International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Reliability and controllability of infrastructure networks : do they match? Li, Jian; Dueñas-Osorio, Leonardo; Chen, Changkun Jul 31, 2015

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Iho1 rC1 n1ihrPCfb1PIrg1 n1 pIiG h1 IiIrIn 1 iCoh1 nio1 n1 pIiG h1rhfRIin 1 iCohN1 Tsr1 Ii1 SI;I 1 hiGIihhfIiGm1 Rs rI5IiIrIn 1nio1Rs rI5rhfRIin 1iCohp1SCRRCi a1h)IprN1<Cf1 h)nR. hm1 Ii1 .CPhf1 ihrPCfbpm1rgh1 lt1 Cc1 n1rhfRIin 1iCoh1HpseprnrICiw1Ip1rgh1siICi1Cc1rgh1lt1ehrPhhi1rgh1rhfRIin 1 iCoh1nio1hnSg1IiIrIn 1 iCoh1H.CPhf1 . nirwN1EC1n.. a1 rgh1U5tvD1 rC1n1Rs rI5IiIrIn 1 iCohp1 lt1 SCR.srnrICim1 rgIp1 prsoa1 sphp1n1 CGISn 1h).nipICi1rC1tvD1HFIR1nio1FniG1k32:wN1EC1 eh1 p.hSIcISm1 noo1 n1 ;Ifrsn 1 iCoh1 HPIrg1fh IneI Ira1 Cc12N3w1 rC1 rgh1 Gfn.g1 nio1 SCiihSr1 rgh1nooho1 iCoh1 PIrg1 n  1 rgh1 IiIrIn 1 iCohpm1 np1SCRRCi a1 oCih1 Ii1 ihrPCfb1 C.rIRI>nrICi1.fCe hRp1 HDgs4nm1 ,nGinirIm1 nio1 0f Ii1 2<<:wN1Egh1lt1ehrPhhi1rgh1Rs rI5IiIrIn 1 iCohp1nio1rgh1rhfRIin 1 iCoh1 ehSCRhp1 rgh1 lt1 ehrPhhi1 rgh1nooho1;Ifrsn 1iCoh1nio1rgh1rhfRIin 1iCohm1PgISg1SCs o1eh1SCR.srho1PIrg1rgh1U5tvDN11EgIp1 .n.hf1 SCipIohfp1 Ci a1 rgh1 cnI sfh1 Cc1iCohpN1jCPh;hfm1 Ir1 pgCs o1 eh1 iCrho1 rgnr1 rgh1U5tvD1 .fCShosfh1 Sni1 RCoh 1 n  1 ;s ihfne h1SCR.Cihirpm1 SCirnIiIiG1KiCohpE1 nio1 K IibpEm1np1iCohpN112.2. Importance measure based on network connectivity reliability Egh1 cnI sfh1 Cc1 IR.Cfrnir1 SCR.Cihirp1 rhiop1 rC1IiSfhnph1 rgh1 cnI sfh1 .fCeneI Ira1 Cc1 rgh1 paprhRpN1Egh1tIpb1DSgIh;hRhir1GCfrg1HtDGw1(snirIcIhp1rgh1IR.CfrniSh1Cc1n1SCR.Cihir1ea1rgh1IiSfhnph1Ii1rgh1 paprhR1 cnI sfh1 .fCeneI Ira1 Pghi1 rgh1SCR.Cihir1 Ip1 fhRC;ho1 cfCR1 rgh1 paprhR1HUCiG1nio1FIsfhGgIni1k33BwN1Egh1iCoh1IR.CfrniSh1HdAw1Ii1rhfRp1Cc1lt1Cc1rgh1i5rg1iCoh1Ip1ohcIiho1ghfh1npy11njjnjijRiRnRnNI22wH2222m111111111111111111111111Hkw1Pghfh1Rj1ohiCrhp1 rgh1 lt1 Cc1 iCoh1jm1 nio1RjHiw1ohiCrhp1rgh1lt1Cc1iCoh1j1PIrg1iCoh1i1fhRC;hoN1:N d?EG0tFU1E0A0J0CAlDJ 