全国数学建模大赛A题获奖论文英文版English.docx
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全国数学建模大赛A题获奖论文英文版English
TheEvaluationofWines
Summary
Thegeneralwayistoemployanumberofqualifiedwinecriticstotastethewineswhenneedingtodeterminethequalityofthewines.Butthegrapesofmakingwinesareabletoinfluencethequalityofthewinesinacertainextent.
InTask1,wefirstlysolvethearithmeticmeantothetwogroupsofthesamesamplewineratingsofAppendixIofthewinecriticMembers,thenproveandverifytwogroupsTastingratingsresultshavetheexistenceofsignificantdifferencesusingSPSSsoftwarebypairedTtest,finallysolvethesecondassessmentwinegroupmorereliablebyanalysisofvariancemethod.
InTask2,byanaccurateanalysisoftheimpactofthephysicalandchemicalindicatorsofwinegrapeandthequalityofwinetowinegrapes,weextracttheprincipalcomponentthatembodiesthebasiccharacteristicsoftheobjectofstudy,sowecanreduceredundancy,andreducethedimensionofthephysicalandchemicalindicatorsofwinegrapes,whichofthevarioussamplesconductacomprehensiveevaluationandrankinggrapes.Redgrapesintofourcategoriesonthisbasis,thethreelevelsofwhitegrape.
InTask3,weanalyzethecorrelationdegreeofbothusingthetypicalcorrelation,itisconcludedthatbothhastheveryhighcorrelation,thatis,thebetterthequalityofwinegrape,thehigherthequalityofthewine.
InTask4,weagainuseSPSSsoftwaretovisuallyshowthecorrelationcoefficientbetweenthethreestudyandconcludedthattheimpactonwinequalityismorethantwo,thereareotherfactorsnottakenintoaccount.ThroughtheThirdSchedulearomaticsubstancesaddedargumentationanalysis,wehaveconfirmedthelargerfactorsexist.Physicalandchemicalindicatorsofwinegrapesandwinecannotbeveryaccurateassessmentofthequalityofthewine,youcanconsidertheintroductionofasensoryanalysisoftasteandsmell.
Keywords:
PairedsamplesT-testPrincipalComponentAnalysisCanonical-correlationanalysisPathAnalysis
Introduction
Thegeneralwayistoemployanumberofqualifiedwinecriticstotastthewineswhenneedingtodeterminethequalityofthewines.First,eachtastingmemberinthetasteofthewinesamplesgiveratesinaccordancewiththeclassificationindex,thensumthetotalscorestodeterminethequalityofthewines.Qualityofwinegrapehasadirectbearingwiththequalityofthewines.thephysicalandchemicalindicatorsofwinegrapeandthewinecanreflectthequalityofthewineandgrapetosomeextent.Followingissuesneedtobeaddressed:
1.AnalysisinAnnex1twogroupsofevaluationofwinememberoftheevaluationresultswhetherthereweresignificantdifferencesofboth,whichasetofresultsmorereliable.
2.Accordingtothephysicalandchemicalindicatorsofthewinegrapeandwinequality,howaboutwerethesewinegrapeclassified?
3.Analyzethelinkbetweenthephysicalandchemicalindicatorsofwinegrapesandwine.
4.Analyzethephysicalandchemicalindexofthewinegrapeandwinetotheinfluenceonthequalityofwine,anddemonstratetheabilitytousethephysicalandchemicalindicatorsofgrapeandwinetoevaluatethequalityofthewine.
Theanalysisofissue
Background
Thehigh-qualitywinesarepopularin2012.It’sseemstobeurgenttostudythatthemainrawmaterials-whetherthequalityoftheredgrapesandwhitegrapesofthewineisgoodorbadadecisiverole.Thereforeanalyzedtherelationshipbetweenwines’andgrapes’qualityandphysicalandchemicalindicatorsoverthirtykindsofphysicalandchemicalindicatorsofgrapeandwine.
Assumptions
1Eachtastingwinesamplesfromanapproximatenormaldistributionofthedistributionoftheoverall；
2Tastingmembersarenormalsenses,thereisnotmuchdifference；
3Annexallthephysicalandchemicalindicatorscanberepresentativeofthenatureofthestudy,omissionoftheobjectofstudyhaveasignificantimpactonphysicalandchemicalindicators；
Symbolicrepresentation
：
Significantparameters；
：
Rejectionregionrange；
：
Thenumberofindicatorvariables；
：
Evaluationobject；
Standardizedindexvalue；
：
Samplemeanandsamplestandarddeviationofthej-thindicator；
:
Correlationcoefficientmatrix；
:
Standardizedmatrix;
Eigenvalue；
Eigenvectors；
Eigenvectorsofthecorrelationcoefficientmatrixofredwinegrapes;
Redwinegrapecorrelationcoefficientmatrixeigenvalue;
Whitewinegrapecorrelationcoefficientmatrixofeigenvectors;
Eigenvaluesofthecorrelationmatrixofwhitewinegrapes;
Thecharacteristicvaluecorrespondingtothefirst,second......pmaincomponen；
Thenumberofindicatorsinthewine；
Thenumberofindicatorsofthewinegrape；
Thecoefficientmatrixofthefirstsetofvariables；
Thecoefficientmatrixofthesecondsetofvariables；
、
Thecorrelationcoefficientofthefirstsetofvariablesandthesecondsetofvariables；
Comprehensiveevaluationfunctionoftheprincipalcomponentofredgrapewinegrape；
Comprehensiveevaluationfunctionoftheprincipalcomponentsofthewhitegrapewinegrape；
TransversesectionofphysicalandchemicalindicatorsinaccordancewithAnnexIItoturnonbehalfofthe27-levelindicatorsofthetotalaminoacids,proteins,VC,......,aswellaswinequalityandwinequalityratings;
Winequality,peelqualityjuicerate（%）,respectively,inturn,said,stemsratio（%）,onehundredquality/g,earquality/gdrymattercontentg/100gsolidacidthantitratableacidity（g/l）,PHvalue,solublesolidsg/l,thereducingsugarsg/L,totalsugarg/L,andflavonols（mg/kg）,resveratrol（mg/kg）andotherphysicalandchemicalindicators；
Modelestablishmentsandsolutions
Task1：
AnalysisinAnnex1twogroupsofevaluationofwinememberoftheevaluationresultswhetherthereweresignificantdifferencesofboth,whichasetofresultsmorereliable.
