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Model, Identification & Analysis of Complex Stochastic Systems:

Sonjoy Das- PhD DefenseThe work presented in this dissertation focuses on characterization, identi¯-cation and analysis of stochastic systems. Stochastic systems refer to a physical
phenomena with inherent uncertainty in it, and are generally characterized by
two forms of representation: (1) a governing conservation law or partial dif-ferential equation (PDE) with some of its parameters interpreted as random
processes, and (2) a model-free random matrix operator. In this work, three
data-driven approaches are ¯rst introduced to characterize and construct consis-tent probability models of non-stationary and non-Gaussian random processes
or ¯elds within the polynomial chaos (PC) formalism. The resulting PC rep-resentations 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 sys-tems by using random matrix theory. Application of this approach to multiscale
mechanics problems is also presented. Also discussed in this work is a simple,
computationally e±cient and experiment-friendly coupling scheme based on fre-quency 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.

Location: Kaprielian Hall (KAP) - 209

Audiences: Everyone Is Invited

Contact: Evangeline Reyes