A local Kriging approximation method using MPP for reliability-based design optimization

• LMPP is developed to enhance the accuracy and efficiency of Kriging-based RBDO.
• LMPP locates samples mainly in a local region around the current MPP.
• Feasibility of probabilistic constraint at the current design is checked in LMPP.
• LEFF criterion is proposed to determine the sequential samples in local region.
• IS using MPP as sampling center is used to perform reliability analysis.

Kriging approximation has been widely used in reliability-based design optimization (RBDO) to replace the complex black-box performance functions. In this paper, a new local approximation method using the most probable point (LMPP) is proposed to improve the accuracy and efficiency of RBDO methods using Kriging model. In the LMPP, the concept of local sampling region is used and the most probable point (MPP) is chosen as the sampling center. The size of the local region is determined by target reliability and the linearity of probability constraint around MPP. Rather than fitting the Kriging model for all the probabilistic constraints, the new method uses the MPP to find feasible constraints, and only these feasible constraints are accurately approximated, which can significantly improve the optimization efficiency. Importance Sampling method using the MPP obtained above as sampling center is utilized to perform reliability analysis and reliability sensitivity calculation. A numerical example, a honeycomb material design problem and a box girder design application are used to demonstrate the computational capability of the LMPP method. The comparison results demonstrate that RBDO using the proposed method is very effective.