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Statistical modeling and process data analytics for smart manufacturing

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Statistical modeling and process data analytics for smart manufacturing

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Content STATISTICAL MODELING AND PROCESS DATA ANALYTICS FOR SMART MANUFACTURING by Yuan Jin A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (CHEMICAL ENGINEERING) December 2018 Copyright 2018 Yuan Jin Dedication To my dear family. ii Acknowledgements First and foremost, I would like to sincerely thank my Ph.D. advisors, Prof. Joe Qin and Prof. Qiang Huang. They encouraged me to learn much and guided me step by step to the exciting and challenging research elds. Without their guidance, encouragement, inspiration and support, this work could not be done. During my Ph.D. journey, they provided me the trainings to develop analytical and technical skills, encouraged me to think critically and innovatively and oered me valuable opportunities to grow better and stronger. Their passion and enthusiasm for science and engineering as well as their rigorous attitude to research will inspire and motivate me through my future career. I would like to express my gratitude to Prof. Pin Wang for serving in my disser- tation committee, Prof. Noah Malmstadt, Prof. Katherine Shing and Prof.Yong Chen for serving in my qualifying exam committee. Their valuable and construc- tive suggestions improved my dissertation and enhanced my understanding of the research elds. I would like to thank Dr. Victor Saucedo and Dr. Zheng Li for mentoring me during my internship at Genentech; their fantastic guidance has inspired me to explore industrial bioprocess data; their serious attitude toward research and work has always inspired me during and after the internship. Also, I would like to thank all my collaborators at Genentech, including Angela Meier, Siddhartha iii Kunda, Briana Lehr and Salim Charaniya for their support and assistance in our collaborative research project. I would like to thank Dr. Brian Post and Dr. Ralph Dinwiddie for mentoring me during my internship at Oak Ridge National Laboratory. Their fantastic support has enhanced my knowledge to the area of additive manufacturing and their enthusiasm for research has encouraged me during my Ph.D. journey. I would like to thank Mr. Curtis Huang for mentoring me during my internship at Facebook. He provided me the opportunity to work on the exciting deep learn- ing project and he was always ready to cheer me up and celebrate our progress. Without his exceptional mentorship, I would not nish a challenging internship in a new area successfully. He made me realize that I could do better than I thought. My Ph.D. study would not be such a memorable experience without the sup- port and company of my friends and fellow graduate students. I would like to thank He Luan and Yanqing Duanmu in Prof. Huang's research lab for being always there and being supportive. I would like to thank Tao Yuan, Johnny Pan, Yining Dong, Zhaohui Zhang, Alisha Deshpande, Qinqin Zhu, Wei Lin, Zheyu Li, Ge An and Yingxiang Liu in Prof. Qin's research lab for useful and ecient discussions. I would like to thank postdoc and visiting scholars including Le Zhou, Gang Li, Qiang Liu, Lijuan Li and Zhengcai Zhao for their constructive sugges- tions. I would like to thank Kai Xu and Huachao Mao in Prof. Yong Chen's lab for providing me tremendous help in collecting research data. All my friends at USC, Tennessee, the bay area and in China have brought me so many joys and mental support, special thanks to Yawen Fan, Yilang Fan, Wangze Du, Ye Wang, Xiangfei Meng, Shaobo Hao, Shuai Li, Xin Miao, Rong Jin and Yu Cao. iv Finally, I would like to give my sincerest thanks to my parents and my ance Ruixin Qiang for their continuous support and encouragement to my life and study. Without their love, I can never arrive at this stage. v Table of Contents Dedication ii Acknowledgements iii List of Tables ix List of Figures x Abstract xii Chapter 1: Introduction 1 1.1 Process Data Analytics for Smart Manufacturing . . . . . . . . . 1 1.2 Overview of AM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Background and Motivation . . . . . . . . . . . . . . . . . 5 1.2.1.1 AM and its Potentials . . . . . . . . . . . . . . . 5 1.2.1.2 Importance of AM Geometric Quality Control . . 7 1.2.1.3 Research Challenges of AM Geometric Quality Con- trol . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 State of the Art on AM Geometric Quality Control . . . . 9 1.2.2.1 Classication of AM Geometric Qualify Control Methodologies . . . . . . . . . . . . . . . . . . . 9 1.2.2.2 FEA Methodology and Physical Modeling . . . . 10 1.2.2.3 Optimal Process Parameter Tuning via Statistical Experimental Investigation . . . . . . . . . . . . 12 1.2.2.4 Statistical Learning and Software Error Compen- sation . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3 Overview of Pharmaceutical Manufacturing for Monoclonal Antibody 18 1.3.1 Background and Motivation . . . . . . . . . . . . . . . . . 19 1.3.1.1 Pharmaceutical Manufacturing for mAbs and its Potentials . . . . . . . . . . . . . . . . . . . . . . 19 1.3.1.2 Importance of Pharmaceutical Manufacturing Vari- ability Analysis . . . . . . . . . . . . . . . . . . . 20 vi 1.3.1.3 Research Challenges of Pharmaceutical Manufac- turing Variability Analysis . . . . . . . . . . . . . 21 1.3.2 State of the Art on Pharmaceutical Manufacturing Variabil- ity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.3.2.1 Classication of Pharmaceutical Manufacturing Vari- ability Analysis Methodologies . . . . . . . . . . 24 1.3.2.2 Glycosylation and Metabolism Modeling . . . . . 24 1.3.2.3 Multivariate Analysis Based Monitoring and Fault Diagnosis . . . . . . . . . . . . . . . . . . . . . . 26 1.3.2.4 ML and Data Analytic based Methods . . . . . . 29 1.4 Outline of this Dissertation . . . . . . . . . . . . . . . . . . . . . 32 Chapter 2: Oine Predictive Control of Out-of-Plane Shape Devi- ation for AM 34 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2 Spatial Deviation Formulation for AM { A Unied Representation of 3D Geometric Errors . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2.1 From In-plane Deviation Representation to 3D Spatial De- viation Representation . . . . . . . . . . . . . . . . . . . . 37 2.2.2 Predictive Modeling of Out-of-Plane Errors . . . . . . . . . 42 2.3 Methodology Illustration and Experimental Validation . . . . . . 44 2.3.1 Experiment Design and Observations from SLA Process . . 45 2.3.2 Predictive Modeling of 3D Geometric Errors . . . . . . . . 46 2.3.2.1 Cylindrical Basis Function . . . . . . . . . . . . . 46 2.3.2.2 Modied Cookie-cutter Function to Predict Poly- gon Shape Deviation in the Vertical Cross Section 49 2.3.2.3 Model Estimation . . . . . . . . . . . . . . . . . 52 2.3.2.4 Model Evaluation . . . . . . . . . . . . . . . . . . 52 2.4 Oine Optimal Compensation and Experimental Validation . . . 53 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Chapter 3: Modeling Inter-layer Interactions for Out-of-Plane Shape Deviation Reduction in AM 58 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.2 Prescriptive Modeling of Out-of-Plane Deviation . . . . . . . . . . 61 3.2.1 Challenges of Prescriptive Modeling of Out-of-Plane Deviation 61 3.2.2 3D Spatial Deviation Representation and Freeform Model- ing Methodology . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.3 Understand the Deviation Accumulation From Layer to Layer Using Eect Equivalence . . . . . . . . . . . . . . . . . . . 65 3.2.4 Prescriptive Modeling of Out-of-Plane Deviation of Freeform Shapes Using Bayesian Approach . . . . . . . . . . . . . . 67 3.3 Methodology Illustration and Experimental Validation . . . . . . 69 vii 3.3.1 Experimental Design and Observations from SLA Process . 71 3.3.2 Prescriptive Modeling for Freeform Shapes . . . . . . . . . 74 3.3.2.1 Cylindrical Basis Function to Incorporate Inter- layer Interaction Eect . . . . . . . . . . . . . . . 74 3.3.2.2 Cookie-cutter Function for Extension to Irregular Polygon Shapes . . . . . . . . . . . . . . . . . . . 75 3.3.3 Out-of-Plane Deviation Model Estimation . . . . . . . . . 75 3.3.4 Prescriptive Modeling via CASC Strategy for Out-of-Plane Freeform Shapes . . . . . . . . . . . . . . . . . . . . . . . 78 3.4 Oine Optimal Compensation and Experimental Validation . . . 80 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Chapter 4: Process Variability Source Analysis and Knowledge Dis- covery for a Multiple-step Bio-process 84 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.2 Process and Problem Description . . . . . . . . . . . . . . . . . . 87 4.3 Data Mining Approaches and Proposed Strategy . . . . . . . . . . 89 4.3.1 PCA and PCA Based Process Monitoring . . . . . . . . . 90 4.3.2 Hierarchical Clustering . . . . . . . . . . . . . . . . . . . . 91 4.3.3 LDA, Robust LDA and LDA Based Contributions Plot . . 92 4.3.4 Proposed Strategy for Multiple-step Bio-process . . . . . . 95 4.4 Case Study on Industrial Manufacturing Bioprocess Data . . . . . 97 4.4.1 Data Pre-processing . . . . . . . . . . . . . . . . . . . . . 97 4.4.2 Stage1: Hierarchical Clustering on PCA Residual Subspace 98 4.4.3 Stage2: Robust LDA Based Modeling on Step-wise Data . 101 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Chapter 5: Conclusion and Future Extensions 108 Bibliography 113 viii List of Tables 1.1 Brief summary of AM technologies . . . . . . . . . . . . . . . . . 6 1.2 Classication of AM geometric qualify control methodologies . . . 9 1.3 Classication of pharmaceutical manufacturing variability analysis methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.1 SLA process settings and test part design parameters . . . . . . . 45 2.2 Model estimation for side surface . . . . . . . . . . . . . . . . . . 52 2.3 Relative total area change: model evaluation . . . . . . . . . . . . 53 2.4 Relative total area change: before and after compensation . . . . 56 3.1 Test part design parameters . . . . . . . . . . . . . . . . . . . . . 71 3.2 Parameter estimation for out-of-plane deviation basis model . . . 77 3.3 Relative total area change: before and after compensation . . . . 82 ix List of Figures 1.1 Overall industry production capacity and supply/demand balance ([107]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.2 Cell culture process operating parameters aect process perfor- mance and product quality ([69]) . . . . . . . . . . . . . . . . . . 23 2.1 Shape deviation representation under polar coordinates . . . . . . 38 2.2 In-plane error of cylindrical parts with r 0 = 0:5 00 ; 1 00 ; 2 00 ; 3 00 ([41]) 39 2.3 In-plane deviation representation . . . . . . . . . . . . . . . . . . 39 2.4 Out-of-plane deviation representation . . . . . . . . . . . . . . . . 40 2.5 Out-of-plane deviation denition . . . . . . . . . . . . . . . . . . . 43 2.6 Prism case study: Printed part and measured data of the right surface 47 2.7 Prism case study: deviation proles and model predictions . . . . 48 2.8 Modied cookie-cutter function . . . . . . . . . . . . . . . . . . . 50 2.9 Modied indicator function . . . . . . . . . . . . . . . . . . . . . 51 2.10 Prism case study: before and after compensation . . . . . . . . . 55 3.1 Observed deviation patterns for in-plane circles and out-of-plane half disks (CAD model in Fig. 3.3) with dierent radii . . . . . . 63 3.2 Schema of the overall modeling and compensation approach . . . 70 3.3 Design and building direction of half disk part, irregular polygon part and freeform part . . . . . . . . . . . . . . . . . . . . . . . . 72 3.4 Printed half disk parts, irregular polygon part and freeform part . 72 x 3.5 Out-of-plane deviation prole and model prediction of irregular polygon and freeform shape (solid line: deviation observation, dashed line: deviation prediction, two dotted lines: 95% condence interval for deviation prediction) . . . . . . . . . . . . . . . . . . . . . . . 73 3.6 Discrepancy measure of each edge for irregular polygon as a func- tion of r 0 () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.7 Out-of-plane deviation prole before and after compensation . . . 81 4.1 The layout of a large scale cell culture process ([69]) . . . . . . . . 88 4.2 Scaled nal lactate concentration distribution . . . . . . . . . . . 89 4.3 Flowchart of the proposed two-stage strategy . . . . . . . . . . . . 95 4.4 3D process data unfolding . . . . . . . . . . . . . . . . . . . . . . 98 4.5 PVE and cumulated PVE plots of PCA model . . . . . . . . . . . 99 4.6 PCA monitoring results for principal component subspace and resid- ual subspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.7 Hierarchical clustering dendrogram in residual subspace . . . . . . 101 4.8 Elbow method to select the number of clusters for hierarchical clus- tering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.9 Visualization of low lactate cluster and 4 high lactate clusters by LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.10 Heatmap of osmolality for 4 high lactate clusters . . . . . . . . . . 104 4.11 Heatmap of PCV for 4 high lactate clusters . . . . . . . . . . . . 105 4.12 Heatmap of sodium for 4 high lactate clusters . . . . . . . . . . . 106 4.13 Distribution of low lactate cluster and one high lactate cluster on the LDA optimal direction . . . . . . . . . . . . . . . . . . . . . . 106 4.14 LDA based contributions plot for high lactate cluster 2 with ad- justable variables in Step N-1 . . . . . . . . . . . . . . . . . . . . 107 4.15 Comparison of contributions with condence limits based on LDA and robust LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 xi Abstract Smart manufacturing is a broad category of advanced manufacturing where man- ufacturing machines are connected through information networks, monitored by sensors and controlled by advanced computational intelligence. The aim of smart manufacturing is to improve product quality, agility, system productivity and sus- tainability while reducing the manufacturing cost. Smart manufacturing has been the focus of many researchers and has been extended to various areas such as addi- tive manufacturing (AM), rapid prototyping, energy, security and pharmaceutical manufacturing. With the increased complexity of the manufacturing process and the variety of data collected from various aspects throughout the process, process data analytics has become one of the major trends for smart manufacturing. While smart manufacturing oers distinct advantages to discover process knowl- edge and predict the future production, there still exist two challenges. Firstly, for many smart manufacturing processes, a conclusive understanding of the process is not available due to the complicated process physics and uncertainty. The com- plexity and uncertainty caused by latent or unobserved factors make the process a grey box. With the limited understanding of the process, it is insucient to use only rst principles models; Secondly, with the development of smart manufac- turing, processes become more integrated and tend to be product-oriented, which bring the variety challenge. For example, a highly integrated system is armed with various sensors that collect multiple types of data from dierent unit operations; xii a product-oriented process has to face the one-of-a-kind demand accurately and eciently. Up to date, process data analytics for smart manufacturing is a fast-growing area. Various advanced statistical models and machine learning methods have been developed to support dierent smart manufacturing processes. This disser- tation will show how the "complexity" and "variety" can be handled for smart manufacturing processes with varying characteristics of manufacturing. The rst research task focuses on how to predict and improve the quality for a variety of products. The application area is AM and we aim to control the geometric accuracy of AM built products with various shapes. AM is a promising one-of-a-kind direct manufacturing technology and makes manufacturing possible to be customer-oriented without signicant cost increase. In this task, a pre- dictive modeling framework is proposed to predict the out-of-plane deviation for AM printed freeform shapes based on disparate and small data. We rst adopt a novel spatial deviation formulation which places both in-plane and out-of-plane geometric deviation under a consistent analytic framework. We then develop a prediction and oine compensation method to reduce the out-of-plane geomet- ric errors. After the feasibility of this approach is proved by a simple rectangular prism case study, we extend the predictive model for arbitrary free-form shapes by statistical learning methods. Experimental investigations using a stereolithogra- phy apparatus (SLA) process successfully validate the eectiveness of the proposed methodology and the optimal compensation. The second task focuses on how to interpret and diagnose on multilevel het- erogeneous datasets. The application area is pharmaceutical manufacturing. We aim to reveal process knowledge and analyze process variability on a complicated process composed of multiple-steps. Pharmaceutical manufacturing requires an xiii integrated precise control to deal with variability from various sources such as manufacturing operation uncertainties, sensor measurement limitations, lot-to-lot raw material variations, media preparation dierence and cell line instability. In this task, a two-stage strategy to explore cell culture manufacturing variability in multiple-step bio-processes was proposed. This strategy is able to make use of the variety of data sets from the manufacturing process, consider their causal relationship, unveil hidden process characteristics and provide insights into factors aecting process quality. Specically, a clustering stage is rstly applied, which performs in the residual subspace found by principal component analysis (PCA) and clusters dierent causes using data in the last step of the bio-processes. After- wards, a fault diagnosis stage based on robust linear discriminant analysis (LDA) contribution analysis is implemented to explore the data in previous steps of bio- processes, supervised by the labels obtained previously. This strategy is used to investigate the process variability of a real manufacturing bioprocess, the ndings are consistent with known process knowledge and have pointed to new clues for domain experts to understand the process better. To summarize, the work in this dissertation not only oers predictive modeling tools for some advanced manufacturing processes such as AM and pharmaceutical manufacturing but also contributes to the process data analytics research for smart manufacturing. For example, the predictive modeling framework for AM accuracy control enhances the understanding of the errors come from the AM built-up process, which can also guide how to predict and improve the quality for product- oriented processes based on disparate and small data. Additionally, the two- stage strategy analysis reveals the hidden process interactions for a multiple-step pharmaceutical manufacturing. It also promises for further study to interpret and diagnose multilevel heterogeneous datasets for smart manufacturing. xiv Chapter 1 Introduction 1.1 Process Data Analytics for Smart Manufacturing Smart manufacturing is a broad category of advanced manufacturing where man- ufacturing machines are connected through information networks, monitored by sensors and controlled by advanced computational intelligence. The aim of smart manufacturing is to improve product quality, agility, system productivity and sus- tainability while reducing the manufacturing cost [22]. Smart manufacturing has been the focus of many researchers and has been extended to various areas such as additive manufacturing (AM), rapid prototyping, energy, security and pharma- ceutical manufacturing. There is a list of characteristics associated with smart manufacturing and they can be categorized into three clusters [76, 63], they are: Modularity and Compositionality Modularity decomposes the manufacturing into identiable, distinct units and sub-units while compositionality deals with the understanding of the whole system based on the units and sub- units. 1 Heterogeneity Heterogeneity means the diversity and dissimilarities in the units and components. Interoperability and networkability Interoperability is the property that sys- tem units exchange and share information. Distributed and decentralized systems are able to communicate and collaborate based on the networkabil- ity. Similarly, various technologies are associated with smart manufacturing; they can also be categorized into roughly four clusters [76, 63], which are: Advanced manufacturing Advanced manufacturing is the use of innovative technology to improve products or processes. For example, AM is estab- lished as a kind of advanced manufacturing; cyber-physical systems and their security are hot topics for AM. Internet of things (IoT) and cloud computing IoT is a system of interrelated computing devices, mechanical and digital machines that communicate with each other; it supports the cloud computing which enables the full sharing of manufacturing resources and capabilities. Data analytics Two hot topics of data analytics are the big data and machine learning (ML). The former is the ability to transfer the volume, variety, velocity and veracity of data into manufacturing insights and the latter uses statistical techniques to give computer systems the ability to learn from data. Other technologies such as modeling, simulation, forecasting, diagnosis and data visualization are also part of this cluster. 2 Visualization technology Visualization technology includes the hologram, virtual reality and augmented reality, which creates or superimposes 3D images with the help of a computer. With the increased complexity of the manufacturing process and the data col- lected from various aspects of the process, process data analytics has become one of the major enabling tools for smart manufacturing [20]. In order to discover knowledge from process data, dierent aspects of data analysis can be imple- mented, i.e., the predictive analysis, the interpretative analysis and the diagnostic analysis. The predictive analysis makes use of the available historical data, ap- plying statistical models and ML models to predict the future production of the process. The interpretative analysis is commonly used to explore the relation- ship among the manufacturing conditions, operation parameters and the quality outputs, for the purpose to better understand the process situational knowledge. When the process suers from unknown large variations, unexpected outcomes or reduced performance, the diagnostic analysis is used to tackle the possible causes of the anomalies. Up to date, process data analytics for smart manufacturing is a fast-growing area. Various advanced statistical models and ML methods have been developed to support dierent smart manufacturing processes [108]. This dissertation studies how process data analytics can be applied considering dierent manufacturing characteristics. In the rst task, we focus on how predictive analysis is applied on a small dataset with a limited number of test cases. The application area is AM, which is a one-of-a-kind direct manufacturing and makes manufacture possible to be customer-oriented without signicant cost increase. Therefore, one major char- acteristic of AM is that for dierent shapes there are only limited numbers of 3 samples. To address this challenge, we propose a statistical modeling method to predict and improve the shape accuracy of AM printed parts that is suitable for small samples. In the second task, we study how interpretative analysis and diagnostic analysis can be applied to a complicated pharmaceutical manufacturing process composed of multiple-steps. This process has multilevel heterogeneous datasets provided by the on-line and o-line measurements as well as the operation logs from various steps in the process. To address the variety challenge accompanied with smart manufacturing, we propose a two-stage strategy to explore cell culture manufac- turing variability in multiple-step bioprocesses with the objective to unveil hidden process characteristics and provide insights into factors aecting process quality. In the following part of this chapter, we will introduce the background and motivation for the two types of smart manufacturing: AM and pharmaceutical manufacturing respectively. The outline of this dissertation will also be presented at the end of this chapter. 4 1.2 Overview of AM AM is a branch of smart manufacturing which fundamentally changes the paradigm of manufacturing operations and makes it possible to make one-of-a-kind prod- ucts without a signicant increase in manufacturing time and cost. Geometric accuracy of AM built products is crucial to fullling the promise of AM. We fo- cus on establishing a generic framework of 3D geometric deviation prediction and compensation strategy to improve the geometric accuracy of AM products. Previous research [41, 133, 98, 44] of in-plane deviation prediction and optimal compensation of AM built products has achieved successful outcomes. To consider realistic situations, the rst task aims to establish an approach to out-of-plane geometric shape deviation control for the variety of shapes. To accomplish this, we rst propose a spatial deviation formulation to enable 3D error control, then develop prediction and compensation methods to reduce the out-of-plane shape deviation, lastly extend this methodology to predict the out-of-plane deviation for arbitrary free-form shapes. Experiments are conducted by a stereolithography machine to validate the proposed approach. In this section, we rst introduce the background and motivation of geometric quality control for AM products, as well as the research challenges. After that, we illustrate the state of the art on AM geometric quality control and review related research work. 1.2.1 Background and Motivation 1.2.1.1 AM and its Potentials AM refers to a class of technologies for direct fabrication. It builds products based on computer-aided design (CAD) through layered fabrication processes. 5 AM has the ability to bring about a revolution in the way products are designed and manufactured. It has gained signicant academic and industrial interest due to the ability to build parts with complex contours, cavities and lattice structures without using xtures, jigs or mold tools [47, 29, 9]. Research interests of AM are concentrated on the geometry design, material design, computational tool development as well as manufacturing tool and processes development. It also has a broad application spectrum, such as automotive, aerospace, medicine, biological systems and food supply chains [29]. Obviously, low cost and time eciency are the two major factors driving the rapid growth of AM rather than traditional manufacturing processes. Also, the ability to reduce product weight and increase its shape accuracy oers signicant energy and cost saving. For example, one notable AM process innovation is in the area of 3D bioprinting, the ability to build cavities allows AM to imitate bone structures [47, 8]. It is clear that AM has many categories, recently, the American Society for Testing and Materials (ASTM) International Standard [114] has classied AM technologies into seven categories: 1. material extrusion. 2. powder bed fusion. 3. vat photopolymerization. 4. material jetting. 5. binder jetting. 6. sheet lami- nation. 