功能性纺织材料设计反问题的数学模型与数值算法

项目名称： 功能性纺织材料设计反问题的数学模型与数值算法

项目编号： No.11471287

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 徐定华

作者单位： 浙江理工大学

项目金额： 65万元

中文摘要： 该项目着力研究具多层结构的功能性纺织材料设计反问题。该项目能为功能性纺织材料（如轻薄型高保温纺织材料、隔热好的热防护服装等）的研发提供理论基础，为多孔介质材料的研制提出新思路。 ..正问题的研究：由于功能性纺织材料的轻薄性、多孔与多层性，并伴随着热力过程（热传导、热辐射、热对流、汽化、凝结等），其数学模型往往是复杂的耦合偏微分方程组定解问题。将基于热湿传递规律建立多区域分数阶耦合偏微分方程组，并利用现代数学理论与方法研究其适定性，构造高性能的数值算法。.. 反问题的研究：提出满足材料设计目标（如高保温、轻薄、防水隔热、人体舒适度等）的若干类反问题，如决定材料的层数与厚度、孔隙率、热传导系数、水汽传递系数等。研究反问题的条件适定性，提出解的概念，并构造目标泛函和数值算法，结合稳定化算法获得反问题的最优解或正则化解，理论上证明算法的稳定性与收敛率。通过贝叶斯推断和随机搜索实现多参数的同时决定。

中文关键词： 反问题；纺织材料设计；分数阶偏微分方程；正则化方法；贝叶斯推断

英文摘要： The project focuses on inverse problems of multilayer functional textiles design. The project will provide theoretical foundation for the development of functional textile materials (such as light-thin insulation clothes, thermal protective clothing etc.) and put forward new strategies for the development of new porous medium materials. The research on Direct Problems (DP): Due to the characteristics of the functional textile materials such as small thickness, porous and multi-layered structure, the mathematial models contain the complicated thermal process (conduction, radiation, convection, vaporization and condensation, etc.), which can be formulated as well-posed problems with complicated coupled differential equations. Accordding to the heat-moisture transfer law, we will propose multidomain fractional partial differential equations and analyse well-posedness of the mathematical model by means of modern mathematical theory, and construct high-performance numerical algorithms. The research on Inverse Problems (IP): Several inverse problems which meet materials design objectives (for example clothing heat-moisture comfort,thermal protective clothing, light weight clothes，etc. ) will be presented, for instance,the determination of material layers and thickness, thermal conductivity, porosity, vapor transfer coefficient and so on. We will present the solution concept of inverse design problems and study the conditional well-poseedness of the inverse problems. Furthermore, we will construct objective functionals and stabilized numerical algorithms, prove the stability and convergence rate of the algorithms theoretically and obtain the optimal solution or regularization solution of the inverse problems. Simultaneous determination of multiple parameters will be realized by means of Bayesian inference methods and stochastic search methods.

英文关键词： Inverse problems;Textile Material Design;Fractional Partial Differential Equations;Regularization Methods;Bayesian Inference