Error propagation for quantile estimation via combining Polynomial Chaos expansions and metalog distributions

Abstract

Introducing parametric uncertainties to models is a quintessential step of simulation-based risk assessment and rare event simulations. A novel quantile estimation method is proposed based on generalized Polynomial Chaos expansions and metalog distribution estimation. We propose to derive the metalog distribution based on the statistical information of an expansion of the random model. The advantage of latter lies in a reduced number of evaluations of the full model, while deriving the metalog distribution avoids sampling-related challenges of quantile estimation. Error estimates and an algorithm to choose the relevant number of statistical moments are developed and analyzed, giving a framework for assessing the method applicability and the accuracy of the quantile estimation. The proposed method and the analysis are demonstrated on numerical examples. The method is applied to a complex fluid flow problem in transpiration cooling.