7. directed energy deposition. Four most commonly used technologies are summarized in Table 1.1. Table 1.1: Brief summary of AM technologies Technologies Categories Materials Power Source Fused lament fabrication (FDM) Material extrusion Thermoplastics Thermal energy Selective laser sintering (SLS) Powder bed fusion Polymer Laser beam Stereolithography (SLA) Photopolymerization Photopolymer Ultraviolet laser Inkjet printing Binder jetting Polymer powder Thermal energy 6 1.2.1.2 Importance of AM Geometric Quality Control While AM oers distinct advantages over traditional manufacturing and has pro- gressed greatly in recent years, many challenges remain to be addressed. Among them, geometric dimensional accuracy is a key issue since the product precision requirement is stringent in some application areas. For instance, dentists have used SLA for dental implants [83, 96] orthodontics and oral surgery [88]. In these cases, small-scale models fabricated by SLA have been used in architecture as a modeling tool. As the AM technology is increasingly applied in the area of medical models, fabricating models from medical images, or creating auxiliary structures for surgery, high accuracy of these applications is required. Moreover, as the AM technology is expanded the scope of applications and forced to meet the specic functional requirements, there is an increasing need for establishing dimensional accuracy control for AM products [101, 11]. AM geometric accuracy is widely studied. Research areas in AM geometric accuracy include improvements in low-end and high-end printers, monitoring and control of the printing processes, improvements to part quality, modeling and simulation of physical processes and development of novel materials. 1.2.1.3 Research Challenges of AM Geometric Quality Control As mentioned in section 1.2.1.2, geometric dimensional accuracy is one of the most signicant issues of AM. Challenges that impede the geometric quality improve- ment in AM come from two aspects, which are "complexity" and "variety": Complex process physics and nonlinear properties make it hard for rst prin- ciples modeling and simulation study. 7 First principles modeling and numerical simulation methods have been ex- tensively applied to model, simulate and predict three-dimensional deviation in AM processes. However, it is dicult to construct delicate mathemat- ical models because of the complicated error sources and unclear process physics. For example, in layer-based fabrication processes, the procedures to separate the built layers from the platform and to rell liquid resin in- volve complicated mechanisms such as uid mechanics and heat transfer. Moreover, the process of layer solidication goes through a material phase change and heterogeneous shrinkage, not to mention the inter-layer bonding eects that happen when layers are built up. Among all the methods, Finite element analysis (FEA) is a wildly used simulation method, which is very versatile and powerful. But the accuracy of the FEA obtained results is usually a function of the mesh resolution and element size. It is time consuming to get the high accuracy due to the high computational complexity. Moreover, FEA is a case-by-case study, which analysis cannot easily extend from one shape to another without additional time and cost. Therefore, improving part accuracy purely relying on such modeling and simulation approaches is far from being eective, and seldomly used in practice. Low volume and high geometric variety make it unsuitable for traditional statistical quality control Statistical Process Control (SPC) has become very important in the manu- facturing and process industries. The objective is to verify that the process is maintained in the normal condition by using statistical methods to mon- itor and control the process performance over time. However, SPC needs a 8 sucient amount of sample data to build the control limit. AM is a product- oriented manufacturing that produces one-of-a-kind product shapes. As a consequence, there does not exist many samples for a particular shape and it is unrealistic to apply SPC for the high volume of distinct shapes. Therefore, the limited collection of data makes SPC not suitable for AM processes. To address these challenges, a bulk of AM research is devoted and we will review the state of the art on AM geometric quality control in the next section. 1.2.2 State of the Art on AM Geometric Quality Control 1.2.2.1 Classication of AM Geometric Qualify Control Methodologies AM geometric quality control is a multidisciplinary research area. To achieve the goal of reducing the geometric error of AM printed parts, researchers have been gradually shifting their eorts from dierent perspectives, such as process mechanism, statistics and quality engineering. In this section, we provide the summary of dierent research methodologies that contribute to the AM geometric quality control. Table 1.2 is a summary of the mainstream methods. Table 1.2: Classication of AM geometric qualify control methodologies Categories Advantages Disadvantages Selected Literature Physical modeling and simulation Extensive application ( i.e. composite materials, irregu- larly shaped boundaries) Large computational load [117, 103, 77, 61, 46, 89, 118, 90, 12, 130, 131, 136, 38, 90, 10] Optimal process parame- ter tuning via statistical experiments Straightforward, appropriate for process calibration Large number of experi- ments, inadequate for com- plex shapes [15, 141, 73, 67, 87, 93, 113, 6, 17, 79, 28] Statistical learning and software compensation Small number of trails, not limited to printing mechanism Limited shape accuracy improvement capability [120, 121, 105, 106, 41, 44, 43, 45, 72, 52] 9 1.2.2.2 FEA Methodology and Physical Modeling The FEA simulation method has been extensively applied to predict 3D deviation and distortion corresponding to dierent part geometries in AM processes [117, 103, 77]. For example, the simulation study of curl distortion due to laser scanning was performed by Koplin et al. [61] and Huang and Jiang [46]. Similar simulation modeling research has been conducted in other AM processes as well [89, 118, 90]. Among the bulk of literature, the distortion in the vertical direction is studied and the geometric distortion is due to the following reasons: 1. The shrinkage of the resin when it solidies. 2. The tendency to shrink the remaining liquid resin in the post-curing process. 3. The liberation of the internal forces when the part is separated from the platform. Bugeda et al. [12] used the FEA simulation to predict the geometric distortion of an SLA process printed part and veried their simulation results by physi- cal experiments. In their paper, they analyzed the in uence of the volumetric shrinkage and layer thickness in the curl distortion and calculated the analytical displacements in both horizontal and vertical directions. However, as they men- tioned in the paper, when it comes to the three dimensional analysis, the small number (e.g., eight noded) elements model had a poor behavior for bending de- viation, while the large number (e.g., twenty noded) elements model had a better behavior with much higher computational cost. Xu and Chen [130] studied the vertical deviation issue in mask image pro- jection based SLA (MIP-SLA) process via both physical experiments and FEA simulations. In their paper, the relationship between the non-uniform tempera- ture distribution and the part curl distortion was studied. In the experimental study, an in-situ temperature monitoring sensor was used to measure the thermal 10 eect in the SLA building process in order to analyze the temperature change with respect to the printed part shapes and thickness. In the FEA simulation, a structural mechanic model was utilized to incorporate the thermal shrinkage eect by calculating the initial stress during the printing process. This study successfully explained the thermal eect and its relation to the deviation. How- ever, a more accurate FEA model is needed to predict the deviation and how to intelligently compensate such curl deviation remains a challenge. The nonlinear and heterogeneous thermal distribution is considered as a primary factor to the shape deviation. Researchers such as Zaeh and Branner [136], Hodge et al. [38] also studied similar topics incorporating mechanical models and residual stresses. Subsequently, Xu and Chen [131] studied the mask image planning method to reduce the shrinkage related deviation in the MIP-SLA process by generating dierent exposure mask patterns for each layer. A full factorial design method had been used in studying signicant factors and levels of the pattern, in order to identify the parameters to achieve the best shape deviation improvement. They claimed that their method could eectively reduce the deviation by 32 % with a trade-o that the new exposure strategy had a longer building time. Generally, the FEA model is based on the assumption that the structural behavior of the resins can be modeled using a linear elastic model with constant Young modulus and a Poisson ratio, which cannot accurately describe the resin behavior during the SLA processes. Therefore, the physics of polymers must be better understood to achieve better fabrication and modeling. Improving part accuracy based purely on such simulation approach is far from being eective[10]. 11 1.2.2.3 Optimal Process Parameter Tuning via Statistical Experimental Investigation A large body of literature is on the statistical experimental investigation of optimal process parameter tuning during the printing processes or during the post-curing processes. Generally, they all follow a two-step procedure: 1. Select the process parameters and set them on dierent levels based on the process knowledge or engineering experience. 2. Apply statistical design of experiments (DOE) to dis- cover the optimal parameter settings under which the printed part has the highest geometric accuracy. Commonly used DOE approaches include Taguchi, analysis of variance (ANOVA), full factorial design, response surface approach and their combinations. For in- stance, Campanelli et al. [15], Zhou et al. [141], Lynn-Charney and Rosen [73], Lee et al. [67] have investigated the shape accuracy of SLA processes, Sood et al. [113], Anitha et al. [6], Chang and Huang [17], Moza et al. [79], Galantucci et al. [28] have studied the shape accuracy or surface roughness for parts printed by FDM processes. Early on, Onuh and Hon [87] applied the Taguchi Method to study and quan- tify the eects of layer thickness, hatch spacing, hatch overcure depth and hatch ll cure depth on the quality of SLA prototypes. Similarly, Anitha et al. [6] conducted the Taguchi Method to analyze the in uence of the parameters on the quality characteristics in an FDM process. In their approach, the signal to noise ratio was calculated to measure the sensitivity to the uncontrollable factors whereas ANOVA was used to provide the signicance rating of the various factors. 12 These two papers are the pioneers to obtain the optimal process parameter set- tings via the statistical experimental investigation; their results show the potential of this approach. Subsequently, Campanelli et al. [15] employed the Taguchi method to study the eects of hatching style parameters in fabricated parts in order to nd a setting combination that results in the best accuracy. To predict the dimensional accuracy separately in three directions (length, width and height) and optimize them simultaneously, Sood et al. [113] applied the Taguchi's parameter design to link the process parameter settings and the part geometric accuracy. In their research, factors such as layer thickness, part build orientation, raster angle, raster width and raster to raster gap (air gap) are varied to evaluate their impacts on geometric accuracy. They modied the Taguchi's parameter design method by means of dening the grey relational grade as the response, and reduce the error in three directions simultaneously. By using Taguchi's parameter design, less number of experiments are required. However, since this work optimizes the combined eects of the error in three directions, it is possible that some small deviation in a particular direction is ignored because the large deviation dominates the combined eects. Raghunath and Pandey [93] had the same interest with Sood et al. [113] and aimed to obtain the best setting in terms of the geometric deviation in three directions and assess the eect of reducing shrinkage phenomena. They conducted research in SLS part and shown that the laser power and scan length were the most in uencing process variables along the X direction, laser power and beam speed were signicant along the Y direction; also, beam speed, hatch spacing and part build temperature were signicant along the Z direction. 13 The open-source, low-cost 3D printers are considered with great potential for the distributed smart manufacturing. Lanzotti et al. [64] applied a full factorial DOE with three factors to assess the main process parameters of a low-cost open- source 3D printer 'RepRap'. In their paper, the three factors were dened as layer thickness, deposition speed and ow rate; the response was the root mean squares error (RMSE). They conducted 27 experiments (each factor had three levels and each level had three replications) on the benchmark and set all the other process parameters as constants throughout the experiments. Based on the DOE methodology, they found the most signicant parameter that aects the part geometric accuracy and the optimal setting combination that obtain the best results. This research gives a new practical insight into calibrating the low-cost, open-source 3D printers and is considerable for low-cost 3D printer since the cost of material and fabricating is low. Optimal process parameter tuning via statistical experimental investigation is a straightforward and easy to implement method that links the process param- eters and the geometric accuracy through limited experimental trials. However, the number of trials is large if we want to test the combination of more process parameters or parameter test levels. Also, process performance is highly depen- dent on the products being experimented and the predictability of this kind of method for new complex shapes is limited. 1.2.2.4 Statistical Learning and Software Error Compensation The methodology of software error compensation aims at reducing the geometric error without changing the printer hardware settings. Hilton and Jacobs [36] rst proposed this idea and utilized it to control the average shrinkage error. Later, researchers have focused on building error models to control the detailed geometric 14 feature and do software compensation based on the models [120, 121, 105, 106]. Recently, this method has been improved by involving the statistical learning method to predict the geometric error. A series of works [41, 44, 43, 45, 72, 52] have been completed to construct a unied predictive modeling framework with a limited number of test trails. In the 3D printing process, the total volumetric shrinkage is caused by the unbalanced cooling in the phase change process, and it varies from process to process and from material to material. Shrinkage compensation factor has been commonly used in practice to apply compensation uniformly to the entire product or to apply dierent factors to the CAD model for each section of a product .Hilton and Jacobs [36] proposed the 'shrinkage factor library' approach to analyze the shrinkage variation of 3D printing. However, shrinkage is never perfectly uniform and the method only controls the average shape shrinkage. Also, the limitation of this line of research is that it is tedious to apply multiple shrinkage factors for complex geometries. On the purpose of precise dimensional control through compensation, Senthilku- maran et al. [105, 106] modeled the percentage of shrinkage for in-plane deviation in x and y direction as linear or nonlinear functions of scan length and proposed an equation to calculate the value of compensation. However, the out-of-plane deviation in z direction was not considered in their work. A similar idea has been implemented by Tong et al. [120, 121], who established polynomial regres- sion models to analyze the product deviation in x, y and z directions separately. The mapped 3D error models were applied to compensate for 3D error reduction. In their study, the volumetric error was reduced around 35%, showing software error compensation was an eective way to increase the geometric accuracy of 3D 15 printed products. However, they also mentioned that the out-of-plane deviation was not signicantly reduced in their experimental studies. Zha and Anand [138] worked in a slightly dierent way to reduce geometric errors. Instead of changing the CAD design, they developed a surface-based mod- ication algorithm (SMA) to locally alter the standard triangle language (STL) le, aiming to reduce the approximation error introduced in the translation pro- cess from CAD to STL. They rst selected the surface to be modied by the value of choral error (the absolute distance between the point on the STL facet and the corresponding point on the CAD surface), then deleted the original facets in the selected surfaces and lled it with more facets using SMA facet formation pattern. The advantage of their approach is that the computational burden is not increased and no physical experiment is required. However, the error caused in the printing process cannot be reduced by their approach since they do compensation before printing. In a series of work [41, 133, 98, 43, 44, 110], Huang and co-authors intended to develop a new predictive learning strategy with the ability of statistical learning from a limited number of tested shapes and deriving compensation plans for new and untested products. This new alternative strategy is motivated by the fact that AM has to build products with huge varieties. It is imperative to establish a methodology independent of shape complexity and specic AM processes. Huang et al. [41] rst established a generic, physically consistent approach to model and predict in-plane shape deviation along product boundary and derive optimal com- pensation plans. The essence of this statistical modeling approach is to decouple the geometric shape complexity from the deviation modeling by transforming in- plane geometric errors from the Cartesian coordinate system into a functional 16 prole dened in the Polar coordinate system (PCS). Huang et al. [43, 44] ex- tended the work in Huang et al. [41] from the cylindrical shape to polyhedrons. However, no detailed discussion has been provided for methodology extension to the 3D case. 17 1.3 Overview of Pharmaceutical Manufacturing for Monoclonal Antibody Mammalian cells such as Chinese hamster ovary (CHO) cells are used to express therapeutic monoclonal antibodies (mAbs) for both clinical studies and commer- cial uses. Large-scale pharmaceutical manufacturing for mAbs has been widely used in biopharmaceutical companies with slightly dierent procedures. For smart manufacturing process development, maintaining desired product quality while improving the product yield and reducing manufacturing cost are the key issues to address. Therefore, it is essential to analyze the process variability and discover new knowledge using data analytics methods [35]. Process variability in the complex bioprocess is challenging to reduce because it comes from various sources such as manufacturing operation uncertainties, sen- sor measurement limitations, lot-to-lot raw material variations, media preparation dierence and cell line instability. Moreover, data of an enormous volume and var- ious kinds are generated and collected from dierent manufacturing stages, which makes it pivotal to uncover the hidden reasons that cause the process variability. Therefore, in this task, the primary objective is to discover process variability sources by analyzing diverse bioprocess data sets. To accomplish this, we propose a two-stage data analytic strategy that investigates the cell culture process vari- ability. The rst stage is applied on the data in the last step of the bioprocess to obtain data labels while the second stage is used on the data in the previous steps of the bioprocess, supervised by the labels dened from Stage 1. In this section, we rst introduce the background and motivation of process variability analysis as well as the research challenges we are facing. After that, 18 we illustrate the state of the art on process variability analysis and review related research work. 1.3.1 Background and Motivation 1.3.1.1 Pharmaceutical Manufacturing for mAbs and its Potentials Cell culture is the process by which cells are grown under controlled conditions, generally outside of their natural environment. CHO cells are selected as host cells for clinical study and manufacturing uses because their capacity for rapid growth, high expression as well as the ability to grow in the chemical-dened media. Cell culture conditions can vary for each cell type, but articial environments typically include a suitable vessel with media that supplies the essential nutrients (amino acids, carbohydrates, vitamins, minerals), growth factors, hormones, gases (CO2, O2) and the physio-chemical environment (pH buer, osmotic pressure, tempera- ture). A large-scale cell culture process consists of a series of unit operations including seed train, inoculum train and production runs. A seed train is used to generate an adequate number of cells for inoculum train [27]; an inoculum train is designed in a stepwise mode with the goal to keep cells grow exponentially while still at a high viability state [1]. The purpose for a production run is to generate as much antibody drug as possible. Therefore, each step has its key performance indicators (KPIs) such as cell growth, viability and titer, along with appropriate product quality attributes. The success of process scale-up is usually measured by these KPIs and product quality attributes that meet pre-dened criteria [69]. The large-scale pharmaceutical manufacturing process is highly industrialized and has a signicant market share. For example, for over 900 biopharma products 19 in US and EU, around 70% are mAbs products and approximately 95% of these biopharma products are produced in mammalian cell culture process. According to Seymour [107], in the year 2015, the top six selling antibody products earn 51 billion with an increased annual revenue of 21%. Figure 1.1 shows the overall in- dustry production capacity and the supply/demand balance from the year 2014 to 2020, which strongly suggests that mAbs production through biopharmaceutical manufacturing has strong growth potential for the foreseeable future. Figure 1.1: Overall industry production capacity and supply/demand balance ([107]) 1.3.1.2 Importance of Pharmaceutical Manufacturing Variability Analysis The vast market share shows the potential of the pharmaceutical manufacturing processes. However, process variability aects the antibody drug productivity. For example, a typical process accumulates mAb titer ranging from 15 g/L. For a production bioreactor with volume 15 kL, the tier variation diers from 1575 kg and the income varies from $ 102510 million considering the median sales price is $ 8 k/g and the average purication rate is 85% [56]. Therefore, it is 20 imperative to analyze the pharmaceutical manufacturing process variability and discover the underlying reasons that cause the variability. The process variability is widely studied and research interests are concen- trated on host cell engineering, feeding media development, process parameters eects and the process operation uncertainties. However, these researches only study a part of the pharmaceutical manufacturing process independently and are obstructed by the complicated process and uncertainties in the cell culture pro- cess. Therefore, in this dissertation, we use data analytic approaches to analyze the data collected throughout dierent manufacturing stages. 1.3.1.3 Research Challenges of Pharmaceutical Manufacturing Variability Analysis There are several challenges for pharmaceutical manufacturing, as Li et al. [69] pointed out, these challenges include: Cell lines capable of synthesizing the required molecules at high productiv- ities that ensure low operating cost. Culture media and bioreactor culture conditions that achieve both the req- uisite productivity and meet product quality specications. Appropriate on-line and o-line sensors capable of providing information that enhances process control. Good understanding of culture performance at dierent process steps. The second task of this dissertation will focus on the last bullet, analyzing process variability and gaining the understanding of the cell culture performance 21 at dierent stages. Specically, there are mainly two challenges related to this work, which also come from "complexity" and "variety": Limited sensor measurements and complicated process variable relationships make it hard for metabolism study in production size It is believed that titer variation is often correlated with the variation of cell growth and lactate production. Therefore, metabolism models have been extensively applied to study these phenomena, such as work in Zagari et al. [137], Mulukutla et al. [80], Larson et al. [65]. However, it is not easy to implement this kind of knowledge-based models to the manufacturing processes because of the lack of specic measurements in commercial man- ufacturing. These types of measurements are not available either due to the expensive cost of precise instruments or the lack of sensitivity measure of low concentration. On the other hand, the cell culture process operating parameters are highly correlated and mainly consist of physiological parameters (viable cell den- sity (VCD), viability and packed cell volume (PCV)) and physio-chemical environment variables (buer pH value, osmotic pressure) and others. When changes happen, it is dicult to tell the cause and the result. For example, when cell growth slows down, lactate is produced at a lower level or even gets consumed, which causes the upward drift in pH, intimately aects the concentration of dissolved CO2 levels, the base consumption level and os- molality. However, the change of osmolality also decreases the cell growth rate, ends up in a loop. Figure 1.2 shows part of the complex relation- ships among these parameters and their eects on the process performance 22 and product quality directly and indirectly. Thus, analyzing the process variability purely relying on such approaches is far from being eective. Figure 1.2: Cell culture process operating parameters aect process performance and product quality ([69]) Multiple-step process and the variety of datasets make it hard to basic process data analysis As mentioned in Section 1.3.1, a typical large-scale cell culture process con- sists of a series of unit operations including seed train, inoculum train and production run with increasing manufacturing scales. Each step has both on-line measurements and o-line measurements, with dierent culture time duration. The initial conditions and nal conditions are recorded as well. Besides, data for media preparation, raw material lots and trace metal con- centration are also available. Therefore, datasets come from dierent steps of the pharmaceutical manufacturing processes have various properties, such as quantitative data and categorical data, 2-D matrix and 3-D tensor, etc. 23 To address these challenges, researchers have focused on analyzing the process data. We will review the state of the art in this research area in the next section. 