A single-loop approach with adaptive sampling and surrogate Kriging for reliability-based design optimization

Surrogate models have been widely used for Reliability-Based Design Optimization (RBDO) to solve complex engineering problems. However, the accuracy and efficiency of surrogate-based RBDO largely rely on the sample size and sampling methods. For this reason, successive sampling methods that update the surrogate successively are more promising. Nowadays, several Kriging-based RBDO approaches have been proposed with different successive sampling techniques. However, these approaches are based on Monte Carlo simulations and double-loop approaches such that most of them would be time consuming for high target reliability levels or high dimensional problems. To improve the efficiency of surrogate-based RBDO, this article proposes a Single-Loop Approach (SLA) combined with the Kriging surrogate. This Kriging model is updated efficiently by using the Most Probable Points (MPPs) from the last SLA iteration. A very simple and effective stopping criterion is proposed. Compared with other sampling methods, the initial Kriging can be started with very few training points and converges to the right optimum very efficiently. Three mathematical examples and a practical engineering problem are used to demonstrate the effectiveness, the advantages and also the limitations of this method.