1l0dEt0JJDTAJAE=1Ej?0 t=13.1. Topological controllability theory Eghfh1nfh1RCoh p1rC1Sn.rsfh1rgh1SCirfC  neI Ira1Cc1n1 fhn 1 paprhR1 rgnr1 Ip1 ofI;hi1 ea1  Iihnf1 nio1 rIRh5Ii;nfInir1 .fCShpphp1HJIsm1 U CrIihm1 nio1Tnfne>pI1k322wm11H wH w H wdx tAx t Bu tdt  m1111111111111111H:w1Pghfh1xHtwIHx2HtwmJNmxd HtwwE1ohiCrhp1rgh1prnrh1Cc1n1paprhR1PIrg1N1iCohp1nr1rIRh1tN1Egh1NLN1RnrfI)1A1ohpSfIehp1rgh1paprhREp1PIfIiG1oInGfnRN1Egh1NLM1RnrfI)1 B1Ip1 rgh1 Ii.sr1 rgnr1 IohirIcIhp1 rgh1 iCohp1SCirfC  ho1ea1ni1CsrpIoh1SCirfC  hf1HM≤NwN1Egh1paprhR1 Ip1 SCirfC  ho1 spIiG1n1 rIRh5oh.hiohir1Ii.sr1;hSrCf1uHtwI1Hu2 twm1JN1mu, HtwwEN112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 1 D1Ar1Ip1.fC;ho1rgnr1rgh1neC;h1 Iihnf1oainRISn 1paprhR1Sni1eh1ofI;hi1cfCR1nia1IiIrIn 1prnrh1rC1nia1ohpIfho1 prnrh1 Ii1 cIiIrh1 rIRhm1 Ic1 nio1 Ci a1 Ic1 rgh1NLNM1SCirfC  neI Ira1 RnrfI)1C1gnp1 cs  1 fnib1HJIsm1U CrIihm1nio1Tnfne>pI1k322M1JCRenfoI1nio1jCfi(sIpr1k33xwm1INhm1k 2tnibH w tnibM m m mNNNm NNC B AB A B A B N  N11111HDwAi1.fnSrISn 1rhfRpm1SCirfC  neI Ira1Sni1eh1n pC1.Cpho1 np1 IohirIcaIiG1 rgh1 RIiIRsR1 isRehf1 Cc1ofI;hf1iCohp1psSg1rgnr1?(N1HDw1Ip1pnrIpcIhoN1Dp1Ii1lt1 SCR.srnrICipm1 cCf1ni1 nfeIrfnfa1 ihrPCfbm1 n1efsrh5cCfSh1phnfSg1Ip1SCR.srnrICin  a1.fCgIeIrI;hN1Ai1.nfrISs nfm1rgh1El1Snph1fh(sIfhp1npphppRhir1Cc1rgh1 fnib1 Cc1C1cCf1 kN521 oIprIiSr1 SCReIinrICip1HJCRenfoI1nio1jOfi(sIpr1k33xwN1JIs1hr1n N1Hk322w1.fC;ho1rgnr1rgh1RIiIRsR1isRehf1Cc1ofI;hf1iCohp1ihhoho1 rC1RnIirnIi1 cs  1 SCirfC 1Cc1 n1 ihrPCfb1 Ip1ohrhfRIiho1 ea1 rgh1 KRn)IRsR1 RnrSgIiGE1 Ii1 rgh1ihrPCfbm1 rgnr1 Ipm1 rgh1Rn)IRsR1phr1Cc1  Iibp1 rgnr1oC1iCr1pgnfh1prnfr1Cf1hio1iCohpN1D1iCoh1Ip1pnIo1rC1eh1RnrSgho1 Ic1n1  Iib1 Ii1 rgh1Rn)IRsR1RnrSgIiG1phr1 .CIirp1 nr1 IrM1CrghfPIph1 Ir1 Ip1 siRnrSghoN10ih1Sni1GnIi1 cs  1 SCirfC 1C;hf1 n1oIfhSrho1 ihrPCfb1 Ic1nio1 Ci a1 Ic1rghfh1 Ip1oIfhSr1 SCirfC 1Cc1hnSg1siRnrSgho1 iCoh1 nio1 rghfh1 nfh1 oIfhSrho1 .nrgp1cfCR1rgh1Ii.sr1pIGin p1rC1n  1RnrSgho1iCohpL rgh1SCirfC  