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STOCHASTIC DATA ASSIMILATION WITH APPLICATION TO MULTI-PHASE
FLOW AND HEALTH MONITORING PROBLEMS
by
George A. Saad
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CIVIL ENGINEERING)
December 2007
Copyright 2007 George A. Saad
Object Description
| Title | Stochastic data assimilation with application to multi-phase flow and health monitoring problems |
| Author | Saad, George A. |
| Author email | gsaad@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Civil Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2007-08-31 |
| Date submitted | 2007 |
| Restricted until | Unrestricted |
| Date published | 2007-09-18 |
| Advisor (committee chair) | Ghanem, Roger |
| Advisor (committee member) |
Masri, Sami Johnson, Erik Ershaghi, Iraj |
| Abstract | Model-based predictions are critically dependent on assumptions and hypotheses that are not based on first principles and that cannot necessarily be justified based on known prevalent physics. Constitutive models, for instance, fall under this category. While these predictive tools are typically calibrated using observational data, little is usually done with the scatter in the thus-calibrated model parameters. In this study, this scatter is used to characterize the parameters as stochastic processes and a procedure is developed to carry out model validation for ascertaining the confidence in the predictions from the model.; Most parameters in model-based predictive tools are heterogeneous in nature and have a large range of variability. Thus the study aims at improving these predictive tools by using the Polynomial Chaos methodology to capture this heterogeneity and provide a more realistic description of the system's behavior. Consequently, a data assimilation technique based on forecasting the error statistics using the Polynomial Chaos methodology is developed. The proposed method allows the propagation of a stochastic representation of the unknown variables using Polynomial Chaos instead of propagating an ensemble of model states forward in time as is suggested within the framework of the Ensemble Kalman Filter (EnKF). This overcomes some of the drawbacks of the EnKF. Using the proposed method, the update preserves all the statistics of the posterior unlike the EnKF which maintains the first two moments only. At any instant in time, the probability density function of the model state or parameters can be easily obtained by simulating the Polynomial Chaos basis. Furthermore it allows representation of non-Gaussian measurement and parameter uncertainties in a simpler, less taxing way without the necessity of managing a large ensemble. The proposed method is used for realistic nonlinear models, and its efficiency is first demonstrated for reservoir characterization using automatic history matching and then for tracking the fluid front dynamics to maximize the waterflooding sweeping efficiency by controlling the injection rates. The developed methodology is also used for system identification of civil structures with strong nonlinear behavior.; History matching, the act of calibrating a reservoir model to match the observed reservoir behavior, has been extensively studied in recent years. Standard methods for reservoir characterization required adjoint or gradient based methods to compute the gradient of the objective function and consequently minimize it. The computational cost of such methods increases exponentially as the number of model parameters or observational data increase. Recently, the EnKF was introduced for automatic history matching . The Ensemble Kalman Filter uses a Monte Carlo scheme for achieving satisfactory history matching results at a relatively low computational cost. In this study, the developed data assimilation methodology is used for improving the prediction of reservoir behavior. To enhance the forecasting ability of a reservoir model, first a better description of the reservoir's geological and petrophysical features using a stochastic approach is adopted, and then the new data assimilation method based on forecasting the error statistics using the Polynomial Chaos (PC) methodology, is employed. The reservoir model developed in this study is that of multiphase immiscible flow in a randomly heterogeneous porous media. The model uncertainty is quantified by modeling the intrinsic permeability and porosity of the porous medium as stochastic processes via their PC expansions. The Spectral Stochastic Finite Element Method (SSFEM) is used to solve the multiphase flow equations. SSFEM is integrated within SUNDANCE 2.0, a software developed in Sandia National Laboratories for solving partial differential equations using finite element methods. Thus, SUNDANCE is used for the analysis or prediction step of the reservoir characterization, and an algorithm using the newmat C++ library is developed for updating the model via the new data assimilation methodology.; Using the same underlying physics, the proposed method is coupled with a control loop for the purpose of optimizing the fluid front dynamics in flow in porous media problem through rate control methods. The rate control is carried out using the developed data assimilation technique; the water injection rates are included as part of the state vector, and are continuously updated so as to minimize the mismatch between the predicted front and a specified target front.; The second application of the proposed method aims at presenting a robust system identification technique for strongly nonlinear dynamics by combining the filtering methodology with a non-parametric representation of the system's nonlinearity. First a non-parametric representation of the system nonlinearity is adopted. The Polynomial Chaos expansion is employed to characterize the uncertainty within the model, and then the proposed data assimilation technique is used to characterize the robust stochastic polynomial representation of the system's non-linearity. This enables monitoring the system's reaction and identifying any obscure changes within its behavior. The presented methodology is applied for the structural health monitoring of a four story shear building subject to a ground excitation. The corresponding results prove that the proposed systemidentification techniques accurately detects changes in the systembehavior in spite of measurement and modeling noises.; The results obtained from these two applications depict the efficiency of the proposed method for parameter estimation problems. The combination of the Ensemble Kalman Filter with the Polynomial Chaos methodology thus proves to be an efficient sequential data assimilation technique that surpasses standard Kalman Filtering techniques while maintaining a relatively low computational cost. |
| Keyword | data assimilation; Kalman Filter; polynomial chaos; flow in porous media; structural health monitoring |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m824 |
| Rights | Saad, George A. |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Saad-20070918 |
| Archival file | uscthesesreloadpub_Volume32/etd-Saad-20070918.pdf |
Description
| Title | Page 1 |
| Full text | STOCHASTIC DATA ASSIMILATION WITH APPLICATION TO MULTI-PHASE FLOW AND HEALTH MONITORING PROBLEMS by George A. Saad A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (CIVIL ENGINEERING) December 2007 Copyright 2007 George A. Saad |
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