Bayesian reliability-based robust design optimization of mechanical systems under both aleatory and epistemic uncertainties

Abstract

Uncertainties can be divided into two general categories: aleatory and epistemic. Conventional reliability-based robust design optimization approaches, which disregard epistemic uncertainties due to lack of knowledge about the physical nature of systems, have previously been developed. To overcome this weakness, unlike previous methods, a Bayesian reliability-based robust design optimization method is proposed in the presence of both aleatory and epistemic uncertainties. The proposed formulation is presented as a multi-objective optimization problem. The univariate dimension reduction method is used to approximate the mean and variance of the design function. The non-dominated sorting genetic algorithm-II is used to solve the multi-objective optimization problem. To find the final optimum design from the Pareto front, Shannon’s entropy-based technique for order of preference by similarity to ideal solution (TOPSIS) algorithm is applied. Finally, to demonstrate the applicability of the proposed method, two case studies are considered and the results are compared and discussed.