ho1 iCohp1 nfh1 Sn  ho1 ofI;hf1 iCohpN1,CfhohrnI p1 Cc1 rgh1El Sni1 eh1 cCsio1 Ii1 JIs1 hr1 n N1Hk322wN11EC1 Rhnpsfh1 rgh1 SCirfC  neI Ira1 nrrfIesrh1 Cc1rgh1ihrPCfbpm1rgIp1.n.hf1ohcIihp1n1SCirfC  neI Ira1Iioh)1HlAwm1cCfRs nrho1np1cC  CPpy1NNNCI D m11111111111111111111111HBwPghfh1N1Ip1 rgh1 isRehf1Cc1 iCohpm1nio1Nv 1Ip1 rgh1RIiIRsR1 isRehf1Cc1ofI;hf1iCohp1ihhoho1rC1cs  a1SCirfC 1rgh1ihrPCfbN11Ar1 Ip1 n pC1biCPi1 rgnr1 spsn  a1 rgh1 RIiIRn 1ofI;hf1iCohp1phrp1nfh1iCr1siI(sh1HuIn1hr1n N1k32:wN1Ai1Crghf1PCfopm1rghfh1nfh1oIcchfhir1SCicIGsfnrICip1cCf1 SCirfC  IiG1 rgh1 ihrPCfb1 PIrg1 rgh1pnRh1RIiIRn 1 isRehf1Cc1ofI;hf1iCohpN1jCPh;hfm1Ir1Ip1n RCpr1 IR.CppIe h1 rC1 hisRhfnrh1 n  1 rgh1SCicIGsfnrICip1 oIfhSr am1 pIiSh1 rgh1 Rn)IRsR1SCReIinrICip1 isRehf1 Ip1cHNv mNwINPQHNv PHN5Nv wPwm1PgISg1Ip1IR.fnSrISn 1cCf1 nfGh1NN1uIn1hr1n N1Hk32:w1.fC.Cpho1 ni1 n GCfIrgR1 rC1 IohirIca1 rgh1SfIrISn m1 IirhfRIrrhir1 nio1 fhosionir1 iCohm1PgISg1nSrp np1n1ofI;hf1iCoh1Ii1n  m1pCRh1Cf1iCih1Cc1rgh1.CrhirIn  a1 SCirfC  ne h1 paprhR1 SCicIGsfnrICip1fhp.hSrI;h aN1 GIrg1n  1rgh1 SfIrISn m1 IirhfRIrrhir1iCohp1IohirIcIho1nio1SfIrISn 1isRehf1iCohp1HNl wm1IirhfRIrrhir1 iCohp1 isRehf1 HNAw1 biCPim1 rgh1isRehf1 Cc1SCReIinrICip1ohSfhnphp1pIGiIcISnir aN1Dp1n1fhps rm1rgIp1.n.hf1cIfpr1noC.rp1uInEp1n GCfIrgR1rC1IohirIca1rgh1SfIrISn 1nio1IirhfRIrrhir1iCohpm1nio1rghi1 hisRhfnrhp1 n  1 rgh1 SCReIinrICip1 Cc1 rgh1ofI;hf1iCohp1PIrgIi1cHNAmHNv 5Nl ww1prh.pN113.2. Importance measure based on networks controllability Ar1 Ip1 inrsfn 1 rC1 h).hSr1 rgnr1 n1 RCfh1 SCirfC  ne h1ihrPCfb1 ihhop1  hpp1ofI;hf1 iCohpN1?;hi1PIrg1 rgh1pnRh1 ofI;hf1 iCohp1 isRehfm1 rgh1 isRehf1 Cc1SCReIinrICip1Cc1 rgCph1RIiIRn 1 ofI;hf1 iCoh1phrp1n pC1 ncchSrp1 rgh1 SCirfC  neI Ira1 nrrfIesrh1 Cc1 rgh1ihrPCfbpN1 ,Cfh1 n;nI ne h1 SCReIinrICip1 Rhnip1hnpIhf1 SCirfC N1 Dp1 n1 fhps rm1 rgIp1 prsoa1 .srp1cCfPnfo1n1SCirfC  neI Ira5enpho1RhrfIS1rC1Rhnpsfh1rgh1dA1Ii1rhfRp1Cc1El m11w CGH22wHwHiConfConfiCiNNbCCaNI  