1.3.2 State of the Art on Pharmaceutical Manufacturing Variability Analysis 1.3.2.1 Classication of Pharmaceutical Manufacturing Variability Analysis Methodologies Process variability analysis is a multidisciplinary research area. To achieve the goal of nding the causes of variability and improving the nal product quantity, researches have been gradually shifting their eorts from dierent perspectives, such as metabolism modeling, multivariate analysis and ML methods. In this section, we provide the summary of dierent research methodologies that contribute to the process variability analysis. Table 1.3 is a summary of the mainstream methods. Table 1.3: Classication of pharmaceutical manufacturing variability analysis methodologies Categories Advantages Disadvantages Selected Literature Glycosylation and metabolism modeling Help understand and im- prove cell life-cycle Hard to nd major contribu- tors when high lactate occurs [137, 80, 65, 75, 134] Multivariate analysis based monitoring and fault diag- nosis Straightforward, easy to un- derstand and visualize VIP plots has smear eects and sometimes misleading [3, 92, 30, 85, 84, 86, 68, 135, 129, 58, 59] ML and data analytic based methods Improve predictive and in- terpretative abilities [18, 16, 109, 50, 18, 19] 1.3.2.2 Glycosylation and Metabolism Modeling The metabolism modeling methods have been extensively applied to study the per- formance of mAbs cell culture, which signicantly aects the antibody product 24 quality and quantity. For example, glycosylation and post-transcriptional mod- ications are considered as two major cell culture metabolisms that are highly correlated with the variation of production titer. Charaniya et al. [19] studied the relationship between the product titer and process variables and claimed that low titer in CHO mAbs production was often correlated to lower cell growth and high lactate production. This assumption has been agreed by most of the researchers and several studies have employed lactate metabolism models or glycosylation models to study these phenomena, such as work in Zagari et al. [137], Mulukutla et al. [80], Larson et al. [65], Mart nez et al. [75], Yang and Butler [134]. For example, Mulukutla et al. [80] was the rst one to explore the bi-stability behavior of glycolysis for the purpose to nd the cues that triggered the metabolic shift to the low lactate production state. In their study, the ordinary dierential equation (ODE) model was built to demonstrate the mass balance of 40 reaction intermediates in the glycolysis cycle. Based on this, the glycolysis bi-stability behavior was studied by simulating the steady state and the transient state. Their results showed that the transitions from high glycolysis ux state to low ux state or vice versa happened when the lactate concentration was in a specied range. Zagari et al. [137] also studied a metabolism model and found a correlation between the high lactate production and a reduced oxidative metabolism. In their research, two kinds of cell lines were cultured in dierent media, various KPIs such as viable cells, glutamine, glucose and lactate were monitored during the cell culture processes. Based on the experimental results they concluded that the correlation between the altered oxidative capacity of mitochondria and the switch of lactate metabolism did exist, but the metabolic models were dierent for dierent cell line in dierent media. 25 The eects of ammonia on CHO cell growth and glycosylation were also studied by a metabolism model [134]. In their experiments, CHO cells were cultured in a serum-free media supplemented with dierent concentrations of ammonia; the number of cells and the viable cell yields were recorded. They claimed that the accumulation of ammonia resulted in a reduction of the growth rate and cell density. Generally, the studies of glycosylation and metabolism are very helpful for host cell engineering, which provide insights on what happened in the cell life- cycle. However, this kind of methods usually explains the correlation between the high lactate production and a few specic pre-dened process parameters, such as glycolysis ux [80], oxidative capacity of mitochondria [137] and ammonia concentration [134]. This type of analysis is not capable of nding the combined eects of multiple process parameters. Moreover, if the high lactate production occurs in a cell culture process, it's impossible to nd the major contributors only relying on this kind of approaches. 1.3.2.3 Multivariate Analysis Based Monitoring and Fault Diagnosis There is a considerable amount of literature on using multivariate data analy- sis (MVA) to explore the knowledge of chemical processes and pharmaceutical manufacturing processes; these methods have been successfully applied and com- mercialized to do process monitoring and fault diagnosis as well [3, 92, 30, 59]. For example, the principal component analysis (PCA) and partial least squares (PLS) algorithms are used to model the correlations from historical data for the continuous process. To get over the limitations of PCA and PLS and to model the nonlinear and dynamic characteristics of the processes, dierent variants have 26 been developed, such as kernel PCA, PLS [102, 70, 95] and probabilistic PCA, PLS [119, 139]. To deal with batch process data, multi-way PCA (mPCA) and multi-way PLS (mPLS) are developed [85, 84, 86]. The key idea behind mPCA and mPLS is to unfold the 3D batch data tensor into the 2D matrix and apply PCA/PLS on the unfolded data afterward. For example, Nomikos and MacGregor [85] proposed and applied mPCA on a simulation study with all process knowledge known. In this paper, they simulated 50 normal batches with typical variations and two ab- normal batches that had the same cause but at dierent abnormal levels. The two abnormal batches were directly detected by the mPCA score plot. Subsequently, Nomikos and MacGregor [86] proposed and applied mPLS on a simulation study of the styrene-butadiene batch reactor, the abnormality was detected by the squared prediction error (SPE) chart. The dierence between using mPCA and mPLS is noticeable. MPCA uses only the process data and it describes how the measurements deviate from the average of the normal variable trajectories. In contrast, mPLS also includes the product quality information and it detects the abnormality correlated with the oset product quality. However, in practice, a major concern for mPLS is the uncertainty whether the number of quality variables is sucient or whether these quality variables can represent the product quality adequately. For instance, usu- ally it's inconclusive to say that only one quality variable can capture all the aspects of the product. MPCA and mPLS also suer from the same issue as PCA and PLS have, to overcome this, dierent variants are developed and ap- plied to batch processes. For example, Lee et al. [68] used multi-way kernel PCA to capture the nonlinear characteristics within normal batch processes and detect 27 faults. Related research work and variations are also introduced in Yu and Qin [135], Wurl et al. [129]. Early on, Garc a-Mu~ noz et al. [30] employed a multi-block PLS model to trou- bleshoot an industrial batch process. In their research, a drying process with three sets of variables was analyzed. To analyze the impact of the initial conditions (Z) on the product quality (Y), a PLS model was built; similarly, another PLS model was constructed to analyze the impact of process variable trajectories (X) on the product quality (Y). Multi-block PLS model also allowed the estimation of each block. By analyzing the contribution plots, the authors claimed that the initial conditions had little impact on the quality while the variations of the process trajectories dominated the variations in the product quality. In the year 2004, the United States Food and Drug Administration (FDA) dened the process analytical technology (PAT) as a mechanism to design, analyze and control pharmaceutical manufacturing processes [25, 26]. In the same year, they outlined a framework for the PAT implementation as well [37]. Since then, the pharmaceutical industry was motivated to use MVA to improve the production processes. For example, Amgen applied MVA to analyze the unit operations and to identify the root causes for their manufacturing processes [58, 59]; Genentech applied MVA to study the characteristics for high productivity processes and analyze the process variations [18, 19]. Kirdar et al. [58] examined the feasibility of using MVA for analyzing the unit operations, process comparability and process characterization. In this study, a comparative study was implemented on both small-scale and large-scale batches of a cell-culture process. They compared the results of score plots, loading plots and variable importance for projection (VIP) plots using the commercial software SIMCA. Because the results were in agreement with the process knowledge, the 28 feasibility is proved. Subsequently, Kirdar et al. [59] applied MVA to make fault diagnosis on the same pharmaceutical manufacturing process, the author claimed that the root causes that adversely impacted the product quantity were identied from the VIP plots and were proved by implementing the pilot runs. From the successful industrial case studies discussed above, the power of MVA has been recognized. However, MVA has drawbacks, i.e., the VIP plots have the smear eects and are sometimes misleading. On the other hand, as the pharma- ceutical manufacturing processes become more complicated and various types of data were collected throughout the pipeline, researchers realize that analysis only relying on MVA can hardly reveal process knowledge. Therefore, an increasing number of researchers start to explore the possibility of using advanced ML and data analysis based methods. 1.3.2.4 ML and Data Analytic based Methods In recent years, many research studies have been carried out using ML and data analytic based methods to explore the process data for pharmaceutical manufac- turing, expecting they could bring new ndings. As Qin [92] pointed out, the advantage of using ML methods to the "variety" challenge is that this category of methods can make use of heterogeneous sources of data during process operations and after products are made; also, imperfect data with outliers and missing values can be easily handled by the robust methods. Unsupervised methods such as clustering are one of the commonly applied methods [18, 16, 109, 50]. The clustering approach nds nature groupings of the time series data under some similarity/dissimilarity measures. For example, Cede~ no et al. [16] dened variable contributions based onT 2 in the original space and then used hierarchical clustering to isolate the suspicious measurements that 29 were faulty. In the prediction stage, they measured the distance between the near- est point in a type of fault and the new sample to determine which faulty type the new sample belonged to. The proposed method was performed on a fermentation process with simulated faults. In the comparative study, the performance of the proposed model beat other kernel methods such as KPCA-RBC and KPCA-CN. Clustering is usually integrated with MVA methods [109, 50]. For instance, Singhal and Seborg [109] developed a modied K-means methodology to cluster multivariate time-series data. In their paper, the similarity was dened as a weighted sum of three parts: SF = 1 S PCA + 2 S x dist + 3 S y dist ( 1 + 2 + 3 = 1). WhereS PCA was based on the rstk PCs that covered the majority of the variance and dened as the sum of the angles between the PCs; S x dist , which was the distance similarity forX, was based on Mahalanobis distance andS y dist was based on Euclidean distance. The authors also dened "purity" and "eciency" as the evaluation metric. A batch fermentation and a continuous reactor process were used as simulation studies and the modied K-means with proposed similarity measures earned the best scores for both metrics compared to other methods. An alternative is the supervised learning methods such as classication and regression. For example, Charaniya et al. [18] attempted to do predictive data analysis on the large-scale pharmaceutical manufacturing processes using support vector regression (SVR). In their study, they rst dened a similarity metric for dierent runs using the exponential of the Euclidean distance; then reduced the dimension of the dataset by selecting top weighted process parameters and em- ployed SVR to predict the nal titer. In their analysis, process data from inoculum train to the production scale was divided into eight datasets, by comparison of the RMSE on the datasets in a stage-wise cumulative manner, the critical time 30 duration was identied; by selection of top weighted process parameters, the ma- jority of pivotal variables were identied. Because carrying experimental study in manufacturing scale is expensive, Charaniya et al. [19] analyzed the importance of the majority of critical variables by both magnitude of regression coecient and the frequency of occurrence, further proved the correctness of their results. The involvement of ML methods and data analytic approaches in pharmaceu- tical manufacturing greatly improves the predictive and interpretative abilities of process data analytics. 31 1.4 Outline of this Dissertation This dissertation focuses on process data analytics for smart manufacturing, dis- cussing how to handle the "variety" challenge accompanying the development of smart manufacturing. The industrial domain of interest includes AM and phar- maceutical manufacturing. The dissertation is organized as follows: In Chapter 2 and 3, a predictive modeling framework is proposed to control and reduce the AM printed part geometric deviation. The advantage of this predictive modeling framework is that it can predict the out-of-plane deviation for freeform shapes based on disparate and small data. Specically, in Chapter 2, an oine out-of-plane shape deviation control ap- proach is established. To formulate the statistical model, a novel spatial deviation formulation is adopted. This spatial representation places both in-plane and out- of-plane geometric deviation under a consistent analytical framework so that the 3D accuracy control is enabled. Under this new formulation, a prediction and o-line compensation method is developed to reduce the out-of-plane geometric errors, to accommodate the unique characteristics of the out-of-plane deviation, this model also provides the exibility of mixed selection for cookie-cutter func- tions. Lastly, the optimal compensation methodology is applied. Experimental validation of a simple rectangular prism on an SLA process is conducted, the out- of-plane deviation is reduced by approximately 50%, validating the eectiveness of the proposed statistical 3D shape accuracy control approach. Motivated by the research in Chapter 2, in Chapter 3, the predictive model mentioned before was extended to predict the out-of-plane deviation for arbitrary free-form shapes. To achieve this, the deviation basis model is generalized by adopting eect equivalence methodology. Then a Bayesian approach is developed 32 to infer the predictive deviation model for complex shapes. Similarly, after the optimal compensation method is applied, experimental validation in an SLA pro- cess is conducted with the out-of-plane deviation reduced by approximately 60% for un-printed polygon shapes and 40% for new freeform shapes. In Chapter 4, a two-stage strategy to explore cell culture manufacturing vari- ability in multiple-step bioprocesses is proposed. This strategy can make use of the variety of data sets from the manufacturing processes, consider the causal re- lationship, unveil hidden process characteristics and provide insights into factors aecting process quality. Specically, this stage includes two parts: 1. A cluster- ing stage performed in the residual subspace found by PCA that clusters dierent causes using data in the last step of the bioprocess. 2. A fault diagnosis stage based on robust LDA contribution analysis, to explore the data in previous steps of the bioprocess, supervised by the labels obtained in Stage 1. This strategy has been used to explore the process viability of a real manufacturing bioprocess from Genentech, the ndings are consistent with known process knowledge and have pointed to new clues for SMEs to understand the process better. Finally, Chapter 5 gives the conclusions for this dissertation 33 Chapter 2 Oine Predictive Control of Out-of-Plane Shape Deviation for AM As mentioned in Chapter 1, AM is a promising direct manufacturing technology and the geometric accuracy of AM built products is crucial to fullling the promise of AM. Prediction and control of three-dimensional (3D) shape deviation, partic- ularly out-of-plane geometric errors of AM built products have been a challenging task. In previous work, we have been establishing an alternative strategy that can be predictive and transparent to specic AM processes based on a limited number of test cases. Successful results have been accomplished in the previous work to control in-plane (x-y plane) shape deviation through oine compensation. In this chapter, we aim to establish an oine out-of-plane shape deviation control ap- proach based on limited trials of test shapes. We adopt a novel spatial deviation formulation in which both in-plane and out-of-plane geometric errors are placed under a consistent mathematical framework to enable 3D accuracy control. Under this new formulation of 3D shape deviation, we develop a prediction and oine compensation method to reduce out-of-plane geometric errors. Experimental val- idation is successfully conducted to validate the developed 3D shape accuracy control approach. 34 2.1 Introduction AM directly builds products based on CAD models through layered fabrication processes [9, 47], it enables building parts with complex contours, cavities and lattice structures, which makes it a promising direct manufacturing technology. However, geometric accuracy control is still one of the major bottlenecks for AM technology, particularly for the control of 3D geometric errors [47, 131, 112]. The layer formation and inter-layer bonding involve complicated mechanisms. Al- though numerical FEA has been extensively used to predict 3D deviation and dis- tortion in AM processes [117, 103, 77, 89, 118, 23], improving part accuracy based purely on such a simulation approach is far from being eective, and seldomly used in practice [10, 40]. A shrinkage compensation factor has been commonly used in practice to apply for compensation uniformly to the entire product or to apply dif- ferent factors to the CAD model for each section of a product [36]. However, it is time-consuming to establish a library of compensation factors for all part shapes. Furthermore, it is proven in the work [41] that the shrinkage compensation factor is optimal only if the geometric deviation is the same everywhere. A large body of the literature has been on experimental investigation of op- timal process settings and on establishing empirical process models to minimize geometric errors. For instance, Taguchi and DOE methods have been applied to investigate SLA processes [15, 141, 140] or FDM processes [113, 6, 39, 64]. Fac- tors such as layer thickness, part build orientation, raster angle, raster width and raster to raster gap (air gap) are varied to evaluate their impacts on geometric ac- curacy. However, process performance is highly dependent on the products being experimented and the predictability for new complex shapes is limited. 35 Tong et al. [121, 120] established polynomial regression models to analyze the product deviation in x, y, and z directions separately. The mapped 3D error models were then applied to compensate 3D error. In their study, the volumet- ric error was reduced around 35%, showing software error compensation was an eective way to improve the geometric accuracy of AM products. However, they also mentioned that the out-of-plane deviation was not obviously reduced in their experimental studies. In a series of work [41, 133, 98, 43, 44, 110, 111], Huang and co-authors in- tended to develop a new predictive learning strategy with the ability of learning from a limited number of tested shapes and deriving compensation plans for new and untried shapes. This new alternative strategy is motivated by the fact that AM has to build products with huge varieties. It is imperative to establish a methodology independent of shape complexity and specic AM processes. Huang et al. rst established a generic, physically consistent approach to model and predict in-plane (xy plane) shape deviation along product boundary and de- rive optimal compensation plans. Huang et al. [43, 44] extended the work in [41] from a cylindrical shape to polyhedrons. However, no detailed discussion has been provided for methodology extension to the 3D case. This work is therefore motivated by extending the methodological framework in [41, 43, 44] from in-plane error to out-of-plane error prediction and oine compensation. Following Introduction, Section 2 presents a novel formulation of spatial error representation to place both in-plane and out-of-plane errors un- der a consistent mathematical framework. Section 3 oers the detailed modeling procedure to establish the out-of-plane error model and its experimental valida- tion using the SLA process. Optimal compensation of out-of-plane errors and its 36 experimental validation are illustrated in Section 4. The conclusion is given in Section 5. 2.2 Spatial Deviation Formulation for AM { A Unied Representation of 3D Geometric Errors 2.2.1 From In-plane Deviation Representation to 3D Spatial Deviation Representation In the previous study the in-plane shape deviation along boundary of an AM printed product is dened as r(;r 0 ();z) =r(;r 0 ();z)r 0 (;z) in the PCS (Fig. 2.1), where r 0 () represents the nominal radius of the product design point at location andz denotes the height of a specic layer in the verticalz direction. The essence of this representation is to decouple the geometric shape complexity from the deviation modeling by transforming in-plane geometric errors from the Cartesian coordinate system into a functional prole dened in PCS. This trans- formation helps to visualize deviation patterns and reduce model complexity. For example, Fig. 2.2 illustrates the in-plane geometric shape deviation r(;r 0 ()jz 0 ) for four cylindrical products built by SLA process [41]. Denote r(;r 0 ()jz 0 ) =f(;r 0 ()jz 0 ), the in-plane shape deviation along its boundary at a given layer z 0 .Huang et al. [41] decomposes the predicted in-plane deviation f(;r 0 ()jz 0 ) into three components: f(;r 0 ()jz 0 ) =f 1 (r 0 ()jz 0 ) +f 2 (;r 0 ()jz 0 ) +f 3 (jz 0 ) + (2.1) 37 where f 1 represents volumetric deviation independent of locations; f 2 is location- dependent deviation aected by local geometric shape features; f 3 represents de- viation not captured by the rst two terms, which might include some high-order terms, and is the noise term. Figure 2.1: Shape deviation representation under polar coordinates To incorporate the out-of-plane deviation, according to Huang (2016) [42], we revise the previous (r;;z) representation to a Spherical coordinate system (SCS) (r;;) to depict both the in-plane and out-of-plane shape deviation in a unied mathematical formulation. The main reason for this change is that it facilitates the representation of the out-of-plane error in the same way as the in-plane error. To illustrate this idea, we rst dene the in-plane and out-of-plane shape deviation in the SCS using the simple cylindrical shape. As shown in Fig. 2.3, for an arbitrary point P 0 (r 0 ; 0 ; 0 ) at a given height = 0 or z =r cos( 0 ), the horizontal cross section view of the product passingP 0 is given as (r sin( 0 );j 0 ), whose shape deviation r(;r 0 (; 0 )j 0 ) represents the in-plane geometric error and its model formulation has been developed in the previous work [44]. 38 0 1 2 3 4 5 6 −0.05 −0.04 −0.03 −0.02 −0.01 0.00 Observed Deformation θ Deformation (in.) 0.5'' 1'' 2'' 3'' Figure 2.2: In-plane error of cylindrical parts with r 0 = 0:5 00 ; 1 00 ; 2 00 ; 3 00 ([41]) (rsin(\ 4 ), E; E y z x 0 E r, E \ 4 0 ¿ ¿ Horizontal Cross Section N 2 4 2 4 4 4 Figure 2.3: In-plane deviation representation 39 Denote the in-plane deviation model r(;r 0 (;)j) ash(r;j). Let us dene the expectation of the in-plane deviations h(r;j) over all : Z h(r;j)d (2.2) Remark Model (2.2) represents the average in-plane deviation over all layers. The previous models developed for cylindrical and polyhedron shapes can be viewed as the average in-plane deviation when the out-of-plane deviation is not considered. On the other hand, the out-of-plane shape deviation, which is the error in the vertical direction , can be represented in the vertical cross section determined by angle (Fig. 2.4). Any point P 0 on the boundary of the vertical cross section = 0 is given as (r;j 0 ). E y z x 0 ¿ Vertical Cross Section N N, \ E 4 0 (N, \; ¿ 2 4 2 4 E 4 E 4 Figure 2.4: Out-of-plane deviation representation Consistent with the in-plane deviation r(;r 0 (;)j), the out-of-plane devi- ation model r(;r 0 (;)j) is denoted asv(r;j). Let us dene the expectation of the out-of-plane deviations v(r;j) over all in the vertical cross section as: Z v(r;j)d (2.3) 40 which can be interpreted as the average out-of-plane deviation in a similar fashion. Remark Geometrically, modelv(r;j) is essentially equivalent toh(r;j). This suggests that the mathematical formulation developed in the previous work for the in-plane errors can be borrowed under this new formulation in the SCS. In this way, the 3D geometric deviation can be described in a unied mathematical framework [42, 52]. Remark It should be noted that v(r;j) and h(r;j) may dier even the hor- izontal and vertical cross-section views share the same shape. Dierent from the in-plane deviation whose representation is along the radial direction, the out-of- plane deviation is dened along the vertical direction. The dierence in repre- sentation leads to dierent error patterns. Furthermore, the vertical deviation is in uenced by extra factors such as layer interactions and gravity, resulting in dierent deviation patterns. Thus, other than presenting a new formulation for 3D geometric errors, another major eort of this chapter is to establish further the out-of-plane deviation model to obtain the 3D representation. The 3D error of any point P 0 on the shape boundary is therefore decomposed into two orthogonal components: in-plane and out-of-plane errors. The orthogo- nality ensures that the model building and error compensation can be conducted separately for two error components. Since the previous work [41, 133, 98, 43, 44, 110] has addressed the issue of in-plane error control, this work will focus more on the method of prediction and control of out-of-plane errors. To summarize, this novel formulation of spatial deviation enables a consistent mathematical formulation of both in-plane and out-of-plane errors, which readily incorporates the previous work on predictive modeling and compensation of in- plane errors. 41 2.2.2 Predictive Modeling of Out-of-Plane Errors Predictive modeling of out-of-plane deviation aims to achieve eective prediction based on a limited number of test shapes. Since the out-of-plane deviation shares the same mathematical formulation with the in-plane deviation, we rst review the predictive in-plane error modelf(;r 0 ()) developed in [43, 44] for cylindrical and polyhedron shapes (in PCS): f(;r 0 ()) =g 1 (;r 0 ()) +g 2 (;r 0 ()) +g 3 (;r 0 ()) +" (2.4) where g 1 represents the basis model for the cylindrical shape, g 2 (;r 0 ()) is the so-called cookie-cutter function added to the cylindrical basis in order to carve out any polygon shape from a circumcircle;g 3 (;r 0 ()) is an optional higher order term, and " is the noise term. Two kinds of cookie-cutter functions have been proposed: the square wave model g 2 (;r 0 ()) = 2 r 0 sign[cos(n( 0 )=2)] (2.5) and the sawtooth cookie-cutter model g 2 (;r 0 ()) = 2 r 0 I( 0 )sawtooth( 0 ) (2.6) where the sawtooth function is dened as: sawtooth( 0 ) = ( 0 )MOD(2=n) (2.7) Although this formulation paves the way to model the out-of-plane deviation in the vertical cross section given 0 , the out-of-plane error modeling faces unique 42 issues. The rst issue is the denition of the deviation in the vertical section. Figure 2.5 illustrates the denition of the out-of-plane error z in a PCS dened vertical cross-section view. Figure 2.5: Out-of-plane deviation denition For representation convenience, we dene: 0 = (=2) MOD 2 (2.8) In the PCS dened vertical cross section view, the nominal shape boundary is represented as r 0 ( 0 ) at angle 0 , while the corresponding actual shape boundary is represented as r( 0 ;r 0 ( 0 )). The out-of-plane deviation z is therefore dened as: z( 0 j 0 ) = (r( 0 ;r 0 ( 0 )j 0 )r 0 ( 0 )j 0 ) sin( 0 j 0 ) (2.9) with this denition, z can adopt the same formulation developed for the in-plane deviation. 