Robust Probability Bounds Analysis for Failure Analysis under Lack of Data and Model Uncertainty

Abstract

The paper serves as a response to the recent challenge problem published by the NAFEMS Stochastic Working Group titled: “Uncertain Knowledge: A Challenge Problem” whereby the participants are to implement current practices and ‘state-of-the-art’ stochastic methods to address numerous uncertainty quantification problems presented in the challenge. In total, two different challenge problems on increasing complexity levels are addressed through the use of the following techniques: 1) Bayesian model updating for the calibration of the distribution models and model selection for the aleatory variables of interest; 2) Adaptivepinching method for the sensitivity analysis; and 3) Probability Bounds Analysis to quantify the uncertainty over the failure probabilities. For the reproducibility of the results and to provide a better understanding of the numerical techniques discussed in the paper, the MATLAB and R codes implemented to address the challenge problems are made available via: https://github.com/Institute-for-Risk-and-Uncertainty/NAFEMS-UQ-Challenge-2022