Methodological Study On Prediction Of Material's Thermal Properties Based On Inverse Heat Conduction Problems

The research on inverse heat conduction problems (IHCP) have been paid more attention since 60s last century. Most of the studies focus on one-dimension IHCP at present, and have good solutions. However, the studies of multi-dimensional IHCP are still in the first step. Because of the ill-posedness and complexity of inverse problems, there is still some obstacle between the researches and actual applications of the inverse problems. Thermal conductivities are important thermal physical properties of material, and inverse problems of estimating thermal conductivities have important academic significance in the field of engineering application and scientific research.Thermal property estimation, boundary heat flux reconstruction, and heat source identification are the most commonly encountered inverse problems in heat conduction. There are many methods to solve inverse heat conduction problems, for instance, a variety of optimizations and regularization approach and so on, in which the regularization approach and Levenberg-Marquardt are used most widely. Bayesian approach, Genetic Algorithms and Levenberg-Marquardt are used to solve the IHCP in this paper.Unlike other techniques that aim at regularizing the ill-posed inverse problem to achieve appoint estimate, the Bayesian method treats the inverse problem as a well-posed problem in an expanded stochastic space and solves for the distribution of random unknown. The primary of Bayesian estimation is to deduce the conditional distribution function of unknown variables on the data, which is also called posterior probability density function (PPDF). And the solution is obtained by computing the expectation of the PPDF. Genetic Algorithms (GAs) are a search procedure modeled on the mechanics of natural selection and natural heredity. GAs can automatically obtain and cumulate the knowledge of the search space, and control the search procedure self-adapting to obtain the optimization solution. Levenberg-Marquardt Algorithm is a blend of vanilla gradient descent and Gauss-Newton iteration. It also can be considered as a trust-region method.The main tasks of this paper are as follow:1) A 2D hierarchical Bayesian PPDF is modeled for parameters estimation.2) Levenberg-Marquardt Algorithm, Genetic Algorithms and Bayesian method are used for 2D inverse heat conduction problems.