An adaptive local range sampling method for reliability-based design optimization using support vector machine and Kriging model

Kriging model is an effective method to overcome huge computational cost for reliability-based design optimization (RBDO) problems. However, the results of RBDO usually depend on constraint boundaries within the local range that contains the RBDO optimum. Determining this local range and building adaptive response surfaces within it can avoid selecting samples in unrelated areas. In this research, a new RBDO process is proposed. In the first phase, Kriging models of constraints are built based on Latin Hypercube sampling method, and updated by two new samples in each iteration. One of these two samples is selected based on SVM and mean squared error to make sure it is located near constraint boundaries. Another one is the deterministic optimum point (DOP) of current Kriging models, which is obtained based on the deterministic optimization and specifies the direction to the RBDO optimum. And the RBDO design point is obtained by SORA. When consecutive RBDO design points are close enough to each other, the local range is determined based on the current RBDO design point and the current DOP. In the second phase, new samples are located on constraint boundaries within the local range to refine Kriging models. The location and the size of the local range is adaptively defined by the RBDO design point and the DOP during each iteration. Several optimization examples are selected to test the computation capability of the proposed method. The results indicate that the new method is more efficient and more accurate.