数模美赛c题论文.docx
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数模美赛c题论文
Problemsolving
Withscienceandtechnologydevelopingrapidlytoday,thehealthproblemofourplanetbecomesincreasinglyseriousatthesametime.SothewholesocietydesirestouseamodeltodescribeandforecasttheEarthhealth.
Task1
Relatedconcepts
Toformamodelthatsuitsfortherequests,forthefirst,wecreateoneindextodescribetheEarthhealth,whichiscalledEHI（AbbreviationofEarthHealthIndex）.
DecisivefactorsofEHIandCorrespondingindex
DecisivefactorsofEHI
Correspondingindex
EarthAirCondition
API（AirPollutionIndex）
EarthWaterCondition
IWS（ImprovedWaterSource）
EarthLandStatus
FAR（ForestAreaRate）
EarthSpeciesstatus
GEF（Biodiversitybenefitsindex）
Reasonsofchoosingthefactorsabove
●TheEarthconsistsoforganiclifeandinorganicenvironment.BothofthetwopartshavetheeffectonEHI.
●BiosphereisthelargestecosystemontheEarth.Itconsistsofatmosphere,hydrosphereandlithosphere.Thefirst3factors,visualperformanceoftheabove3parts,cancomprehensivelystandforinorganicenvironment.
●SpecieistheonlyobjectiveexistingformoforganiclifeontheEarth.Sothespeciesstatuscanmostlymeasuretheconditionoforganiclifehealthlevel.
●ToimplementthequalitativecalculationofEHI,wechoosecorrespondingindexonbehalfofthe4factors.
CalculatingmethodsofEHI
●LocalEHI
Providingthatwe‘dliketocalculatetheEHIofthewholeplanet,it’sobvioustochooseoneplaceandcalculateitslocalEHIfirst.Afterthat,wecanusethedataofsingleplacestocalculatethewholeplanet’sEHI.
Setting;
（onecertainplace,certaintime）
Accordingtotheinterrelationoffactors,thelocalEHIcanbedescribedbytheareaofthequadrilateralwhichisformedbyfoursegments.Eachsegmentindicatesonekindofindex.Theleveloftheindexcanbeindicatedbythelengthofthesegment.
AccordingtotheSchematicdiagram;
●globalnetworkmodelbuilding
Knowingeachplace’slocalEHI,,westartedtochooseconnectingnodesandbuildglobalnetworkmodelofEHI.Wechoose12connectingnodesamongtheplanet.Thedistributionofnodesisbelow;
Principiumofchoosingnetworkconnectingnodes
●Selectthenodesaccordingtothegeographicaldivision.
●EachnodemustindicatetheEHIofAparticularregion.
●Theareaof12regionsshouldmaintainarelativebalance.
●Thenetworkformedbyallthenodesshouldreachtheglobalcoveragetothemaximumextent
●GlobalEHIcalculating
Setting;
●Numbertheconnectingnodesoftheletter“i”
●Theareaofeachregion=Ai
●ThelocalEHIofeachnode=Si
●GlobalEHIThree-dimensionalgraphic
Accordingtothecalculatingprinciple,theglobalEHIcanbedescribedbythevolumeofgraphic.
.
Usingthefinalresult“S”,theglobalEHIisobvious.Peoplecanusethisindextojudgethehealthconditionofthewholeplanet.
Theglobalnetworkmodelcandealwithallkindsoffactor-changingincludingnaturalfactorsandsocialfactors.Nomatterwhichkindoffactorchanges,itmaycausethechangeofthe4decisivefactors.Withthebasicfactorschanging,thefinalresultofEHIwillchangeintoanewnumber.Itthusreflectsthelevelchangingofglobalhealth.
TASK2
Theglobalnetworkcanbeusedtopredictthefuturedevelopmentofplanethealthcondition.Usingthemodel,youwillknowthedevelopingtrendofEHI.Theprocedureisbelow.
