基于动态热湿传递的纺织材料孔隙率决定的反问题  

The Inverse Problem of Textile Porosity Determination in Dynamic Heat and Moisture Transfer

作　　者：徐定华[1,2] 文雷[2] 

机构地区：[1]浙江理工大学浙江省服装工程技术中心 [2]浙江理工大学理学院数学系

出　　处：《数学年刊（A辑）》2014年第2期129-144,共16页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11071221,No.10561001);浙江省自然科学基金(No.LQ12A01024);浙江省重中之重纺织材料与工程一级学科和浙江省服装工程技术研究中心开放基金(No.2013KF10)的资助

摘　　要：除纺织材料的厚度与导热系数外,其孔隙率也是影响人体热湿舒适性的一个重要因素.基于动态热湿传递模型,作者提出了满足人体热湿舒适性的纺织材料孔隙率决定反问题.通过吉洪诺夫正则化方法将纺织材料孔隙率决定反问题归结为目标函数极小值问题.应用巴拿赫不动点理论证明了正问题解的存在唯一性,揭示了织物内热湿传递变化规律.应用L-曲线方法获得了正则化参数的最优选择,采用粒子群最优化算法随机搜索目标函数极小值点,得到反问题的广义解.数值模拟结果验证了纺织材料孔隙率决定反问题提法的合理性和算法的有效性.Besides the thickness and thermal conductivity of fabrics, the porosity of fabrics is an important factor on the heat-moisture comfort of human body. This paper presents an inverse problem of textile porosity determination （IPTPD for short） in dynamic heat and moisture transfer. The IPTPD is formulated into a function minimization problem by means of the Tikhonov regularization method. The law of heat-moisture transfer in fabrics is displayed by proving the existence and uniqueness of the solution to the direct problem by means of the Banach＇s fixed-point theorem. The authors adopt the L-curve method todetermine the optimal regularized parameter, and use the particle swarm optimization （PSO for short） method to stochastically search the minimizer of the objective function and hence obtain the generalized solution to the IPTPD. The result of the numerical simulation shows the reasonability of IPTPD and the efficiency of the proposed algorithms.

关 键 词：反问题 最优孔隙率决定 吉洪诺夫正则化 粒子群算法 纺织材料 适定性 

分 类 号：O241.8[理学—计算数学]