全国数学建模大赛A题获奖论文英文版English.docx

1、全国数学建模大赛A题获奖论文英文版EnglishThe Evaluation of WinesSummaryThe general way is to employ a number of qualified wine critics to taste the wines when needing to determine the quality of the wines. But the grapes of making wines are able to influence the quality of the wines in acertain extent. In Task 1, we

2、 firstly solve the arithmetic mean to the two groups of the same sample wine ratings of Appendix I of the wine critic Members , then prove and verify two groups Tasting ratings results have the existence of significant differences using SPSS software by paired T test ,finally solve the second assess

3、ment wine group more reliable by analysis of variance method.In Task 2, by an accurate analysis of the impact of the physical and chemical indicators of wine grape and the quality of wine to wine grapes ,we extract the principal component that embodies the basic characteristics of the object of stud

4、y, so we can reduce redundancy, and reduce the dimension of the physical and chemical indicators of wine grapes, which of the various samples conduct a comprehensive evaluation and ranking grapes .Red grapes into four categories on this basis, the three levels of white grape.In Task 3, we analyze th

5、e correlation degree of both using the typical correlation, it is concluded that both has the very high correlation, that is, the better the quality of wine grape, the higher the quality of the wine.In Task 4, we again use SPSS software to visually show the correlation coefficient between the three

6、study and concluded that the impact on wine quality is more than two, there are other factors not taken into account. Through the Third Schedule aromatic substances added argumentation analysis, we have confirmed the larger factors exist .Physical and chemical indicators of wine grapes and wine can

7、not be very accurate assessment of the quality of the wine, you can consider the introduction of a sensory analysis of taste and smell.Keywords: Paired samples T-test Principal Component Analysis Canonical- correlation analysis Path AnalysisIntroductionThe general way is to employ a number of qualif

8、ied wine critics to tast the wines when needing to determine the quality of the wines. First,each tasting member in the taste of the wine samples give rates in accordance with the classification index, then sum the total scores to determine the quality of the wines. Quality of wine grape has a direc

9、t bearing with the quality of the wines. the physical and chemical indicators of wine grape and the wine can reflect the quality of the wine and grape to some extent. Following issues need to be addressed :1. Analysis in Annex 1 two groups of evaluation of wine member of the evaluation results wheth

10、er there were significant differences of both, which a set of results more reliable.2. According to the physical and chemical indicators of the wine grape and wine quality, how about were these wine grape classified ?3. Analyze the link between the physical and chemical indicators of wine grapes and

11、 wine.4. Analyze the physical and chemical index of the wine grape and wine to the influence on the quality of wine, and demonstrate the ability to use the physical and chemical indicators of grape and wine to evaluate the quality of the wine.The analysis of issueBackgroundThe high-quality wines are

12、 popular in 2012. Its seems to be urgent to study that the main raw materials - whether the quality of the red grapes and white grapes of the wine is good or bad a decisive role. Therefore analyzed the relationship between wines and grapes quality and physical and chemical indicators over thirty kin

13、ds of physical and chemical indicators of grape and wine.Assumptions1 Each tasting wine samples from an approximate normal distribution of the distribution of the overall；2 Tasting members are normal senses, there is not much difference；3 Annex all the physical and chemical indicators can be represe

14、ntative of the nature of the study, omission of the object of study have a significant impact on physical and chemical indicators；Symbolic representation： Significant parameters；： Rejection region range；： The number of indicator variables；： Evaluation object； Standardized index value；： Sample mean a

15、nd sample standard deviation of the j-th indicator；: Correlation coefficient matrix；: Standardized matrix; Eigenvalue； Eigenvectors； Eigenvectors of the correlation coefficient matrix of red wine grapes; Red wine grape correlation coefficient matrix eigenvalue; White wine grape correlation coefficie

16、nt matrix of eigenvectors; Eigenvalues of the correlation matrix of white wine grapes; The characteristic value corresponding to the first, second . p main componen； The number of indicators in the wine； The number of indicators of the wine grape； The coefficient matrix of the first set of variables

