基于成分数据的古代玻璃制品的成分分析与鉴别  

Composition Analysis and Identification of Ancient Glass Products Based on Compositional Data

作　　者：黄慧婷 李春明 刘思语 毛睿[1] HUANG Huiting;LI Chunming;LIU Siyu;MAO Rui(School of Mathematics and Computing Science,Guilin University of Electronic Science and Technology,Guilin,Guangxi 541004,China;School of Computer and Information Security,Guilin University of Electronic Science and Technology,Guilin,Guangxi 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]桂林电子科技大学计算机与信息安全学院,广西桂林541004

出　　处：《数学建模及其应用》2023年第2期52-62,124,共12页Mathematical Modeling and Its Applications

摘　　要：根据一批我国古代玻璃制品的相关检测数据,对这些古代玻璃制品进行风化规律的研究,并根据风化规律进行分类,同时给出玻璃制品风化前的预测模型.首先,利用卡方检验分析风化与颜色、玻璃类型以及纹饰间的关系,并通过回归方程建立化学成分趋势变换模型以预测风化前的化学成分含量;然后,采用决策树法和以R型聚类法得到特征变量为基础的Q型聚类对玻璃制品进行亚类分类,并进行了合理性和敏感性分析;第三,利用前述分类模型对未知类别玻璃文物的化学成分进行分析并得到其所属类型;最后,应用灰色关联分析,针对不同的玻璃文物,分析其化学成分之间的关联关系.Based on a group of ancient glass objects in China,we studied the weathering pattern of these ancient glass objects,classified them according to the weathering pattern,and gave a prediction model for the weathering of glass objects before weathering.First,the relationship between weathering and color,glass type and ornamentation was analyzed by chi-square test,and the chemical composition trend transformation model was established by regression equation to predict the chemical composition content before weathering;then,the decision tree method and Q-type clustering based on R-type clustering method were used to classify the glass artifacts into subcategories,and the rationality and sensitivity analysis were conducted;third,the chemical composition of the un Third,the chemical composition of glass artifacts in the middle category was analyzed and their genus types were obtained using the aforementioned classification model;finally,grey correlation analysis was applied to analyze the correlations between the chemical composition of different glass artifacts.

关 键 词：中心化对数变换 卡方检验 决策树法 聚类分析 灰色关联分析 

分 类 号：O29[理学—应用数学]