m11111111HFw1Pghfh1C1Ip1rgh1lA1Cc1rgh1ihrPCfbm1HIw1Ip1rgh1lA1Cc1rgh1ihrPCfb1PIrg1iCoh1i1fhRC;hom1nio1NSCic1Ip1rgh1isRehf1 Cc1SCirfC  ne h1SCicIGsfnrICip1 PIrg1 rgh1RIiIRn 1ofI;hf1iCohp1isRehfm1PgI h1NSCicHIw1Ip1rgh1isRehf1 Cc1 SCicIGsfnrICip1 PIrg1 rgh1 RIiIRn 1ofI;hf1iCohp1isRehf1Pghi1iCoh1i1Ip1fhRC;hoN1Ai1nooIrICim1a1ni o1b1nfh1SChccISIhirp1rC1en niSh1rgh1fh nrI;h1 IR.nSr1 Ci1 eCrg1 rgh1 lA1 nio1 isRehf1 Cc1SCicIGsfnrICipN1Ai1rgIp1prsoam1aI3N@m1bI3Nkm1pIiSh1Ir1Ip1eh Ih;ho1rgnr1SgniGhp1Ii1rgh1RIiIRn 1ofI;hf1iCohp1isRehf1gnp1 nfGhf1IR.nSr1rgni1SgniGhp1Ii1rgh1 SCicIGsfnrICip1 isRehfN10c1 SCsfphm1 RCfh1PCfbp1 nfh1 prI  1 ihhoho1 Ci1 rgh1SCirfC  neI Ira5enpho1 iCoh1 IR.CfrniSh1Rhnpsfhpm1cCf1 h)nR. h1rgh1;hfIcISnrICi1Cc1rgh1neC;h1SChccISIhirp1a1nio1bN1DN CJ0TDJ1,?EtAlUE1A,ADlEU10d1lt1Ddv1 El 1Ai1 Cfohf1 rC1 h). Cfh1 gCP1 rgh1 lt1 nio1El1.hfp.hSrI;hp1 RnrSgm1 pI)1 SIra5 h;h 1 .CPhf112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 1 B1rfnipRIppICi1 GfIop1 cfCR1 SIrIhp1 nSfCpp1c sf1BNUN1prnrhp1 rgnr1 nfh1 pspSh.rIe h1 rC1 onRnGh1 cfCR1gsffISnihp1 Cf1 hnfrg(snbhp1 HCf1 eCrgwm1 nfh1hR. CahoN1Egh1GfIop1SCipIpr1Cc1223bH rC1xFBbH1rfnipRIppICi5 h;h 1 .CPhf1  Iihp1 SCiihSrIiG1GhihfnrCfp1nio1pseprnrICipN1Egh1fnP1ihrPCfb1onrn1Ip1 CernIiho1 Ii1 CAU1 cCfRnr1 cfCR1 rgh1 RA nrrpS1HA nrrp1k323w1fh.CpIrCfa1cCf1Rn.p1nio1GhCp.nrIn 1onrnN1Egh1ihrPCfb1pI>h1fniGhp1cfCR1Dx1iCohp1nio1Fk1 hoGhp1 HDRnfI  Cm1 ETw1 rC1xDiCohp1 nio1<@1hoGhp1HAn R1Tnam1<JwN11Ai1 rgh1 cC  CPIiGm1 rgIp1 .n.hf1 h). Cfhp1gCP1 Iib1ohipIra1HINhN1n;hfnGh1ohGfhh1Cc1rgh1ihrPCfbw1nio1 ohGfhh1 ghrhfCGhihIra1HINhN1 rgh1;nfIneI Ira1Cc1rgh1 ohGfhhw1ncchSr1 eCrg1 lt1 nio1El m1 np1 Ph  1 np1Pghrghf1rgha1RnrSg1PIrg1hnSg1Crghf1Ii1 rhfRp1Cc1h hRhir1 IR.CfrniShN1 Egh1.CPhf1 rfnipRIppICi1ihrPCfb1 HAEdw1 Cc1 DRnfI  Cm1 ET1nio1 nfrIcISIn 1ihrPCfbp1Ghihfnrho1enpho1Ci1rgh1AEd1nfh1spho1np1ni1I  sprfnrICi1eh CPN11Egh1 AEd1 Ii1 DRnfI  Cm1 ET1 SCipIprp1Cc1Fk1hoGhp1nio1Dx1 iCohpm1 nRCiG1 PgISg1@1 iCohp1 nfh1.CPhf1 . nirp1 