17、； The coefficient matrix of the second set of variables；、 The correlation coefficient of the first set of variables and the second set of variables； Comprehensive evaluation function of the principal component of red grape wine grape； Comprehensive evaluation function of the principal components of

18、the white grape wine grape； Transverse section of physical and chemical indicators in accordance with Annex II to turn on behalf of the 27-level indicators of the total amino acids, proteins, VC, ., as well as wine quality and wine quality ratings; Wine quality, peel quality juice rate (%), respecti

19、vely, in turn, said, stems ratio (%), one hundred quality / g, ear quality / g dry matter content g/100g solid acid than titratable acidity (g/l), PH value, soluble solids g/l, the reducing sugars g/L, total sugar g/L, and flavonols (mg/kg), resveratrol (mg/kg) and other physical and chemical indica

20、tors；Model establishments and solutionsTask1：Analysis in Annex 1 two groups of evaluation of wine member of the evaluation results whether there were significant differences of both, which a set of results more reliable.To review the wine member of the evaluation result, significant difference and c

21、redibility evaluation calculation methods are varied，mainly including Sensory evaluation of significant differences, based on the evaluation of the credibility of the Analytic Hierarchy Process, discriminant analysis, T value analysis, F value analysis,etc.Firstly, in accordance with the principle o

22、f the score with the same sample that 10 Tasting average score obtained in Schedule I of the first and second sets each red and white wine sample tasting ratings. Are listed below:Table 1 Red wine tasting Average Rating of the first and second SetsWine samples123456789FirstSet62.780.380.468.673.372.

23、271.572.381.5SecondSet68.17474.671.272.166.365.36678.2Wine samples101112131415161718FirstSet74.270.153.974.67358.774.979.359.9SecondSet68.861.668.368.872.665.769.974.565.4Wine samples192021222324252627FirstSet78.678.677.177.285.67869.273.873SecondSet72.675.872.271.677.171.568.27271.5Table 2 White wi

24、ne tasting Average Rating of the first and second SetsWine samples12345678910FirstSet8274.278.379.47168.477.571.472.974.3SecondSet77.975.875.676.981.575.574.272.380.479.8Wine samples111213141516171819FirstSet72.363.365.97272.47478.873.172.2SecondSet71.472.473.977.178.467.380.376.776.4Wine samples202

25、122232425262728FirstSet77.876.47175.973.377.181.364.881.3SecondSet76.679.279.477.476.179.574.37779.6Comparing of the two sets of data, we can visually see the values in the above two tables of very difference.Establishments of Model 11-1 For the evaluation of red wine :First of all by the data obser

26、vation, it is known that on the whole, in view of the same sample wine in the first group and the second group of score difference are more prominent，therefore the relationship between the two with a Broken line vividly expressed. From the sensory ,image display greater differences in two groups Tas

27、ting set of evaluation criteria, shown in the following figure line chart:Figure 1 the overall rating of FirstSet and SecondSet for each of the red wine samplesThen, the overall rating results of the two rating wine group in a significant level are made a significant difference test. Firstly, each w

28、ine sample is selected from the large number of the same kind of samples wine from testing samples ,sample population can be approximated as a normal distribution . Secondly, Of all samples tested constitute 27 paired samples tested overall. Therefore we paired samples T-test two samples. The result

29、s are as follows:Table 3 The paired samples T-test the first and second Sets(The red)Inspectionobjectthe difference with95% confidence intervaltNPLower limitCeilingFirst and Second0.415694.665792.458260.021 In fact, Pand, the result falls into Rejection region.Therefore the overall evaluation criter

30、ia of the members of the two groups of wine critic has a significant difference.Which is trustworthier : The smaller the variance,the trustworthier the groups evaluate ,when we study a single kind of wine sample. In that ,we compare the variance of these two groups to define the trustworthier group which have a smaller variance .Table 4 The credibility test for red wineWine samplesFirstSetsVariance SecondsVarianceThe trustworthier groupWine samplesFirstSetsVariance SecondsVarianceThe trustworthier group1236.1736.9一15770.1372.1二2358.1146二16112.9180.9一3412