A Sequential Algorithm for Reliability-Based Robust Design Optimization Under Epistemic Uncertainty

In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some probabilistic constraints in a reliability based design optimization (RBDO) problem. It is important to ensure that the probabilistic constraints at the optimum in a RBDO problem are insensitive to the variations of design variables. In this paper, we propose a novel concept and procedure for reliability based robust design in the context of random uncertainty and epistemic uncertainty. The epistemic uncertainty of design variables is first described by an info gap model, and then the reliability-based robust design optimization (RBRDO) is formulated. To reduce the computational burden in solving RBRDO problems, a sequential algorithm using shifting factors is developed. The algorithm consists of a sequence of cycles and each cycle contains a deterministic optimization followed by an inverse robustness and reliability evaluation. The optimal result based on the proposed model satisfies certain reliability requirement and has the feasible robustness to the epistemic uncertainty of design variables. Two examples are presented to demonstrate the feasibility and efficiency of the proposed method.