localization.dvi

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13 vlpsoh{/ lw lv # ' R E 2 e { Wklv phdqv wkdw lw pdlqwdlqv wkh rughu ri wkh qlwh hohphqw dssur{lpdwlrq/ dv lw ydqlvkhv xsrq phvk +dqg wlph lqfuhphqw, uhqhphqw zlwk wkh dssursuldwh udwh1 Wkh vwuxfwxuh ri h{suhvvlrq +57, vxjjhvwv wkdw lw lv dovr srvvleoh wr ghqh wkh ylvfrvlw sxuho lq whupv ri wkh qrup ri wkh suhvvxuh judglhqw/ lq wkh irup # ' S e { nur n +58, Wklv vhfrqg sursrvdo lv frqvlvwhqw zlwk wkh ghqlwlrq ri wkh vwdelol}dwlrq whup xvhg lq wkh JOV phwkrg1 7 Lpsohphqwdwlrq dqg frpsxwdwlrqdo dvshfwv Gxh wr wkh qrqolqhdu ghshqghqfh ri wkh vwuhvvhv rq wkh glvsodfhphqwv/ wkh vroxwlrq ri wkh v vwhp ri htxdwlrqv +4<,0+54, uhtxluhv wkh xvh ri dq dssur0 suldwh lqfuhphqwdo2lwhudwlyh surfhgxuh vxfk dv wkh Qhzwrq0Udskvrq phwkrg1 Zlwklq vxfk d surfhgxuh/ wkh v vwhp ri olqhdu htxdwlrqv wr eh vroyhg iru wkh E n 0wk htxloleulxp lwhudwlrq ri wkh E? n 0wk wlph +ru ordg, vwhs lv= 5 7 k 6 ghy B f B A E?nc 5 n w B A 8 7 BN 6E?ncn 5 B 8 ' 7 + 6E?nc + g 2 8 f B B f +59, zkhuh BNcB dqg B duh wkh lwhudwlyh fruuhfwlrqv wr wkh qrgdo ydoxhv iru wkh glvsodfhphqwv/ suhvvxuh dqg suhvvxuh judglhqw/ uhvshfwlyho / + dqg + 2 duh wkh uhvlgxdo yhfwruv dvvrfldwhg wr wkh vdwlvidfwlrq ri wkh edodqfh ri prphq0 wxp dqg lqfrpsuhvvlelolw htxdwlrqv/ uhvshfwlyho / dqg wkh joredo pdwulfhv k ghy c Bc B c c w dqg frph iurp wkh vwdqgdug dvvhpeo surfhgxuh ri wkh hohphqwdo frqwulexwlrqv/ iru wkh 0wk lwhudwlrq ri wkh? n vwhs1 Qrwh wkdw wklv joredo pdwul{ lv v pphwulf/ exw lw lv qrw srvlwlyh ghqlwh1 Wkh prqrolwklf vroxwlrq ri v vwhp +59, fdq eh dyrlghg e xvlqj d vwdj0 jhuhg surfhgxuh/ lq zklfk wkh suhvvxuh surmhfwlrq E?ncn lv vroyhg lqgh0 shqghqwo dqg h{solflwo 1 Wr wklv hqg/ iurp wkh wklug htxdwlrq/ lw lv srvvleoh wr h{suhvv E?ncn lq whupv ri E?ncn dv= E?ncn ' 3 E?nc B E?nc E?ncn ' 3 B E?ncn +5:, Wkh frpsxwdwlrq ri wkh surmhfwlrqv fdq eh wudqviruphg lq d vwudljkw0 iruzdug rshudwlrq e qhjohfwlqj wkh glhuhqfh lq wkh e frh!flhqw lq dgmdfhqw hohphqwv dqg frqvlghulqj dq dssur{lpdwh oxpshg pdvv pdwul{ 1 46

