The Design Optimization Based On Euclidean Distance Sampling And Kriging Surrogate Model

The Structural optimization not only can effectively reduce the structural weight and the cost of design, but also can improve the structural performances. From now to the future, it will always play an important role in the scientific research field of structural design and manufacture. The solution of optimization can be roughly classified into the following methods:mathematical programming method and optimality criterion method, randomly search method, etc. In recent years, the intelligent algorithms such as the Simulated Annealing algorithm (SA) and Genetic algorithm (GA) have attracted more and more attentions. Compared with the traditional optimization algorithm, they have more advantages in global searching and dealing with discrete variable. But in dealing with the complicated model, the new intelligent algorithms also exposed the defect in the low computational efficiency. In order to reduce the computational time of finite element analysis (FEA) in the process of design optimization, we introduce the surrogate model instead of complicated FEA. It effectively reduces the computational time, and greatly improve the efficiency of design optimization.The main content of this paper are as follows:Firstly, the engineering background of this paper is briefly introduced. Then the basic theory of Kriging surrogate model and its construction process, several common regression equations and the correlation functions representing sample points'spatial characteristics are described in detail. Besides, two kinds of optimization method based on Kriging surrogate model, and their advantages and disadvantages are also discussed.Secondly, as we all know, the selection of sample points is the key step in the surrogate model fitting and the distribution of the sampling points in the fitting process, directly determines the fitting accuracy and convergence speed. According to advantages and disadvantage sof the Latin Hypercube Sampling and Grid Rectangular Sampling, a new sampling method is proposed based on Euclidean distance in this paper. The purpose of the new method is to make the sample points as evenly as possible and improve the accuracy of the fitting model. Numerical examples of the fitting function demonstrate the effectiveness of the sampling method proposed in this paper, which provides a good basis for the subsequent design optimization.Then, we detailed introduce the two kinds of common criteria for increasing points based on Kriging surrogate model in the design optimization. Considering the sequential quadratic programming, the procedure of optimization solution is given. Based on Maximum Expected Improvement (EI), the numerical examples of the function optimization and structural optimization are employed, which shows the effectiveness of the sampling method proposed in this paper.Finally, combining SA, new sampling method, the Kriging surrogate model and Maximum Expected Improvement, a solution procedure is presented for structural optimization. The numerical examples show that, compared with the traditional SA and GA, on the basis of the same computational precision, the number of FEA can be significantly reduced by using the procedure. Besides, compared with the procedure of using SQP to update the sample points, the procedure has the obvious advantages in the computational precision and the number of FEA. These indicate that the mixed uses of Euclidean distance sampling, Kriging surrogate model based on the El criterion and SA is effective for structural optimization.