43 To achieve prediction of an arbitrary polygon or circular shapes in the vertical cross-section, we still adopt the cookie-cutter concept proposed in the previous work. However, we have to accommodate the out-of-plane deviation. Similarly, the out-of-plane deviation model is dened as: z( 0 ;r 0 ( 0 )j 0 ) =g 1 ( 0 ;r 0 ( 0 )j 0 ) +g 2 ( 0 ;r 0 ( 0 )j 0 ) +" 0j 0 (2.10) whereg 1 is the cylindrical basis model andg 2 is the revised cookie-cutter function to be developed in Section III, and " 0j 0 is the noise term. Remark: This formulation works more eciently for axial symmetric products such as prisms and cylinders, whose vertical cross-sections along the z axis are in the same shape. In this case, we normally need one predictive model for the out-of-plane deviation. Otherwise, for products with entirely dierent vertical cross-section shapes, several predictive models are required to cover every point on the shape boundary, making the generic model much more complicated. Due to page limitation, this work illustrates the proposed method using symmetric products. 2.3 Methodology Illustration and Experimental Validation In this section, we demonstrate how the generic out-of-plane deviation model (2.10) can be applied to a rectangular prism. There are two reasons why we choose rectangular prism as the experimental investigation example. 1. With the vertical cross-section shape being polygons, in-plane deviation models developed in [43, 44] for polygons can be directly applied; 44 2. It is easy to get the measurement data from the prism part using the Micro- Vu vertex measuring machine, for all the six surfaces of the prism part. 2.3.1 Experiment Design and Observations from SLA Process A variant of the SLA process (MIP-SLA) machine is used to build the test parts, where a digital micromirror device projects the designed pattern to the resin tank. The light exposure initiates the resin solidication process for each layer and the platform moves down vertically for the next layer. The size of the test part is 1.6 inch1.2 inches0.5 inches (LWH). The part is positioned at the center of the platform. Since we are interested in the deviation of every point on the part surfaces, including the bottom surface, we add the support under the part to separate the test part from the printing base. The specic parameters in the SLA process and the design for the part are listed in Tab. 2.1. Table 2.1: SLA process settings and test part design parameters Thickness of each layer 0.00197 00 Resolution of the mask 19201200 Dimension of each pixel 0.005 00 Illuminating time of each layer 7 s Average waiting time between layers 15 s Type of the resin SI500 Prism part size (length width height) 1.6 00 1.2 00 0.5 00 Circumcircle radius of top surface 1 inch Support height 0.19685 00 The printed part is shown in Fig. 2.6. A non-symmetric sunk cross with the line thickness of 0.02 00 is designed at the center of each surface to help identify the orientation of the test part and reduce measurement errors (errors caused by part shift and rotation during measurement). A Micro-Vu precision machine is used to measure and evaluate the geometric accuracy of all six surfaces of the prism 45 part. The same measurement procedure is followed for each surface to reduce the measurement errors. Figure 2.6 shows a side view of the measured surface, where the black line is the designed shape boundary and the blue line is the measured shape boundary. The deviation occurs everywhere on the boundary, especially the obvious deviation at the bottom. In Fig. 2.7, the geometric deviations of four side surfaces are presented in the PCS (curves in solid lines). By comparing the deviation proles of four side surfaces, it is clear that all the systematic deviation patterns follow the same trend, indicating the out-of-plane deviation is caused by the same factors with slightly dierent impact. For simplicity of method illustration, in the following section, we apply a unied model to describe the out-of-plane deviation. 2.3.2 Predictive Modeling of 3D Geometric Errors This section demonstrates the proposed method of constructing the out-of-plane deviation model. 2.3.2.1 Cylindrical Basis Function The cylindrical basis function g 1 ( 0 ;r 0 ( 0 )) in model (2.10) represents the devi- ation pattern for a cylinder. For the SLA process in the experiment, we have shown in [41] that cos(2 0 ) basis function captures the deviation pattern well. To test the generality of the identied basis and its applicability to the out-of-plane deviation, we still adopt its form: g 1 ( 0 ;r 0 ( 0 )) = 0 r 0 + 1 r 0 cos(2 0 ) (2.11) 46 (a) Printed rectangular prism part −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 −0.2 0.0 0.1 0.2 x z (b) Measured data of the prism right surface Figure 2.6: Prism case study: Printed part and measured data of the right surface 47 −0.005 0.010 Front Surface φ ' = (π 2 − φ) MOD (2π) Δz 0 π 2 π 3π 2 2π −0.005 0.005 Back Surface φ ' = (π 2 − φ) MOD (2π) Δz 0 π 2 π 3π 2 2π (a) Front and back side surfaces −0.005 0.010 Left Surface φ ' = (π 2 − φ) MOD (2π) Δz 0 π 2 π 3π 2 2π −0.005 0.010 Right Surface φ ' = (π 2 − φ) MOD (2π) Δz 0 π 2 π 3π 2 2π (b) Left and right side surfaces Figure 2.7: Prism case study: deviation proles and model predictions 48 2.3.2.2 Modied Cookie-cutter Function to Predict Polygon Shape Deviation in the Vertical Cross Section The two cookie-cutter models proposed in [43] are applied to regular polygons. They have to be modied when applying to irregular polygons according to their geometric characteristics, particularly, the transitions at the corners. Assume the position of the ith corner is ( 0 c;i ;r c;i ) in the PCS and let n be the number of the polygon sides in the vertical cross section. We propose a one- to-one mapping from ( 0 c;i ; 0 c;i+1 ) to ((i 3 2 ); (i 1 2 )), which is the domain for trigonometric function cos that all the points in this domain are positive or negative. The mapping is proposed as: 0 7! : where = 0 0 c;i 0 c;i+1 0 c;i +i 3 2 (2.12) Using this relationship, the modied square wave cookie-cutter function is dened as: squarewave( 0 ) =r c;i sign[cos(( 0 0 c;i 0 c;i+1 0 c;i +i 1) 2 )] for 0 c;i 0 < 0 c;i+1 ; 0i<n 1; 0 c;0 = 0 c;n (2.13) Similarly, the one-to-one mapping from ( 0 c;i ; 0 c;i+1 ) to (1; 1) is: 0 7! : where = 2 ( 0 0 c;i )MOD( 0 c;i+1 0 c;i ) ( 0 c;i+1 0 c;i ) 1 (2.14) 49 And the sawtooth wave cookie-cutter is modied as: sawtooth( 0 ) =r c;i [1 2 ( 0 0 c;i )MOD( 0 c;i+1 0 c;i ) ( 0 c;i+1 0 c;i ) ] for 0 c;i 0 < 0 c;i+1 ; 0i<n 1; 0 c;0 = 0 c;n (2.15) For the prism part studied in the experiment, Fig. 2.8 shows its modied square wave cookie-cutter function (middle) and the modied sawtooth wave cookie-cutter function (bottom). The top curve shows the nominal radius r( 0 ) as a reference for catching the transition at corners. φ ' = (π 2 − φ) MOD (2π) cookie−cutter for irregular shape 0 π 2 π 3π 2 2π Figure 2.8: Modied cookie-cutter function Another signicant generalization of the cookie-cutter model g 2 ( 0 ;r 0 ( 0 )j 0 ) from [43] is that we allow the mixed selection of square wave and sawtooth wave functions in model (2.10). The cookie-cutter function in [43] is only applied to in-plane deviation in the horizontal cross-section view. It is expected that a single type of square wave or sawtooth wave function can be applied to each polygon side. In the vertical section view, however, deviation patterns of the left and right sides are expected to be quite dierent from those of the top and bottom 50 φ ' = (π 2 − φ) MOD (2π) indicators for irregular shape 0 π 2 π 3π 2 2π Figure 2.9: Modied indicator function sides. This rationale leads to a mixed selection among cookie-cutter functions for dierent sides in the vertical cross-sections. This mixed selection is through an indicator function dened as: 1 [ 0 c;i ; 0 c;i+1 ] ( 0 ) = 1 2 (sign[cos(( 0 0 c;i 0 c;i+1 0 c;i +i 1) 2 )] + 1) for 0 c;i 0 < 0 c;i+1 ; 0i<n 1; 0 c;0 = 0 c;n (2.16) For the four side surfaces of the rectangular prism, the indicator functions are shown in Fig. 2.9. They are the indicator function 1 h ( 0 ) for left and right sides (middle) and the indicator function1 v ( 0 ) for top and bottom sides (bottom) with the top curve showing the nominal radius r( 0 ) as a reference for the transition at corners. Thus, the out-of-plane deviation model in a specic vertical cross section is derived as: z( 0 ) = 0 r 0 + 1 r 0 cos(2 0 ) + 2 r 0 squarewave1 h ( 0 ) + 3 r 0 sawtooth1 v ( 0 ) +" 0 (2.17) 51 2.3.2.3 Model Estimation To estimate model (2.17), we take advantage of the observation that similar de- viation patterns exist among the four side surfaces shown in Fig. 2.7. So we make use of the front and back side surface data to obtain the predictive model for the vertical cross section given 0 = 0, and use the left and right side surface data to obtain the predictive model for the vertical cross section given 0 ==2. The maximum likelihood estimation of model parameters for the two out-of-plane deviation models are listed in Tab. 2.2. The tted model results are shown as the dashed line in Fig. 2.7 . Table 2.2: Model estimation for side surface Side surface Parameter Estimate Std. Error t-value 0 1.329e-03 5.788e-05 22.96 front & back 1 -2.254e-03 1.457e-04 -15.47 surfaces 2 1.804e-03 9.555e-05 18.88 1.60.5 in 3 3.092e-03 1.053e-04 29.37 0 0.0033386 0.0001557 21.442 left & right 1 -0.0073289 0.0003335 -21.974 surfaces 2 0.0012638 0.0001276 9.907 1.20.5 in 3 -0.0015888 0.0001486 -10.695 2.3.2.4 Model Evaluation We use the relative total area change as a criterion to evaluate the predictive model. The total area change is dened as the absolute area outlined by the deviation prole. It quanties the total deviation of the printed part in a vertical cross section. It is dened as: S(r( 0 )) = Z 2 0 r 0 ( 0 )jr( 0 )jd 0 (2.18) 52 And the relative total area change is proposed as: R S = S model =S measurement (2.19) IfR S is close to 1, it indicates that the model predicts the average deviation well. The relative total area change of the four side surfaces are listed in Tab. 2.3. As can be seen, the out-of-plane deviation models capture the major deviation patterns in four vertical cross-sections. Table 2.3: Relative total area change: model evaluation Front Back Left Right R S 0.9366841 1.116051 0.7667575 0.6895701 2.4 Oine Optimal Compensation and Experimental Validation To control geometric error of AM built products, we adopt the oine compensa- tion strategy by adjusting CAD design. The amount of adjustment is based on the predicted geometric shape deviations and original design. Following the com- pensation approach proposed in [41], we denote f( 0 ;r 0 ( 0 );x( 0 )) as the prole deviation at angle 0 when compensation x( 0 ) is applied at angle 0 . As derived in [41], the optimal compensation function is: x ( 0 ) = g( 0 ;r 0 ( 0 )) 1 +g 0 ( 0 ;r 0 ( 0 )) (2.20) where x ( 0 ) satises the objective that E[f( 0 ;r 0 ( 0 )x ( 0 )j 0 )] = 0 and g(;) is the deviation model, g 0 (;) is the rst order derivative with respect to r 0 ( 0 ) 53 The out-of-plane deviation model for the prism is substituted into the com- pensation function to obtain the optimal compensation policy at each point along the boundary: x () = 0 r 0 + 1 r 0 cos(2 0 ) + 2 r 0 squarewave1 h ( 0 ) + 3 r 0 sawtooth1 v ( 0 ) 1 + 0 r 0 + 1 r 0 cos(2 0 ) + 2 r 0 squarewave1 h ( 0 ) + 3 r 0 sawtooth1 v ( 0 ) (2.21) By adjusting CAD design based on Eq. (21), another prism part is printed for validation of compensation eectiveness. As shown in Fig. 2.10, the out-of-plane deviation before compensation is represented by the black line, while the out-of- plane deviation after compensation is represented by the red line. The nominal value 0 is also plotted. Apparently, the out-of-plane deviation is, in general, decreased under compensation. Relative total area change is used as a criteria to evaluate the impact of com- pensation, which is proposed as: R S = S after =S before (2.22) A small value of R S indicates that the compensation reduces the geometric error of AM products. The relative total area change of the four side surfaces are summarized in Tab. 2.4. As can be seen, compensation methodology performs well for out-of-plane geometric shape control with approximately 50% deduction of the geometric errors. 54 −0.005 Front Surface φ ' = (π 2 − φ) MOD (2π) Δz 0 π 2 π 3π 2 2π −0.005 Back Surface φ ' = (π 2 − φ) MOD (2π) Δz 0 π 2 π 3π 2 2π (a) Front and back side surfaces −0.005 Left Surface φ ' = (π 2 − φ) MOD (2π) Δz 0 π 2 π 3π 2 2π −0.005 Right Surface φ ' = (π 2 − φ) MOD (2π) Δz 0 π 2 π 3π 2 2π (b) Left and right side surfaces Figure 2.10: Prism case study: before and after compensation 55 Table 2.4: Relative total area change: before and after compensation Side surface Area before comp:S before Area after comp: S after S after =S before front 0.01037927 0.006563249 63.23% back 0.01037927 0.003832391 36.92% left 0.01325666 0.00729557 55.03% right 0.01474055 0.005779417 39.21% 2.5 Summary This study extends the previous work on control of in-plane shape deviation to out- of-plane shape deviation of AM built products. This is accomplished by adopting a novel spatial formulation of three-dimensional geometric errors which places the in-plane and out-of-plane errors under a unied and consistent framework. Under the spherical coordinate system, the in-plane error and out-of-plane error are two orthogonal components depicted in horizontal and vertical cross sections, respec- tively. Thanks to the mathematical consistency, the out-of-plane error modeling can be derived from the previously developed in-plane error modeling framework. Deriving out-of-plane deviation models, however, is not a trivial extension of in-plane error modeling due to the complicated eects of inter-layer bonding. With the proper denition of out-of-plane error, we revise the previously proposed cookie-cutter modeling framework. The revised model provides the exibility of mixed selection of cookie-cutter functions to accommodate the unique charac- teristics of errors in the vertical direction. Furthermore, the optimal compensa- tion methodology is applied in an SLA process and the out-of-plane deviation is reduced by approximately 50%. The error can be further reduced when more training data is available to understand the eect of inter-layer bonding eects. The study provides a methodological prospect of fully integrating both in-plane and out-of-plane errors for three-dimensional deviation reduction. Not limited to 56 the SLA process, the developed methodology can be applied to a broad category of AM processes. 57 Chapter 3 Modeling Inter-layer Interactions for Out-of-Plane Shape Deviation Reduction in AM Shape accuracy is an important quality measure of nished parts built by additive manufacturing (AM) processes. In Chapter 2, we have established a generic and prescriptive methodology to represent, predict and compensate out-of-plane shape deviation of AM built products using a limited number of test cases. The feasi- bility of the proposed methodology is proved by a rectangular prism case study. However, the extension to control the out-of-plane shape deviation still faces a signicant challenge due to complex inter-layer interactions and error accumula- tion. One direct manifestation of such complication is that products with various sizes exhibit dierent deviation patterns along z direction even for the same type of shapes. In this chapter, we devise an economical experimental plan and a data analyt- ical approach to model out-of-plane deviation for improving the understanding of inter-layer interactions. The key strategy is to discover the transition of deviation patterns from a smaller shape with fewer layers to a bigger one with more lay- ers. This transition is established through the eect equivalence principle which 58 enables the model predicting a smaller shape to digitally \reproduce" the big- ger shape by identifying the equivalent amount of design adjustment. Besides, a Bayesian approach is established to infer the deviation models capable of predict- ing deviation of complex shapes along the z direction. Furthermore, prediction and compensation of out-of-plane deviation for freeform shapes are accomplished with experimental validation in an SLA process. 3.1 Introduction AM refers to a class of technologies that build 3D objects from digital models through layered fabrication [62, 11, 29]. It enables one-of-a-kind manufacturing of complex shapes without extra tooling and xturing. Despite AM's great po- tentials, lack of shape accuracy is a critical barrier and customized parts with high-precision are in demand [11, 101]. In many cases, however, the printed parts still need post-processing to meet design specications. Therefore, The need for shape accuracy control is of vital importance to AM [9, 123]. Ef- forts have been made to improve the shape accuracy of the AM products. There are two categories, one category of research focuses on modeling critical process variables, such as temperature eld and melt pool size, as proxies of product quality [77, 117, 103, 57, 13], trying to optimize and characterize the process set- tings. However, high-delity physical AM models are costly to build [10]. In addition, these studies are often benchmarked by products with relatively simple geometries. Another category of research focuses on adding compensation during the work ow, such as CAD design, STL le or even 3D optical scanning data [132, 142, 2]. Even so, few have demonstrated the feasibility of predicting and 59 compensating freeform shape deviation using a limited number of test cases. Pre- vious work intends to address this issue by establishing a data-driven methodology to represent, predict and compensate in-plane (xy plane) shape deviation of AM built products using a limited number of test cases [41, 44, 42, 126, 72]. The developed approach can be applied to a broad category of AM process since no specic printing machine settings and underlying physical variables are involved in the model. However, extension to control of the out-of-plane (z plane) devia- tion faces a signicant challenge due to intricate inter-layer interactions and error accumulation. Inter-layer interactions are caused by heat penetration and residual stresses that arise from the contraction, which is associated with the solidication of each layer during the building process [12, 82]. One direct manifestation of such com- plication is that products with various sizes are exhibiting dierent deviation patterns along the z direction even for the same type of shapes. FEA has been applied to model shape distortion caused by inter-layer interactions. To name some previous FEA approaches, Huang and Lan [48] simulate the photopolymer- ization process and conclude that the behavior of the cure distortion is a function of the laser exposure intensity and the elapsed time. Nickel et al. examine the layer deposition process for metal parts in layered manufacturing and show that the part stresses and de ections are aected by the layer deposition pattern [82]. However, FEA has limited applicability due to its large computational load and sensitivity to boundary conditions [10, 40]. Processing techniques have been developed to limit the inter-layer interactions for improved material structure, for example, through modifying the polymeriza- tion process in 3D printed polymers. In FDM processes, chemical cross-linkers are applied to improve the adhesion between adjacent layers [115]. Preheating of the 60 targeted portion of material are developed to increase the inter-layer bonding for Fused lament fabrication (FFF) processes [34]. This line of research, however, is only applicable to specic materials and processes. This chapter aims at modeling and compensating the out-of-plane deviation of freeform shapes with the consideration of interlayer interactions. Following In- troduction, Section 2 presents the overall modeling approach for the out-of-plane deviation and the method to achieve the understanding of the inter-layer inter- actions. Section 3 discusses the detailed modeling procedure for the out-of-plane deviation, which has been validated by an SLA process. Optimal compensation of out-of-plane deviation and its experimental validation are illustrated in Section 4. Conclusions and limitation discussion are given in Section 5. 3.2 Prescriptive Modeling of Out-of-Plane Deviation 3.2.1 Challenges of Prescriptive Modeling of Out-of-Plane Deviation To predict the out-of-plane deviation of freeform shapes, two major challenges have yet to be addressed. The rst one is to model the complicated inter-layer interactions and deviation accumulation. Unlike the in-plane deviation which is mainly caused by non-uniform material shrinkage and shows similar deviation pattern for the same shape of dierent sizes [72], the out-of-plane deviation pat- terns vary with sizes of the same shape, due to additional error sources such as the inter-layer bonding eect, the curl distortion and the complicated eect ac- cumulations. Fig. 3.1 shows the observed deviation patterns for in-plane circles and out-of-plane half-disks. We measure the points on the boundary of the shape 61 and transfer the points in the Cartesian Coordinate System (CCS) to the PCS. As shown in Fig.3.1a, the in-plane deviation r(;r 0 ()) for circles with dierent radii exhibits repeatable patterns. In Fig.3.1b, however, the out-of-plane deviation z(;r 0 ()) for half disks with dierent radii vary with part sizes. The second challenge is the prescriptive modeling of out-of-plane deviation. Prescriptive modeling means the prediction of geometric deviations for new and untried categories of shapes, while traditional predictive modeling usually predicts within its experimental categories [72]. AM has the characteristic of high product varieties and low production volumes. An initial study of out-of-plane deviation of AM built products applies to simple shapes [52]. The substantial extension is required to understand and control out-of-plane deviations of arbitrary freeform shapes by using only a limited number of trial shapes. To address these two challenges, Section 3.2.2 brie y reviews previous work on deviation modeling of 3D shapes and of in-plane freeform shapes. Section 3.2.3 presents the prescriptive modeling methodology to understand the out-of-plane deviation caused by inter-layer interactions. Section 3.2.4 introduces the out-of- plane modeling approach to freeform shapes based on the cookie-cutter modeling framework proposed in [44]. 3.2.2 3D Spatial Deviation Representation and Freeform Modeling Methodology In previous work [42, 52], 3D shape deviation is represented in SCS (r;;). The in-plane deviation is dened in any horizontal cross-section determined by angle 0 where=2 0 =2, and the out-of-plane deviation is dened in any vertical cross-section determined by angle 0 where 0 0 . Any point P 0 62 !0.05 !0.04 !0.03 !0.02 !0.01 0.00 ! Deformation (inch) 0 " 2 " 3" 2 2" 0.5 in 1 in 2 in 3 in (a) In-plane deviation observation ([41]) !0.005 0.000 0.005 0.010 0.015 ! Deformation (inch) 0 " 4 " 2 3" 4 " 0.5 in 0.8 in 1.5 in 2 in (b) Out-of-plane deviation observation Figure 3.1: Observed deviation patterns for in-plane circles and out-of-plane half disks (CAD model in Fig. 3.3) with dierent radii 63 on the boundary of the vertical cross-section = 0 is given as (r;j 0 ), and the out-of-plane deviation model is denoted as z(;r 0 (;)j). Modeling and predicting of the in-plane deviation has been reported in [41, 44, 126, 72]. The primary interest of this chapter is to model the out-of-plane deviation in a specic vertical cross-section. In subsequent discussion, we use z(;r 0 ()) to denote the out-of-plane deviation with omitted for simplicity of notation. Given the representation of geometric shape deviations, we propose the pre- scriptive modeling of the out-of-plane deviation to achieve eective prediction. As shown in [52], the out-of-plane deviation model is dened as: z(;r 0 ()) =g 1 (;r 0 ()) +g 2 (;r 0 ()) +" (3.1) where g 1 (;r 0 ()) = 0 r 0 + 1 r 0 cos(2) exemplies a cylindrical basis model; g 2 depicts the cookie-cutter model [44] with the square wave function proposed as g 2 (;r 0 ()) = 2 r 0 sign[cos(n( 0 )=2)] or the sawtooth function asg 2 (;r 0 ()) = 2 r 0 I( 0 )[( 0 )MOD(2=n)]. The validation example in [52] shows the model eectiveness, however, the pre- vious simple cylindrical basis model g 1 cannot capture the out-of-plane deviation patterns in Fig. 3.1b that vary with part sizes. That is because the inter-layer interactions and error accumulation have not been considered therein. Moreover, the pre-dened classes of the cookie-cutter functiong 2 are not able to capture local deviation accurately and consistently, especially for complex shapes not printed before. The prescriptive in-plane deviation model of freeform shapes has been built following the circular approximation with selective cornering (CASC) strategy in [72]. This is a generic methodology that can predict the deviation for freeform 64 shapes based on a number of test shapes using the cylindrical basis model and the cookie-cutter model described above. Therefore, we intend to extend the CASC strategy to model and predict the out-of-plane deviation for arbitrary freeform shapes. The CASC strategy consists of two steps, the rst step is to use a series of sectors to approximate the curvature of the freeform shape boundary and predict each sector by the generalized cylindrical basis modelg F 1 (;r 0 ()); the second step is to insert the extended cookie-cutter functiong F 2 (;r 0 ()) at corners with sharp transitions. With the generalized cylindrical basis model and extended cookie-cutter model, the prescriptive model for freeform deviation is extended from Equation 3.1 to: z F (;r 0 ()) =g F 1 (;r 0 ()) +g F 2 (;r 0 ()) +" (3.2) 3.2.3 Understand the Deviation Accumulation From Layer to Layer Using Eect Equivalence The cylindrical basis function is a key functional component to achieve high pre- diction accuracy. As stated in Section3.2.2, the cylindrical basis function g 1 from Equation 3.1 cannot capture the out-of-plane deviation pattern transition with various part sizes. Therefore, it needs to be improved to consider the intricate inter-layer interactions and error accumulation as well. The rationale of the proposed data analytical method in this chapter is as follows. Given the understanding of in-plane deviation with a few layers, we wish to predict the potential out-of-plane shape deviation with more layer build-up. The connection between these two situations needs to be discovered by building 65 the transition function that links the settings with fewer layers to the one with more layers. However, the latent variables in the printing process obscure the model construction. Thus, to understand the pattern transition from fewer layers to more layers, we adopt the "eect equivalence" principle and associated modeling approach. The eect equivalence concept is rstly proposed for machining process con- trol [128]. It represents a common engineering phenomenon that dierent factors could potentially generate the same outcome. Then