Quantile-based optimization under uncertainties for complex engineering structures using an active learning basis-adaptive PC-Kriging model

The Reliability-Based Design Optimization (RBDO) of complex engineering structures considering uncertainties has problems of being high-dimensional, highly nonlinear, and time-consuming, which requires a significant amount of sampling simulation computation. In this paper, a basis-adaptive Polynomial Chaos (PC)-Kriging surrogate model is proposed, in order to relieve the computational burden and enhance the predictive accuracy of a metamodel. The active learning basis-adaptive PC-Kriging model is combined with a quantile-based RBDO framework. Finally, five engineering cases have been implemented, including a benchmark RBDO problem, three high-dimensional explicit problems, and a high-dimensional implicit problem. Compared with Support Vector Regression (SVR), Kriging, and polynomial chaos expansion models, results show that the proposed basis-adaptive PC-Kriging model is more accurate and efficient for RBDO problems of complex engineering structures.