An efficient RBDO process using adaptive initial point updating method based on sigmoid function

Abstract

Using Kriging model in the reliability-based design optimization (RBDO) process can reduce the computational cost effectively. However, the constraints in practical problems are often highly nonlinear and black box functions, and the cost of evaluations at design points is very high, such as the finite element analysis (FEA). So building accurate Kriging models will consume a huge amount of computing resources. Moreover, complex constraint functions will lead to the local minimum in the design space, which makes it difficult to get the global optimum. To cope with this problem, an adaptive sampling method based RBDO process (AS-RBDO) is proposed by introducing two new sampling criterions. The first criterion is built based on the support vector machine (SVM) and the sigmoid function. And the second criterion is built based on the improvement of the constraint boundary sampling (CBS) method. With the use of new strategies, AS-RBDO can not only guide the optimization to the global optimal direction, but also update the Kriging model only in the local range that has the greatest impact on the results of RBDO. Thus the unnecessary sampling and evaluations can be avoided effectively. Several examples are selected to test the computation capability of the proposed method. The results show that AS-RBDO can effectively improve the efficiency of the RBDO process.