Efficient Conditional Reliability Updating with Sequential Importance Sampling. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Ehre, Max; Papaioannou, Iason; Straub, Daniel
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800282
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Data on the performance of engineering systems can and should be used to learn system parameters and update the system reliability estimate. This can be achieved in a Bayesian framework. In order to capture the dependence of the reliability estimate on the data used, we consider the probability of failure conditional on the updating variables, i.e. those variables on which data is available. Thus, the probability of failure becomes a random variable itself. In practice, the distribution of the conditional probability of failure may be obtained by solving a reliability problem at several samples from the updating variable space which causes a considerable increase in required computational effort. To address this challenge, we devise a procedure for the fast re‐computation of failure probabilities within a sequential sampling method. We exploit the similarity of reliability problems with small distance in a suitable norm by sequentially initializing computations with failure samples of similar problem solutions.