Sequential approximate robust design optimization using radial basis function network

Abstract

This paper proposes a sequential approximate robust design optimization (SARDO) with the radial basis function (RBF) network. In RDO, the mean and the standard deviation of objective should be minimized simultaneously. Therefore, the RDO is generally formulated as bi-objective design optimization. Our goal is to find a robust optimal solution with a small number of function evaluations, not identifying a set of Pareto-optimal solution using Multi-Objective Evolutionary Algorithms. The weighted sum is often used to find a robust optimal solution. In contrast, the weighted lp norm method is used in this paper. Through illustrative examples, some validations of the weighted lp norm method to the RDO are clarified. Next, SARDO with the RBF network is discussed. In general, the standard deviation of functions is obtained by using the finite difference method. Thus, in order to obtain the standard deviation of functions, the finite difference method is directly applied to the response surface. High accuracy of the finite difference method will leads to highly accurate robust optimal solution. In order to avoid the inaccurate numerical calculation, the standard deviation is expressed by only the Gaussian kernel. As the result, it is expected that a highly accurate robust optimal solution can be found with a small number of function evaluations. Through numerical examples, the validity of the proposed approach is examined. Finally, the variable blank holder force trajectory for reducing springback is examined.