纺织材料设计反问题的贝叶斯统计推断方法

Bayesian statistical inference method for inverse problems of textile material design

针对具有不适定性纺织材料设计反问题,给出了利用贝叶斯蒙特卡洛方法求解纺织材料单参数和多参数反演问题的一种新方法。因织物稳态热湿传递模型的非线性和反问题的不适定性,基于贝叶斯统计推断方法的纺织材料类型、厚度、孔隙率等参数的后验概率分布推断是一种有效的方法。这种方法将参数的先验信息描述为先验概率密度,构建了纺织材料设计反问题的数值算法。数值实验结果表明,与马尔科夫链蒙特卡洛抽样算法相匹配的贝叶斯推理可用来求解纺织材料设计反问题。

Aiming at the ill-posed of the inverse problem of textile material design （IPTMD）,a new approach based on Bayesian Markov Chain Monte Carlo （Bayesian-MCMC） method was proposed for solving the problem of single and multiple parameter determination.Since the heat and moisture transfer model is non-linear and the IPTMD is ill-posed,it is proved that posterior distribution for the model parameters such as the heat conductivity,thickness and porosity of the material is an effective method.This method describes prior information of parameters as prior probability density,constructing numerical algorithms of the IPTMD.The numerical results show that Bayesian inference method agreed with Markov Chain Monte Carlo sampling algorithm can be applied to solve the IPTMD.