R_2O-MO-Al_2O_3-SiO_2玻璃配方与热膨胀系数关系的支持向量回归研究  

Study on the relationship between thermal expansion coefficient and oxide composition of R_2O-MO-Al_2O_3-SiO_2 system glass via support vector regression approach

作　　者：温玉锋[1] 蔡从中[1] 裴军芳[1] 朱星键[1] 肖婷婷[1] 

机构地区：[1]重庆大学应用物理系,重庆400044

出　　处：《功能材料》2009年第1期66-70,74,共6页Journal of Functional Materials

基　　金：教育部新世纪优秀人才支持计划资助项目(NCET-07-0903);教育部留学回国人员科研启动基金资助项目(教外司留[2008]101-1);重庆市自然科学基金资助项目(2006BB5240);国家大学生创新性实验计划资助项目(CQUCX-G-2007-016)

摘　　要：不同配方的玻璃一般具有不同的热膨胀系数。根据R2O-MO-Al2O3-SiO2(R为碱金属元素,M为碱土金属元素)系统玻璃在不同氧化物组成(SiO2,MgO,CaO,SrO,BaO,Na2O和K2O)下的热膨胀系数实测数据集,应用基于粒子群算法(PSO)寻优的支持向量回归(SVR)方法,建立了玻璃的不同配方与其热膨胀系数关系的SVR预测模型,并与基于BPNN神经网络模型的预测结果进行了比较。结果表明:对于相同的训练样本和检验样本,支持向量回归的玻璃的热膨胀系数模型始终比BPNN模型具有更高的预测精度;增加训练样本数有助于提高所建SVR预测模型的泛化能力;基于留一交叉验证法(LOOCV)的SVR预测的均方根误差(RMSE)、平均绝对误差(MAE)和平均绝对百分误差(MAPE)均为最小。本研究表明:SVR是一种预测不同配方玻璃的热膨胀系数的有效方法。In general, glass with different composition possesses different thermal expansion coefficients. Based on the experimental dataset, the support vector regression （SVR） approach combined with particle swarm optimization （PSO） for parameter optimization, is proposed to establish a model for simulating the relationship between thermal expansion coefficient and oxide composition （i. e. , SiO2, MgO, CaO, SrO, BaO, Na2O and K2O） of R2O-MO-Al2O3-SiO2 system glass （R stands for alkali metal element and M stands for alkaline earth element）. The comparison of prediction results demonstrates that the generalization ability of SVR model consistently surpasses that of BP neural network （BPNN） by applying identical training and test samples. For SVR, it was revealed that the estimated error, such as root mean squared error （RMSE）, mean absolute error （MAE） and mean absolute percentage error （MAPE）, can be all efficiently reduced by increasing the number of training samples. Therefore, the best forecast results along with the smallest RMSE, MAE and MAPE of glass thermal expansion coefficient dataset are provided by LOOCV test of SVR. This suggests that SVR is an effective and powerful technique for the estimation of glass thermal expansion coefficient with different oxide composition.

关 键 词：玻璃 热膨胀系数 支持向量机 粒子群算法 留一交叉验证法 回归分析 预测 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O551.3[自动化与计算机技术—控制科学与工程]