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research-article

Uncertainty Quantification Using Generalized Polynomial Chaos Expansion for Nonlinear Dynamical Systems with Mixed State and Parameter Uncertainties

[+] Author and Article Information
Rajnish Bhusal

Graduate Student, Department of Mechanical and Aerospace Engineering, The University of Texas at Arlington, Arlington, TX 76019
rajnish.bhusal@mavs.uta.edu

Kamesh Subbarao

Associate Professor, Department of Mechanical and Aerospace Engineering, The University of Texas at Arlington, Arlington, TX 76019
subbarao@uta.edu

1Corresponding author.

ASME doi:10.1115/1.4041473 History: Received May 31, 2018; Revised September 10, 2018

Abstract

This paper develops a framework for propagation of uncertainties, governed by different probability distribution functions in a stochastic dynamical system. More specficially, it deals nonlinear dynamical systems, wherein both the initial state and parametric uncertainty have been taken into consideration and their effects studied in the model response. A sampling based non-intrusive approach using pseudospectral stochastic collocation is employed to obtain the coefficients required for the generalized Polynomial Chaos (gPC) expansion in this framework. The samples are generated based on the distribution of the uncertainties, which are basically the cubature nodes to solve expectation integrals. A mixture of one-dimensional Gaussian quadrature techniques in a sparse grid framework are used to produce the required samples to obtain the integrals. The familiar problem of degeneracy with high order gPC expansions is illustrated and insights into mitigation of such behavior are presented. To illustrate the efficacy of the proposed approach, numerical examples of dynamic systems with state and parametric uncertainties are considered which include the simple linear harmonic oscillator system and a two-degree-of-freedom nonlinear aeroelastic system .

Copyright (c) 2018 by ASME
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