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Unified reliability analysis by active learning Kriging model combining with random‐set based Monte Carlo simulation method
Author(s) -
Yang Xufeng,
Liu Yongshou,
Gao Yi
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5255
Subject(s) - kriging , monte carlo method , curse of dimensionality , reliability (semiconductor) , random variable , uncertainty quantification , computer science , set (abstract data type) , mathematical optimization , mathematics , algorithm , artificial intelligence , machine learning , statistics , power (physics) , physics , quantum mechanics , programming language
Summary Reliability analysis with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described with random variables, and epistemic uncertainties are tackled with evidence theory. To estimate the bounds of failure probability, several methods have been proposed. However, the existing methods suffer the dimensionality challenge of epistemic variables. To get rid of this challenge, a so‐called random‐set based Monte Carlo simulation (RS‐MCS) method derived from the theory of random sets is offered. Nevertheless, RS‐MCS is also computational expensive. So an active learning Kriging (ALK) model that only rightly predicts the sign of performance function is introduced and closely integrated with RS‐MCS. The proposed method is termed as ALK‐RS‐MCS. ALK‐RS‐MCS accurately predicts the bounds of failure probability using as few function calls as possible. Moreover, in ALK‐RS‐MCS, an optimization method based on Karush–Kuhn–Tucker conditions is proposed to make the estimation of failure probability interval more efficient based on the Kriging model. The efficiency and accuracy of the proposed approach are demonstrated with four examples. Copyright © 2016 John Wiley & Sons, Ltd.