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Asymptotic sampling – a tool for efficient reliability computation in high dimensions
Author(s) -
Bucher Christian
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510265
Subject(s) - monte carlo method , curse of dimensionality , reliability (semiconductor) , computer science , computation , importance sampling , sampling (signal processing) , scaling , scale (ratio) , monte carlo integration , reliability engineering , monte carlo molecular modeling , mathematical optimization , algorithm , mathematics , statistics , markov chain monte carlo , engineering , artificial intelligence , power (physics) , physics , geometry , filter (signal processing) , quantum mechanics , computer vision
Monte Carlo methods are most versatile regarding applications to the reliability analysis of high‐dimensional nonlinear structural systems. In addition to its versatility, the computational efficacy of Monte Carlo method is not adversely affected by the dimensionality of the problem. Crude Monte Carlo techniques, however, are very inefficient for extremely small failure probabilities such as typically required for sensitive structural systems. Therefore methods to increase the efficacy for small failure probability while keeping the adverse influence of dimensionality small are desirable. On such method is the asymptotic sampling method. Within the framework of this method, well‐known asymptotic properties of the reliability index regarding the scaling of the basic variables are exploited to construct a regression model which allows to determine the reliability index for extremely small failure probabilities with high precision using a moderate number of Monte Carlo samples. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)