Rare event simulation in finite-infinite dimensional space

Au, Siu-Kui ORCID: 0000-0002-0228-1796 and Patelli, Edoardo ORCID: 0000-0002-5007-7247 (2016) Rare event simulation in finite-infinite dimensional space. RELIABILITY ENGINEERING & SYSTEM SAFETY, 148. pp. 67-77.

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Official URL: http://dx.doi.org/10.1016/j.ress.2015.11.012

Abstract

Modern engineering systems are becoming increasingly complex. Assessing their risk by simulation is intimately related to the efficient generation of rare failure events. Subset Simulation is an advanced Monte Carlo method for risk assessment and it has been applied in different disciplines. Pivotal to its success is the efficient generation of conditional failure samples, which is generally non-trivial. Conventionally an independent-component Markov Chain Monte Carlo (MCMC) algorithm is used, which is applicable to high dimensional problems (i.e., a large number of random variables) without suffering from 'curse of dimension'. Experience suggests that the algorithm may perform even better for high dimensional problems. Motivated by this, for any given problem we construct an equivalent problem where each random variable is represented by an arbitrary (hence possibly infinite) number of 'hidden' variables. We study analytically the limiting behavior of the algorithm as the number of hidden variables increases indefinitely. This leads to a new algorithm that is more generic and offers greater flexibility and control. It coincides with an algorithm recently suggested by independent researchers, where a joint Gaussian distribution is imposed between the current sample and the candidate. The present work provides theoretical reasoning and insights into the algorithm.

Item Type:	Article
Uncontrolled Keywords:	Curse of dimension, Rare Event, Markov Chain Monte Carlo, Monte Carlo, Subset Simulation
Depositing User:	Symplectic Admin
Date Deposited:	11 Apr 2016 15:25
Last Modified:	15 Dec 2022 12:17
DOI:	10.1016/j.ress.2015.11.012
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3000283