Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

Kanjilal, Oindrila and Manohar, C S (2017) Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics. In: JOURNAL OF COMPUTATIONAL PHYSICS, 341 . pp. 278-294.

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Abstract

The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, visa-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations. (C) 2017 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	JOURNAL OF COMPUTATIONAL PHYSICS
Additional Information:	Copy right for this article belongs to the ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	16 Jun 2017 10:03
Last Modified:	16 Jun 2017 10:03
URI:	http://eprints.iisc.ac.in/id/eprint/57226

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