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Non-Intrusive Global Sensitivity Analysis for Linear Systems with Process Noise

[+] Author and Article Information
Souransu Nandi

Control, Dynamics and Estimation Laboratory, Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, New York 14260
souransu@buffalo.edu

Tarunraj Singh

Control, Dynamics and Estimation Laboratory, Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, New York 14260
tsingh@buffalo.edu

1Corresponding author.

ASME doi:10.1115/1.4041622 History: Received May 29, 2018; Revised September 21, 2018

Abstract

The focus of this paper is on the global sensitivity analysis of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problem help illustrate that it is conceivable that parameters which are not so significant in contributing to the uncertainty of the mean can be extremely significant in contributing to the uncertainty of the variances. The paper uses a Polynomial Chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

Copyright (c) 2018 by ASME
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