Research On Inverse Heat Conduction Problems Based On Markov Chain Monte Carlo Method

The main difficulties of the solution for heat conduction inverse problems lies in the ill-posed and the complexity of inverse problems. It comes from the uncertainties of the heat conduction systems. There are many uncertainties factors in the heat conduction systems, so how to face directly and solve these problems is dire need. In the view of probability theory, a statistics method is adopted to set up the inverse models. The measurement data, prior information and the solution of the inverse problems are all expressed in the probability language. The traditional inverse problem solving algorithm though the approximation to the result, which is refinement, but estimated solving is probability result. Thus the uncertainty problems of the inverse research is solved conveniently.The model for solving an inverse heat conduction problem based on Bayesian inference is set up. Using the Markov Chain Monte Carlo method to solve the Bayesian model. Building tools to solve the problem for one dimensional unsteady heat conduction mathematical model by the Finite Control Volume method. It take result as measure temperature, Building the mathematical model on solving the coefficient of thermal conductivity and boundary heat flow,With the Bayesian inference of MCMC sampling method to obtain the samples for the thermal conductivity and the boundary heat flux. Samples of the statistical results show that the MCMC method about heat conduction inverse problem of heat conduction coefficient and boundary heat flux, which is effective.The analysis of the dynamic characteristics of the temperature sensor,Building mathematical model of the sensor dynamic characteristics. By analyze the impaction on result for calculating the inverse heat conduction problem about the time constant. The conclusion show a greater influence on the dynamic characteristics of inversion, by according to the actual situation of inversion process.The temperature of material by measuring the boundary. The result based on MCMC method on the material coefficient of thermal conductivity inversionshow that the MCMC method is effective in application inversion coefficient of thermal conductivity.