Bayesian reliability-based design optimization using eigenvector dimension reduction (EDR) method

In practical engineering design, most data sets for system uncertainties are insufficiently sampled from unknown statistical distributions, known as epistemic uncertainty. Existing methods in uncertainty-based design optimization have difficulty in handling both aleatory and epistemic uncertainties. To tackle design problems engaging both epistemic and aleatory uncertainties, reliability-based design optimization (RBDO) is integrated with Bayes theorem. It is referred to as Bayesian RBDO. However, Bayesian RBDO becomes extremely expensive when employing the first- or second-order reliability method (FORM/SORM) for reliability predictions. Thus, this paper proposes development of Bayesian RBDO methodology and its integration to a numerical solver, the eigenvector dimension reduction (EDR) method, for Bayesian reliability analysis. The EDR method takes a sensitivity-free approach for reliability analysis so that it is very efficient and accurate compared with other reliability methods such as FORM/SORM. Efficiency and accuracy of the Bayesian RBDO process are substantially improved after this integration.