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Research Papers

Nonintrusive 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, NY 14260
e-mail: souransu@buffalo.edu

Tarunraj Singh

Control, Dynamics and Estimation Laboratory,
Department of Mechanical
and Aerospace Engineering,
University at Buffalo,
Buffalo, NY 14260
e-mail: tsingh@buffalo.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 29, 2018; final manuscript received September 21, 2018; published online January 7, 2019. Assoc. Editor: Paramsothy Jayakumar.

J. Comput. Nonlinear Dynam 14(2), 021003 (Jan 07, 2019) (12 pages) Paper No: CND-18-1238; doi: 10.1115/1.4041622 History: Received May 29, 2018; Revised September 21, 2018

The focus of this paper is on the global sensitivity analysis (GSA) 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 problems 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 (LIPs) 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.

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Figures

Grahic Jump Location
Fig. 1

PC realization nodes for n1=n2=3

Grahic Jump Location
Fig. 2

Evolution of Sobol' indices corresponding to the diagonal elements of μ over time: (a) μ1, (b) μ2, (c) μ3, and (d) μ4

Grahic Jump Location
Fig. 3

Evolution of Sobol' indices corresponding to the diagonal elements of Σ over time: (a) Σ(1,1), (b) Σ(2,2), (c) Σ(3,3), and (d) Σ(4,4)

Grahic Jump Location
Fig. 4

Schematic diagram of the quarter car model

Grahic Jump Location
Fig. 5

Sobol' indices for μ2

Grahic Jump Location
Fig. 6

Sobol' indices for Σ(2,2)

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