Efficient imprecise reliability analysis using the Augmented Space Integral

Abstract

This paper presents an efficient approach to compute the bounds on the reliability of a structure subjected to uncertain parameters described by means of imprecise probabilities. These imprecise probabilities arise from epistemic uncertainty in the definition of the hyper-parameters of a set of random variables that describe aleatory uncertainty in some of the structure's properties.Typically, such calculation involves the solution of a so-called double-loop problem, where a crisp reliability problem is repeatedly solved to determine which realisation of the epistemic uncertainties yields the worst or best case with respect to structural safety. The approach in this paper aims at decoupling this double loop by virtue of the Augmented Space Integral. The core idea of the method is to infer a functional relationship between the epistemically uncertain hyper-parameters and the probability of failure. Then, this functional relationship can be used to determine the best and worst case behaviour with respect to the probability of failure. Three case studies are included to illustrate the effectiveness and efficiency of the developed methods.

A Review of Uncertainty-Based Multidisciplinary Design Optimization Methods Based on Intelligent Strategies

“…There are currently two main types of solving strategies for Equation (11). Firstly, some alternative approximation methods are utilized to translate the constraints with uncertainty into quasi-deterministic constraints with simplifications and assumptions [72], such as worst-case analysis method [108] and variation pattern formulation [109], which can greatly reduce computational costs. However, the results of these methods need to be confirmed through reliability analysis because the reliability of constraint is not calculated precisely during the solving process.…”

Bayesian probabilistic propagation of hybrid uncertainties: Estimation of response expectation function, its variable importance and bounds

“…For an review of the computation methods for propagating p-boxes, the reader is referred to [42]. Besides, some progress has also been made in the context of hybrid uncertainty propagation, e.g., surrogate modelling-based methods [43][44][45][46][47][48], stochastic simulation-based methods [49][50][51] and others [52,53]. For propagating probabilistic-interval hybrid uncertainty, one can refer to the review [54].…”