nio1 rgh1 fhpr1 nfh1 pseprnrICipN1 Egh1cnI sfh1fnrh1Cc1hnSg1iCoh1Ip1nppsRho1rC1eh13N21rC1rfIGGhf1 cnI sfhp1 nio1 hine h1 (snirIcISnrICi1 Cc1h hRhir1fhRC;n 1hcchSrp1Ci1lt1nio1ElN1Egh1lt1Cc1hnSg1iCoh1HRIw1Ip1rgh1fh IneI Ira1rgnr1rgh1iCoh1Ip1SCiihSrho1PIrg1nr1 hnpr1Cih1.CPhf1. nirN1DSfCpp1n  1 iCohpm1 rgh1 n;hfnGh1 SCiihSrI;Ira1 fh IneI Ira1HDltw1 Ip1 Sn Ss nrhoN1Egh1 RIiIRn 1 ofI;hf1 iCohp1ihhoho1 rC1 cs  a1 SCirfC 1 rgh1 ihrPCfb1 Ip1 n pC1hprne Ipghom1hprIRnrIiG1 rgh1lA1 Cc1 rgh1 ihrPCfbN1EgIp1 .n.hf1n pC1SCR.srhp1rgh1Dlt1nio1 lA1Cc1n1RIiIRn 1 p.niiIiG1 rfhh1 H,UEw1 Cc1 rgh1 ihrPCfbm1PgISg1 Ip1 Ghihfnrho1 PIrg1 Ffspbn Ep1 n GCfIrgR1HTsg 1 hr1 n N1 k33FwN1 D1 ,UE1 Ip1 n1 p.niiIiG1 rfhh1PIrg1PhIGgr1  hpp1 rgni1Cf1 h(sn 1 rC1 rgh1PhIGgr1Cc1h;hfa1Crghf1p.niiIiG1rfhhm1PgCph1ohcIiIrICi1 Ip1n1pseGfn.g1rgnr1Ip1n1rfhh1HiC1 CC.pw1nio1SCiihSrp1n  1rgh1;hfrIShp1rCGhrghfN11Ai1 Cfohf1 rC1 ohrhSr1 rgh1 IR.nSr1 cfCR1  Iib1ohipIra1 Hn;hfnGh1 ohGfhhwm1 rgIp1 .n.hf1n pC1Ghihfnrhp1 nfrIcISIn 1 ihrPCfbp1 rgfCsGg1 nooIiG1 Iibp1 Cf1 oh hrIiG1  Iibp1 fnioCR a1rC1rgh1 CfIGIin 1AEd1PgI h1bhh.IiG1rgh1iCoh1isRehf1siSgniGhoN1Egh1n;hfnGh1ohGfhh1fniGhp1cfCR1kNk1rC1:Nkm1nio1nr1hnSg1 n;hfnGh1ohGfhhm1 rgIp1 .n.hf1 Ghihfnrhp1 23331ihrPCfbp1rC1Sn.rsfh1fnioCRihpp 1;In1n;hfnGhp1nio1;nfIneI IraN1Egh1 Rhni1 n;hfnGh1 SCiihSrI;Ira1 H,Dltw1nio1 Rhni1 SCirfC  neI Ira1 Iioh)1 H,lAw1 Cc1rgh1ihrPCfbp1PIrg1oIcchfhir1n;hfnGh1ohGfhh1Ip1pgCPi1Ii1<IGsfh12N1JCPhf1eCsio p1cCf1Dlt1nio1 lA1nfh1.fC;Ioho1ea1rgh1,UEN1Ar1Sni1n pC1eh1phhi1rgnr1np1rgh1 n;hfnGh1 ohGfhh1 IiSfhnphpm1 eCrg1 ,Dlt1 nio1,lA1IiSfhnph1PIrg1n1pIRI nf1rfhioN111Figure 1: Mean average connectivity reliability (MACR) and mean controllability index (MCI) in terms of average degree (<k>) of network.  