An efficient Kriging based method for time-dependent reliability based robust design optimization via evolutionary algorithm

Uncertainty inadvertently exists in various stages of engineering system design, development, and operating conditions. During the system design and development stages, a design engineer encounters the reliability and robustness measures of a dynamic uncertain system. Due to the existence of dynamic uncertainties, incorporating the time-dependent reliability of an engineering system in reliability based robust design optimization (RBRDO) is crucial. However, the time-dependent and highly non-linear performance functions present a new challenge to the RBRDO problem. This paper presents a multiobjective integrated framework and corresponding algorithms to handle a time-dependent RBRDO problem. The mean and coefficient of variation of the cost function are taken as a multiobjective problem that needs to be optimized to maximize the robustness without destabilizing the system performance. An evolutionary algorithm is employed to find the optimal design points. The performance functions used to estimate the time-dependent reliability are taken as dynamic probabilistic constraints. The dynamic probabilistic constraints are then converted into deterministic constraints by predicting the corresponding time-dependent reliability. A transfer learning based method integrated with the Kriging surrogate models is proposed to predict the time-dependent reliability for a given time interval. Various examples are used to demonstrate the effectiveness of the proposed approach.