A hybrid adaptive Kriging-based single loop approach for complex reliability-based design optimization problems

•A hybrid adaptive Kriging-based single loop approach (HAK-SLA) is proposed.•The Kriging model is applied to single loop approach (SLA).•The Kriging model is adaptively updated by approximate or accurate MPP.•Two improved modified chaos control methods are presented to locate accurate MPP.•The performance of HAK-SLA is verified through five benchmark examples. The study proposed a hybrid adaptive Kriging-based single loop approach (HAK-SLA) to prevent the conventional single loop approach (SLA) from being less efficient, converging to an inaccurate solution or encountering significant difficulty in convergence when dealing with complex RBDO problems with highly nonlinear constraints. The procedural strategy here is to apply surrogate modeling approach in SLA, in which the constraints were surrogated specifically by Kriging models updated using most probable points (MPPs) in each loop. Since the MPPs obtained directly from the Kriging-based SLA may be insufficiently accurate, two different enhanced chaos control methods are developed here to obtain robustly accurate MPPs. Nonetheless, searching for accurate MPPs would increase considerable computational cost; thus, a criterion combining Karush-Kuhn-Tucker (KKT) optimality condition of performance measure approach (PMA) with Kriging model is utilized to determine whether it is necessary to update the Kriging models using accurate MPPs. When the criterion is satisfied, the accurate MPPs are then used to update Kriging models. In this study, performance of the proposed HAK-SLA is demonstrated by comparing with the other conventional RBDO methods through five illustrative RBDO examples. The results exhibit that the proposed approach is of high efficiency and robustness in solving complex RBDO problems.