非齐次线性方程组在求解最优玻璃料方中的应用  

Application of Non⁃Homogeneous Linear Equations in Solving Optimal Glass Squares

作　　者：黄钰 骞少阳 任强 马骏 张新新 李宁 HUANG Yu;QIAN Shaoyang;REN Qiang;MA Jun;ZHANG Xinxin;LI Ning(Hebei Panel glass Co.,Ltd.,Lang fang 065000,China;Hebei Province Company Technology Center,Lang fang 065000,China;Hebei Province Ultra-Thin Electronic Glass Technology Innovation Center,Lang fang 065000,China)

机构地区：[1]河北视窗玻璃有限公司,廊坊065000 [2]河北省企业技术中心,廊坊065000 [3]河北省超薄电子玻璃技术创新中心,廊坊065000

出　　处：《玻璃搪瓷与眼镜》2024年第4期1-5,19,共6页Glass Enamel & Ophthalmic Optics

摘　　要：浮法玻璃生产中料方成分的变更或波动对成品玻璃质量有显著的影响。通过解析原料及其所含化合物的数据结构,确定各种原料的用量,挖掘最接近目标料方的优化方案,是浮法玻璃料方计算领域中的重要研究内容。研究发现,原料及其所含化合物、目标料方可用非齐次线性方程组的系数矩阵、常数项列向量表示,计算最优料方中各原料的用量问题可以转化为非齐次线性方程组求解。在方程组有解的情况下,求解得到最优料方;在方程组无解但有最优解的情况下,通过搭配使用非齐次线性方程组和最小二乘法可以求解最优料方。此计算方案能维持或提高料方计算结果的精度,同时也能提高原料工程师在计算料方中的工作效率,从而产生实际的经济效益,可广泛应用于浮法玻璃料方计算。In the production of float glass processes,changes or fluctuations in the composition of the material side have a significant impact on the quality of the finished glass.By analyzing the data structure of raw materials and compounds contained in raw materials,determining the amount of various raw materials,getting the optimal material side closest to the target material side,the application in the field of float glass material calculation is particularly important and necessary.Through the analysis,it is found that the raw materials and the compounds and target materials contained in the raw materials can be expressed by the coefficient matrix and constant term series vectors of the non-homogeneous linear equation system,respectively,so that the calculation of the amount of each raw material in the optimal material square can be converted into a problem solved by the non-homogeneous linear equation system.It is concluded that when there is a solution to the nonhomogeneous linear equation system,the optimal material square can be solved by the non-homogeneous linear equation system.In the case where there is no solution but there is an optimal solution,the optimal material square can be solved by combining a system of non-homogeneous linear equations and the least squares method.This calculation scheme can be widely used in float glass side calculation,which can not only maintain or improve the accuracy of the material side calculation results,but also improve the work efficiency of raw material engineers in calculating the material side,thereby generating actual economic benefits.

关 键 词：非齐次线性方程组 浮法玻璃 玻璃料方 应用数学 

分 类 号：TQ171.1[化学工程—玻璃工业]