基于遗传算法的多层热防护服装的热传递模型

Thermal Transfer Model of Multilayer Thermal Protective Clothing Based on Genetic Algorithm

摘要: 本文以2018年全国大学生数学建模A题为例，利用热传导方程建立数学规划模型，研究了不同温度约束下的最佳防护服厚度问题。首先，用遗传算法求解得防护服温度空间分布表。其次，利用最小二乘法求第II层最优厚度d₂ = 10.6 mm。目标函数为服装质量时d₂ = 11.4 mm，d₄ = 1.6 mm；目标函数为服装体积时d₂ = 9.8 mm，d₄ = 5.8 mm；目标函数为服装厚度时d₂ = 10.7 mm，d₄ = 20 mm。该模型在战场、消防、石油化工、金属冶炼等环境中均能得到较好的推广，保护工作人员免受高温高辐射危害，为处于特定环境下的人体提供保护屏障。

Abstract: In this paper, we used the heat conduction equation to establish a mathematical programming model and studied the optimal protective clothing thickness model under different temperature constraints by taking the problem A in the Contemporary Undergraduate Mathematical Contest (CUMCM) in 2018 as an example. Firstly, we used the genetic algorithm to obtain the temperature spatial distribution table of the protective clothing. Secondly, we used the least-squares method to find the optimal thickness of the second layer of the clothing, d₂ = 10.6 mm. When the optimization goal is the weight of the clothing, d₂ = 11.4 mm, d₄ = 1.6 mm; when the optimization goal is the volume of the clothing, d₂ = 9.8 mm, d₄ = 5.8 mm; when the optimization goal is the thickness of the clothing, d₂ = 10.7 mm, d₄ = 20 mm. The model can be better promoted in the battlefield, fire, pet-rochemical, metal smelting and other environments to protect the staff from high temperature. High radiation hazard provides a protective barrier for the human body in a specific environment.