Uncertain Optimization Method Based On Bayesian Model And Its Application

With the improvement and development of computer computing power,the mixed method of numerical experiments has become the mainstream method for determining design parameters.However,this method can’t consider the general uncertainty existing in the problem,and can only get the point estimation of design parameters.The Bayesian calculation method has attracted much attention from scholars because it can effectively solve complex design problems and consider uncertainties in the problems.However,in practical engineering practice,the difficulty of obtaining likelihood functions in Bayesian calculation framework hinders its wide application.In order to effectively solve optimization problems in practical engineering,this paper presents an uncertain analysis method based on Bayesian model from the point of view of approximate Bayesian computation method,and verifies the feasibility of the proposed method through specific engineering cases.Finally,this method is applied to different engineering problems.The main contents of this paper are as follows:Approximate Bayesian computation does not need to obtain the likelihood function in Bayesian inference,and is suitable for dealing with the problem models with output response.In the framework of approximate Bayesian computation,the choice of sufficient statistics is a difficult problem for a long time.The sufficient statistics can be understood as the low dimensional expression of the observed data,and its dimensions need to be low enough to adequately represent the original observation data.In this paper,the Variational autoencoder is used as the dimensionality reduction method of observation data,and latent variables in the model are taken as the sufficient statistics to approximate Bayesian computation.In order to determine the dimension of latent variables,this paper uses structural similarity to calculate the similarity between reconstructed chart and original chart,which is the basis of the information contained in latent variables,and determines the specific dimensions of latent variables,thus improving the accuracy of calculation.In approximate Bayesian computation,we need a target as approximation value.In this paper,a target cloud chart is synthesized by traversing the sample cloud chart.The target cloud chart is an ideal set of sample cloud chart,and the sufficient statistics of the target cloud chart is used as approximate value in the approximate Bayesian computation framework.Approximate Bayesian computation requires continuous sampling to generate simulated samples to approximate the target value.If the simulation sample is acquired by finite element simulation,it will lead to computation impossible.In order to solve this problem,the least squares support vector regression model is applied to construct the fast response between the optimized parameters and the sufficient statistics.At the same time,in order to improve the sampling efficiency of approximate Bayesian calculation,Non-Parametric Population Monte Carlo is selected for sampling in this paper.Finally,the parameters of a sheet metal stamping problem and a static strength analysis problem are analyzed by using the proposed optimization method,and the required parameter distribution interval is obtained,which verifies the correctness and effectiveness of the optimization method.