A framework for global reliability sensitivity analysis in the presence of multi-uncertainty

Abstract

In reliability analysis with numerical models, one is often interested in the sensitivity of the probability of failure estimate to changes in the model input. In the context of multi-uncertainty, one whishes to separate the effect of different types of uncertainties. A common distinction is between aleatory (irreducible) and epistemic (reducible) uncertainty, but more generally one can consider any classification of the uncertain model inputs in two subgroups, type A and type B. We propose a new sensitivity measure for the probability of failure conditional on type B inputs. On this basis, we outline a framework for multi-uncertainty-driven reliability sensitivity analysis. A bi-level surrogate modelling strategy is designed to efficiently compute the new conditional reliability sensitivity measures. In the first level, a surrogate is constructed for the model response to circumvent possibly expensive evaluations of the numerical model. By solving a sequence of reliability problems conditional on samples of type B random variables, we construct a level 2-surrogate for the logarithm of the conditional probability of failure, using polynomial bases which allow to directly evaluate the variance-based sensitivities. The new sensitivity measure and its computation are demonstrated through two engineering examples.

Uncertainty and sensitivity analysis for probabilistic weather and climate risk modelling: an implementation in CLIMADA v.3.1.

“…CLIMADA is such a deterministic computer code. In order to describe truly stochastic models on 65 would have to use other techniques, for instance which allow to take into account correlations between input parameters, or which are directly built for probabilistic computer codes (Ehre et al, 2020;Étoré et al, 2020;Zhu and Sudret, 2021). Eberenz et al, 2020) for all combinations of the nightlight and population exponents m and n considered in the uncertainty analysis (c.f.…”

“…In practice, the quantification of risk with climate risk models are particularly challenging as they involve dealing with the absence of robust verification data (Matott et al, 2009;Pianosi et al, 2016) when setting-up the hazard, exposures and vulnerability sub-models, as well as dealing with large uncertainties in the input parameters and the model structure itself (Knüsel, 2020b). For example, in hazard modelling, many authors have shown large uncertainties affecting the computation of flood maps through hydraulic modelling (Merwade et al, 2008;Dottori et al, 2013) and, similarly, alternative models have been proposed for modelling tropical cyclones tracks and intensities (Emanuel, 2017;Bloemendaal et al, 2020). For exposures, notable uncertainties are associated with the quality of the data being used, their resolution and, as often proxy data are used (Ceola et al, 2014;Eberenz et al, 2020), their fitness-for-purpose.…”

Global sensitivity analysis of rare event probabilities

“…An early work [21] combines rare event estimation techniques with the traditional Monte Carlo approach for GSA of the hyper-parameters. Several studies introduce new sensitivity measures [9,12,13,17] which are tailored to make the rare event SA process more tractable.…”

“…Others perform sensitivity analysis in the joint space of both input parameters and hyper-parameters [9,13,30,31]. These methods increase computational efficiency through use of local SA methods [9], surrogate models [13], kernel density estimates [31], and Kriging [30]. A thorough overview of current methods at the intersection of SA and rare event simulation can be found in [8] .…”

Decision-theoretic reliability sensitivity

“…The FORM α-factors are briefly reviewed in Section 3.3. As an alternative, classical global sensitivity metrics, specifically variance-based and distribution-based metrics, have been adapted for reliability analyses [18,19,20,21]. In addition, quantile-based sensitivity metrics can be utilized in the context of reliability and risk analysis [22].…”