Experiment Design And Optimization Of The Nested Computer Models

Computer experiment is the simulation experiment of simulating real physical and chemical processes with the help of computer models such as mathematical statistical model and computer code.When the traditional physical experiment is difficult to implement or timeconsuming,laborious and expensive,using computer experiments to replace the traditional physical experiment has become an important research method.With the development of computer science,computer simulation experiment becomes more and more complex.Many computer simulation processes involve multiple nested computer models,that is,the output of the inner computer model is the input of the outer computer model.This dissertation focuses on the simulation model which is nested by two computer models.The main research work includes the experiment design and bayesian optimization of nested computer model.Space filling design is a common design method in the field of computer experiment,which aims to distribute the test points evenly in the design space.For the nested computer model,because the output of the inner model is the input of the outer model,affected by the inner model,the input of the outer computer model often has the phenomenon that some design points are close or even overlapped,which makes the outer computer input have poor space filling property,therefore it is not conducive to the modeling of the nested computer experiment.In order to solve this problem,this dissertation proposes a maximum and minimum inner layer output experimental design method,which ensures that the inner layer design meets the space filling property,and improves the space filling property of the outer layer computer input by maximizing the minimum distance between the inner layer computer simulation outputs.Numerical simulation results show that the proposed method can effectively improve the space filling of the outer computer input,and improving the prediction effect of the outer computer model.Bayesian optimization is a very efficient method to solve the global optimization of black box function.The main steps of this method include:(1)the existing sample points are used to establish the proxy model of the objective function,such as gaussian process model;(2)an acquisition function is selected,such as expected improvement function,and the global optimal point of the objective function is obtained by increasing the maximum point of the acquisition function sequentially.In order to solve the global optimization problem of the nested computer model with black box functions,based on bayesian optimization theory,this dissertation first uses the nested gaussian process model to approximate the computer simulation output,and proves that the nested gaussian process model is not necessarily gaussian.Then,when the nested gaussian process model is gaussian or non gaussian,the calculation methods of the expected improvement function are given respectively.The results of numerical simulation show that,compared with the traditional bayesian optimization algorithm which regards the nested computer model as a black box function,the bayesian optimization method proposed in this dissertation has the advantages of high computational efficiency and it is not easy to fall into the local optimum because it makes full use of the intermediate information of the nested computer model.