Efficient local adaptive Kriging approximation method with single-loop strategy for reliability-based design optimization

The classical reliability-based design optimization (RBDO) methods, due to the ever increasing complexity of designs and contingent engineering situations, incur more and more intricate numerical models. The consequent intractable computational intensity has imposed great challenges for practical application of RBDO. Thus, the surrogate-based RBDO methods, and especially those using Kriging model, have received widespread attention recently for their superior computational efficiency without compromise of computational accuracy. On the other hand, the Kriging-based RBDO methods still ensue high computational demands for complex RBDO problems and especially those with implicit objective and constraint functions. To enhance the computational efficiency of the Kriging-based RBDO methods, this study proposes an efficient local adaptive Kriging approximation method with single-loop strategy (LAKAM-SLS), in which Kriging models are employed to replace both the objective and constraint functions. Two different criteria are developed to identify whether Kriging model of performance function in probability constraint is active in each iteration. If the criterion is satisfied, approximate inverse most probable point (IMPP) derived by combining sing-loop approach with Kriging will be used to refine the corresponding Kriging model. For the objective function, its Kriging model is sequentially refined through points selected by a newly proposed learning function from the sample pool generated by taking the optimal solution from each iteration as the sampling center. Four benchmark examples and an application example of head pressure shell are implemented to evaluate the computational performance of the currently proposed LAKAM-SLS against other Kriging-based RBDO methods. The result comparison shows that the currently proposed LAKAM-SLS substantially reduces the computational expense to a relatively low level.