EC1 (snirIca1 rgh1 SCffh nrICi1 ehrPhhi1 rgh1IiSfhnpIiG1rfhio1cCf1,Dlt1nio1,lA1Hnp1n;hfnGh1ohGfhh1 IiSfhnphpwm1 rgIp1 .n.hf1sp p1rgh1 AhnfpCiUp1SCffh nrICi1SChccISIhir1HDiG1nio1EniG1k33DwN1Egh1 AhnfpCiEp1 SCffh nrICi1 SChccISIhir1 Ip13N<x<F1cCf1rgh1SCffh nrICi1ehrPhhi1rgh1IiSfhnpIiG1rfhio1cCf1,Dlt1nio1,lA N1EC1 nin a>h1 rgh1 IR.nSrp1 cfCR1 ohGfhh1ghrhfCGhihIram1n1RhrfIS1rgnr1Rhnpsfhp1Ir1Ip1cIfpr a1ohcIiho1np1eh CPy1nii kknH2kwH2m11111111111111Hxw1Pghfh1kI1Ip1 rgh1ohGfhh1Cc1 iCoh1i1nio1VkW1Ip1 rgh1n;hfnGh1ohGfhh1Cc1rgh1ihrPCfbN11EgIp1 .n.hf1 Ghihfnrhp1 2m3331 ?foCp5thiaI1H?tw1fnioCR1 ihrPCfbp1H?foCp1nio1 thiaI1 2<F3w1nio1 2m3331USn h5cfhh1 ihrPCfbp1HTnfne>pI1 nio1D ehfr12<<<wN1Egh1?t1 ihrPCfb1 Ip1 n1 fnioCR1ihrPCfb1 PgCph1 ohGfhh1 oIprfIesrICi1 Cehap1 n1ACIppCi1oIprfIesrICi1PgI h1rgh1USn h5cfhh1ihrPCfb1Ip1n1 ihrPCfb1PIrg1ohGfhh1oIprfIesrICi1CehaIiG1n112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 1 F1.CPhf1  nPN1EC1 n;hfr1 rgh1 IR.nSrp1 cfCR1  Iib1ohipIra1 nio1 ihrPCfb1 pSn h1 Ci1 lt1 nio1 Elm1 rgh1isRehf1Cc1iCohp1nio1 Iibp1nfh1 .fhphf;ho1osfIiG1GhihfnrIiGN1<IGsfh1 k1 .fhphirp1 rgh1 ,Dlt1 nio1,lA1 Cc1 rghph1Ghihfnrho1ihrPCfbp1 Ii1 rhfRp1 Cc1oIcchfhir1 ohGfhhp1 Cc1ghrhfCGhihIra1HN1 Ar1 Sni1 eh1phhi1 np1 eCrg1 ,Dlt1 nio1 ,lA 1 ohSfhnphm1H1IiSfhnphpN1 Egh1 SCffh nrICi1 SChccISIhir1 ehrPhhi1rgh1rPC1Ssf;hp1Ip13N<<3:N111Figure 2: Mean average connectivity reliability (MACR) and mean controllability index (MCI) in terms of degrees of network heterogeneity (H). DSSCfoIiG1 rC1 rgh1.fh;ICsp1 fhps rpm1 n1 ohiph1nio1gCRCGhihCsp1ihrPCfb1Ip1ehrrhf1rgni1n1p.nfph1nio1 ghrhfCGhihCsp1 ihrPCfb1 siohf1 eCrg1 lt1 nio1El1 SCipIohfnrICipL n1 bha1 IipIGgr1 cCf1 pRnfr1IicfnprfsSrsfh1ihrPCfb1ohpIGiN1EgIp1cIioIiG1SCs o1n pC1 GsIoh1 rgh1 IR.fC;hRhir1 Cc1 h)IprIiG1IicfnprfsSrsfh1ihrPCfbpm1PgISg1rhio1rC1eh1p.nfphm1niom1oh.hioIiG1 Cc1 rgh1 paprhRm1.Cpphpp1;nfICsp1ohGfhhp1 Cc1 ghrhfCGhihIraN10rghf1cnSrCfp1 pgCs o1n pC1 eh1 rnbhi1 IirC1 SCipIohfnrICi1 Ii1 .fnSrISn 1hiGIihhfIiG1ohpIGim1IiS soIiG1SCprpm1esr1rgha1nfhohchffho1cCf1csrsfh1fhphnfSgN11BN d0v?1A,A0tEDdl? 1DSSCfoIiG1 rC1 rgh1 ohcIiIrICi1 Cc1 iCoh1IR.CfrniSh1Ii1rhfRp1Cc1lt1nio1El1 pgCPi1Ii1?(N1Hkw1 nio1 ?