数学建模：建筑物人员疏散方案的数学模型研究

321120106JOURNALOFWUHANUNIVERSITYOFTECHNOLOGYVol.32No.11Jun.2010DOI:10.3963/j.issn.167124431.2010.11.0381,2,3(1.,443002;2.,443002;3.,443002):,,,,:;;;:TU972+.4:A:167124431(2010)1120155204MathematicalModelofEvacuationPrograminaBuildingWANGWei2hua1,WUShu2xian2,CHENGJian3(1.SchoolofScience,ChinaThreeGorgesUniversity,Yichang443002,China;2.ResearchCenterforEmergencyManagement,ChinaThreeGorgesUniversity,Yichang443002,China;3.SchoolofMechanicalandMaterials,ChinaThreeGorgesUniversity,Yichang443002,China;Abstract:Thisarticleresearchesthathowtoorganizepersonneltoescapeofabuildingintheshortesttime.Inordertofindoutthebestevacuationprogram,thispaperestablishesamathematicalmodelofflowofpeopletoevacuate.Themodeltakestherelationshipbetweenflowvelocityandflowdensityintoaccounttoevacuatetheshortestoftheobjectivefunction.Accordingtothismodelsolutionwegetaquicklyevacuateoptimizationprogramofaclassroombuilding.Throughthemodeltests,theau2thoritiesmakeanumberofconstructivecomments.Keywords:evacuationprogram;evacuationmodel;flowdensity;flowvelocity:2010201210.:(19662),,.E2mail:[e-mail]21,,,,,,,,,,2080,,2Helbing[1],,(grid2gas)[2,3],,,2090,,[4],,,[5]PredtechenskiiMilinskiiFruin,Maclennan&NelsonSmithAndoPaul,,2,,,,[6],1,,,,,A,,TniLijL;dbb0v,(),t0(s),minT=t0+g1(n1,Li,j,L)minT=t0+g2(d,b,b0,v)(1)(1)TT=t0+g3(n1,Li,j,L,d,b0,v),,22.12.1.1,Fegress[7],,p=nf((n-1)d0+nw)b0/2(2),n;f(m2);d0(m);w(m);b0(m)(2)Fegress[7]3:,,,f=xa+yb+zc(3),f(m2);xyz(m2);abc2.1.2,,:v=f(p),,,,65120106Fegress,,12.1.3,,m=int[(b0-0.238)/b3](4),b3,int2.1.4PredtechenskiiMilinskii[8],v=(112p4-380p3+434p2-217p+57)/60(5),p0.92,,v1=vu1(6),u1=1.49-0.36p()v2=u1v(7)2.21),;2);3);4),B;5);6)2.3,2:1),t0(s)2),,T02,,d0(m);,v1(m/s);,v2(m/s);ini,iXi(m),iALi(m),d(m),L(m),b0(m),b(m),21((n1-1)d0+n1w)/(mv1),1,t21=(L1+(n1-1)d0+n1w)/(mv1),i((ni-1)d0+niw)/(mv1),t2i=Limv1+(ni-1)d0+niwmv1(i=1,2,,5),2,,211,1,27513211,,:,32[10](n1-1)d0+n1wmv1L2-L1v1(n1-1)d0+n1wm(L2-L1),5()T25=L5+(n5-1)d0+n5wmv1,(n1-1)d0+n1wm(L2-L1)L1+Ld0/(w+d0)+nwmv1,(n1-1)d0+n1wm(L2-L1)n=n1+n2+n3+n4+n5,,T25=T210,,T25,26,21AT2=Lv2,AminT=t0+T25+L+nw(j-2)mv2(8)2.4,,,0.25m,0.16m2,,,f=xax,f=0.16,0.7m:1)11.6m,1.0m2)69.7m,2.4m3)6.4m,2.0m4)60,2400II0.5m,,201s,23460,190s,,3,,,,,,:a.,,;b.,,,,,,;c.,,,;d.,;e.,,,,,(162)85120106,,EXCEL,,2;3;4,V=92.18,,MATLABDELPHI5,,,,MATLABDELPHI,,,,,[1].[J].,2008,45(1):124.[2].[J].,2008(3):2272330.[3],.[J].:,2005,37(3):3812385.[4],.[J].,2004(11):1192121.[5],.DELPHIAHPKPI[J].,2008,30(2):37238.[6],.MATLABDELPHI[J].,2007(1):1532154.(158)[1]DHelbingDL,FarkasDI,VicsekT.SimulatingDynamicFeaturesofEscapePanic[J].Ature,2000(407):4872490.[2]NagataniT.DynamicalTransaitioninMergingPedestrianFlowWithoutBottleneck[J].Physica,2002,307:5052515.[3]TajimaY,TakimotoK,NagataniT.PattenFormationandJammingTransitioninPedestrianCounterFlow[J].Physics,2002,313:7092723.[4],.[J].,2001,22(5):5642567.[5],.[J].:,2002,35(2):66270.[6].[J].,2006,16(2):982103.[7]StahlF.BFIRESII,ABehaviorBasedComputerSimulationofEmergencyEgressDuringFires[J].FireTechnology,1982,18(1):49265.[8],.[M].:,2005.26120106