one factor can be transformed into the equivalent amount of the other factors in terms of equal outcomes. In machining processes [127, 128], for example, the eect equivalence among xture, machine tool, and datum errors is represented by the total equivalent amount (TEA) of the xture error (base error) using a mapping obtained through kine- matic analysis. For AM processes, if one well-studied AM process and its model can always reproduce the outcome of another through "proper adjustment", we can use the learned process model to predict the new processes. The critical issue is to iden- tify the equivalent amount of adjustments. Recent work in [100] addresses this issue through a generic causal modeling formulation. This approach enables us to transfer the model in one environment to another for the case containing lurking variables. For example, in the SLA process studied in [41], light exposure is a lurking variable that holds up the model construction since it cannot be directly measured. The established model for an ideal SLA process without light-exposure issue can be transferred to the actual SLA process by nding the TEA of design compensation (base error). For the complicated case of out-of-plane deviation with inter-layer interactions, we take advantage of the established in-plane cylindrical basis model (without 66 inter-layer interactions) and transfer it to the case of out-of-plane cylindrical basis model with inter-layer interactions, if we can identify the equivalent of adjustment. The vertical basis model is prescriptively dened as in Equation 3.3. We generalize the basis model and assume it consists of two parts: the basis function f 1 characterizes the shared eects of in-plane and out-of-plane deviation (e.g., non-uniform shrinkage and material phase change); the equivalent eect function f 2 captures the extra eects that specically happen in vertical direction (e.g., inter-layer bonding eect and distortion eect). Details will be shown in Section 3.3.2. g 1 (;r 0 ()) = 0 r 0 + 1 f 1 f 2 (3.3) 3.2.4 Prescriptive Modeling of Out-of-Plane Deviation of Freeform Shapes Using Bayesian Approach Extending a cylindrical shape model to other freeform shapes is nontrivial. We address this problem by extending the cookie-cutting modeling framework. Pre- viously, the cookie-cutter function with mixed selection is adopted as g 2 in the out-of-plane deviation model [52]. Though the rectangular case study shows the eectiveness, it is dicult to extend the mixed selected cookie-cutter function to model the out-of-plane shapes. Another limitation is that the pre-specied func- tional forms of cookie-cutter (square wave function and sawtooth function) cannot completely capture the local deviation of a variety of new shapes. Therefore, we wish to build an appropriate cookie-cutter model that can cap- ture the local deviation for new complex shapes with the small samples of the deviation data and the out-of-plane cylindrical model derived in section 3.2.3. To 67 achieve this, we adopt the Bayesian posterior predictive checks methodology in [31, 32]. Bayesian posterior predictive checks oer a feasible method for model parameter estimation by looking for systematic discrepancies between the real observed data and simulated data from the tted model [33]. In [99], it is used to eectively combine 2D deviation data and previously learned models of a small sample of disparate shapes to aid in model specication. Consequently, the local deviation feature can be captured by the dierence between the newly observed deviation data and the existing cylindrical basis model. We dene the discrepancy measure T as: T = r(;r 0 ())g 1 (;r 0 ()) (3.4) The discrepancy measure focuses on the construction of the cookie-cutter model g 2 (;r 0 ()) since the deviation feature of the basis function is removed from the observed data. We then generate the generalized cookie-cutter function according to the discrepancy measure T and the local shape feature. Consider a polygon with E edges, let e = 1; 2;:::;E, for each edge e, dene m(e) as the angle that minimized the nominal radius on edge e: m(e) =argmin (r 0 ()) (3.5) Accordingly,r 0 (m(e)) is the minimum nominal radius of all points on the same edge. For each edge, the local shape feature can be represented as the dierence between the nominal radius with any points on the boundary and the minimum nominal radius. Therefore, the generalized cookie-cutter function is dened as a function of local shape features as follows: g 2 (;r 0 ()) = 0;e + 1;e [r()r 0 (m(e))] b + (3.6) 68 Prescriptive modeling of out-of-plane deviation aims to achieve eective pre- diction for untried shapes based on a limited number of test trials. After the two issues being addressed, the out-of-plane deviation model becomes: z(;r 0 ()) =g 1 (;r 0 ()) +g 2 (;r 0 ()) + (3.7) where g 1 and g 2 are dened in Equation 3.3 and Equation 3.6. 3.3 Methodology Illustration and Experimental Validation In this section, we validate the eectiveness of the proposed general modeling ap- proach with experimentation on an SLA process. The half disk shapes are printed to aid the model estimation of the vertical cylindrical basis function. The full cylindrical shape is not considered since the downward face has to be connected with the support structures, and the data prole collected from it would be im- pacted. As demonstrated in [44, 72], polygon shapes has played an essential role in the prescriptive model for freeform shapes. So the measurements of irregular polygon shapes are used to estimate the complete out-of-plane deviation model. The deviation prediction of freeform shapes built along the vertical direction based on prescriptive models for half disks and irregular polygons with a number of trials is also illustrated at the end of this section. The schema of the overall modeling and compensation approach is as shown in Fig. 3.2. In practice, the following procedure can be followed: Print 3-5 cylindrical shapes with dierent radii and 2-3 regular or irregular polygon shapes as training cases 69 Figure 3.2: Schema of the overall modeling and compensation approach Represent shape deviations of training products in SCS and build the cylin- drical basis model to capture the global deviations Calculate discrepancy measure and build the cookie-cutter model to capture the local deviations The cylindrical basis model in step 1 and the cookie-cutter model in step 3 compose the prescriptive model for freeform shapes For a new, untried product, we apply CASC strategy to approximate the shape of its CAD design, use the prescriptive model to predict the deviation and use the optimal compensation approach to compensate the CAD design. 70 3.3.1 Experimental Design and Observations from SLA Process A commercial ULTRA machine is used in all experiments. In the printing pro- cess, the UV laser exposes the design onto the surface of the resin to motivate the solidication process. An elevating platform then descends a predetermined distance, and so forth [112]. The specications of the manufacturing process are the same as in [53]. Four half disks with dierent radii are built in order to estimate the parameters of the vertical cylindrical basis model. An irregular polygon part with circumcircle radius of 1:8 inch and a vertical freeform part with circumcircle radius of 2 inch are printed to verify the out-of-plane cookie-cutter model and the prescriptive modeling through CASC strategy respectively. The experimental part design parameters are listed in Tab.3.1: Table 3.1: Test part design parameters Vertical cross section geometry Circumcircle radius half disk r = 0.5 00 , 0.8 00 , 1.5 00 , 2 00 Irregular polygon r = 1.8 00 Freeform r = 2 00 Figure 3.3 shows how the printed parts are represented in the SCS as described in Section 3.2.2, the printing direction is also shown in Fig.3.3. The printed parts are shown in Fig.3.4. In order to reduce the measurement error, a nonsymmetric sunk cross is designed for each part as the measurement coordinate origin. We use the Micro-Vu precision machine to measure the shape boundary of each part with an amplication factor as 64 and follow the same measurement procedure for each part. 71 It is observed in [41] and [44] that under the same printing process setting, through variability exists, parts with the same geometric shape have the same deviation pattern. Thus, for this study, we assume the printing process is relatively stable and repeatability is not an issue. Figure 3.3: Design and building direction of half disk part, irregular polygon part and freeform part Figure 3.4: Printed half disk parts, irregular polygon part and freeform part The out-of-plane shape deviation is represented in SCS at a dened vertical cross-section. The solid lines in Fig.3.1b show the deviation observation of four half disks, solid lines in Fig.3.5a and Fig.3.5b show the shape deviation observation of the irregular polygon shape and freeform shape respectively. 72 −0.015 −0.010 −0.005 0.000 0.005 0.010 φ Deformation (in.) 0 π 4 π 2 3π 4 π (a) For irregular polygon shape (b) For freeform shape Figure 3.5: Out-of-plane deviation prole and model prediction of irregular poly- gon and freeform shape (solid line: deviation observation, dashed line: deviation prediction, two dotted lines: 95% condence interval for deviation prediction) 73 3.3.2 Prescriptive Modeling for Freeform Shapes 3.3.2.1 Cylindrical Basis Function to Incorporate Inter-layer Interaction Eect The generalized basis function in Equation 3.3 represents the pattern of the radial deviation. From Fig.3.1b, notice that larger cylinders with more layers (i.e. r 0 = 1:5 00 ; 2 00 ) have similar patterns. When the number of layers decreases, the common deviation pattern disappears, changing to a dierent one. We formulated the following rationale for this phenomenon: for small parts with fewer layers, the deviation pattern is dominated by the basis function f 1 , the deviation caused by inter-layer interaction, which characterized by f 2 , is relatively small. As the number of layers increases, the total equivalent eect f 2 become more and more signicant in the predictive model. Therefore, there exists a deviation pattern transition as the number of layers increase. We want to represent the complicated accumulated eects. The basis func- tion f 1 is used to characterize the common eect of both the in-plane and the out-of-plane deviations, so it follows the same functional form as the in-plane de- viation location-dependent function. Moreover, by the assumption that the total equivalent eectf 2 is the aggregated error from multiple sources, we dene it as a weighted summation of trigonometric functions, each of which has a similar form as f 1 . Thus, we propose the vertical cylindrical basis function to model the deviation pattern: g 1 (;r 0 ()) = 0 r d 0 + 1 r c 0 sin ( 0 ) [ X i r a i cos ( 0 ) + 1] (3.8) 74 where f 1 =r c 0 sin ( 0 ) f 2 = X i r a i cos ( 0 ) + 1 (3.9) 3.3.2.2 Cookie-cutter Function for Extension to Irregular Polygon Shapes The discrepancy measure T in Equation 3.4 is supposed to capture the major trend of the local deviation features. As can be seen in Fig.3.6, for each edge, the discrepancy measure with respect to the nominal radius follows the similar pattern. The observation of the discrepancy measure as a function of the local shape feature suggests the generalized cookie-cutter function in Equation 3.6 to become: g 2 (;r 0 ()) = 0;e + 1;e [r()r 0 (m(e))] b 1 1() + 2;e [r()r 0 (m(e))] b 2 (11()) + (3.10) For each edge, the deviation proles have two opposite trends, we model them simultaneously by using the indicator function: 1() = 8 > > < > > : 1 if >m(e) 0 if <m(e) (3.11) 3.3.3 Out-of-Plane Deviation Model Estimation To estimate the parameters of the basis function f 1 in Equation 3.9, we use least square estimation (LSE) over the half disk measurement data. The resulting model is illustrated in Fig.3.1b as dashed lines, with parameters listed in Tab.3.2. We can see that the tted generalized cylindrical basis model predicts the deviation 75 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1.775 1.785 1.795 −0.008 −0.004 0.000 edge 1 Discrepancy (in.) ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1.65 1.70 1.75 1.80 0.000 0.002 0.004 0.006 edge 2 Discrepancy (in.) ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1.55 1.60 1.65 1.70 1.75 1.80 0.010 0.014 0.018 edge 3 Discrepancy (in.) ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 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● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1.66 1.70 1.74 1.78 −0.002 0.002 0.006 edge 4 Discrepancy (in.) Figure 3.6: Discrepancy measure of each edge for irregular polygon as a function of r 0 () accurately, for both small and large parts, while there is a potential improvement for transition prediction. Armed with the generalized cookie-cutter model, we then use the Bayesian pos- terior predictive check to t the integrated out-of-plane deviation model in Equa- tion 3.7 suitable for both the cylindrical shape and the polygon shape. Bayesian posterior predictive check compares the observed data to a reference distribution based on the posterior that obtained by Bayesian formulation. The reference dis- tribution is the predictive distribution of the data sets if the model is true [31, 116]. We assume that all the parameters are independent a prior. Flat priors are placed on 0 and 1 , The prior for other parameters are specied as follows: 76 Table 3.2: Parameter estimation for out-of-plane deviation basis model Parameter Estimated value Standard deviation 0 0.0038 2:0646 10 5 1 0.0058 4:2389 10 5 c 0.0084 1:7290 10 4 d 1.4239 1:0318 10 3 1 1.4278 5:1612 10 4 2 0.3938 1:2717 10 4 0 0.0145 1:2783 10 3 1 sN(1:4278; 1) 2 sN(0:3938; 1) csN(0:0084; 1) dsN(1:4239; 1) log( = 1= )sN(0:0145; 1) i;j sN(0; 2) where i = 0; 1; 2 j = 1; 2; 3; 4 b i;j sN(1=2; 1) where i = 1; 2 j = 1; 2; 3; 4 k sN(0; 2 ) where k = 1; 2;:::K (3.12) Note that i;j denotes parameter i for the j th edge of the irregular polygon; b i;j denotes parameterb i for the j th edge; and k denotes the residual at thek th point (K is the number of the total measured points). We t the deviation model via Hamiltonian Monte Carlo (HMC) with 800 draws. The HMC algorithm [24] is a Markov Chain Monte Carlo (MCMC) tech- nique. It rst draws new momentum vector p by Gibbs sampling update, then simulates the complex distributions using Hamiltonian dynamics by the leapfrog algorithm [4, 81]. Fig.3.5a shows the result for the irregular polygon shape. The posterior mean (dashed line), 2.5% and 97.5% posterior quantiles (two dotted lines) are also plotted. 77 It can be observed that in Fig.3.5a, the tting for edge 2 shows a dierent trend with the observed data prole, which negatively aects the compensation accu- racy. This local discrepancy between model prediction and actual measurement is mainly due to the compromise between model robustness and model accuracy. Because we intend to use a few training shapes to predict the shape deviation of freeform products, simpler model structures with robustness will be preferred to avoid overtting of the training data. Approximation error is inevitable. On the other hand, the small set of training data can introduce variations as well. Specically, in Equation 3.10 and 3.12, we assume all the parameters in g 2 follow certain distributions, for example, i;j sN(0; 2) where i = 0; 1; 2 j = 1; 2; 3; 4. However, from Fig. 3.6, subgure "edge 2", we can see that 2;2 (the slope) does not follow the same distribution, and this is the cause of the unex- pected tting for edge 2. Once more training cases are accumulated, the model accuracy is expected to improve through learning. 3.3.4 Prescriptive Modeling via CASC Strategy for Out- of-Plane Freeform Shapes We then adopt the CASC strategy to predict the out-of-plane deviation for freeform shape with all model parameters estimated from previous experiments. The rst step of CASC strategy is to capture the curvature from the freeform shape bound- ary. We obtain a series of sectors with dierent radiir i ( i ) at i that approximate 78 the boundary of freeform shape. The deviation of each sector can be predicted by the generalized cylindrical basis model: g F 1 (;r 0 ()) = 0 r i ( i ) + 1 r i ( i ) cos(2) where i1 << i ; 1in; 0 = n (3.13) Secondly, we select corners with sharp transitions along the freeform shape boundary and impose cookie-cutter functions. Assuming there are m selected cornersf 1 ; 2 ;:::; m g. When j = k is satised, the square wave function is extended as: g F 2 (;r 0 ()) = 2 r j ( j ) sign[cos( (2 + (1) j ) 2 j )] where j1 << j ; 1in; 0 = n (3.14) and the sawtooth wave function is extended as: g F 2 (;r 0 ()) = 2 r j ( j ) ( j1 )MOD( j j1 ) 2( j j1 ) where j1 << j ; 1in; 0 = n (3.15) The observed deviation prole for the freeform is represented in Fig.3.5b (solid lines), 41 sectors of circular curves have been determined by the CASC strategy, with the vertical basis modelg 1 adopted to every sector. The predicted deviation (dashed line) and its 95% condence interval (two dotted lines) are also shown in Fig. 3.5b. 79 3.4 Oine Optimal Compensation and Experimental Validation To improve the shape accuracy of AM built products, we adopt an oine compen- sation strategy by adjusting the CAD directly. The amount of compensation is calculated based on the prescriptive out-of-plane deviation model. Following the compensation approach established in [41, 42] and substituting the out-of-plane deviation model into the compensation function, the optimal oine compensation at each point along the boundary is derived as follows: x () = g(;r 0 ()) 1 +g 0 (;r 0 ()) = g 1 (;r 0 ()) +g 2 (;r 0 ()) 1 +g 1 0 (;r 0 ()) +g 2 0 (;r 0 ()) (3.16) According to the new CAD with compensation added by Equation.3.16, a new vertical irregular polygon part and a new vertical freeform part are printed for the validation of eectiveness. As shown in Fig.3.7, the out-of-plane deviation before compensation is represented by the dotted lines, while the out-of-plane deviation after compensation is represented by the solid lines. The nominal value 0 is also plotted in dotted lines. Apparently, the out-of-plane deviation is, in general, decreased under compensation. As [5, 78] states, Y14.5 standards can be used as a benchmark to evaluate specic feature tolerance ( i.e., atness and straightness). However, we aim to minimize the overall error for arbitrary shapes, which potentially aggregate all features including both dimensional and geometric error. Therefore, the relative total area change R S , dened in [42, 52] is used as a criterion to evaluate the impact of compensation. 80 !0.015 !0.010 !0.005 0.000 0.005 ! Deformation (inch) 0 " 4 " 2 3" 4 " Before compensation After compensation (a) Vertical irregular polygon !0.02 0.00 0.02 0.04 ! Deformation (inch) 0 " 4 " 2 3" 4 " After compensation Before compensation (b) Vertical freeform shape Figure 3.7: Out-of-plane deviation prole before and after compensation 81 Tab.3.3 summarizes the compensation performance of the two vertical parts evaluated by R S . As can be seen, compensation methodology performs well for the out-of-plane shape control with approximately 60% and 40% deduction of the shape errors respectively. Table 3.3: Relative total area change: before and after compensation Vertical irregular polygon Deviation Before After Reduction 0.0187 0.0078 57:9837% Vertical freeform Deviation Before After Reduction 0.0309 0.0195 36:7954% 3.5 Summary In this work, we establish a prescriptive analytic method to model the out-of-plane deviation. We rst generalize the in-plane deviation basis function by adopting eect equivalence methodology. A Bayesian approach is developed to infer the predictive deviation model for out-of-plane complex shapes, where the inter-layer interactions and error accumulation are captured. Applicable to a wide category of AM processes, this data-analytical method leads a way to predict the out-of-plane deviation for freeform shapes based on disparate and small data. Experimental validation and analysis show that the prescriptive out-of-plane deviation model is capable of predicting the deviation prole for out-of-plane com- plex shapes and even free-form shapes. Furthermore, the optimal compensation methodology is applied in an SLA process with the out-of-plane deviation reduced by approximately 60% for un-printed polygon shapes and 40% for new freeform shapes. However, because this work aims to reduce the out-of-plane deviation 82 with inter-layer interactions, it is suggested to be applied to shapes with freeform in the vertical cross-section and simple shape in horizontal cross-sections, but not to model and compensate 3D freeform shapes. The experimental validation further indicates that the developed prescriptive methodology has the potential of predicting 3D deviation for arbitrary shapes by learning from a limited number of tested shapes. The insight and results obtained from this study are promising for controlling the shape accuracy of 3D freeform shapes. 83 Chapter 4 Process Variability Source Analysis and Knowledge Discovery for a Multiple-step Bio-process As introduced in Chapter 1, commercial bio-processes are comprised of multiple- step batch operations. However, their productivity is often aected by abnormal variations that lead to undesirable results. Though multivariate statistical meth- ods such as PCA and PLS have been in use in recent years to monitor, detect and diagnose faults for bioprocesses, it is still dicult to identify the causes of multiple-step process variability. In this chapter, we propose a two-stage strategy to explore cell culture man- ufacturing variability in multiple-step bio-processes with the objective to unveil hidden process characteristics and provide insights into factors aecting process quality. The proposed strategy includes two parts: 1. a clustering stage performed to explore the residual subspace found by PCA for dierent causes using data in the nal production of the bioprocess; 2. a fault diagnosis stage based on robust LDA s analysis, to explore the data in previous steps of bioprocess, supervised by the cluster knowledge obtained in Stage 1. The proposed strategy is applied 84 to multiple-step batch processes from Genentech, showing its ability to categorize and diagnose the sources of multiple-step process variability. 4.1 Introduction Multiple-step batch processes are widely used in pharmaceutical manufacturing to utilize mammalian cells for the production of recombinant protein therapeutics and process variability may be experienced in these complex bioprocesses [19, 122]. Data of enormous volume and various kinds are generated and collected from various cell culture process stages. Therefore, mining the historical data is pivotal to uncover the hidden reasons that cause the process variability, and potentially provide means to detect them in early stages to improve process performance [19, 66]. Low titer in CHO mAbs production is often correlated with lower cell growth and with high lactate production [19]. Several studies have employed lactate metabolism models to study this phenomena [137, 80, 65]. For example, a steady state topological metabolic model is proposed in [80], indicating the mechanism of lactate consumption and accumulation can explain the cause of high lactate. Nev- ertheless, these knowledge-based models are built with lactate metabolic pathway simulation and can hardly be applied to the large-scale manufacturing process since the concentration of additional metabolites are needed, which is not mea- sured routinely in commercial manufacturing. In a dierent vein, data-driven modeling is also a useful way to explore the knowledge of bioprocess and has a vast body of literature. In particular, MVA has been successfully applied to process monitoring and fault diagnosis for bioprocess [3, 92, 30, 59]. For example, The PCA and PLS algorithms were used to model 85 the correlations from historical data, mPCA and mPLS were used to deal with batch process data. The key idea behind mPCA and mPLS is to unfold the 3D batch data tensor into the 2D matrix and apply PCA or PLS on the unfolded data afterward. For example, Nomikos [84], Nomikos and MacGregor [86] applied mPCA and mPLS to extract the information in the trajectory data and developed simple monitoring charts for process fault detection. Lee et al. [68] used multi- way kernel PCA to capture the nonlinear characteristics within normal batch processes and detect faults. Related research work and variations were introduced in [135, 129] as well. An alternate approach to MVA methods can be found in [18, 16], which used clustering methods to group dierent process runs into subgroups according to the similarity of certain variables based on the distance measure. For example, in [16], a clustering technique was used to identify the fault contributors by calculating the Euclidean distance between pairs of contributors. Moreover, MVA methods and data clustering have been integrated. For example, Singhal and Seborg [109] developed a modied K-means methodology to cluster multivariate time-series data from similarity factors based on PCA. Husson et al. [50] proposed Hierarchical Clustering on Principal Components (HCPC) that combined PCA, hierarchical clustering and partitional clustering to enrich the description of the data and obtain a better visualization. In this chapter, we propose a data mining strategy that investigates the cell culture process variability in multiple manufacturing steps with diverse bio-process data sets. This strategy includes the following two stages: 1. use hierarchical clus- tering method on the residual subspace found by PCA to better separate normal data and dierent types of fault data; 2. use robust LDA based contributions 86 analysis on normal-fault data clusters pair-wisely to nd fault direction and vari- able contributions. The rst stage is applied on the data in the last step of the bioprocess to obtain data labels while the second stage is applied on the data in the previous steps of the bioprocess, supervised by the labels dened from stage 1. Following the introduction, Section 4.2 presents a large-scale cell culture process and describes the problem. Section 4.3 introduces the data mining approaches and the proposed procedure for multiple-step bio-process variability source anal- ysis. Comparative case studies on a real industrial manufacturing bio-process are shown in Section 4.4, the advantages of the strategy can be shown clearly in this section. Conclusions are shown in Section 4.5. 