| 徐定华,文雷.基于动态热湿传递的纺织材料孔隙率决定的反问题[J].数学年刊A辑,2014,35(2):129~144 |
| 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 andMoisture Transfer |
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| DOI： |
| 中文关键词: 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 |
| 英文关键词:Inverse problems, Optimal porosity determination, Tikhonov regularization, Particle swarm optimization method,
Textile materials, Well-posedness |
| 基金项目: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) |
| Author Name | Affiliation | E-mail | | XU Dinghua | Engineering Research Center of Clothing of Zhejiang Province, Zhejiang Sci-Tech University,
Hangzhou 310018, China
Department of Mathematics, College of Sciences, Zhejiang Sci-Tech University,
Hangzhou 310018, China. | dhxu6708@zstu.edu.cn | | WEN Lei | Department of Mathematics, College of Sciences, Zhejiang Sci-Tech University,
Hangzhou 310018, China. | wen llei@163.com |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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 to determine 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. |
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