Adaptive Gaussian process emulators for efficient reliability analysis

Abstract

ReuseThis article is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs (CC BY-NC-ND) licence. This licence only allows you to download this work and share it with others as long as you credit the authors, but you can't change the article in any way or use it commercially. More information and the full terms of the licence here: https://creativecommons.org/licenses/ TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. AbstractThis paper presents an approximation method for performing efficient reliability analysis with complex computer models. The computational cost of industrial-scale models causes problems when performing sampling-based reliability analysis. This is due to the fact that the failure modes of the system typically occupy a small region of the performance space and thus require relatively large sample sizes to accurately estimate their characteristics. The sequential sampling method proposed in this article, combines Gaussian process-based optimisation and subset simulation. Gaussian process emulators construct a statistical approximation to the output of the original code, which is both affordable to use and has its own measure of predictive uncertainty. Subset simulation is used as an integral part of the algorithm to efficiently populate those regions of the surrogate which are likely to lead to the performance function exceeding a predefined critical threshold. The emulator itself is used to inform decisions about efficiently using the original code to augment its predictions. The iterative nature of the method ensures that an arbitrarily accurate approximation of the failure region is developed at a reasonable computational cost. The presented method is applied to an industrial model of a biodiesel filter.

A novel two-stage reliability analysis method combining improved cross-entropy adaptive sampling and relevant vector machine

“…However, it is highly unsuitable for implicit reliability analysis and rare event reliability analysis. Variance reduction techniques are developed based on MCS, which include importance sampling (IS) [7], subset simulation (SS) [8][9][10][11] and others. By constructing an IS density function (ISD), IS improves the efficiency of reliability analysis.…”

Robust optimisation of computationally expensive models using adaptive multi-fidelity emulation

“…Adaptive sampling approaches tend to involve a utility function which measures some form of model improvement to select additional sample points. The most popular choice is expected improvement [7] , which has been widely used in reliability [8] , optimisation [9] and robust optimisation problems [10] , amongst others. Further, the concept can be extended to multiple performance functions by considering the expected improvement of the current Pareto front via hypervolume expected improvement [11] .…”

Efficient estimation of extreme quantiles using adaptive kriging and importance sampling

“…Several algorithms have been proposed to deal with very small failure probabilities (10 −5 −10 −9 ) and multiple failure regions: Meta‐IS, MetaAK‐IS 2 , BSS, ASVR, 2 SMART, AK‐MCSi, GPSS, AK‐MCS‐IS, S4IS, and SS‐KK . Some other methods such as SORM or AK‐IS are suitable for very small failure probabilities, but rely on the existence of an assumed unique so‐called most probable failure point.…”