(N1 HFwm1 rgIp1 prsoa1 SCR.srhp1 rgh1IR.CfrniSh1cCf1n  1rgh1iCohp1Cc1rgh1pI)1SIra5 h;h 1AEdp1prsoIho1 Ii1 rgIp1 .n.hfN1<IGsfh1 :1pgCPp1 rgh1Rhni1 iCoh1 IR.CfrniSh1 Ii1 rhfRp1 Cc1 lt1 HMNIt w1nio1 rgh1 Rhni1 iCoh1 IR.CfrniSh1 Ii1 rhfRp1 Cc1ElHMNIl wN1Ar1Ip1cCsio1rgnr1gIGg1ohGfhh1iCohp1rhio1rC1gn;h1gIGghf1IR.CfrniSh1Ii1rhfR1Cc1eCrg1lt1nio1El N1Egh1SCffh nrICi1SChccISIhir1Ip13N<x@3N11 Figure 3: Mean NI of different degree nodes in terms of CR and TC.   Figure 4: Correlation between node importance rankings in terms of CR and TC: (a) generator nodes; (b) substation nodes.  EgIp1 .n.hf1 n pC1 h). Cfhp1 dA1 cCf1 IioI;Iosn 1iCohpy1 Ir1 cIfpr1 fnibp1n  1 rgh1 iCohp1 nSSCfoIiG1 rC1rghIf1IR.CfrniSh1Ii1ohpShioIiG1CfohfN1?nSg1iCoh1gnp1 rPC1 fnibIiGpm1 lt5enpho1 nio1 El5enpho1 Hx5n)Ip1 nio1y5n)Ip1 Ii1 <IGsfh1 Dm1 fhp.hSrI;h awN1 Egh1iCohp1 nfh1 oI;Ioho1 IirC1 rPC1 SnrhGCfIhpy112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 1 x1pseprnrICip1 nio1GhihfnrCfpm1PgISg1 nfh1 pgCPi1 Ii1<IGsfh1DHnw1nio1DHewm1fhp.hSrI;h aN1Ar1Sni1eh1phhi1rgnr1 cCf1 RCpr1 Cc1 rgh1 pseprnrICi1 iCohpm1 gIGg1fnibIiG1 Ii1 rhfRp1 Cc1 El1 SCffhp.Ciop1 rC1 gIGg1fnibIiG1 Ii1 rhfRp1 Cc1 ltm1 nio1 rgIp1 ohRCiprfnrhp1rgnr1 lt1 ps..Cfrp1El1cCf1RCpr1Cc1 rgh1pseprnrICi1iCohpN1jCPh;hfm1cCf1GhihfnrC1i ohpm1rghfh1Ip1iC1prfCiG1SCffh nrICi1ehrPhhi1El1 fnibIiGp1nio1lt1fnibIiGpm1 RnIi a1 ehSnsph1 Cc1 rgh1 rC.C CGISn 1hR.gnpIp1Cc1rgh1Ssffhir1prsoam1np1GhihfnrCfp1nfh1IR.Cfrnir1 h hRhirp1 cfCR1 n1 csiSrICin Ira1.hfp.hSrI;hN1 Eghph1 .fh IRIinfa1 cIioIiGp1 pgCP1rgnr1 fh IneI Ira5enpho1 Rhnpsfhp1 Sni1 IohirIca1 nio1IicCfR1C.hfnrCfp1neCsr1IR.Cfrnir1iCohpm1iCr1Ci a1cCf1 cnI sfh1 .fh;hirICi1 esr1 n pC1 cCf1 csrsfh1SCirfC  neI IraN1? hRhirp1IohirIcIho1np1SfIrISn 1cCf1fh IneI Ira5enpho1paprhR1ohpIGim1RnIirhiniSh1nio1fhprCfnrICi1 Rna1 ps..Cfr1rgh1 hRefnShRhir1 Cc1pRnfr1rhSgiC CGIhp1rgnr1hine h1SCirfC  neI Ira1nio1fhSCicIGsfneI IraN11FN l0dlJBUA0dU 1EgIp1 .n.hf1 rnbhp1 pI)1 SIra5 h;h 1 . 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