2016美赛E题参考答案(8)

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Table 10:Data comparison

year 2008 2009 2010 2011 2012 2013 2014 Water consumption industrial 4.07 3.6 3.88 4.2 4.3 4.42 4.5 Water agricultural ecological supply 18.15 18.45 18.2 18.6 18.66 18.7 18.89 0.68 0.75 0.9 1.15 1.3 1.48 1.63 33.88 34.11 34.62 35.99 36.96 38.11 39.21 According to China's water resources for water supply and water consumption data and water resources allocation model of data comparison, it can be seen through the construction of reservoirs, water diversion, water desalination, wastewater treatment methods such as water supply has obvious improvement. By raising people's consciousness of water saving, adjusting industrial structure, optimizing the irrigation method and other methods, we have significant lower water consumption. So by raising water reduce water consumption or reduce water consumption can increase speed to solve the water shortage in the future, which has obvious effects. The model of water allocation of water resources of planning water supply, water in the North China can be very good to alleviate water crisis.

454035302520151050IndustryIndustry'AgricultureAgriculture'EcologyEcology'OutputOutput'20084.774.0720.0518.150.780.6830.9333.8820094.383.620.2518.450.870.7530.8934.1120104.563.8820.3718.21.070.931.5234.6220115.114.220.5718.61.261.1532.9335.9920125.024.320.7318.661.411.333.8636.9620135.124.4220.918.71.571.4834.9738.1120145.254.521.0618.891.731.6336.1139.21 Figure 13:Actual water supply and water consumption and water

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resources allocation model the data table

In the same way, we can predict that water crisis will ease in 2020 through the water allocation of water resources model. Compared with task 1, the result will be five years ahead. Through the prediction of the model, if we can constantly improve the reservoir, sea water desalination technology, wastewater reuse, the adjustment of industrial structure and the citizens' consciousness of water-saving in the future, then the solution will come ahead of schedule.

Conclusions

We give a brief introduction about our work in this part, and conclude as follows: ☆The model of water supply capacity is not only a simple estimate for the North China, but also suitable for other areas.

☆The Grey Metabolism GM model with the known objective characteristics can predict the characteristics of the future at some point. Through the metabolism of grey, this article predicts system for water supply in the next 15 years, the calculation is simple, easy to operate.

☆Analytic hierarchy process (AHP) starts from the actual situation of the North China, analyzing various factors that are accounted for in the area. By contrast, normalizing the regularization matrix, and then, we give the weight of each index, and finally calculated the optimal decision scheme.

Further discussions

We simplify some problems because of the limited time, and in the next step we plan to finish some further work:

☆If we divide the world into developed countries, developing countries and underdeveloped countries, adopting the same method，we can improve the precision of the model which is used for the whole world.

☆It can also be extended to other known partial information, which is small in the prediction of other information.

☆Analytic hierarchy process (AHP) can be applied to all areas of decision problems.

Reference

[1] Kefeng Duan. China's population prediction model based on a composite model [D]. Lanzhou university institute of mathematics and statistics, 2012.20. [2] Songqian Huang, Weiming Wang, Cong Zeng, Shuang Hao, Xiaojuan Cao .Based on the grey metabolism GM (1, 1) model of China's annual production of aquatic products[J].Chinese Agriculutural Science Bulletin, 2012(28):126-131. [3]Beijing Municipal Statistics Bureau.The Beijing statistics yearbook2009[EB/OL].[2016].http://www.bjstats.gov.cn/nj/main/2009-tjnj/index.htm.

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[4] The national bureau of statistics,http://www.stats.gov.cn/，2015.07. [5] China's ministry of water resources.Water China[EB/OL].[2016].http://www.mwr.gov.cn/zwzc/hygb/szygb/.

Resources

of

[6] Jian'e Chang, Taili Jiang.Analytic hierarchy process (ahp) to determine weights of research[J].Journal of wuhan university of technology, 2007.29(1). [7] Jinghai,Lli.Based on the rules of water resources allocation model[D].The China institute of water resources and hydropower research:The China institute of water resources and hydropower research, 2005.03.

[8] Huiling He.Study on the Water Use and Water[D].Tsinghua University, 2010.05.

[9] Chonghui Fu, Wenjun Wang, Xuchun Zeng.China's population fertility change and the influence factors, based on the analysis of the sixth census[J].South China Population, 2014.02.

[10] Shunjiu Wang, Yu Hou, Xinli Zhang, Jing Ding.Progress in the study of Chinese water resources optimal allocation and prospect[J].Water Resources Development Research, 2002.09.

[11] Yong Zhao,YuanSheng Pei.The urban water shortage[J].Advances in Water Science, 2006.5.3(7):389-394.

[12] zhengtao shi, xinyou liu, overwhelmed with. Urban water security evaluation index system research [j]. Journal of urban problems. 2008.155 (6), 30-34. [13] Xu shen. water supply security multi-index evaluation method research [D]. China institute of water resources and hydropower research, 2013.06.

[14] Xinmin xie, Haiqing,Zhang, Mingwan Yin,the sustainable utilization of water resources evaluation and planning theory and practice” , the Yellow River water conservancy press, 2003.

Appendix

We mainly enumerate the programs of the software Matlab. The gray forecast metabolism: function gmcal=gm1(x) sizexd2 = size(x,2); k=0; for y1=x k=k+1; if k>1

x1(k)=x1(k-1)+x(k);

z1(k-1)=-0.5*(x1(k)+x1(k-1));

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yn1(k-1)=x(k); else

x1(k)=x(k); end end

%x1,z1,k,yn1 sizez1=size(z1,2); %size(yn1); z2 = z1';

z3 = ones(1,sizez1)'; YN = yn1'; %YN B=[z2 z3];

au0=inv(B'*B)*B'*YN; au = au0'; %B,au0,au afor = au(1); ufor = au(2); ua = au(2)./au(1); afor,ufor

constant1 = x(1)-ua; afor1 = -afor; x1t1 = 'x1(t+1)'; estr = 'exp'; tstr = 't'; leftbra = '('; rightbra = ')';

%constant1,afor1,x1t1,estr,tstr,leftbra,rightbra

strcat(x1t1,'=',num2str(constant1),estr,leftbra,num2str(afor1),tstr,rightbra,'+',leftbra,num2str(ua),rightbra)

%***************************************************** k2 = 0; for y2 = x1

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k2 = k2 + 1; if k2 > k else

ze1(k2) = exp(-(k2-1)*afor); end end %ze1

sizeze1 = size(ze1,2); z4 = ones(1,sizeze1)'; G=[ze1' z4]; X1 = x1';

au20=inv(G'*G)*(G'*X1); au2 = au20'; %z4,X1,G,au20 Aval = au2(1); Bval = au2(2); %Aval,Bval

strcat(x1t1,'=',num2str(Aval),estr,leftbra,num2str(afor1),tstr,rightbra,'+',leftbra,num2str(Bval),rightbra)

%

nfinal = sizexd2-1 + 1; %nfinal = sizexd2 - 1 + 1; for k3=1:nfinal

x3fcast(k3) = constant1*exp(afor1*k3)+ua; end %x3fcast

for k31=nfinal:-1:0 if k31>1

x31fcast(k31+1) = x3fcast(k31)-x3fcast(k31-1); else if k31>0

x31fcast(k31+1) = x3fcast(k31)-x(1); else

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