玻璃文物成分分析与鉴别的数学模型  

Mathematical Model of Composition Analysis and Identification of Glass Relics

作　　者：张梦婷 游慧玲 张和涛 全然[1] Zhang Mengting;You Huiling;Zhang Hetao;Quan Ran(School of Science,Henan University of Technology,Zhengzhou 450001,China;School of Chemistry and Chemical Engineering,Henan University of Technology,Zhengzhou 450001,China;School of Management,Henan University of Technology,Zhengzhou 450001,China)

机构地区：[1]河南工业大学理学院,郑州450001 [2]河南工业大学化学化工学院,郑州450001 [3]河南工业大学管理学院,郑州450001

出　　处：《黑龙江科学》2024年第4期44-50,共7页Heilongjiang Science

基　　金：“常微分方程”课程的教学改革探索。

摘　　要：针对2022年全国大学生数学建模竞赛C题“玻璃文物的成分分析与鉴别问题”中的4个问题分别进行建模分析,根据玻璃文物的化学成分含量、纹饰及颜色等数据,基于单因素方差分析,探究玻璃文物的表面风化与玻璃类型、纹饰及颜色的关系,建立ARIMA模型,预测风化前玻璃文物的化学成分含量;通过主成分分析提取玻璃文物的分类特征,结合聚类算法进行亚类划分;通过基于欧氏距离的聚类算法鉴别未知玻璃文物的类别,分析玻璃文物分类结果的敏感性;通过K-Means++聚类算法分析不同类别玻璃文物的关联关系,对不同类别玻璃文物关联关系的差异性进行判断,给出结论。According to the four problems in the question C“Composition Analysis and Identification of Glass Relics”in 2022 China Undergraduate Mathematical Contest in Modeling,the corresponding mathematical models are built and analyzed respectively.Based on the data of chemical composition content,decoration and color of the glass relics,and based on the one-way ANOVA,the study establishes ARIMA model to explore the relationship between the surface weathering of glass relics and the type,decoration and color of glass,and to predict the chemical content of glass relics before weathering.The classification characteristics of the glass relics are extracted by principal component analysis,and the subcategory division is given by cluster algorithm.The unknown categories of the glass relics are identified by Euclidean distance cluster algorithm and the sensitivity of the classification results of the glass relics is analyzed.The K-Means++cluster algorithm is used to analyze the relationship between different categories of the glass relics and to judge the difference of relationship between different categories of the glass relics.Finally,the conclusion is given.

关 键 词：玻璃文物 单因素方差分析 聚类分析 主成分分析 ARIMA模型 K-Means++聚类 

分 类 号：O29[理学—应用数学]