●Factualbasis
Data
4basicfactors
Time
2003-2008
Object
12connectingnodes
From
WorldBankdatabase
Weusesomecountries’datatodescribe12connectingnodes’data.Thecorrespondisbelow;
Number
Region
Area（SQtkm2）
Country
1
NorthAmerica
24230
Unitedstates,Canada
2
Asia
36210
Russia,China
3
Europe
10160
FranceItalyGreece
4
SoutheastAsia
4570
Indonesia
5
Oceania
8970
Australia
6
MiddleEast
12320
EgyptSaudiArabia
7
SouthAmerica
17840
Brazil
8
AtlanticOcean
94300
Dominican
9
PacificOcean
181344
Fiji
10
IndianOcean
74920
Maldives
11
ArcticOcean
14750
Norway
12
Africa
21200
Congo（DEM,REP）
BasicDatabase
GEF
2003
2004
2005
2006
2007
2008
US
90
90
90
94
94
94
Canada
22
22
22
22
22
22
China
65
65
65
67
67
67
Russia
37
37
37
34
34
34
Italy
4
4
4
4
4
4
France
4
4
4
5
5
5
Greece
3
3
3
3
3
3
Indonesia
90
90
90
81
81
81
Australia
96
96
96
88
88
88
Egypt
3
3
3
3
3
3
SaudiArabia
3
3
3
3
3
3
Brazil
100
100
100
100
100
100
Fiji
100
100
100
100
100
100
DominicaRepublic
100
100
100
100
100
100
Maldives
100
100
100
100
100
100
Norway
100
100
100
100
100
100
API
2003
2004
2005
2006
2007
2008
US
22
22
22
21
20
19
Canada
20
19
19
17
17
16
China
82
82
78
75
69
66
Russia
23
20
19
17
16
16
Italy
30
28
27
26
25
23
France
15
14
14
14
13
13
Greece
40
38
36
34
33
32
Indonesia
97
97
90
83
77
74
Australia
16
15
15
15
14
14
Egypt
124
126
119
111
103
99
SaudiArabia
135
127
118
112
107
104
Brazil
29
27
25
23
21
21
Fiji
25
24
23
21
19
19
DominicaRepublic
24
22
19
18
17
17
Maldives
38
35
35
31
32
29
Norway
17
17
16
16
15
16
Congo
89
89.8
90
91
91
92
FAR
1990
2000
2005
2010
US
32.4
32.8
33
33.2
Canada
34.1
34.1
34.1
34.1
China
16.8
19
20.7
22.2
Russia
49.4
49.4
49.4
49.4
Italy
25.8
28.5
29.8
33.1
France
26.5
28
28.7
29.1
Greece
25.6
27.9
29.1
30.3
Indonesia
65.4
54.9
54
52.1
Australia
20.1
20.2
20
19.4
Egypt
0
0
0.1
0.1
SaudiArabia
0.5
0.5
0.5
0.5
Brazil
68
64.5
62.7
61.4
Fiji
0
0
0
0
DominicaRepublic
0
0
0
0
Maldives
0
0
0
0
Norway
0
0
0
0
Congo
70.1
68.4
69.7
768.0
IWS
2003
2004
2005
2006
2007
2008
US
99
99
99
99
99
99
Canada
100
100
100
100
100
100
China
84
85
87
87
89
89
Russia
88
88
88
88
88
88
Italy
100
100
100
100
100
100
France
100
100
100
100
100
100
Greece
100
100
100
100
100
100
Indonesia
79
79
80
80
80
81
Australia
100
100
100
100
100
100
Egypt
97
97
98
98
98
99
SaudiArabia
0
0
0
0
0
0
Brazil
95
97
96
97
97
97
Fiji
100
100
100
100
100
100
DominicaRepublic
100
100
100
100
100
100
Maldives
100
100
100
100
100
100
Norway
100
100
100
100
100
100
Congo
44
44
44
45
45
45
Usingthemethodsabove,wecancalculatethelocalEHIofeachnetworknode,Thecalculatingresultisbelow;
2003
2004
2005
2006
2007
2008
1
0.4993
0.4998
0.4999
0.5074
0.5079
0.5087
2
0.4342
0.4371
0.4412
0.4392
0.4438
0.4449
3
0.0626
0.0634
0.0654
0.0665
0.0676
0.0688
4
0.324
0.3249
0.3255
0.3286
0.3294
0.3297
5
0.5702
0.5694
0.578
0.5515
0.5548
0.5591
6
0.5727
0.5734
0.5733
0.5493
0.5497
0.5491
7
0.7683
0.7764
0.7727
0.7773
0.778
0.7767
8
0.4750
0.4760
0,4770
0.4790
0,4760
0,4750
9
0.4760
0.4780
0.4810
0.4820
0.4830
0.4830
10
0.4830
0.4840
0.4840
0.4850
0.4850
0.4840
11
0.4620
0.4650
0.4650
0.4690
0.4680
0.4710
12
0.2409
0.2419
0.2423
0.2592
0.2603
0.2604
Usingthedataabove,wedrawtheimagesofeachconnectingnode.