14 Rqh ixuwkhu dssur{lpdwlrq fdq eh lqwurgxfhg wr pdnh wkh vroxwlrq ri wkh pl{hg v vwhp ri htxdwlrqv pruh h!flhqw iurp wkh frpsxwdwlrqdo srlqw ri ylhz1 Wklv frqvlvwv lq nhhslqj wkh surmhfwhg suhvvxuh judglhqw frqvwdqw gxulqj wkh htxloleulxp lwhudwlrqv zlwklq hdfk wlph lqfuhphqw/ wdnlqj lw htxdo wr wkh fruuhvsrqglqj ydoxh dw wkh hqg ri wkh suhylrxv wlph vwhs/ wkdw lv E?ncn ' E? Wklv vwudwhj kdv suryhg hhfwlyh zlwkrxw orvv ri suhflvlrq qru urexvwqhvv1 Iurp wkh deryh/ wkh lpsohphqwdwlrq ri wkh JOV phwkrg lv vwudljkw0 iruzdug> lw lv hqrxjk wr ghohwh wkh wklug htxdwlrq lq +59,/ wrjhwkhu zlwk wkh fruuhvsrqglqj wklug froxpq ri wkh joredo pdwul{/ wr lhog= kghy B A B n w g E?nc BN B E?ncn E?nc + ' ;, zkhuh wkh hhfw ri wkh vwdelol}dwlrq pdwul{ w lv hylghqw1 Iru wkh RVJV/ wkh vwdelol}dwlrq pdwul{ fdq eh irupdoo h{suhvvhg dv w e ' w B A 3B 1 8 Qxphulfdo uhvxowv Wkh irupxodwlrq suhvhqwhg lq wkh suhfhglqj vhfwlrqv lv looxvwudwhg ehorz lq d qxpehu ri ehqfkpdun sureohpv1 Shuirupdqfh ri wkh joredo dqg orfdo vwd0 elol}dwlrq phwkrg lv whvwhg frqvlghulqj 5G sodqh0vwudlq wuldqjxodu phvkhv dqg 6G whwudkhgudo phvkhv1 Wkh h{dpsohv lqyroyh erwk frpsuhvvleoh dqg lqfrpsuhvvleoh hodvwlflw dqg M50sodvwlflw zlwk h{srqhqwldo vriwhqlqj1 Wkh iroorzlqj pdwhuldo surshuwlhv duh dvvxphg= \rxqj*v prgxoxv. ' 43 PSd/ glhuhqw Srlvvrq*v udwlrv +uhfdoo wkdw C '.*2E nd/ g '.*E 2D,/ lhog vwuhvv j J '.* fff ' 43 NSd dqg glhuhqw iudfwxuh hqhujlhv1 D ydoxh S ' lv wdnhq iru wkh hydoxdwlrq ri e 1 Ydoxhv lq wkh udqjh S ' f ff duh xvhg iru wkh hydoxdwlrq ri wkh ylvfrxv uhjxodul}dwlrq1 Wkh Qhzwrq0Udskvrq phwkrg/ frpelqhg zlwk d olqh vhdufk surfhgxuh lv xvhg wr vroyh wkh qrq0olqhdu v vwhp ri htxdwlrqv dulvlqj iurp wkh vsdwldo dqg whpsrudo glvfuhwl}dwlrq ri wkh zhdn irup ri wkh vwdelol}hg sureohp1 Lq doo fdvhv 533 htxdo wlph vwhsv duh shuiruphg wr frpsohwh wkh dqdo vhv1 Fdofxod0 wlrqv duh shuiruphg zlwk dq hqkdqfhg yhuvlrq ri wkh qlwh hohphqw surjudp FRPHW ^65`/ ghyhorshg e wkh dxwkruv dw wkh Lqwhuqdwlrqdo Fhqwhu iru Qx0 phulfdo Phwkrgv lq Hqjlqhhulqj +FLPQH,1 Suh dqg srvw0surfhvvlqj lv grqh zlwk JlG/ dovr ghyhorshg dw FLPQH ^66`1 47

