 28(7), 495-508. https://doi.org/10.1111/mice.12016.
[114] Kumar, A., Kumar, R., Tang, H., & Xiang, J. (2024). A comprehensive study on developing
an intelligent framework for identification and quantitative evaluation of the bearing defect
size. Reliability Engineering & System Safety, 242.
https://doi.org/10.1016/j.ress.2023.109768.
[115] Li, J., Dackermann, U., Xu, Y.-L., & Samali, B. (2011). Damage identification in civil
engineering structures utilizing PCA-compressed residual frequency response functions
and neural network ensembles. Structural Control and Health Monitoring, 18(2), 207-226.
https://doi.org/10.1002/stc.369.
[116] Esfandiari, A., Nabiyan, M. S., & Rofooei, F. R. (2020). Structural damage detection using
principal component analysis of frequency response function data. Structural Control and
Health Monitoring, 27(7). https://doi.org/10.1002/stc.2550.
[117] White, P. R., Tan, M. H., & Hammond, J. K. (2006). Analysis of the maximum likelihood,
total least squares and principal component approaches for frequency response function
estimation. Journal of Sound and Vibration, 290(3-5), 676-689.
https://doi.org/10.1016/j.jsv.2005.04.029.
[118] Mahmoudi, H., Bitaraf, M., Salkhordeh, M., & Soroushian, S. (2023). A rapid machine
learning-based damage detection algorithm for identifying the extent of damage in concrete
shear-wall buildings. Structures, 47, 482-499. https://doi.org/10.1016/j.istruc.2022.11.041.
[119] Abdeljaber, O., Avci, O., Kiranyaz, S., Gabbouj, M., & Inman, D. J. (2017). Real-time
vibration-based structural damage detection using one-dimensional convolutional neural
networks. Journal of Sound and Vibration, 388, 154-170.
https://doi.org/10.1016/j.jsv.2016.10.043.
[120] Afshari, S. S., Enayatollahi, F., Xu, X., & Liang, X. (2022). Machine learning-based
methods in structural reliability analysis: A review. Reliability Engineering & System
Safety, 219. https://doi.org/10.1016/j.ress.2021.108223.
[121] Vy, V., Lee, Y., Bak, J., Park, S., Park, S., & Yoon, H. (2023). Damage localization using
acoustic emission sensors via convolutional neural network and continuous wavelet
transform. Mechanical Systems and Signal Processing, 204.
https://doi.org/10.1016/j.ymssp.2023.110831.

162
[122] Yessoufou, F., & Zhu, J. (2023). One-class convolutional neural network (OC-CNN) model
for rapid bridge damage detection using bridge response data. KSCE Journal of Civil
Engineering, 27(4), 1640–1660. https://doi.org/10.1007/s12205-023-0063-7.
[123] Gulgec, N. S., Takáč, M., & Pakzad, S. N. (2019). Convolutional neural network approach
for robust structural damage detection and localization. Journal of Computing in Civil
Engineering, 33(6). https://doi.org/10.1061/(ASCE)CP.1943-5487.0000820.
[124] Zhuang, B., Gencturk, B., Oberai, A., Ramaswamy, H., & Meyer, R. (2023). Impurity gas
monitoring using ultrasonic sensing and neural networks: forward and inverse problems.
Measurement, 223. https://doi.org/10.1016/j.measurement.2023.113822.
[125] Zhuang, B., Gencturk, B., Oberai, A., Ramaswamy, H., Meyer, R., Sinkov, A., & Good, M.
(2024). Impurity gas detection for SNF canisters using probabilistic deep learning and
acoustic sensing. SSRN Preprint. https://doi.org/10.2139/ssrn.4675917.
[126] Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., & Salakhutdinov, R. (2014).
Dropout: A simple way to prevent neural networks from overfitting. Journal of Machine
Learning Research, 15(56), 1929–1958. https://jmlr.org/papers/v15/srivastava14a.html.
[127] Gal, Y., & Ghahramani, Z. (2015). Dropout as a Bayesian approximation: Representing
model uncertainty in deep learning. arXiv preprint, arXiv:1506.02142.
https://doi.org/10.48550/arXiv.1506.02142.
[128] Modarres, C., Astorga, N., Droguett, E. L., & Meruane, V. (2018). Convolutional neural
networks for automated damage recognition and damage type identification. Structural
Control and Health Monitoring, 25(10). https://doi.org/10.1002/stc.2230.
[129] Goodfellow, I. J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S.,
Courville, A., & Bengio, Y. (2014). Generative adversarial networks. arXiv preprint,
arXiv:1406.2661. https://doi.org/10.48550/arXiv.1406.2661.
[130] Luleci, F., Catbas, F. N., & Avci, O. (2022). Generative Adversarial Networks for Data
Generation in Structural Health Monitoring. Frontiers in Built Environment, 8.
https://doi.org/10.3389/fbuil.2022.816644.
[131] Salimans, T., Goodfellow, I., Zaremba, W., Cheung, V., Radford, A., & Chen, X. (2016).
Improved techniques for training GANs. arXiv preprint, arXiv:1606.03498.
https://doi.org/10.48550/arXiv.1606.03498.
[132] Arjovsky, M., Chintala, S., & Bottou, L. (2017). Wasserstein GAN. arXiv preprint,
arXiv:1701.07875. https://doi.org/10.48550/arXiv.1701.07875.