HerearethelocalEHIimageofeachnode.Also,wecanobviouslycalculatetheglobalEHIofeachyear.Thedataandimagearebelow;
Data
Year
2003
2004
2005
2006
2007
2008
EHI
0.4474
0.4491
0.4505
0.4495
0.4507
0.4514
Image
TopredictthefuturetrendofEHI,weusetheSoftwareMATLABtodothefuctionfitting.
Operating
Weuseexistingdatatofindanadaptablefuctionwhichsuitsforit.Asresultsreachedbythesoftware,thesuitablefuctionisbelow;
Explanation;
●Intheformula,letterA,B,C,D,E,F,Marecoefficients.
●Allthecoefficientsaredeterminedbythecomplexconditionsofspecificconnectingnodes.
●The12solutionsofeachkindofcoefficientcanbeexpressedasacertainmatrix.
A:
p1=[0.0023290.0022360.001331
0.001339-0.003669-0.006524
0.0009730.0014740.001561
0.00047940.0013110.005169];
B:
p2=[-4.167-4.043-2.604
-2.3587.92213.64
-1.176-2.478-2.65
-0.4775-2.162-10.11];
C:
p3=[-0.0021820.001647-2.91e-006
0.0095450.007509-0.001384
-0.00050950.00074185.447e-005
0.001176-0.005093-0.008302];
D:
p4=[2.82.83.4
32.82.8
2.43.63.6
2.82.42.8];
M:
p5=[1.5491.590.9853;
1.571.4131.744
1.7052.0121.168
1.6722.321.749];
E:
p6=[5531,3.08,-9.827,
1.46,12.05,4334,
-5.738,4670,4507
13.09,1.558,4732];
F:
p7=[3257,-2001,0.3918,
0.8031,-1993,2584,
-2001,2009,1991,
-2000,-2003,3357];
●Localimageofthetrend
●WecanalsogetthefuctioncoefficientsofglobalEHI.
Coefficient
A
B
C
D
M
E
F
Result
0.0006675
-0.8887
-0.008302
2.8
-0.09785
2505
2542
●AccordingtothefuctionoftheglobalEHI,wecangettheimageofitsfuturetrend.
Fromtheimageabove,wefindthat;
●TheimagecanberegardedasaspecialkindofDampedoscillation.
●Thelineofoscillatingspindle.canbedescribedasatimefuction.Itsanalyticformulaisp（x）=0.0006675x-0.8887.SinceAisminimum.theprincipalvalueofthefuctionp（x）growslowly.
●Onefactoroftheformula（x+E）/Fcandescribetheamplitudeofthefunction.Fromtheimageabove,weknowthatthefactorbasicallykeepsstable.Andthefactor
almostdoesn’t
attenuate.Soit’sobviousthatamplitudebasicallykeepsstable.
Fromthefeaturesofthefunction,wecanmakeapredictionaboutthefuturetrendofglobalhealth.
●Inalongdecade,theEHIgrowsslowly.Sowecanpredictthatthe
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