A Heat Conduction Model With Stochastic Boundary Data And Related Inverse Problems Of Parameters Determination

In the real world,the changing process usually contains some randomness or uncertainty factors.Numerous studies have shown definite solution of the problem of partial differential equations under random noise boundary can be regarded as a kind of stochastic partial differential equation system,which is broadly noticed by scholars of domestic and overseas.As the intersection of partial differential equations and probability theory,stochastic partial differential equation system plays an important role in finance,medicine,engineering,physics,chemistry and other applied disciplines.In this paper,a mathematical model of heat transfer with random Robin boundary conditions is established to describe the heat transfer law in the environment-thermal protective clothing-air layer-skin system.Combined with the evaluation criteria of burn degree of human skin,the inverse problems of parameters determination of thermal protective clothing is proposed.Aiming at the inverse problem of thickness parameter determination,a random search algorithm is established and the inverse problem is solved numerically.The main contents of this paper are as follows:In chapter 1,we introduced the background and significance of stochastic partial differential equations and thermal protective clothing.The results of previous research and relevant preparatory knowledge of stochastic theory are reviewed,and the main research content of this paper is briefly summarized.In chapter 2,a definite solution problem for a class of three-layer parabolic equations with random Robin boundary conditions is established to describe the heat transfer process in the environment-thermal protective clothing-air layer-skin system.In order to describe the heat transfer between fabric and high temperature more accurately,the random Robin boundary conditions is used on the boundary.The composite finite difference method is used to calculate the stochastic model,the temperature distribution with time and space is obtained,and its rationality is explained.In chapter 3,the main goal of the inverse problems of thermal protective clothing design is to ensure that the high-temperature workers do not have thermal damage or reduce the degree of burn as far as possible.Based on the stochastic heat transfer model of thermal protective clothing established in the previous chapter,we combined it with the evaluation criteria of burn degree of human skin,the inverse problem of thickness parameter determination in the sense of probability is presented.On the basis of the idea of interval algorithm,a random search algorithm for inverse problem is constructed.In chapter 4,we used random search algorithm for the numerical solution of the inverse problems of stochastic parameter determination.The confidence interval of the thickness parameter under the given design objective is obtained.The calculation results are substituted into the direct problem model,combined with the evaluation criteria of burn degree of human skin for verification.The results have shown that the model is reasonable and the algorithm is effective.In chapter 5,we concluded the main research content and innovation of this paper,and put forward some directions worthy of further research.