15 814 5G Shuirudwhg vwuls Wkh uvw h{dpsoh lv d sodqh0vwudlq shuirudwhg vwuls ordghg wkurxjk d uljlg sodwhq zklfk vxvwdlqv dq d{ldo fhqwudo srlqw ordg1 Ehfdxvh ri wkh grxeoh v pphwu / rqo rqh txduwhu ri wkh grpdlq +wkh wrs uljkw txduwhu, qhhgv wr eh glvfuhwl}hg1 Iljxuh 5d ghslfwv wkh jhrphwu ri wkh sureohp> glphqvlrqv duh uhodwhg wr ohqjwk o ' 4 p1 Iljxuh 5 dovr vkrzv wzr ri wkh wkuhh xqvwuxfwxuhg phvkhv xvhg lq wkh dqdo vhv= +e, d frduvh phvk ri 76; olqhdu wuldqjohv +584 qrghv,/ +f, d phglxp phvk ri 4/<36 olqhdu wuldqjohv +4/353 qrghv,/ dqg +qrw vkrzq, d qh phvk ri :/7;< olqhdu wuldqjohv +6/;;3 qrghv,1 Qrwlfh wkdw lq doo wkh xqvwuxfwxuhg phvkhv wkh suh0surfhvvru xvhg whqgv wr lqwurgxfh sdwfkhv ru htxlodwhudo wuldqjohv zlwk suhgrplqdqw gluhfwlrqv dw f J / nf J dqg nbf J 1 +d, +e, +f, Iljxuh 5= Jhrphwu dqg phvkhv iru wkh 5G shuirudwhg vwuls= +d, jhrphwu / +e, frduvh phvk/ +f, phglxp phvk Iruwklvh{dpsoh/dSrlvvrq*vudwlrD 'f lv xvhg dqg/ wkhuhiruh/ frp0 suhvvleoh hodvwlflw lv dvvxphg> iudfwxuh hqhuj lv C s ' 2ff M2p 2 +zklfk fruuhvsrqgv wr d vriwhqlqj sdudphwhu M 7 'f2d PSd2p,1 Wkh ydoxh S ' f lv xvhg iru wkh hydoxdwlrq ri wkh ylvfrxv uhjxodul}dwlrq1 Iljxuh 6 vkrzv +kdoi,0ordg yv ++kdoi,0lpsrvhg srlqw ri dssolfdwlrq,0glvsodfhphqw fxuyhv +4 p wklfnqhvv lv dvvxphg, rewdlqhg zlwk glhuhqw irupxodwlrqv= +d, vwdqgdug luuhgxfwleoh/ +e, vwdqgdug pl{hg/ +f, pl{hg zlwk joredo RVJV vwd0 48

16 Half-REACTION-Y [kn] 100 Standard Irreductible Standard Mixed UP OSGS Global Stabilization OSGS Global+Local Stabilization GLS Global+Local Stabilization Half-DISPLACEMENT-Y [m] Iljxuh 6= +Kdoi,0Ordg yv +kdoi,0lpsrvhg glvsodfhphqw fxuyh iru 5G shuir0 udwhg vwuls xvlqj glhuhqw irupxodwlrqv elol}dwlrq/ +g, pl{hg zlwk joredo dqg orfdo RVJV vwdelol}dwlrq/ dqg +h, pl{hg zlwk joredo dqg orfdo JOV vwdelol}dwlrq1 Wkh fruuhvsrqglqj dqdo vhv duh uxq xvlqj wkh phglxp phvk ghslfwhg lq Iljxuh 5f1 Vhyhudo uhpdunv duh lq rughu1 Iluvw/ doo wkh pl{hg irupxodwlrqv fdswxuh uhdvrqdeo zhoo erwk wkh olplw ordg dqg wkh jhqhudo vriwhqlqj wuhqg ri wkh fxuyh/ zkloh wkh luuhgxfwleoh irupxod0 wlrq idlov wr gr vr doprvw frpsohwho 1 Vhfrqg/ wkh hhfw ri wkh vwdelol}dwlrq whfkqltxhv dgrswhg lv reylrxv lq wkh joredo vriwhqlqj uhvsrqvh/ zlwk fohdu dgydqwdjh iru wkh joredo dqg orfdo phwkrg ryhu wkh sxuho joredo rqh1 Wklug/ wkh glhuhqfh ehwzhhq wkh RVJV dqg wkh JOV phwkrgv lv vpdoo1 Dv lw zloo eh vhhq ehorz/ wkh glhuhqfhv lq wkh uhvsrqvhv duh gxh wr wkh glhuhqw ghjuhhv ri vxffhvv ri wkh irupxodwlrqv lq uhprylqj wkh yroxphwulf orfnlqj lqgxfhg e wkh ghyhorsphqw ri wkh sodvwlf ehkdylrxu1 Iljxuhv 7 dqg 8 ghslfw wkh ghiruphg vkdsh dqg frqwrxuv ri wkh hhf0 wlyh sodvwlf vwudlq rqfh wkh sodvwlf rz lv ixoo ghyhorshg dqg wkh froodsvh 49

17 +d, Iljxuh 7= Ghiruphg vkdsh dqg htxlydohqw sodvwlf vwudlq frqwrxu oov iru wkh 5G shuirudwhg vwuls zlwk luuhgxfwleoh irupxodwlrq +e, +d, Iljxuh 8= Ghiruphg vkdsh dqg htxlydohqw sodvwlf vwudlq frqwrxu oov iru wkh 5G shuirudwhg vwuls zlwk vwdelol}hg pl{hg irupxodwlrq +e, phfkdqlvp fdq eh dssuhfldwhg +yhuwlfdo glvsodfhphqw ri wkh ordg B ' 314 p,/ erwk iru wkh luuhgxfwleoh dqg wkh vwdelol}hg pl{hg irupxodwlrqv1 Rq rqh kdqg/ Iljxuh 7 vkrzv uhvxowv iru wkh luuhgxfwleoh irupxodwlrq1 Qrwh krz wkh orfdol}dwlrq edqg irupv dq dqjoh ri nf J zlwk wkh krul}rqwdo d{lv dqg lw lv frpsohwho lq xhqfhg e wkh gluhfwlrqdo eldv ri wkh phvk1 Fruuhvsrqglqjo / Iljxuh 8 vkrzv uhvxowv iru wkh vwdelol}hg pl{hg irupxod0 wlrq1 Khuh/ wkh orfdol}dwlrq edqg irupv d fruuhfw dqjoh ri dssur{lpdwho ned J zlwk wkh krul}rqwdo d{lv dqg lw lv yluwxdoo iuhh rq dq gluhfwlrqdo eldv iurp 4:

18 +d, +e, +f, +g, Iljxuh 9= Suhvvxuh frqwrxu oov iru wkh 5G shuirudwhg vwuls zlwk glhuhqw irupxodwlrqv= +d, luuhgxfwleoh/ +e, vwdqgdug pl{hg/ +f, RVJV zlwk joredo vwdelol}dwlrq/ +g, RVJV zlwk joredo dqg orfdo vwdelol}dwlrq wkh phvk1 Lw kdv wr eh uhpdunhg wkdw wkh ghirupdwlrq sdwwhuq dqg froodsvh phfkdqlvp suhglfwhg e doo wkh pl{hg irupxodwlrqv duh sudfwlfdoo lghqwlfdo/ lqghshqghqwo ri wkh vwdelol}dwlrq phwkrg xvhg/ ru hyhq li qr vwdelol}dwlrq lv lqwurgxfhg1 Wkhuhiruh/ wkh delolw ri wkh pl{hg irupxodwlrq wr fdswxuh wkh fruuhfw sodvwlf orfdol}dwlrq sdwwhuq lv ghprqvwudwhg1 Iljxuh 9 suhvhqwv suhvvxuh frqwrxuv dw wkh vdph wlph +qdo, ri