Model, identification & analysis of complex stochastic systems: applications in stochastic partial differential equations and multiscale mechanics

Description

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[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.

Title:

Model, identification & analysis of complex stochastic systems: applications in stochastic partial differential equations and multiscale mechanics

Record ID:

usctheses-m1242

Names & Dates

Created:

2008

Issued:

[published] 2008-05-13

Modified:

[defended] 2008-04-25

Creator:

[author] Das, Sonjoy
[author email] sdas@usc.edu

Contributor:

[advisor: dissertation committee chair] Ghanem, Roger
[advisor: committee member] Masri, Sami F.
[advisor: committee member] Johnson, Erik A.
[advisor: committee member] Bardet, Jean-Pierre
[advisor: committee member] Newton, Paul
[school] Viterbi School of Engineering

Publisher:

[host] University of Southern California. Libraries

Subject

Topic:

[program] Civil Engineering , [keyword] random matrix theory , [keyword] polynomial chaos representation , [keyword] homogenization , [keyword] multiscale mechanics , [keyword] data uncertainty , [keyword] modeling uncertainty , [keyword] non-Gaussian and nonstationary random processes and fields

Relationships

Part Of:

[collection] University of Southern California dissertations and theses

Physical

Type:

texts

Format:

[document type] Dissertation
[degree] Doctor of Philosophy

Access

Identifiers

Record ID:

usctheses-m1242

Language:

en_us