关键词: 反问题, Bayes推理, 热源识别, 遗传算法

Abstract: Bayesian genetic algorithm was used to solve the heat source parameters of twodimensional heat conduction equation. Firstly, the posterior probability density function of the heat source parameters was obtained by Bayesian inference and twodimensional heat conduction equation. Secondly, combined with the genetic algorithm, according to maximum likelihood principle, we gave the posterior probability distribution and statistical results of the location and the time parameters of the heat source. Numerical experiments show that when the iteration number reaches 50 times, the relative error of the parameters converge stably within 1%. Adding 5% and 10% noise to the observation data respectively, and the relative error of the parameters is controlled within 5% and 9% respectively.

Key words: inverse problem, Bayesian inference, heat source identification, genetic algorithm