Reliability-based robust design optimization using anchored ANOVA expansion and truncated Edgeworth series approximation

Based on the basic concept of reliability-based design optimization and robust design optimization, a reliability-based robust design optimization is achieved with the moment method in this work. At the first step, two methods, i.e. the anchored ANOVA expansion and truncated Edgeworth series approximation, are combined to solve the reliability constraints in the optimization procedure. The computational effort of the reliability analysis involved in the reliability-based design optimization is then reduced by the moment method. The reliability-based robust design optimization is then formulated by introducing the reliability sensitivity into the reliability-based design optimization as a sub-objective function, which is derived based on the truncated Edgeworth series expansion. The numerical examples illustrate the effectiveness and applicability of the proposed methodology and that the moment-based reliability-based robust design optimization satisfies (1) the reliability target of each constraint and (2) the minimum reliability sensitivity with respect to the mean value of the input random variables. The proposed reliability-based robust design optimization procedure could be applied to the product design under uncertain environment.