汕头大学学报（自然科学版）

本文是对2012年全国大学生数学建模竞赛A题的解答,建立了葡萄酒质量的评价模型,对葡萄和葡萄酒的理化指标与其质量的关系进行了分析.在问题1中,通过非参数检验方法检验这两组品酒员对酒的打分是否有显著性差异,利用协和系数分析检验两组品酒员对酒的打分的可靠程度.在问题2中,采用了基于SOM网络的等级分类和SPSS的聚类分析对酿酒葡萄进行分类,然后根据每一类葡萄酒得分均值对葡萄进行分级.在问题3中,以葡萄的指标数据为输入层,葡萄酒的指标数据为输出层,建立BP广义回归神经网络模型,得到两者之间的定量关系.在问题4中,首先采用灰关联模型,得出酿酒葡萄和葡萄酒理化指标和葡萄酒质量的关联度,然后建立支持向量机的回归拟合模型,得到葡萄酒和酿酒葡萄的理化指标与葡萄酒质量之间的定量关系.

In this paper,a solution is presented for the Problem A of Contemporary Undergraduate Mathematical Contest in Modeling in 2012.Several evaluation models of grape wine quality were built.The relationship between physical-chemical indexes of grape and the quality of grape wine was discussed.Whether there is some significant differences between the scores of two groups of wine tasters was analyzed using non parametric testing method for Question 1.The degree of reliability of two groups of wine tasters by coefficient of concordance was verified.Two models were setup for Question 2.One is the SOM neural network model and the other is the cluster analysis model.The average score of grape wine was used to classify the degree of grape.Using a BP generalized regression neural network model,a quantitative relationship between physical-chemical indexes of grape and indexes of grape wine is obtained for Question 3.The grey relational model was adopted for Question 4.The grey correlation degree between physical-chemical indexes of grape and the quality of grape wine was obtained.Using support vector machine(SVM) regression fitting model,a quantitative relationship between physical-chemical indexes of grape and the quality of grape wine was examined.