Time variant reliability estimation of randomly excited uncertain dynamical systems by combined Markov chain splitting and Girsanov�s transformation

Kanjilal, O and Manohar, CS (2020) Time variant reliability estimation of randomly excited uncertain dynamical systems by combined Markov chain splitting and Girsanov�s transformation. In: Archive of Applied Mechanics, 90 (11). pp. 2363-2377.

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Abstract

The problem of estimating the time variant reliability of randomly parametered dynamical systems subjected to random process excitations is considered. Two methods, based on Monte Carlo simulations, are proposed to tackle this problem. In both the methods, the target probability of failure is determined based on a two-step approach. In the first step, the failure probability conditional on the random variable vector modelling the system parameter uncertainties is considered. The unconditional probability of failure is determined in the second step, by computing the expectation of the conditional probability with respect to the random system parameters. In the first of the proposed methods, the conditional probability of failure is determined analytically, based on an approximation to the average rate of level crossing of the dynamic response across a specified safe threshold. An augmented space of random variables is subsequently introduced, and the unconditional probability of failure is estimated by using variance-reduced Monte Carlo simulations based on the Markov chain splitting methods. A further improvement is developed in the second method, in which, the conditional failure probability is estimated by using Girsanov�s transformation-based importance sampling, instead of the analytical approximation. Numerical studies on white noise-driven single degree of freedom linear/nonlinear oscillators and a benchmark multi-degree of freedom linear system under non-stationary filtered white noise excitation are presented. The probability of failure estimates obtained using the proposed methods shows reasonable agreement with the estimates from existing Monte Carlo simulation strategies. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

Item Type:	Journal Article
Publication:	Archive of Applied Mechanics
Publisher:	Springer
Additional Information:	Copy right for this article belongs to Springer Science and Business Media Deutschland GmbH.
Keywords:	Degrees of freedom (mechanics); Dynamical systems; Failure analysis; Importance sampling; Linear systems; Markov chains; Parameter estimation; Random variables; Ultrasonic devices; Uncertainty analysis; White noise, Analytical approximation; Conditional failure probability; Conditional probabilities; Multi degree-of-freedom; Probability of failure; Single degree of freedoms; Time-variant reliability; Uncertain dynamical systems, Monte Carlo methods
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	19 Nov 2020 10:28
Last Modified:	19 Nov 2020 10:28
URI:	http://eprints.iisc.ac.in/id/eprint/66117

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