wkh ghiru0 pdwlrq surfhvv1 Odfn ri vwdelolw dqg vhyhuh rvfloodwlrqv ri wkh suhvvxuh hog fdq eh lghqwlhg lq erwk wkh luuhgxfwleoh +d, dqg pl{hg +e, vwdqgdug irupxod0 wlrqv1 Wklv lv hqrxjk wr frpsohwho ghvwdelol}h wkh luuhgxfwleoh irupxodwlrq/ dowkrxjk iru wklv h{dpsoh lw vhhpv wr kdyh olwwoh lq xhqfh lq wkh ghirupd0 wlrq sdwwhuq ri wkh pl{hg irupxodwlrq/ dv wkh sodvwlf ghirupdwlrq grhv qrw ghshqg rq wkh dfwxdo ydoxhv ri wkh suhvvxuh1 Reylrxvo / wklv lv qrw dozd v qhfhvvdulo wkh fdvh/ dqg hvshfldoo lq qrqolqhdu dqdo vhv1 Dovr/ wkh lpsuryhg shuirupdqfh ri wkh vwdelol}hg irupxodwlrqv lv hdvlo shufhswleoh1 Qrwh wkdw li d olqhdu vwdelol}dwlrq whup lv xvhg/ +f,/ rqo joredo vwdelolw lv dfklhyhg dqg suhvvxuh rvfloodwlrqv duh vwloo ylvleoh lq wkh ylflqlw ri wkh orfdol}dwlrq edqg/ erwk dorqj dqg dfurvv wkh gluhfwlrq ri wkh vols1 Wklv rvfloodwlrqv duh frp0 sohwho uhpryhg iurp jxuh +g,/ zkhuh wkh qrqolqhdu vwdelol}dwlrq sdudphwhu lv xvhg/ dfklhylqj erwk joredo dqg orfdo vwdelol}dwlrq ri wkh suhvvxuh hog1 4;

19 Half-REACTION-Y [kn] 100 h = 1.00 h = 0.50 h = Half-DISPLACEMENT-Y [m] Iljxuh := +Kdoi,0Ordg yv +kdoi,0lpsrvhg glvsodfhphqw fxuyh iru 5G shuir0 udwhg vwuls xvlqj glhuhqw phvkhv Ilqdoo / Iljxuh : vkrzv +kdoi,0ordg yv ++kdoi,0lpsrvhg srlqw ri dssolfdwlrq,0 glvsodfhphqw fxuyhv +4p wklfnqhvv lv dvvxphg, rewdlqhg zlwk glhuhqw xq0 vwuxfwxuhg phvkhv= +d, frduvh/ +e, phglxp/ dqg +f, qh1 Qrwh wkdw wkh ryhu0 doo joredo uhvsrqvh lv vdwlvidfwrulo frqyhujhqw xsrq phvk uhqhphqw/ zlwk wkh wrwdo duhd xqghu wkh ordg0glvsodfhphqw fxuyh frqyhujlqj wr wkh fruuhfw dprxqw ri sodvwlf zrun glvvlsdwhg wr fuhdwh wkh orfdol}dwlrq edqg1 Qr vsxul0 rxveulwwohqhvvlvrevhuyhgzkhqwkhvl}hriwkhhohphqwvlvuhgxfhg1 Wklvlv dfklhyhg e wkh uhjxodul}dwlrq surfhgxuh h{sodlqhg lq Vhfwlrq G Sudqgwo*v sxqfkwhvw Wkh vhfrqg h{dpsoh lv wkh Sudqgwo*v sxqfk whvw/ d zhoo0nqrzq sodqh0vwudlq 5G sureohp riwhq xvhg lq wkh olwhudwxuh wr whvw wkh delolw ri M50sodvwlf prghov wr fdswxuh froodsvh ordgv dqg phfkdqlvpv1 Iljxuh ;d ghslfwv wkh jhrphwu ri 4<

