Study Of Using Gaussian Process To Construct The Agent Model Of The Electromechanical Simulation Problem

In the field of modern engineering design,in order to reduce the design cost and design time,people often develop computer models to simulate on the physical system of the real world process,which also can help people get a deeper understanding of the physical process.However,on one hand,because the complexity of specific practical problems lead to the actual problems have lots of known or unknown physical process,people are unable to only use a single scientific physical process to simulate of the practical problems.On the other hand,the input and output data of the model,due to the randomness of the actual problem and the error and uncertainty of the observation.This requires the theory of uncertainty analysis from the strategy of Verification and Validation(V&V).Gaussian process theory is developed at the base of the Bayes theorem,which regard the unknown and uncertain function as stochastic process.According to Bayes theorem,one can calculate and obtain the prior distribution by the observed data or design data.Gaussian process model is a non parametric or semi parametric model and suitable for simulating and handling complex and nonlinear problems with high dimension,also has better flexibility and higher accuracy,which is able to quantify the uncertainty specially and developed by combining Gaussian process theory with statistical knowledge,Bayes theory and uncertainty quantification theory.Research shows that the Gaussian process model can be use as the substitution of the complex mechanical and electrical engineering problem simulation model to calibrate its model and predict the result.In this article the research of Gaussian process theory and application of Gaussian process model is of great significance in promoting further research of the Gaussian process theory and improving applicability and of the universality application of Gaussian process model in actual project.This article is organized as follows.First of all,we introduce the basic theory of Gaussian process,namely the Bayes method of Gaussian process.We derive the formula of the Gaussian process in detail,apply it in the one-dimensional input function and the two-dimensional input function,and obtain the posterior result.Then we discuss the influence of the number and distribution of the known design data points,the form of the prior expectation function and the size of the covariance function parameters on posterior results of Gaussian process,and draw the conclusion.we classify the source of uncertainty which help decompose the Gaussian process model.The MCMC sampling is introduced and used to obtain the posterior results according to the posterior distribution of the Gaussian process model.We introduce the process of set up Gaussian process model.First,we divide the Gaussian process model into three parts,the simulation model,the discrepancy model and observation error.Second,in the Gaussian process model,we input the simulation data and observation data,and obtain the the output of posterior simulation and posterior discrepancy by calculation and derivation.In the end,we add them together and get the final posterior results.Secondly,we introduce the knowledge of the proton exchange membrane fuel cell and its model and show that traditional methods of calibrating the parameter cannot obtain the accurate result of parameter calibration because of the uncertain factor,and are unable to predict the result.In order to handle the problem,in this article we use Gaussian process to construct Gaussian process agent model for the process of the actual proton exchange membrane fuel cell by studying its basic theory of Gaussian process,quantify its uncertainty,calibrate the parameter of empirical formula of proton exchange membrane fuel cell and predict the output result of fuel cell.Finally,we introduce the theory of crack propagation and its method of extending the finite element(XFEM)and show that when people use the traditional method of finite element to solve complex engineering problems,because the construction of the model is difficult,the computing time is long and the parameters or data of the input and output must be deterministic,the output result is only an reference value,not a accurate value.In this article we use Gaussian process to set up Gaussian process agent model for the problem of the finite element analysis,quantify its uncertainty,and predict the result.