BEPU robustness analysis via perturbed law-based sensitivity indices

Abstract

The “best-estimate plus uncertainty” (BEPU) methodology is the term used in the nuclear engineering community when dealing with uncertainty quantification issues in realistic numerical simulation models. One of the most critical hypothesis in these studies is the choice of the probability distributions of uncertain input variables which are propagated through the model. Bringing stringent justifications to the BEPU approach, especially in a safety study, requires quantifying the impact of potential uncertainty on the input variable distribution. To solve this problem, this paper deepens the robustness analysis based on the “Perturbed Law-based sensitivity Indices” (PLI). The PLI quantifies the impact of a perturbation of an input distribution on the quantity of interest (as a quantile of a model output or a safety margin) in the BEPU study. The mathematical formalism of the PLI is applied to two particular quantities of interest: the quantile and the superquantile. For both quantities, the PLI can be easily computed using a unique Monte-Carlo sample containing model inputs and output. Numerical tests are developed in order to define validity criteria of a PLI-based robustness analysis. The practical use of the method is illustrated on thermal-hydraulic computer experiments, simulating a cold leg Intermediate Break Loss Of Coolant Accident (IBLOCA) in a pressurized water nuclear reactor.

An information geometry approach for robustness analysis in uncertainty quantification of computer codes

“…• For each {f We emphasize that this approach only restricts to expensive computer models. Indeed, the bootstrap variance of the estimated quantile with reverse importance sampling tends to become very large as illustrated in Iooss et al (2020). This is due to the likelihood ratio that punctually explodes.…”

“…One of the key issue of the methodology is to determine how far the input distribution should be perturbed. We propose to adapt the empirical criterion from Iooss et al (2020) in order to establish a maximal perturbed level δ max . The number of points in the output sample Y N , smaller or larger than the δ-perturbed quantile has to be sufficient.…”

“…Amongst all densities with shifted mean or variance of a δ value, f iδ is defined as the one minimizing the Kullback-Leibler divergence from f i . This method has been applied on the computation of a probability of failure (Iooss and Le Gratiet, 2019;Perrin and Defaux, 2019), a quantile (Sueur et al, 2017;Larget, 2019) and a superquantile (Iooss et al, 2020;Larget and Gautier, 2020) as the QoI.…”

Computation of parametric uncertainty margin using stability boundary locus: An application to load frequency control

“…In Hu et al (2019), a generalized polynomial chaos expansion (PCE) technique is implemented for the assessment of parametric uncertainty in hydrological modeling. In Iooss et al (2021), best estimate plus uncertainty (BEPU) quantification and robustness analysis has been done using a perturbed law-based sensitivity indices (PLI) in a pressurized water nuclear reactor. In Ghiasi et al (2021), a non-probabilistic modeling has been implemented by employing wavelet weighted least squares support vector machine (WWLS-SVM) for tackling the uncertainties in structural damage detection.…”