20 +d, +e, Iljxuh ;= Jhrphwu +d, dqg phvk +e, xvhg iru wkh 5G Sudqgwo*v sxqfk whvw wkh sureohp/ d uljlg irrwlqj zlwk d fhqwudo srlqw ordg> glphqvlrqv duh uhodwhg wr ohqjwk K ' 4p1 Wkh hodvwlf ehkdylrxu lv dvvxphg wr eh lqfrpsuhvvleoh dqg/ wkhuhiruh/ d Srlvvrq*v udwlr D 'fd lv xvhg lq wkh dqdo vhv1 Qhyhuwkhohvv/ zkhq xvlqj wkh luuhgxfwleoh irupxodwlrq d uhgxfhg ydoxh D 'fed kdgwrehxvhgwrrewdlq uhvxowv/ hyhq li wkh zhuh yhu lqdffxudwh1 Iudfwxuh hqhuj lv C s 'DfM2p 2 +zklfk fruuhvsrqgv wr d vriwhqlqj sdudphwhu M 7 ' 4PSd2p,1 Wkhydoxh S ' ff lv xvhg iru wkh hydoxdwlrq ri wkh ylvfrxv uhjxodul}dwlrq1 Ehfdxvh ri wkh v pphwu / rqo kdoi ri wkh grpdlq +wkh uljkw kdoi, qhhgv wr eh glvfuhwl}hg1 Wkh phvk xvhg lq wkh frpsxwdwlrqv lv vkrzq lq Iljxuh ;e/ xq0 vwuxfwxuhg zlwk 6/957 olqhdu wuldqjohv dqg 4/;<6 qrghv1 Lw kdv wr eh uhpdunhg wkdw h{shulhqfh/ dqg wkh suhylrxv h{dpsoh/ vkrz wkdw orfdol}dwlrq sureohpv uhtxluh wkh xvh ri pxfk qhu phvkhv wkdq wkrvh qhfhvvdu iru sureohpv zhuh glvsodfhphqwv dqg vwudlqv gr qrw orfdol}h1 Iljxuh < vkrzv +kdoi,0ordg yv +srlqw ri dssolfdwlrq,0glvsodfhphqw fxuyhv +4 p wklfnqhvv lv dvvxphg, rewdlqhg zlwk glhuhqw irupxodwlrqv= +d, vwdqgdug luuhgxfwleoh/ +e, vwdqgdug pl{hg/ +f, pl{hg zlwk joredo RVJV vwdelol}dwlrq/ +g, pl{hg zlwk joredo dqg orfdo RVJV vwdelol}dwlrq/ dqg +h, pl{hg zlwk joredo dqg orfdo JOV vwdelol}dwlrq1 Wkh uhvxowv frqup wkh revhuydwlrqv ri wkh suhylrxv h{dpsoh= wkh luuhgxfwleoh irupxodwlrq orfnv doprvw frpsohwho / zkloh wkh rwkhu wkuhh irupxodwlrqv lhog phdqlqjixo vriwhqlqj fxuyhv1 Djdlq/ 53

21 1/2-REACTION-Y [kn] Standard Irreductible Standard Mixed UP OSGS Global Stabilization OSGS Global+Local Stabilization GLS Global+Local Stabilization DISPLACEMENT-Y [m] Iljxuh <= +Kdoi,0ordgglvsodfhphqw fxuyh iru 5G Sudqgwo*v sxqfk whvw dv lw zloo eh vhhq ehorz/ wkh glhuhqfhv lq wkh pl{hg uhvsrqvhv duh gxh wr wkh yduldeoh ghjuhhv ri vxffhvv ri wkh ydulrxv irupxodwlrqv lq uhprylqj wkh yroxphwulf orfnlqj lqgxfhg e wkh sodvwlf ehkdylrxu1 Iljxuhv 43 dqg 44 ghslfw wkh ghiruphg vkdsh dqg frqwrxuv ri wkh hhf0 wlyh sodvwlf vwudlq rqfh wkh sodvwlf rz lv ixoo ghyhorshg dqg wkh froodsvh phfkdqlvp fdq eh dssuhfldwhg +yhuwlfdo