4.2 Process and Problem Description Cell culture is the process by which cells are grown under controlled conditions. The layout of a large-scale cell culture process is shown in Fig. 4.1, it consists of a series of unit operations including cell bank, seed train, inoculum train and production runs. The inoculum train and the production run also consist of multiple-steps such as N-3, N-2, N-1 and N with increasing manufacturing scale from 20L to 12,000L. Each step has its KPI such as cell growth rate, nal viabil- ity and titer, along with appropriate product quality attributes. The success of process scale-up is usually measured by these KPIs and product quality attributes that meet pre-dened criteria [69]. In this study, 241 historical runs of large-scale cell culture process data during the year 2008 - 2015 from Genentechs facility were investigated and all batches were within the pharmacopoeial specications and approved by the legal require- ments. Process data was obtained from inoculum train which was cultured for 87 Figure 4.1: The layout of a large scale cell culture process ([69]) approximate 4 days with one measurement per day and production run which was cultured for approximate 11 days with two measurements per day. For each stage, data includes 11 oine measurements, 11 initial batch conditions and seven media preparation measurements (such as media prep osmolality and media prep dura- tion). These variables are highly correlated and mainly consist of physiological parameters such as VCD, PCV and physio-chemical environment variables such as buer pH value, osmotic pressure and others. As an essential quality metric, the concentration of lactate at the end of the cell culture process was measured, scaled to range [0; 1] based on the min and max reading. The distribution of the scaled nal lactate concentration is shown in Figure 4.2. Based on the process knowledge, if the normalized nal lactate value of a run is larger than 0.4, this run is recognized as a high lactate run; otherwise, it is recognized as a low lactate run. There are 75 high lactate runs and 166 low lactate runs. This study aims to explore the process variability and 88 diagnose the causes of high lactate runs by analyzing the diverse process data from multiple-step bio-processes. Figure 4.2: Scaled nal lactate concentration distribution 4.3 Data Mining Approaches and Proposed Strategy In this section, we brie y introduce the methods that are applied in the proposed strategy. The PCA and PCA based monitoring methods are introduced rstly, they are used to decompose the process data into dierent subspaces; we then introduce the hierarchical clustering method which is used to assist multiple fault detection. Finally, to gure out feature contributions to the fault clusters, we introduce LDA, robust LDA and LDA based contributions analysis. The work ow of the proposed strategy is also introduced at the end of this section. 89 4.3.1 PCA and PCA Based Process Monitoring PCA in many ways is the basis of MVA. Given the scaled process matrixX2R nm consisting of m variables and n samples, PCA aims to maximize the covariance of the process matrix under certain constrain: max p p T X T Xp s.t.jjpjj = 1 (4.1) and decompose the data into principal subspace and residual subspace: X =TP T + ~ T ~ P T (4.2) whereT andP are the score matrix and loading matrix in the principal subspace respectively, ~ T and ~ P are the score matrix and loading matrix in the residual subspace respectively. They hold the relationship ~ P ~ P T =IPP T For a sample x k , its PCA model estimate ^ x k and residual estimate ~ x k are: ^ x k =PP T x k ~ x k = ~ P ~ P T x k = (IPP T )x k (4.3) PCA based fault detection monitors PCs and residuals with dierent statistics [54, 91] , for example Hotelling's T 2 is used to monitor the PC scores for the observations, SPE is used to monitor the residuals which are the distances from the model hyper plane. The T 2 index and SPE index for the kth sample are calculated as: T 2 k =x T k P 1 P T x k SPE k =x T k (IPP T )x k (4.4) 90 where = diag[ 1 ; 2 ;:::; l ] with i to be the ith largest eigen-value and l to be the number of PCs selected for PCA model. The control limit with (1) condence are: T 2 k 2 l; SPE k g 2 h; (4.5) where the coecientg and the degree of freedom (DOF)h for SPE are calculated by g = P m l+1 2 i P m l+1 i and h = ( P m l+1 i ) 2 P m l+1 2 i . 4.3.2 Hierarchical Clustering The goal of data clustering is to group similar data points into the same cluster so that data points in the same group have similar properties and in dierent groups have dissimilar properties. Hierarchical clustering does not require a pre-specied number of clusters. The hierarchy of clusters is represented as a dendrogram with the height of the dendrogram corresponding to the dissimilarity of the clusters [51, 55]. In the proposed strategy, the dissimilarity is dened as Euclidean distance and we use hierarchical clustering with complete linkage since it tends to yield a more balanced dendrogram. The elbow method which looks at the total within- cluster sum of squares (WSS) as a function of the number of clusters is used to decide the optimal number of clusters [60]. This algorithm is described as follows to nd the number of clusters k. 91 Algorithm 1: Elbow algorithm to decide the number of clusters k Compute clustering algorithm for dierent values of k and for each k, calculate corresponding WSS; Plot the curve of WSS according to the number of clusters k; The location of a knee in the plot is considered as an indicator of the appropriate number of clusters. 4.3.3 LDA, Robust LDA and LDA Based Contributions Plot Both LDA and PCA are commenly used linear transformation techniques. The major dierence is that PCA is a unsupervised learning algorithm which does not take use of the data labels; in contrast, LDA is a supervised learning algorithm which seeks the optimal direction that maximize the separation of dierent classes. Given the scaled process matrix X2R nm , assume there are K classes in data label and X k represents the set of samples from class k, then the scatter matrix for class k is: S k = 1 n k X x2X k (x x k )(x x k ) T (4.6) The within-class scatter matrix is: S w = 1 K K X k=1 S k (4.7) and the between-class scatter matrix is: S b = K X k=1 1 K ( x k x)( x k x) T (4.8) 92 The optimal direction that maximizes the separation of dierent classes can be found by maximizing the ratio of the between-class scatter matrix and the within-class matrix: J() = T S b T S w (4.9) Let @J() @ = 0, the optimal direction is obtained by solving the generalized eigenvalue problem: S b =S w (4.10) When there exists strong collinearity in the process data matrix X, S w will be ill-conditioned. Thus the optimal direction found by LDA is very sensitive to the noise in the data, which make the result not convincing. To avoid this issue, robust LDA is proposed by adding the regularization term to S w such that: S w =S w + (1)I 2 [0; 1] (4.11) where the hyper-parameter is selected based on cross-validation. Notice if = 1, this is the original LDA and if = 0, Equation 4.9 becomes the same as the objective function of PCA. The robust LDA method can be used in fault diagnosis and characterize the variable contributions to the fault cluster. Assume there exists a class of normal process data X 0 and a class of fault data X i , for this bi-class LDA problem, we can and only can nd one optimal direction that discriminates fault data X i to normal data X 0 . This direction is dened as the fault direction for X i and the weights of variables projected onto this direction are dened as the contributions of variables to the fault class i. Therefore, the robust LDA based contributions plot algorithm is proposed as in Algorithm 2: 93 The comparison of LDA based contributions plot and robust LDA based con- tributions plot is discussed in Section 4.4. We use bootstrapping to calculate the condence interval (CI) for each variable, which is used evaluated the eect of robustness, the smaller the range, the better the robustness. Algorithm 2: Robust LDA based contributions with CIs Calculate scatter matrix for normal data and the ith class of fault data: S 0 = 1 n 0 X x2X 0 (x x 0 )(x x 0 ) T S i = 1 n i X x2X i (x x i )(x x i ) T (4.12) Calculate within-class scatter matrix and between-class scatter matrix: S w =S 0 +S i S b = X j=0;i ( x j x)( x j x) T (4.13) Add a regularization term to S w , where 2 (0; 1) is selected based on cross validation S w =S w + (1)I (4.14) Optimize the objective function max J() = S b T Sw T by solving the generalized eignevalue problem S b =S w Obtain the optimal direction , weights in are used to generate the contributions plot = 1 ; 2 ;:::; j ;:::; m T (4.15) Apply boot-strapping to get CI for each contributor 94 4.3.4 Proposed Strategy for Multiple-step Bio-process We propose a strategy to analyze the process variability for bio-process in multiple steps and the schema of the proposed strategy is shown in Fig 4.3. There are two stages in this strategy: intra-batch data analysis for the last step of the bioprocess and the step-wise data analysis. Figure 4.3: Flowchart of the proposed two-stage strategy Stage 1: The rst stage focuses on analyzing intra-batch data in the last step of the bioprocess with the hope to discover additional process knowledge from the data perspective and provide data labels for the next stage. The underlying assumption is that for high lactate batches caused by specic reasons, they behave similarly and are spatially close to each other, or in other words, they are in the same cluster. We rst unfold the 3D data into the 2D matrix, then construct a PCA model for the normal batches and obtain the fault data projected in the residual subspace. After that, we perform hierarchical clustering on the residual 95 subspace to discover hidden patterns of the process data. The results of how dif- ferent clusters are separated and look like can be visualized by LDA and heatmap for each variable. Instead of clustering on the raw data, which contains process information along with noise, we cluster on the residual subspace, which is suitable to show the variability that breaks the normal correlation. We use the Calinski-Harabasz Index as a metric to evaluate the clustering performance [14, 71]. As shown in Equation 4.16, this index is dened as a ratio of between-class scatter matrix and the within-class scatter matrix, where a higher score relates to better-dened clusters. The comparison of clustering on the raw data X and in the residual space ~ X is also shown in Section 4.4. I CH = Tr(S b ) Tr(S w ) NK K 1 (4.16) Stage 2: The second stage of the strategy is to do step-wise data analysis which aims to diagnose the variable contributors from multiple-steps. We use the data labels resulting from the clustering in the last stage to supervise modeling in the previous process steps such as the inoculum train. The assumption is that if something abnormal happens in the previous steps, it would result in a dierent batch behavior in the last step of the process and show dierent patterns in the data. We use the robust LDA method as introduced in Section 4.3.3 to model the normal data and clusters of fault data pair-wisely. If the normal batches and the fault batches could be separated by using data from a certain process step, the fault direction can be found by the robust LDA and the corresponding variable contributors can be found from the contributions plot as described in Algorithm 2. 96 4.4 Case Study on Industrial Manufacturing Bioprocess Data In this section, we introduce how the proposed strategy is applied to the large- scale manufacturing bio-process introduced in Section 4.2. We start from data pre-processing, then discuss how the two stages in the strategy are applied in the real process to do fault detection and diagnosis. The advantages of the proposed procedure can be shown in two comparative case studies. 4.4.1 Data Pre-processing Data cleaning As described in Section 4.2, 11 variables related to the cell physiology and chemical environment are measured oine (twice a day), these variables are PCV, viability, VCD, oine pH, pO2, pCO2, lactate, glucose, am- monium, sodium and osmolality. We remove the trace of lactate in the data because lactate concentration at the nal state is the quality metric. Also, we clean the data by removing the duplicates whose sampling time dier within one hour and interpolate missing data using local linear regression. After prepro- cessing, the dataset contains 241 batch runs, where each of them has 10 process variables with 13 samples. Data unfolding The process measurement data is a three-dimensional array and is organized into a cubic X(NMK) as shown in Figure 4.4. To analyze the batch-wise data, we decompose X into a 2D matrix (N (MK)) following [86, 85]. The new matrix has dimension 241 130, with each column representing a physical variable at a certain time. Due to the low sampling frequency, process dynamics is not a consideration in this chapter. 97 Figure 4.4: 3D process data unfolding 4.4.2 Stage1: Hierarchical Clustering on PCA Residual Subspace PCA residual subspace We apply PCA on the intra-batch data for all 166 low lactate batches, Figure 4.5 shows the proportion of variance explained (PVE) and cumulative PVE, both by the number of PCs. The number of PCs is selected as 48 with 95% of the total variance explained. The T 2 limit is calculated as 65.17 and SPE limit is 9.55, both based on the 95% CI. From Figure 4.6, we see that in the principal subspace (left gure), the high lactate batches and the low lactate batches can hardly be dierentiated, while in the residual subspace (right gure), the high lactate batches and the low lactate batches can be easily separated apart. This also explains why we cluster on the residual subspace ~ X. It is necessary to emphasize that the out of control limit condition of those high lactate batches does not mean that they are above the legal requirements and batches employed in this study are all within the pharmacopoeial specications. Hierarchical clustering analysis As described in Section 4.3, we use hierar- chical clustering with complete linkage. Figure 4.7 shows the dendrogram obtained 98 Figure 4.5: PVE and cumulated PVE plots of PCA model by hierarchical clustering and Figure 4.8 shows the result of elbow method to de- cide the optimal number of clusters. The number of clusters is 4, which gives a balance for the number of clusters and number of batches in each cluster. The four clusters of high lactate batches can be visualized by LDA along with the low lactate cluster. From Figure 4.9 we see that as expected, there is no overlapping among the low lactate cluster and four high lactate clusters. Comparison: hierarchical clustering in raw data X vs. in residual sub- space ~ X We use the Calinski-Harabasz Index to evaluate the clustering perfor- mance. The I CH for clustering in the raw data X is 4.7369 and for clustering in the residual subspace is 8.2725, indicating the clustering results in the residual subspace is better. This can also be visualized from heatmaps of dierent variables such as osmolality, PCV and sodium as in Figure 4.10, 4.11 and 4.12 respectively. 99 Figure 4.6: PCA monitoring results for principal component subspace and residual subspace In these gures, the left plots show the clustering results in raw data while the right plots show the clustering results in the residual subspace. It is hard to see the dierence among clusters in the raw data. However, it's easier to distinguish the dierent patterns among clusters in the residual subspace. For example, it can be observed that for batches in cluster 2, sodium has lower concentration, for batches in cluster 3, osmolality and sodium have the higher concentration at the beginning and for batches in cluster 4, PCV density is higher than other clusters. These unusual patterns in dierent clusters are benecial to understand the pro- cess and dig out correlation among dierent variables for certain types of process variability. In conclusion, by applying stage 1 in the proposed strategy, we can separate low lactate batches and clusters of high lactate batches. There are 4 clusters of high lactate batches; each is related to specic reasons, we label low lactate batches as 0, high lactate batches as 1, 2, 3 and 4 based on their cluster numbers, these data labels will be used to supervise the modeling in Stage 2. 100 Figure 4.7: Hierarchical clustering dendrogram in residual subspace 4.4.3 Stage2: Robust LDA Based Modeling on Step-wise Data In this section, we analyze the process data from previous steps (i.e., N-3, N-2, N-1 in inoculum train) or early stage in the production run from the bioprocess, and use the adjustable variables in N-1 as an example case study to show how the variable contributors are diagnosed by robust LDA. The potentially adjustable variables are selected from initial states, oine measurements and media prepa- ration data based on process knowledge. Data labels are obtained from clustering analysis. Robust LDA based fault diagnosis on N-1 data We use robust LDA to model the normal data and clusters of fault data pair-wisely. The intuition behind the pair-wisely robust LDA based fault diagnosis is that the main contributors to separate the two clusters are the variables that have large projections on the optimal direction found by robust LDA. Figure 4.13 shows the data distribution of 101 Figure 4.8: Elbow method to select the number of clusters for hierarchical clus- tering low lactate cluster and one high lactate cluster on their own robust LDA optimal direction. It can be observed from Figure 4.13 that high lactate cluster 2 is separated from low lactate cluster using the Step N-1 adjustable dataset, which means the process variability in Step N-1 could potentially be the cause of high lactate for cluster 2. Thus we apply the Algorithm 2 to nd the main contributors and the result is in Figure 4.14. The top ve ranked main contributors are : 1. N-1 media-prep Osmo (mOsm/kg); 2. pO2 accepted at day 3; 3. N-1 initial Osmo (mPsm/kg); 4. N-1 Prelnoc media hold duration (hours); and 5. oine pH accepted at day 2. These main contributors are consistent with the known process knowledge and point to new clues for SMEs to better understand the process. For example, N-1 initial osmolality concentration is potentially caused by the variability of osmo- lality media preparation, while the latter could point to some dilution operations. Besides, this is the rst time SMEs see the eects of media hold duration and 102 Figure 4.9: Visualization of low lactate cluster and 4 high lactate clusters by LDA decided to investigate if the media hold variation impacts the nal lactate based on its handling and preparation. Comparison: LDA based contributions plot vs. robust LDA based contributions plot We use bootstrapping to calculate CIs for each contributor [7], the number of simulation is set as 500 and the percentage of samples in each bag is set as 70%. The result is also shown in Figure 4.14. The small range of 95% CI for each variable shows the robustness of the method. Because the adjustable data in N-1 is not highly correlated, the CI range for LDA based contributions plot and robust LDA based contributions plot does not have a distinct dierence. To show the advantage of the robust LDA, we use the 103 Figure 4.10: Heatmap of osmolality for 4 high lactate clusters oine measurement data in production run before 72 hours (temperature shift) and compare the contributions plot for both methods. This dataset contains 60 variables after data unfolding. Figure 4.15 shows the contributions plots based on LDA and robust LDA. It can be observed that in the left gure the CIs for variable contributors are very large while in the right gure, CIs are much smaller, which shows the advantage of robust LDA. 4.5 Summary This chapter proposes a two-stage strategy to analyze the process variability and discover new process knowledge for a multiple-step bio-process. The rst stage analyzes the data in the last step of bioprocess, obtaining data labels by applying hierarchical clustering on the PCA residual subspace; The second stages takes use of the data labels from stage 1, using robust LDA based contributions anal- ysis on normal-fault data clusters pair-wisely to nd fault direction and variable contributions in dierent steps of the bioprocess. 104 Figure 4.11: Heatmap of PCV for 4 high lactate clusters This strategy has been used to explore the process viability of a real man- ufacturing bio-process from Genentech, the ndings are consistent with known process knowledge and have pointed to new clues for SMEs to understand the process better. 105 Figure 4.12: Heatmap of sodium for 4 high lactate clusters Figure 4.13: Distribution of low lactate cluster and one high lactate cluster on the LDA optimal direction 106 Figure 4.14: LDA based contributions plot for high lactate cluster 2 with ad- justable variables in Step N-1 Figure 4.15: Comparison of contributions with condence limits based on LDA and robust LDA 107 Chapter 5 Conclusion and Future Extensions Smart manufacturing has been the focus of many researchers and has been ex- tended to various areas. With the increased complexity of the manufacturing process and the variety of data collected from multiple aspects throughout the process, process data analytics is thus essential to reveal process knowledge and predict the future production. In this dissertation, we introduce two challenges accompanied by smart manufacturing and discuss how we handle the challenges for processes with dierent manufacturing characteristics. The two challenges are "complexity" and "variety"; the areas of applications are AM and pharmaceutical manufacturing. We rst study a statistical modeling and optimal compensation approach to predict and improve the shape accuracy of AM printed parts, especially for the out-of-plane deviation. This method is data-driven and thus, not hampered by the complicated AM physical mechanisms. Moreover, this method can deal with low volume sample data and high product variety. The feasibility and eectiveness of this approach are proved by experimental studies. We then explore the pharmaceutical manufacturing domain and propose a two-stage strategy to study the process variability for a large-scale cell culture 108 manufacturing process. This strategy not only adopts MVA and ML methods on intricate multiple-step bio-processes but also makes use of multilevel heteroge- neous datasets to unveil hidden process characteristics and provide insights into factors aecting process quality. This strategy has been applied to a real anti- body pharmaceutical manufacturing, pointing to new cues for domain experts to understand the process better. To summarize, the work in this dissertation not only oers predictive modeling tools for some advanced manufacturing processes such as AM and pharmaceutical manufacturing, but also contributes to the process data analytics research for smart manufacturing. In the future, we may extend the dissertation work to further support smart manufacturing. Possible directions include but not limited to the following: A statistical learning methodology for 3D free-form shape accuracy modeling In Chapter 2 and 3 of this dissertation, we analyze and model the out-of- plane deviation in the vertical direction, further exploration to model the 3D free-form shape accuracy is necessary and essential. To achieve this, we need to overcome data collection limitation and extend the current model to 3D. 3D scanner and coordinate measurement machine (CMM) are two commonly used machines to measure 3D data. However, the 3D scanner is primarily designed for reverse engineering; though it provides a large amount of point cloud data, they are not accurate enough for precise accuracy control. On the contrary, CMM uses the probe to attach the part surface and provides precise measurements, however, it can only oer a few measurement points. Therefore, to get 3D measurement data with high volume and high precision, 109 it is necessary to study how to align high volume low precision samples and low volume high precision samples. Multisensor data fusion is potentially a methodology to deal with this, research work in this topic can be considered as a regression problem, which combines the datasets in a way the error is minimized. Possible models could be iterative closest point (ICP), weighted least squares or Gaussian process models [49, 104, 21, 94]. To predict the 3D deviation for free-form shapes, the model for in-plane and out-of-plane shape deviation is a good start for the extension. However, it is challenging to model shape deviation for parts with holes, cavities and chan- nels because the geometric of these features and the part boundary surface are interdependent. The eect equivalence modeling framework introduced in Chapter 3 could potentially provide a way because under its framework, the interrelationship can be transferred to TEA. As a result, the causal un- derstanding of TEA regarding the base factor in the shapes without holes, cavities or channels can be extended to the shapes with those complicated features [97, 100]. An accuracy control framework for cyber-physical additive manufacturing systems As introduced in Chapter 1, for smart manufacturing, manufacturing ma- chines are connected through networks, monitored by sensors and controlled by advanced computational intelligence. With the fast development of IoT and cloud computing, the cyber-manufacturing system is potentially the next generation of AM and an accuracy control framework for cyber-physical AM systems is on demand. The systems should consist of three key compo- nents: 1. Open-source, low-cost clients such as 3D printers and 3D scanners. 110 2. Smart calibration interfacing Apps on mobiles or individual PCs. 3. A cloud-based accuracy control server. The major challenge is the construction of a cloud-based accuracy control server. ML and deep learning (DL) models are good choices to run on the cloud-based server due to their capability to make use of a large amount of the data collected from the distributed clients. Possible DL models to be considered include convolutional neural networks (CNNs), recurrent neural networks (RNNs) and recently developed graph attention networks (GATs) [125]. A ML modeling framework that involves more multilevel heterogeneous datasets with a better visualization As mentioned in Chapter 4, we propose a two-stage strategy to analyze the process data from inoculum train to production run. Datasets include process variable trajectories, initial conditions, nal conditions and measure- ments for media preparation in multiple steps. Further exploration could also involve more multilevel heterogeneous datasets and develop more pow- erful ML methods with stronger interpretability and better visualization. Process variability comes from various sources such as manufacturing oper- ation uncertainties, sensor measurement limitations, lot-to-lot raw material variations, media preparation dierence and cell line instability. Therefore, further exploration may consider including diverse datasets that provide de- tailed information for cell bank and raw material. It would be better if the feedback control system logs and human operator logs are available. On the other hand, the current way to interpret data mainly relies on the contribu- tion plots or heatmap plots. Therefore, a more powerful ML method with stronger interpretability and better visualization is in need. 111 An alternative would be t-distributed Stochastic Neighbor Embedding (t- SNE), which is a prize-winning technique that has been applied on datasets with up to 30 million examples. T-SNE is a non-linear visualization method; it converts similarities between data points to joint probabilities and tries to minimize the Kullback-Leibler divergence between the joint probabilities of the low-dimensional embedding and the high-dimensional data [74, 124]. Further exploration can use a pairwise Euclidean distance matrix or a pair- wise similarity matrix as input into t-SNE. A transfer learning approach that reuses the knowledge from current product manufacturing to others Process variability exists for most of the pharmaceutical manufacturing pro- cesses. In Chapter 4, we study a commercial pharmaceutical manufacturing for a mAbs drug at one of Genentechs facilities. It is also essential to study the processes for the same product manufactured in dierent sites and for dierent mAbs drugs with similar manufacturing operations. Consequently, a methodology that can reuse the models from the current process to other processes considering the similarities and dierences is needed. Transfer learning could be a possible solution; it is an ML research topic where a model developed for a task is reused as the starting point for a model on another task. Optionally, this transferred model may need to be adapted or rened. Transfer learning allows fast progress or improved performance when modeling the new task, even better, if transfer learning is applied to study similar pharmaceutical manufacturing processes, we may not have to have a large amount of data for the new processes. 