The Research Of Adaptive Sampling Strategies For Kriging Metamodel Based On Delaunaly Triangulation And TOPSIS

Numerical simulation technology has been widely used in engineering design optimization,such as finite element analysis model and computational fluid dynamics model,which greatly reduces the manpower and material resources needed for product design only depending on physical experiments.However,numerical simulation analysis of complex engineering products often requires expensive time cost.In the process of designing and optimizing the design of complex engineering products based on numerical simulation,it is often necessary to call the numerical simulation model repeatedly to obtain the optimal design scheme,resulting in the computational cost being unacceptable to designers.In this context,approximate modeling technology came into being.It can substitute the numerical simulation model or physical experiment by establishing the surrogate model,which effectively reduces the design cost.The quality of the metamodel has a great influence on the computing cost or convergence characteristics of the design optimization problem based on metamodels,which largely depends on the selection of the sample points in the simulation,that is,the design of experiments.Generally,a large number of sample points are needed to construct a high precision metamodel,which will lead to an increase in computational cost.If less sample points are selected to reduce the cost of calculation,the accuracy of the metamodel will be low.Therefore,adaptive sampling methods based on the Kriging model are proposed in two cases of single output and multiple output to effectively balance the contradiction between high precision metamodel and low computational cost.The proposed methods are based on the Kriging model,combined with the Delaunay triangulation and the TOPSIS method,where global exploration and local exp loitation are simultaneously considered in the design space,i.e.the discreteness of the sample points and the estimation error provided by the Kriging model.In this paper,the Delaunay triangulation method is used to divide the design space into multiple triangular regions.The discrete degree of the sample points which is the area of the triangular region is selected as the global exploration index.And the prediction error at the centroid of the triangular region is used as the local exploration index.Finally,the sensitive region is selected by the TOPSIS method,and a new sample point is added at the centroid of the region.Besides,since there are often multiple responses in the engineering design optimization problem,the above method is discussed to solve the multiple response problems.To verify the validity of the proposed methods,the proposed methods are tested by some numerical examples and engineering examples of NACA 0012 airfoil lift coefficient prediction and the pressure vessel.The results show that the proposed methods can effectively improve the modeling accuracy and reduce the computational cost.