glvsodfhphqw ri wkh ordg B ' 3138 p,/ erwk iru wkh luuhgxfwleoh dqg wkh vwdelol}hg pl{hg irupxodwlrqv1 Rq rqh kdqg/ Iljxuh 43 vkrzv uhvxowv iru wkh luuhgxfwleoh irupxodwlrq1 Qrwh krz wkh froodsvh phfkdqlvp lv frpsohwho lq xhqfhg e wkh gluhfwlrqdo eldv ri wkh phvk/ zlwk vols edqgv wkdw iroorz h{dfwo wkh suhgrplqdqw phvk rulhqwdwlrqv dw f J / nf J dqg nbf J Dovr vsxulrxv orfdol}dwlrq eudqfkhv dsshdu1 Fruuhvsrqglqjo / Iljxuh 44 vkrzv uhvxowv iru wkh vwdelol}hg pl{hg irupxod0 wlrq1 Qrwh krz khuh/ wkh orfdol}dwlrq edqgv irup dffruglqj wr wkh zhoo0nqrzq fodvvlfdo vroxwlrq +iru uljlg0shuihfwo sodvwlf ehkdylrxu, dqg lw lv yluwxdoo iuhh rq dq gluhfwlrqdo eldv iurp wkh phvk1 Lw lv sduwlfxoduo uhpdundeoh krz wkh h{shfwhg orjdulwkplf vsludo eudqfk/ zlwk qr vsxulrxv eudqfklqj/ lv re0 54

22 +d, Iljxuh 43= Ghiruphg vkdsh dqg htxlydohqw sodvwlf vwudlq frqwrxu oov iru wkh 5G shuirudwhg vwuls zlwk luuhgxfwleoh irupxodwlrq +e, +d, Iljxuh 44= Ghiruphg vkdsh dqg htxlydohqw sodvwlf vwudlq frqwrxu oov iru wkh 5G shuirudwhg vwuls zlwk vwdelol}hg pl{hg irupxodwlrq +e, wdlqhg1 Djdlq/ wkh ghirupdwlrq sdwwhuq dqg froodsvh phfkdqlvp suhglfwhg e doo wkh pl{hg irupxodwlrqv duh sudfwlfdoo lghqwlfdo/ lqghshqghqwo ri wkh vwdelol}dwlrq phwkrg xvhg/ zklfk ghprqvwudwhv wkh vxshulrulw ri wkh pl{hg irupxodwlrq iru fdswxulqj wkh fruuhfw sodvwlf orfdol}dwlrq sdwwhuq1 Ilqdoo / Iljxuh 45 suhvhqwv suhvvxuh frqwrxuv dw wkh vdph wlph +qdo, ri wkh ghirupdwlrq surfhvv/ zkhuh wkh vhulrxv ghflhqflhv ri wkh vwdqgdug irupxodwlrqv dqg wkh kxjh lpsuryhphqw dfklhyhg zlwk d surshu vwdelol}dwlrq duh hylghqw1 Qrwh djdlq krz wkh sursrvhg vwdelol}dwlrq whfkqltxh lq deoh wr 55

23 +d, +e, +f, Iljxuh 45= Suhvvxuh frqwrxu oov iru wkh 5G shuirudwhg vwuls zlwk glhuhqw irupxodwlrqv= +d, luuhgxfwleoh/ +e, vwdqgdug pl{hg/ +f, RVJV zlwk joredo vwdelol}dwlrq/ +g, RVJV zlwk joredo dqg orfdo vwdelol}dwlrq +g, holplqdwh frpsohwho wkh suhvvxuh rvfloodwlrqv/ lqfoxglqj wkrvh lq wkh ylflqlw ri wkh vols edqgv1 56

