A Bayesian Approach to Engineering Reliability Estimation

Description

The advent of modern computing technology has allowed engineering systems to be analyzed with much greater detail than ever before. Along side are increasing expectation of high performance reliability and robustness in functionality, calling for a rational assessment of the effects of uncertainties and their mitigation in the design decision making process. Quantitative risk analysis of engineering systems often requires the estimation of reliability, or equivalently the failure probability, of satisfactory performance under uncertainties modeled in a given scenario. Monte Carlo methods have shown great promise for applications in complex systems but its direct version is computationally prohibitive for rare failure scenarios, which are often the main interest in reliability analysis. An advanced Monte Carlo method called Subset Simulation has been developed by the PI which generates samples that progressively populate the rare failure region by crossing intermediate failure boundaries. In view of some bottleneck problems faced by Subset Simulation reported recently, a novel approach is proposed in this project that formulates the Monte Carlo reliability problem as a Bayesian inference problem using the simulated samples as ‘data’. This approach allows greater flexibility in the design of samples for exploring rare failure events and resolves the bottleneck problems arising from frequency-occurrence formulation of estimators in Subset Simulation. Both theoretical and computational aspects of the proposed approach shall be investigated, which are backed up by benchmark studies of realistic structural and aerospace systems.