Bayes Method For The Inverse Problem Of Convection-diffusion Models Based On Atmospheric Pollution

In recnet years,air pollution problem has become more and more serious in the society.The composition and behavior of air pollutants as well as the accumulation process and the migration and transport law of air pollutants are key scientific problems in the control and prevent work for the air pollution.It is of important scientific meanings for the air pollution problems to put forward suitable mathematical models to describe the migration and diffusion processes of the air pollutants,and to determine the unknown parameters in the models by using the inverse problem theory.There are many uncertainties in the transport and diffusion system of air pollutant and the measurement data contains more or less random errors.The ill-posedness in the inverse problem of air pollution parameter identification,especially the non-uniqueness and instability of the solution,brings challenges to the numerical solution.Based on the two-dimensional convection-diffusion equation,an inverse problem model for pollutant parameter identification based on Bayesian inference is established.Unknown parameters are treated as random variables,and the available prior information and noise information of the parameters are introduced into the parameter identification process.Beyesian method of parameter inference is given,and the posterior probability distribu tion and estimator of the parameters are obtained through the posterior sampling of Markov Chain Monte Carlo method to deal with the uncertainty of model.Numerical solution of parameter identification is obtained.The paper is divided into five chapters.The first chapter introduces the research background and research progress.The second chapter formulates the mathematical model of transport and diffusion system of air pollutant based on the two-dimensional convection-diffusion equation and gives the numerical simulation.The third chapter discusses the inverse problem of diffusion coefficients identification in transport and diffusion system of air pollutant by Bayesian theory of statistical inferences.In the forth chapter,the numerical simulation is presented for the diffusion coefficients determination.In the final,some conclusions and further research are concluded.