112 Bibliography [1] Susan Fugett Abu-Absi, LiYing Yang, Patrick Thompson, Canping Jiang, Sunitha Kandula, Bernhard Schilling, and Abhinav A Shukla. Dening process design space for monoclonal antibody cell culture. Biotechnology and bioengineering, 106(6):894{905, 2010. [2] Shukri Afazov, Annestacy Okioga, Adam Holloway, Willem Denmark, An- drew Triantaphyllou, Sean-Anthony Smith, and Liam Bradley-Smith. A methodology for precision additive manufacturing through compensation. Precision Engineering, 2017. [3] Carlos F Alcala and S Joe Qin. Analysis and generalization of fault diagnosis methods for process monitoring. Journal of Process Control, 21(3):322{330, 2011. [4] Mohammed Alfaki. Improving eciency in parameter estimation using the hamiltonian monte carlo algorithm. Master's thesis, The University of Bergen, 2008. [5] Gaurav Ameta, Paul Witherell, Shawn Moylan, and Robert Lipman. Toler- ance specication and related issues for additively manufactured products. In ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE 2015, 2015. [6] R Anitha, S Arunachalam, and P Radhakrishnan. Critical parameters in- uencing the quality of prototypes in fused deposition modelling. Journal of Materials Processing Technology, 118(1):385{388, 2001. [7] Hamid Babamoradi, Frans van den Berg, and Asmund Rinnan. Condence limits for contribution plots in multivariate statistical process control using bootstrap estimates. Analytica chimica acta, 908:75{84, 2016. [8] Joseph Beaman, Dave Bourell, and Darryl Wallace. Special issue: Additive manufacturing (am) and 3d printing. Journal of Manufacturing Science and Engineering, 136(6):060301, 2014. 113 [9] Christiane Beyer. Strategic implications of current trends in additive man- ufacturing. Journal of Manufacturing Science and Engineering, 136(6): 064701, 2014. [10] David L. Bourell, Ming C. Leu, and David W. Rosen. Roadmap for additive manufacturing: Identifying the future of freeform processing. Technical report, Sponsored by National Science Foundation and the Oce of Naval Research, 2009. [11] DL Bourell, JJ Beaman, Ming C Leu, and DW Rosen. A brief history of additive manufacturing and the 2009 roadmap for additive manufacturing: looking back and looking ahead. Proceedings of RapidTech, pages 24{25, 2009. [12] G. Bugeda, M. Cervera, G. Lombera, and E. Onate. Numerical analysis of stereolithography processes using the nite element method. Rapid Proto- typing Journal, 1(2):13{23, 1995. [13] Carlos Cajal, Jorge Santolaria, David Samper, and Jesus Velazquez. E- cient volumetric error compensation technique for additive manufacturing machines. Rapid Prototyping Journal, 22(1):2{19, 2016. [14] Tadeusz Cali nski and Jerzy Harabasz. A dendrite method for cluster anal- ysis. Communications in Statistics-theory and Methods, 3(1):1{27, 1974. [15] SL Campanelli, G Cardano, R Giannoccaro, AD Ludovico, and Erik LJ Bohez. Statistical analysis of the stereolithographic process to improve the accuracy. Computer-Aided Design, 39(1):80{86, 2007. [16] Marco V Cede~ no, Leandro PF Rodr guez Aguilar, and Mabel C S anchez. Bioprocess statistical control: Identication stage based on hierarchical clus- tering. Process Biochemistry, 51(12):1919{1929, 2016. [17] Dar-Yuan Chang and Bao-Han Huang. Studies on prole error and extrud- ing aperture for the rp parts using the fused deposition modeling process. The International Journal of Advanced Manufacturing Technology, 53(9-12): 1027{1037, 2011. [18] Salim Charaniya, Wei-Shou Hu, and George Karypis. Mining bioprocess data: opportunities and challenges. Trends in biotechnology, 26(12):690{ 699, 2008. [19] Salim Charaniya, Huong Le, Huzefa Rangwala, Keri Mills, Kevin Johnson, George Karypis, and Wei-Shou Hu. Mining manufacturing data for discovery of high productivity process characteristics. Journal of biotechnology, 147 (3-4):186{197, 2010. 114 [20] Ying Cheng, Ken Chen, Hemeng Sun, Yongping Zhang, and Fei Tao. Data and knowledge mining with big data towards smart production. Journal of Industrial Information Integration, 9:1{13, 2018. [21] Bianca Maria Colosimo, Massimo Pacella, and Nicola Senin. Multisensor data fusion via gaussian process models for dimensional and geometric ver- ication. Precision Engineering, 40:199{213, 2015. [22] Jim Davis, Thomas Edgar, Robert Graybill, Prakashan Korambath, Brian Schott, Denise Swink, Jianwu Wang, and Jim Wetzel. Smart manufacturing. Annual review of chemical and biomolecular engineering, 6:141{160, 2015. [23] Erik R Denlinger, Je Irwin, and Pan Michaleris. Thermomechanical model- ing of additive manufacturing large parts. Journal of Manufacturing Science and Engineering, 136(6):061007, 2014. [24] Simon Duane, Anthony D Kennedy, Brian J Pendleton, and Duncan Roweth. Hybrid monte carlo. Physics letters B, 195(2):216{222, 1987. [25] Food, Drug Administration, et al. Guidance for industry, pat-a framework for innovative pharmaceutical development, manufacturing and quality as- surance. http://www. fda. gov/cder/guidance/published. html, 2004. [26] US Food, Drug Administration, et al. Pharmaceutical cgmps for the 21st centurya risk-based approach. Final report. Rockville, MD, 2004. [27] Bj orn Frahm. Seed train optimization for cell culture. In Animal Cell Biotechnology, pages 355{367. Springer, 2014. [28] Luigi Maria Galantucci, Fulvio Lavecchia, and Gianluca Percoco. Experi- mental study aiming to enhance the surface nish of fused deposition mod- eled parts. CIRP annals, 58(1):189{192, 2009. [29] Wei Gao, Yunbo Zhang, Devarajan Ramanujan, Karthik Ramani, Yong Chen, Christopher B Williams, Charlie CL Wang, Yung C Shin, Song Zhang, and Pablo D Zavattieri. The status, challenges, and future of additive man- ufacturing in engineering. Computer-Aided Design, 2015. [30] Salvador Garc a-Mu~ noz, Theodora Kourti, John F MacGregor, Arthur G Mateos, and Gerald Murphy. Troubleshooting of an industrial batch process using multivariate methods. Industrial & engineering chemistry research, 42 (15):3592{3601, 2003. [31] A. Gelman, X.L. Meng, and H. Stern. Posterior predictive assessment of model tness via realized discrepancies. Statistica Sinica, 6:733{759, 1996. 115 [32] Andrew Gelman. A bayesian formulation of exploratory data analysis and goodness-of-t testing. International Statistical Review, 71(2):369{382, 2003. [33] Andrew Gelman, John B Carlin, Hal S Stern, and Donald B Rubin. Bayesian data analysis, volume 2. Chapman & Hall/CRC Boca Raton, FL, USA, 2014. [34] M. Gordon. Increased inter-layer bonding in 3d printing, May 17 2016. URL https://www.google.com/patents/US9339972. US Patent 9,339,972. [35] Q Peter He and Jin Wang. Statistical process monitoring as a big data analytics tool for smart manufacturing. Journal of Process Control, 67: 35{43, 2018. [36] P.D. Hilton and P.F. Jacobs. Rapid tooling: technologies and industrial applications. CRC, 2000. [37] Dirk C Hinz. Process analytical technologies in the pharmaceutical industry: the fdas pat initiative. Analytical and bioanalytical chemistry, 384(5):1036{ 1042, 2006. [38] NE Hodge, RM Ferencz, and JM Solberg. Implementation of a thermome- chanical model for the simulation of selective laser melting. Computational Mechanics, 54(1):33{51, 2014. [39] Mohammad Shojib Hossain, David Espalin, Jorge Ramos, Mireya Perez, and Ryan Wicker. Improved mechanical properties of fused deposition modeling- manufactured parts through build parameter modications. ASME Trans- actions, Journal of Manufacturing Science and Engineering, 136(6):061002, 2014. [40] Yongxiang Hu, Zhi Li, Kangmei Li, and Zhenqiang Yao. Predictive modeling and uncertainty quantication of laser shock processing by bayesian gaussian processes with multiple outputs. Journal of Manufacturing Science and Engineering, 136(4):041014, 2014. [41] Q. Huang, J. Zhang, A. Sabbaghi, and T. Dasgupta. Optimal oine com- pensation of shape shrinkage for 3d printing processes. IIE Transactions on Quality and Reliability, 47(5):431{441, 2015. [42] Qiang Huang. An analytical foundation for optimal compensation of three- dimensional shape deformation in additive manufacturing. ASME Trans- actions, Journal of Manufacturing Science and Engineering, 138(6):061010, 2016. 116 [43] Qiang Huang, Hadis Nouri, Kai Xu, Yong Chen, Sobambo Sosina, and Tirthankar Dasgupta. Predictive modeling of geometric deviations of 3d printed products-a unied modeling approach for cylindrical and polygon shapes. In 2014 IEEE International Conference on Automation Science and Engineering (CASE), pages 25{30, Taipei, Taiwan, August 18-22 2014. IEEE. [44] Qiang Huang, Hadis Nouri, Kai Xu, Yong Chen, Sobambo Sosina, and Tirthankar Dasgupta. Statistical predictive modeling and compensation of geometric deviations of three-dimensional printed products. ASME Trans- actions, Journal of Manufacturing Science and Engineering, 136(6):061008{ 061018, 2014. [45] Qiang Huang, Jizhe Zhang, Arman Sabbaghi, and Tirthankar Dasgupta. Optimal oine compensation of shape shrinkage for three-dimensional print- ing processes. IIE Transactions, 47(5):431{441, 2015. [46] Y.M. Huang and C.P. Jiang. Curl distortion analysis during photopolymeri- sation of stereolithography using dynamic nite element method. The In- ternational Journal of Advanced Manufacturing Technology, 21(8):586{595, 2003. [47] Yong Huang, Ming C Leu, Jyoti Mazumder, and Alkan Donmez. Additive manufacturing: Current state, future potential, gaps and needs, and recom- mendations. ASME Transactions, Journal of Manufacturing Science and Engineering, 137(1):014001, 2015. [48] You-Min Huang and Hsiang-Yao Lan. Dynamic reverse compensation to increase the accuracy of the rapid prototyping system. Journal of materials processing technology, 167(2):167{176, 2005. [49] Yunbao Huang, Xiaoping Qian, and Shiliang Chen. Multi-sensor calibration through iterative registration and fusion. Computer-Aided Design, 41(4): 240{255, 2009. [50] Francois Husson, Julie Josse, and Jerome Pages. Principal component methods-hierarchical clustering-partitional clustering: why would we need to choose for visualizing data. Applied Mathematics Department, 2010. [51] Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani. An introduction to statistical learning, volume 112. Springer, 2013. [52] Yuan Jin, Sizhao Qin, and Qiang Huang. Oine predictive control of out- of-plane geometric errors for additive manufacturing. ASME Transactions on Manufacturing Science and Engineering, 138(12):121005(7 pages), 2016. 117 [53] Yuan Jin, Sizhao Qin, and Qiang Huang. Prescriptive analytics for un- derstanding of out-of-plane deformation in additive manufacturing. Dallas, TX, August 21-24 2016. 2016 IEEE International Conference on Automation Science and Engineering (CASE 2016). [54] S Joe Qin. Statistical process monitoring: basics and beyond. Journal of chemometrics, 17(8-9):480{502, 2003. [55] Stephen C Johnson. Hierarchical clustering schemes. Psychometrika, 32(3): 241{254, 1967. [56] Brian Kelley. Industrialization of mab production technology: the biopro- cessing industry at a crossroads. In MAbs, volume 1, pages 443{452. Taylor & Francis, 2009. [57] W. E. King, A. T. Anderson, R. M. Ferencz, N. E. Hodge, C. Kamath, S. A. Khairallah, and A. M. Rubenchik. Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges. Applied Physics Reviews, 2(4), 2015. [58] Alime Ozlem Kirdar, Jeremy S Conner, Jerey Baclaski, and Anurag S Rathore. Application of multivariate analysis toward biotech processes: case study of a cell-culture unit operation. Biotechnology progress, 23(1):61{67, 2007. [59] Alime Ozlem Kirdar, Ken D Green, and Anurag S Rathore. Application of multivariate data analysis for identication and successful resolution of a root cause for a bioprocessing application. Biotechnology progress, 24(3): 720{726, 2008. [60] Trupti M Kodinariya and Prashant R Makwana. Review on determining number of cluster in k-means clustering. International Journal, 1(6):90{95, 2013. [61] Christof Koplin, Matthias Gurr, R M ulhaupt, and Raimund Jaeger. Shape accuracy in stereolithography: a ma-terial model for the curing behavior of photo-initiated resins. In International User's Conference on Rapid Pro- totyping & Rapid Tooling & Rapid Manufacturing (Euro-uRapid), Berlin, 2008. [62] J-P Kruth, Ming-Chuan Leu, and T Nakagawa. Progress in additive manu- facturing and rapid prototyping. CIRP Annals-Manufacturing Technology, 47(2):525{540, 1998. [63] Andrew Kusiak. Smart manufacturing. International Journal of Production Research, 56(1-2):508{517, 2018. 118 [64] Antonio Lanzotti, Massimo Martorelli, and Gabriele Staiano. Understand- ing process parameter eects of reprap open-source three-dimensional print- ers through a design of experiments approach. ASME Transactions, Journal of Manufacturing Science and Engineering, 137(1):011017, 2015. [65] Tina M Larson, Martin Gawlitzek, Heather Evans, Urs Albers, and Jerry Cacia. Chemometric evaluation of on-line high-pressure liquid chromatog- raphy in mammalian cell cultures: Analysis of amino acids and glucose. Biotechnology and bioengineering, 77(5):553{563, 2002. [66] Huong Le, Santosh Kabbur, Luciano Pollastrini, Ziran Sun, Keri Mills, Kevin Johnson, George Karypis, and Wei-Shou Hu. Multivariate analy- sis of cell culture bioprocess datalactate consumption as process indicator. Journal of biotechnology, 162(2-3):210{223, 2012. [67] Byoung Hun Lee, J Abdullah, and Zahid A Khan. Optimization of rapid prototyping parameters for production of exible abs object. Journal of materials processing technology, 169(1):54{61, 2005. [68] Jong-Min Lee, ChangKyoo Yoo, and In-Beum Lee. Fault detection of batch processes using multiway kernel principal component analysis. Computers & chemical engineering, 28(9):1837{1847, 2004. [69] Feng Li, Natarajan Vijayasankaran, Amy Shen, Robert Kiss, and Ashraf Amanullah. Cell culture processes for monoclonal antibody production. In MAbs, volume 2, pages 466{479. Taylor & Francis, 2010. [70] Fredrik Lindgren, Paul Geladi, and Svante Wold. The kernel algorithm for pls. Journal of Chemometrics, 7(1):45{59, 1993. [71] Yanchi Liu, Zhongmou Li, Hui Xiong, Xuedong Gao, and Junjie Wu. Under- standing of internal clustering validation measures. In Data Mining (ICDM), 2010 IEEE 10th International Conference on, pages 911{916. IEEE, 2010. [72] He Luan and Qiang Huang. Prescriptive modeling and compensation of in- plane geometric deviations for 3d printed freeform products. IEEE Trans- actions on Automation Science and Engineering, 14(1):73{82, 2017. [73] Charity Lynn-Charney and David W Rosen. Usage of accuracy models in stereolithography process planning. Rapid Prototyping Journal, 6(2):77{87, 2000. [74] Laurens van der Maaten and Georey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(Nov):2579{2605, 2008. 119 [75] Ver onica S Mart nez, Stefanie Dietmair, Lake-Ee Quek, Mark P Hodson, Peter Gray, and Lars K Nielsen. Flux balance analysis of cho cells be- fore and after a metabolic switch from lactate production to consumption. Biotechnology and bioengineering, 110(2):660{666, 2013. [76] Sameer Mittal, Muztoba Ahmad Khan, David Romero, and Thorsten Wuest. Smart manufacturing: characteristics, technologies and enabling factors. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, page 0954405417736547, 2017. [77] K. Mori, K. Osakada, and S. Takaoka. Simplied three-dimensional sim- ulation of non-isothermal lling in metal injection moulding by the nite element method. Engineering Computations, 13(2):111{121, 1996. [78] Shawn P Moylan. Nist perspective on additive manufacturing standards. 2015. [79] Zoi Moza, Konstantinos Kitsakis, John Kechagias, and Nikos Mastorakis. Optimizing dimensional accuracy of fused lament fabrication using taguchi design. In 14th International Conference on Instrumentation, Measurement, Circuits and Systems, Salerno, Italy, 2015. [80] Bhanu Chandra Mulukutla, Andrew Yongky, Simon Grimm, Prodromos Daoutidis, and Wei-Shou Hu. Multiplicity of steady states in glycolysis and shift of metabolic state in cultured mammalian cells. PloS one, 10(3): e0121561, 2015. [81] Radford M Neal et al. Mcmc using hamiltonian dynamics. Handbook of Markov Chain Monte Carlo, 2(11), 2011. [82] AH Nickel, DM Barnett, and FB Prinz. Thermal stresses and deposition patterns in layered manufacturing. Materials science and Engineering: A, 317(1):59{64, 2001. [83] Sakineh Nikzad and Abbas Azari. A novel stereolithographic surgical guide template for planning treatment involving a mandibular dental implant. Journal of Oral and Maxillofacial Surgery, 66(7):1446{1454, 2008. [84] Paul Nomikos. Detection and diagnosis of abnormal batch operations based on multi-way principal component analysis world batch forum, toronto, may 1996. ISA transactions, 35(3):259{266, 1996. [85] Paul Nomikos and John F MacGregor. Monitoring batch processes using multiway principal component analysis. AIChE Journal, 40(8):1361{1375, 1994. 120 [86] Paul Nomikos and John F MacGregor. Multi-way partial least squares in monitoring batch processes. Chemometrics and intelligent laboratory sys- tems, 30(1):97{108, 1995. [87] SO Onuh and KKB Hon. Improving stereolithography part accuracy for in- dustrial applications. The International Journal of Advanced Manufacturing Technology, 17(1):61{68, 2001. [88] Oguz Ozan, Ilser Turkyilmaz, Ahmet Ersan Ersoy, Edwin A McGlumphy, and Stephen F Rosenstiel. Clinical accuracy of 3 dierent types of computed tomography-derived stereolithographic surgical guides in implant placement. Journal of Oral and Maxillofacial Surgery, 67(2):394{401, 2009. [89] Deepankar Pal, Nachiket Patil, Kai Zeng, and Brent Stucker. An inte- grated approach to additive manufacturing simulations using physics based, coupled multiscale process modeling. ASME Transactions, Journal of Man- ufacturing Science and Engineering, 136(6):061022, 2014. [90] Ratnadeep Paul, Sam Anand, and Frank Gerner. Eect of thermal deforma- tion on part errors in metal powder based additive manufacturing processes. Journal of Manufacturing Science and Engineering, 136(3):031009, 2014. [91] S Joe Qin. Survey on data-driven industrial process monitoring and diag- nosis. Annual reviews in control, 36(2):220{234, 2012. [92] S Joe Qin. Process data analytics in the era of big data. AIChE Journal, 60(9):3092{3100, 2014. [93] N. Raghunath and P.M. Pandey. Improving accuracy through shrinkage modelling by using taguchi method in selective laser sintering. International Journal of Machine Tools and Manufacture, 47(6):985{995, 2007. [94] MJ Ren, LJ Sun, MY Liu, CF Cheung, YH Yin, and YL Cao. A weighted least square based data fusion method for precision measurement of freeform surfaces. Precision Engineering, 48:144{151, 2017. [95] Roman Rosipal and Leonard J Trejo. Kernel partial least squares regression in reproducing kernel hilbert space. Journal of machine learning research, 2(Dec):97{123, 2001. [96] J org Ruppin, Aleksandra Popovic, Mario Strauss, Elmar Sp untrup, Alexan- der Steiner, and Christian Stoll. Evaluation of the accuracy of three dierent computer-aided surgery systems in dental implantology: optical tracking vs. stereolithographic splint systems. Clinical oral implants research, 19(7):709{ 716, 2008. 121 [97] A. Sabbaghi and Q. Huang. Predictive model building across dierent pro- cess conditions and shapes in 3d printing. pages 774{779, Dallas, TX, Au- gust 21-24 2016. 2016 IEEE International Conference on Automation Science and Engineering (CASE 2016). [98] A. Sabbaghi, T. Dasgupta, Q. Huang, and J. Zhang. Inference for defor- mation and interference in 3d printing. Annals of Applied Statistics, 8(3): 1395{1415, 2014. [99] A Sabbaghi, Q Huang, and T Dasgupta. Bayesian model building from small samples of disparate data in 3d printing. Technometrics, in press, 2018. [100] Arman Sabbaghi and Qiang Huang. Model transfer across additive manu- facturing processes via mean eect equivalence of lurking variables. Annals of Applied Statistics, in press, 2018. [101] Mika Salmi, Kaija-Stiina Paloheimo, Jukka Tuomi, Jan Wol, and Antti M akitie. Accuracy of medical models made by additive manufacturing (rapid manufacturing). Journal of Cranio-Maxillofacial Surgery, 41(7):603{609, 2013. [102] Bernhard Sch olkopf, Alexander Smola, and Klaus-Robert M uller. Kernel principal component analysis. In International Conference on Articial Neu- ral Networks, pages 583{588. Springer, 1997. [103] J. Secondi. Modeling powder compaction from a pressure-density law to continuum mechanics. Powder Metallurgy, 45(3):213{217, 2002. [104] N Senin, BM Colosimo, and M Pacella. Point set augmentation through tting for enhanced icp registration of point clouds in multisensor coordinate metrology. Robotics and Computer-Integrated Manufacturing, 29(1):39{52, 2013. [105] K Senthilkumaran, Pulak Mohan Pandey, and PV Madhusudan Rao. Shrinkage compensation along single direction dexel space for improving accuracy in selective laser sintering. In Automation Science and Engineer- ing, 2008. CASE 2008. IEEE International Conference on, pages 827{832. IEEE, 2008. [106] K Senthilkumaran, Pulak M Pandey, and PVM Rao. New model for shrink- age compensation in selective laser sintering. Virtual and Physical Proto- typing, 4(2):49{62, 2009. [107] Patti Seymour. Global biomanufacturing trends, capacity and technology drivers. DCAT Week, pages 14{17, 2016. 122 [108] Michael Sharp, Ronay Ak, and Thomas Hedberg Jr. A survey of the ad- vancing use and development of machine learning in smart manufacturing. Journal of Manufacturing Systems, 2018. [109] Ashish Singhal and Dale E Seborg. Clustering multivariate time-series data. Journal of Chemometrics: A Journal of the Chemometrics Society, 19(8): 427{438, 2005. [110] Suoyuan Song, Andi Wang, Qiang Huang, and Fugee Tsung. Shape de- viation modeling for fused deposition modeling processes. In 2014 IEEE International Conference on Automation Science and Engineering (CASE), pages 758{763, Taipei, Taiwan, August 18-22 2014. IEEE. [111] Suoyuan Song, Andi Wang, Qiang Huang, and Fugee Tsung. Shape devi- ation modeling and compensation for fused deposition modeling processes. IEEE Transactions on Automation Science and Engineering, Accepted as regular, 2016. [112] Xuan Song, Yong Chen, Tae Woo Lee, Shanghua Wu, and Lixia Cheng. Ceramic fabrication using mask-image-projection-based stereolithography integrated with tape-casting. Journal of Manufacturing Processes, 20:456{ 464, 2015. [113] A.K. Sood, RK Ohdar, and SS Mahapatra. Improving dimensional accuracy of fused deposition modelling processed part using grey taguchi method. Materials & Design, 30(10):4243{4252, 2009. [114] ASTM Standard. F2792. 2012 standard terminology for additive manu- facturing technologies. West Conshohocken, PA: ASTM International. See www. astm. org.(doi: 10.1520/F2792-12), 2012. [115] Madeline S Stark. Improving and understanding inter-lament bonding in 3d-printed polymers. 2016. [116] LLC Statisticat. Bayesian inference. Farmington, Connecticut: Statistical Consulting and Support, 2013. [117] B. Stor akers, N.A. Fleck, and R.M. McMeeking. The viscoplastic com- paction of composite powders. Journal of the Mechanics and Physics of Solids, 47:785{815, 1999. [118] Gustavo Tapia and Alaa Elwany. A review on process monitoring and control in metal-based additive manufacturing. Journal of Manufacturing Science and Engineering, 136(6):060801, 2014. 123 [119] Michael E Tipping and Christopher M Bishop. Probabilistic principal com- ponent analysis. Journal of the Royal Statistical Society: Series B (Statis- tical Methodology), 61(3):611{622, 1999. [120] K. Tong, E.A. Lehtihet, and S. Joshi. Parametric error modeling and soft- ware error compensation for rapid prototyping. Rapid Prototyping Journal, 9(5):301{313, 2003. [121] K. Tong, S. Joshi, and E.A. Lehtihet. Error compensation for fused depo- sition modeling (fdm) machine by correcting slice les. Rapid Prototyping Journal, 14(1):4{14, 2008. [122] Adamastor R T^ orres, Ant^ onio Di ogenes P de Oliveira, Severino Grangeiro J unior, and Wallace D Fragoso. Multivariate statistical process control in annual pharmaceutical product review. Journal of Process Control, 69:97{ 102, 2018. [123] Brian N Turner and Scott A Gold. A review of melt extrusion additive manufacturing processes: Ii. materials, dimensional accuracy, and surface roughness. Rapid Prototyping Journal, 21(3):250{261, 2015. [124] Laurens Van der Maaten and Georey Hinton. Visualizing non-metric sim- ilarities in multiple maps. Machine learning, 87(1):33{55, 2012. [125] Petar Velickovic, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. Graph attention networks. arXiv preprint arXiv:1710.10903, 2017. [126] Andi Wang, Suoyuan Song, Qiang Huang, and Fugee Tsung. In-plane shape- deviation modeling and compensation for fused deposition modeling pro- cesses. IEEE Transactions on Automation Science and Engineering, 14(2): 968{976, 2017. [127] H. Wang and Q. Huang. Error cancellation modeling and its application in machining process control. IIE Transactions on Quality and Reliability, 38: 379{388, 2006. [128] Hui Wang and Qiang Huang. Using error equivalence concept to auto- matically adjust discrete manufacturing processes for dimensional variation control. ASME Transactions, Journal of Manufacturing Science and Engi- neering, 129:644{652, 2007. [129] Robin C Wurl, Susan L Albin, and Irwin J Shier. Multivariate monitoring of batch process startup. Quality and Reliability Engineering International, 17(4):269{278, 2001. 124 [130] Kai Xu and Yong Chen. Deformation control based on in-situ sensors for mask projection based stereolithography. ASME Paper No. MSEC2014- 4055, 2014. [131] Kai Xu and Yong Chen. Mask image planning for deformation control in projection-based stereolithography process. Journal of Manufacturing Science and Engineering, 137(3):031014, 2015. [132] Kai Xu, Tsz-Ho Kwok, Zhengcai Zhao, and Yong Chen. A reverse com- pensation framework for shape deformation control in additive manufactur- ing. Journal of Computing and Information Science in Engineering, 17(2): 021012, 2017. [133] L. Xu, Q. Huang, A. Sabbaghi, and T. Dasgupta. Shape deviation mod- eling for dimensional quality control in additive manufacturing. Number IMECE2013-66329, San Diego, USA, November 15{21 2013. Proceedings of the ASME 2013 International Mechanical Engineering Congress & Exposi- tion. [134] M Yang and M Butler. Eects of ammonia on cho cell growth, erythropoietin production, and glycosylation. Biotechnology and bioengineering, 68(4):370{ 380, 2000. [135] Jie Yu and S Joe Qin. Multiway gaussian mixture model based multiphase batch process monitoring. Industrial & Engineering Chemistry Research, 48 (18):8585{8594, 2009. [136] Michael F Zaeh and Gregor Branner. Investigations on residual stresses and deformations in selective laser melting. Production Engineering, 4(1):35{45, 2010. [137] Francesca Zagari, Martin Jordan, Matthieu Stettler, Herv e Broly, and Flo- rian M Wurm. Lactate metabolism shift in cho cell culture: the role of mitochondrial oxidative activity. New biotechnology, 30(2):238{245, 2013. [138] Wentao Zha and Sam Anand. Geometric approaches to input le modi- cation for part quality improvement in additive manufacturing. Journal of Manufacturing Processes, 2015. [139] Junhua Zheng, Zhihuan Song, and Zhiqiang Ge. Probabilistic learning of partial least squares regression model: Theory and industrial applications. Chemometrics and Intelligent Laboratory Systems, 158:80{90, 2016. [140] Chi Zhou. A direct tool path planning algorithm for line scanning based stereolithography. Journal of Manufacturing Science and Engineering, 136 (6):061023, 2014. 125 [141] J.G. Zhou, D. Herscovici, and C.C. Chen. Parametric process optimiza- tion to improve the accuracy of rapid prototyped stereolithography parts. International Journal of Machine Tools and Manufacture, 40(3):363{379, 2000. [142] Zuowei Zhu, Nabil Anwer, and Luc Mathieu. Deviation modeling and shape transformation in design for additive manufacturing. Procedia CIRP, 60: 211{216, 2017. 126

