Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network

Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estimate proposed by Nakayama, four sufficient conditions are introduced. Then, a new simple estimate of the width in the Gaussian kernel is proposed. Second, a new sampling strategy with the RBF network is also proposed. In order to find the sparse region, the density function with the RBF network is developed. The proposed width and sampling strategy are examined through benchmark problems. Finally, the proposed SAO is applied to the optimal variable blank holder force (VBHF) trajectory for square cup deep drawing. The objective is taken as the minimization of the deviation of whole thickness. The constraints are quantitatively defined with the forming limit diagram in which no wrinkling and tearing can be observed. The design variables are the blank holder force. In particular, the risk of both tearing and wrinkling can be handled as the constraints separately. Numerical simulation is carried out by the optimal VBHF trajectory with SAO. It is clear from the numerical simulation that no tearing and wrinkling can be observed.