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MODEL, IDENTIFICATION & ANALYSIS OF COMPLEX STOCHASTIC SYSTEMS:
APPLICATIONS IN STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND MULTISCALE
MECHANICS
by
Sonjoy Das
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 AND ENVIRONMENTAL ENGINEERING)
August 2008
Copyright 2008 Sonjoy Das
Object Description
| Title | Model, identification & analysis of complex stochastic systems: applications in stochastic partial differential equations and multiscale mechanics |
| Author | Das, Sonjoy |
| Author email | sdas@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Civil Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2008-04-25 |
| Date submitted | 2008 |
| Restricted until | Unrestricted |
| Date published | 2008-05-13 |
| Advisor (committee chair) | Ghanem, Roger |
| Advisor (committee member) |
Masri, Sami F. Johnson, Erik A. Bardet, Jean-Pierre Newton, Paul |
| Abstract | This dissertation focusses on characterization, identification and analysis of stochastic systems. A stochastic system refers to a physical phenomenon with inherent uncertainty in it, and is typically characterized by a governing conservation law or partial differential equation (PDE) with some of its parameters interpreted as random processes, or/and a model-free random matrix operator. In this work, three data-driven approaches are first introduced to characterize and construct consistent probability models of non-stationary and non-Gaussian random processes or fields within the polynomial chaos (PC) formalism. The resulting PC representations would be useful to probabilistically characterize the system input-output relationship for a variety of applications. Second, a novel hybrid physics- and data-based approach is proposed to characterize a complex stochastic systems by using random matrix theory. An application of this approach to multiscale mechanics problems is also presented. In this context, a new homogenization scheme, referred here as "nonparametric" homogenization, is introduced. Also discussed in this work is a simple, computationally efficient and experiment-friendly coupling scheme based on frequency response function. This coupling scheme would be useful for analysis of a complex stochastic system consisting of several subsystems characterized by, e.g., stochastic PDEs or/and model-free random matrix operators. While chapter 1 sets up the stage for the work presented in this dissertation, further highlight of each chapter is included at the outset of the respective chapter. |
| Keyword | random matrix theory; polynomial chaos representation; homogenization; multiscale mechanics; data uncertainty; modeling uncertainty; non-Gaussian and nonstationary random processes and fields |
| 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-m1242 |
| Contributing entity | University of Southern California |
| Rights | Das, Sonjoy |
| 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-Das-20080513 |
| Archival file | uscthesesreloadpub_Volume23/etd-Das-20080513.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Full text | MODEL, IDENTIFICATION & ANALYSIS OF COMPLEX STOCHASTIC SYSTEMS: APPLICATIONS IN STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND MULTISCALE MECHANICS by Sonjoy Das 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 AND ENVIRONMENTAL ENGINEERING) August 2008 Copyright 2008 Sonjoy Das |