Abstract (if available)

Abstract Smart manufacturing is a broad category of advanced manufacturing where manufacturing machines are connected through information networks, monitored by sensors and controlled by advanced computational intelligence. The aim of smart manufacturing is to improve product quality, agility, system productivity and sustainability while reducing the manufacturing cost. Smart manufacturing has been the focus of many researchers and has been extended to various areas such as additive manufacturing (AM), rapid prototyping, energy, security and pharmaceutical manufacturing. With the increased complexity of the manufacturing process and the variety of data collected from various aspects throughout the process, process data analytics has become one of the major trends for smart manufacturing. ❧ While smart manufacturing offers distinct advantages to discover process knowledge and predict future production, there still exist two challenges. Firstly, for many smart manufacturing processes, a conclusive understanding of the process is not available due to the complicated process physics and uncertainty. The complexity and uncertainty caused by latent or unobserved factors make the process a grey box. With the limited understanding of the process, it is insufficient to use only first principles models

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Creator Jin, Yuan (author)

Core Title Statistical modeling and process data analytics for smart manufacturing

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Chemical Engineering

Publication Date 11/08/2020

Defense Date 10/02/2018

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

Tag OAI-PMH Harvest,process data analytics,smart manufacturing

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Language English

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Advisor Qin, Joe (committee chair), Huang, Qiang (committee member), Wang, Pin (committee member)

Creator Email jinyuan.zju@gmail.com,yuanjin@usc.edu

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