Adaptive decoupled robust design optimization

Abstract

Robust design optimization (RDO) is a valuable technique in the design of engineering structures as it can provide an optimum design solution that is relatively insensitive to input uncertainties. However, the nested double-loop estimation process required in RDO often results in significant computational costs. To address this issue, we propose an adaptive decoupled RDO method based on the Kriging surrogate model. This method transforms the nested double-loop estimation process into a traditional deterministic optimization procedure, thus reducing computational costs. Furthermore, a novel estimation expression for the performance standard deviation that can simultaneously reflect the uncertainties in both the prediction and the performance mean is established. The closed-form expressions of the performance mean and performance standard deviation under different design parameters are deduced, which are further implemented to the uncertainty propagation during the design optimization. Moreover, an adaptive framework is introduced to improve the computational accuracy of uncertainty propagation as well as optimization procedure to guarantee the estimation accuracy of RDO problems. Several numerical examples along with engineering cases are introduced to illustrate the effectiveness of the established adaptive decoupled adaptive RDO method, and the results demonstrate that the proposed method can effectively optimize the design of structures while reducing computational costs.