163
[133] Li, Z.-D., He, W.-Y., & Ren, W.-X. (2024). Structural damage identification based on
Wasserstein Generative Adversarial Network with gradient penalty and dynamic
adversarial adaptation network. Mechanical Systems and Signal Processing, 221.
https://doi.org/10.1016/j.ymssp.2024.111754.
[134] Luleci, F., Catbas, F. N., & Avci, O. (2022). A literature review: Generative adversarial
networks for civil structural health monitoring. Frontiers in Built Environment, 8.
https://doi.org/10.3389/fbuil.2022.1027379.
[135] Gao, S., Zhao, W., Wan, C., Jiang, H., Ding, Y., & Xue, S. (2022). Missing data imputation
framework for bridge structural health monitoring based on slim generative adversarial
networks. Measurement, 204. https://doi.org/10.1016/j.measurement.2022.112095.
[136] van der Maaten, L., & Hinton, G. (2008). Visualizing data using t-SNE. Journal of Machine
Learning Research, 9(86), 2579–2605. https://jmlr.org/papers/v9/vandermaaten08a.html.
[137] Chen, T., & Guestrin, C. (2016). XGBoost: A scalable tree boosting system. In Proceedings
of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data
Mining (pp. 785–794). Association for Computing Machinery.
https://doi.org/10.1145/2939672.2939785.
[138] Lim, S., & Chi, S. (2019). Xgboost application on bridge management systems for proactive
damage estimation. Advanced Engineering Informatics, 41, 100922.
https://doi.org/10.1016/j.aei.2019.100922.
[139] Dong, W., Huang, Y., Lehane, B., & Ma, G. (2020). XGBoost algorithm-based prediction
of concrete electrical resistivity for structural health monitoring. Automation in
Construction, 114, 103311. https://doi.org/10.1016/j.autcon.2020.103155.
[140] Friedman, J. H. (2001). Greedy function approximation: A gradient boosting machine. The
Annals of Statistics, 29(5), 1189–1232. https://doi.org/10.1214/aos/1013203451.
[141] XGBoost Documentation. (2023). Python package.
https://xgboost.readthedocs.io/en/stable/. (Accessed October 18, 2024).

Abstract (if available)

Abstract Nuclear fuel assemblies (FA) become high-level radioactive waste known as spent nuclear fuel (SNF) after several years of operation in nuclear reactors. Due to the lack of a permanent disposal solution, FA are stored in sealed stainless-steel canisters for extended periods. These canisters may sustain accidental damage during handling or transportation events, but since they are sealed, non-destructive evaluation (NDE) is necessary to assess internal FA integrity. Therefore, in this study, an NDE technique was developed using dynamic modal analysis and machine learning (ML) to identify FA damage from measurements taken on the canister’s exterior surface. An experimental mock-up SNF canister was fabricated, and a high-fidelity finite element model (FEM) was developed as its digital twin. Modal analysis was performed to obtain frequency response functions (FRF) under healthy and damaged canister conditions. The root mean square error (RMSE) between experimental FRF successfully detected missing FA but was insufficient for identifying smaller FA damage modes. To improve damage detection capabilities, differences in FRF were used to train multi-task ML models for (1) identifying the FA damage level, and (2) localizing the damage. The classifiers demonstrated high testing accuracy for both classification tasks. To simulate damage scenarios difficult to replicate experimentally, the FEM was modified to include additional damage modes. To align numerical and experimental FRF, Wasserstein generative adversarial networks (WGAN) were trained to generate experimental noise signals. The generated noise signals were added to numerical data, which were then analyzed by a multi-task ML model to identify the additional damage modes. This ML-aided NDE method addresses the limitations of visual inspection and provides a non-invasive solution for detecting FA damage in sealed SNF canisters.

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Asset Metadata

Creator Arcaro, Anna (author)

Core Title Damage identification in spent nuclear fuel canisters using dynamic modal analysis and machine learning

School Andrew and Erna Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Civil Engineering

Degree Conferral Date 2025-05

Publication Date 03/25/2025

Defense Date 02/24/2025

Publisher University of Southern California (original), Los Angeles, California (original), University of Southern California. Libraries (digital)

Tag Damage Detection,damage localization,dry storage,machine learning,non-destructive evaluation,OAI-PMH Harvest,spent nuclear fuel,Structural dynamics

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Language English

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Advisor Gencturk, Bora (committee chair), Ghanem, Roger (committee member), Oberai, Assad (committee member)

Creator Email arcaro@usc.edu,arcaroanna@yahoo.com

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