Toreviewthewinememberoftheevaluationresult,significantdifferenceandcredibilityevaluationcalculationmethodsarevaried，mainlyincludingSensoryevaluationofsignificantdifferences,basedontheevaluationofthecredibilityoftheAnalyticHierarchyProcess,discriminantanalysis,Tvalueanalysis,Fvalueanalysis,etc.
Firstly,inaccordancewiththeprincipleofthescorewiththesamesamplethat10Tasting'averagescoreobtainedinScheduleIofthefirstandsecondsetseachredandwhitewinesampletastingratings.Arelistedbelow:
Table1RedwinetastingAverageRatingofthefirstandsecondSets
Winesamples
1
2
3
4
5
6
7
8
9
FirstSet
62.7
80.3
80.4
68.6
73.3
72.2
71.5
72.3
81.5
SecondSet
68.1
74
74.6
71.2
72.1
66.3
65.3
66
78.2
Winesamples
10
11
12
13
14
15
16
17
18
FirstSet
74.2
70.1
53.9
74.6
73
58.7
74.9
79.3
59.9
SecondSet
68.8
61.6
68.3
68.8
72.6
65.7
69.9
74.5
65.4
Winesamples
19
20
21
22
23
24
25
26
27
FirstSet
78.6
78.6
77.1
77.2
85.6
78
69.2
73.8
73
SecondSet
72.6
75.8
72.2
71.6
77.1
71.5
68.2
72
71.5
Table2WhitewinetastingAverageRatingofthefirstandsecondSets
Winesamples
1
2
3
4
5
6
7
8
9
10
FirstSet
82
74.2
78.3
79.4
71
68.4
77.5
71.4
72.9
74.3
SecondSet
77.9
75.8
75.6
76.9
81.5
75.5
74.2
72.3
80.4
79.8
Winesamples
11
12
13
14
15
16
17
18
19
FirstSet
72.3
63.3
65.9
72
72.4
74
78.8
73.1
72.2
SecondSet
71.4
72.4
73.9
77.1
78.4
67.3
80.3
76.7
76.4
Winesamples
20
21
22
23
24
25
26
27
28
FirstSet
77.8
76.4
71
75.9
73.3
77.1
81.3
64.8
81.3
SecondSet
76.6
79.2
79.4
77.4
76.1
79.5
74.3
77
79.6
Comparingofthetwosetsofdata,wecanvisuallyseethevaluesintheabovetwotablesofverydifference.
EstablishmentsofModel1
1-1Fortheevaluationofredwine:
Firstofallbythedataobservation,itisknownthatonthewhole,inviewofthesamesamplewineinthefirstgroupandthesecondgroupofscoredifferencearemoreprominent，thereforetherelationshipbetweenthetwowithaBrokenlinevividlyexpressed.Fromthesensory,imagedisplaygreaterdifferencesintwogroupsTastingsetofevaluationcriteria,showninthefollowingfigurelinechart:
Figure1theoverallratingofFirstSetandSecondSetforeachoftheredwinesamples
Then,theoverallratingresultsofthetworatingwinegroupinasignificantlevel
aremadeasignificantdifferencetest.Firstly,eachwinesampleisselectedfromthelargenumberofthesamekindofsampleswinefromtestingsamples,samplepopulationcanbeapproximatedasanormaldistribution.Secondly,Ofallsamplestestedconstitute27pairedsamplestestedoverall.ThereforewepairedsamplesT-testtwosamples.Theresultsareasfollows:
Table3ThepairedsamplesT-testthefirstandsecondSets（Thered）
Inspection
object
thedifferencewith
95%confidenceinterval
t
N
P
Lowerlimit
Ceiling
FirstandSecond
0.41569
4.66579
2.458
26
0.021
Infact,P<
and
theresultfallsintoRejectionregion
.Thereforetheoverallevaluationcriteriaofthemembersofthetwogroupsofwinecritichasasignificantdifference.
Whichistrustworthier:
Thesmallerthevariance,thetrustworthierthegroup’sevaluate,whenwestudyasinglekindofwinesample.Inthat,wecomparethevarianceofthesetwogroupstodefinethetrustworthiergroupwhichhaveasmallervariance.
Table4Thecredibilitytestforredwine
Winesamples
FirstSet’s
Variance
Second’s
Variance
Thetrustworthier
group
Winesamples
FirstSet’s
Variance
Second’s
Variance
Thetrustworthier
group
1
236.1
736.9
一
15
770.1
372.1
二
2
358.1
146
二
16
112.9
180.9
一
3
412
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