Reliability-based design optimization using kriging surrogates and subset simulation

Abstract

20 pages, 6 figures, 5 tables. Preprint submitted to Springer-VerlagInternational audienceThe aim of the present paper is to develop a strategy for solving reliability-based design optimization (RBDO) problems that remains applicable when the performance models are expensive to evaluate. Starting with the premise that simulation-based approaches are not affordable for such problems, and that the most-probable-failure-point-based approaches do not permit to quantify the error on the estimation of the failure probability, an approach based on both metamodels and advanced simulation techniques is explored. The kriging metamodeling technique is chosen in order to surrogate the performance functions because it allows one to genuinely quantify the surrogate error. The surrogate error onto the limit-state surfaces is propagated to the failure probabilities estimates in order to provide an empirical error measure. This error is then sequentially reduced by means of a population-based adaptive refinement technique until the kriging surrogates are accurate enough for reliability analysis. This original refinement strategy makes it possible to add several observations in the design of experiments at the same time. Reliability and reliability sensitivity analyses are performed by means of the subset simulation technique for the sake of numerical efficiency. The adaptive surrogate-based strategy for reliability estimation is finally involved into a classical gradient-based optimization algorithm in order to solve the RBDO problem. The kriging surrogates are built in a so-called augmented reliability space thus making them reusable from one nested RBDO iteration to the other. The strategy is compared to other approaches available in the literature on three academic examples in the field of structural mechanics

Stochastic Reliability Measurement and Design Optimization of an Inventory Management System

“…This paper develops a novel reliability measure and reliability-based robust design optimization (RBRDO) approach. Reliability focuses on the subset stimulation technique to achieve numerical efficiency [6]. Reliability is described as the tendency towards consistency of performance and responsibility or as the fulfillment of a service provider's promises to customers.…”

Novel procedure for reliability-based cost optimization of seismically isolated structures for the protection of critical equipment: A case study using single curved surface sliders

“…[24][25][26] Other efficient newly developed methods for simulation-based reliability analyses, which can significantly reduce computation size, involve estimating the limit states using the response surface [27] or surrogate models. [28] The former methods, generally called response-surface methods, are mainly used in RBDO. Rathi and Chakraborty developed a numerical solution scheme for optimizing the design of a tuned mass damper operating in an uncertain environment.…”

Adaptive Emulation-Based Reliability Analysis

“…The authors of [6] use constraint boundary sampling to select improvement points. A combination between a MCMC sampling and k-means clustering is used to select new data points in [7]. An approach based on the first order reliability method is used in [8] and a probabilistic classification function is presented in [9].…”

“…These issue are addressed in the present article.The other major part of all adaptive algorithms is the stopping condition. This ranges from the use of reliability indices [7,8] through error in the estimation of the failure probability [5,13,15,16,17] and forms of measure of the discrepancy between the GPE predictions and code observations [4,6,9,18] to thresholds on the learning function [3,12,14]. Most frameworks use some form of statistic related to the surrogate, which, depending on the use and complexity of the problem, could prove insufficiently robust.…”