功能性纺织材料设计反问题的数学模型与数值算法

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.

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。

该项目聚焦具多层结构的功能性纺织材料设计反问题研究。该项目的研究为功能性纺织材料（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，也为多孔介质材料的研制提出新思路。..针对正问题：获得了耦合偏微分方程组定解问题、分数阶偏微分方程模型。基于热湿传递规律建立了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条件适定性，构造了高性能的数值算法。发表了正问题论文八篇。..针对反问题：提出了满足材料设计目标的若干类反问题，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。研究了反问题的条件适定性，提出了解的概念，并构造了目标泛函和数值算法，获得了反问题的最优解或正则化解。通过贝叶斯推断和随机搜索实现多参数的同时决定。发表了论文十三篇。