Bayesian Updating for Reliability with Imprecise Probabilities: Julia Implementation and Application to the NASA Langley UQ Challenge 2019

Model updating has emerged as a technique of great importance in a number of engineering contexts where measurements are employed to infer the parameters of systems. In many applications, the limited availability of experimental data, coupled with significant model uncertainties, presents a considerable challenge for inferring accurate model parameters, particularly in the context of hybrid uncertainties. Nevertheless, accurately quantifying these uncertain parameters is of key importance in order to ensure the reliability of systems within an engineering context. This highlights the need for flexible yet robust methodologies to address systems with imprecise probability models in the context of stochastic model updating. In light of these considerations, we present a Julia implementation of a Bayesian updating technique within a structural reliability framework. The objective is to infer parameters represented by imprecise probabilistic models and obtain imprecise failure probabilities. The methodology is illustrated with reference to the NASA Langley UQ Challenge 2019, which demonstrates the application of Bayesian techniques in updating the uncertainty model of a black-box system and conducting subsequent reliability analysis. A two-step Bayesian updating procedure is employed here. This procedure uses the Transitional Markov Chain Monte Carlo algorithm and applies model reduction techniques to construct an approximate likelihood function from coefficients of time series data using the Euclidean and Bhattacharyya distances.

Keywords: Bayesian updating, Imprecise probabilities, Reliability analysis, Hybrid uncertainty, Transitional Markov chain Monte Carlo, Uncertainty quantification, Julia programming, NASA langley UQ challenge.