Adaptive ensemble model-based approach for estimating failure probability function using global error measures with application in reliability optimization

The failure probability of structure associated with random input design parameter is defined as the failure probability function (FPF), which is commonly essential for reliability-based design optimization (RBDO). The estimation of FPF requires multiple calls to the time-consuming original model, leading to the computational costs are often unaffordable for complex engineering problems. In this work, we proposed a novel adaptive ensemble model-based approach to estimate FPF, leveraging Bayes’ rule and augmented reliability theory. A new ensemble learning function is implemented to select optimal sample points for updating the ensemble model, which is then used to recognize failure samples and effectively estimate the FPF. Each of the individual surrogate in the proposed ensemble models provides statistical information on the predicted points and no additional samples are needed to validate the ensemble model's accuracy. Furthermore, our proposed ensemble model integrates the predictive capabilities for each individual model by assigning specific weights to them, which enhances the accuracy and efficiency of our proposed ensemble model compared to a single individual model. Several benchmark examples demonstrate that our proposed method enhances both computational efficiency and accuracy. Finally, the proposed method is adopted to solve the RBDO problem of aeronautical hydraulic pipeline system effectively.