How Adaptively Constructed Reduced Order Models Can Benefit Sampling-Based Methodsfor Reliability Analyses

Abstract

Many sampling-based approaches are currently available for calculating the reliability of a design. The most efficient methods can achieve reductions in the computational cost by one to several orders of magnitude compared to the basic Monte Carlo method. This paper is specifically targeted at sampling-based approaches for reliability analysis, in which the samples represent calls to expensive finite element models. The aim of this paper is to illustrate how these methods can further benefit from reduced order modeling to achieve drastic additional computational cost reductions, in cases where the reliability analysis is carried out on finite element models. Standard Monte Carlo, importance sampling, separable Monte Carlo and a combined importance separable Monte Carlo approach are presented and coupled with reduced order modeling. An adaptive construction of the reduced basis models is proposed. The various approaches are compared on a thermal reliability design problem, where the coupling with the adaptively constructed reduced order models is shown to further increase the computational efficiency by up to a factor of six.

A Reduced Order Model Approach for Fuzzy Field Analysis

“…To control the error introduced by the reduced order model, one can investigate the residual error associated with the equilibrium equations considering the approximate response (see Gogu et al [13]). That is,…”

Adaptive coupling of reduced basis modeling and Kriging based active learning methods for reliability analyses

“…In practice, the exact error between the reduced solution and the real one is not computed (since it would defeat any computational savings). Various error estimation techniques exist such as [16,38,39,40,41]. In this paper, we first propose the following residual based error estimator [16] (low computational cost) to approximate the accuracy associated to reduced basis solutions :…”

“…In this section, the application considered is a reliability analysis, which involves the heat transfer through the combustion chamber wall of a regeneratively cooled rocket engine [46,47,16]. In such an engine, liquid hydrogen (LH2) flowing through cooling channels in the combustion chamber wall at a temperature of 40K is used for cooling the engine.…”

“…Following this concept, reduced basis techniques have already been combined with several reliability analysis techniques such as first or second-order reliability method or sampling based methods (i.e. Monte Carlo Simulations or even Importance Sampling) [15,16,17,18] and were shown to be able to lead to substantial computational savings. Presently, some of the most promising 2 methods for reliability analysis are the ones based on an adaptive sampling approach.…”