基于热湿传递二维模型的纺织材料孔隙率决定反问题
Inverse Problem of DeterminingPorosity in Textile Materials Based on a Two-Dimensional Heat and Moisture Transfer Model
摘要: 本文研究了基于织物的二维动态热湿传递模型的纺织材料孔隙率最优决定反问题。首先改进一个低温条件下织物的二维动态热湿传递模型，将其边界条件修正为第二类边界条件，使其更符合实际情况，采用有限差分方法求解该模型,接着基于该二维热湿传递模型，根据低温条件下服装保暖透湿性最佳提出反问题，利用透湿指数建立反问题数学模型，并用粒子群算法进行计算。最后给出数值实例，将粒子群算法计算结果与遍历算法结果进行比较，说明算法的有效性。
Abstract: This paper explores the inverse problem of optimally determining the porosity of tex-tile materials based on a two-dimensional dynamic heat and moisture transfer model tailored for fabrics. Initially, an existing two-dimensional dynamic heat and moisture transfer model for fabrics under low-temperature conditions is refined by adjusting its boundary conditions to the second-type boundary conditions, enhancing its realism. The finite difference method is utilized to solve this refined model. Furthermore, based on this two-dimensional heat and moisture transfer model, an inverse problem is formulated with the aim of optimizing the thermal insulation and moisture perme- ability of clothing under low-temperature conditions. A mathematical model for this inverse problem is constructed using the moisture permeability index, and is solved through the application of the Particle Swarm Optimization (PSO) algorithm. Lastly, numerical examples are presented, comparing the results obtained from the PSO al- gorithm with those derived from the exhaustive search algorithm, thereby illustrating the effectiveness of the proposed algorithm.
文章引用：黄涛玺. 基于热湿传递二维模型的纺织材料孔隙率决定反问题[J]. 理论数学, 2024, 14(12): 138-154. https://doi.org/10.12677/PM.2024.1412415

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