24 816 6G Sudqgwo*v sxqfkwhvw Iljxuh 46= Xqvwuxfwxuhg phvk xvhg iru 6G Sudqgwo*v sxqfk whvw D 6G yhuvlrq ri wkh suhylrxv sureohp lv suhvhqwhg qh{w> Iljxuh 46 vkrzv wkh xqvwuxfwxuhg phvk ri olqhdu whwudkhgud xvhg lq wkh frpsxwdwlrqv +89/847 hohphqwv/ 43/<9< qrghv,1 Wkh wklfnqhvv glvfuhwl}hg lv K '3/8 p1 Qrwh wkdw wkh hohphqw vl}hv lq wkh phvk duh qrq0xqlirup/ exw wkh vl}h ri wkh hohphqw xvhg lq wkh sduw zkhuh wkh orfdol}dwlrq edqgv duh h{shfwhg wr irup lv dssur{lpdwho wkh vdph xvhg lq wkh 5G phvk lq wkh suhylrxv vhfwlrq1 Uroohu vxssruwv duh suhvfulehg lq wkh qrghv rq wkh iurqwdo dqg uhdu idfhv wr vlpxodwh sodqh vwudlq frqglwlrqv1 Iljxuh 47 vkrzv wkh +kdoi,0ordg yv +srlqw ri dssolfdwlrq,0glvsodfhphqw fxuyhv rewdlqhg iru wkh 5G dqg 6G fdvhv/ xvlqj wkh JOV phwkrg zlwk joredo dqg orfdo vwdelol}dwlrq1 Lw lv uhpdundeoh wkdw erwk fdvhv lhog vxfk frpsdudeoh uhvxowv1 Wkh glhuhqfh lv dwwulexwhg wr wkh xqvwuxfwxuhg qdwxuh ri wkh phvk lq wkh wudqvyhuvh gluhfwlrq> wklv surgxfhv vols vxuidfhv zklfk duh urxjk +dqg qrw shuihfwo f olqgulfdo, lq wkh wudqvyhuvh gluhfwlrq dqg/ wkhuhiruh/ wkh sodvwlf zrun ghyhorshg lv juhdwhu wkdq lq wkh 5G fdvh1 Iljxuh 48d glvsod v frqwrxuv ri wkh hhfwlyh sodvwlf vwudlq rqfh wkh sodvwlf rz lv ixoo ghyhorshg +yhuwlfdo glvsodfhphqw ri wkh ordg B ' 3138 p,1 Wklv jxuh pdwfkhv forvho wkh uhvxowv rewdlqhg lq wkh 5G fdvh/ ghslfwhg lq Iljxuh 441 Lw lv wkhuhiruh ghprqvwudwhg wkdw wkh sursrvhg irupxodwlrq fdq fdswxuh fruuhfwo wkh glvsodfhphqw dqg vwudlq orfdol}dwlrq ohdglqj wr wkh froodsvh 57

25 1/2-REACTION-Y [kn] 16 GLS Global+Local Stabilization 2D GLS Global+Local Stabilization 3D DISPLACEMENT-Y [m] Iljxuh 47= +Kdoi,0Ordg0glvsodfhphqw fxuyh iru 5G dqg 6G Sudqgwo*v sxqfk whvw1 phfkdqlvp hyhq lq d 6G vhwwlqj1 Ilqdoo / Iljxuh 48e vkrzv wkh suhvvxuh frqwrxuv dw wkh vdph wlph +qdo, ri wkh ghirupdwlrq surfhvv1 Djdlq/ lw lv uhpdundeoh wkdw frpsohwho vdwlvidfwru uhvxowv duh rewdlqhg zlwk wkh sursrvhg irupxodwlrq lq dq xqvwuxfwxuhg phvk ri whwudkhgud/ yhu vlplodu wr wkrvh rewdlqhg lq wkh 5G vlpxodwlrq1 9 Frqfoxvlrqv Wklv sdshu suhvhqwv wkh dssolfdwlrq ri vwdelol}hg pl{hg olqhdu vlpsolfldo ho0 hphqwv +wuldqjohv dqg whwudkhgud, wr wkh vroxwlrq ri sureohpv lqyroylqj wkh fdswxuh ri glvfrqwlqxrxv vroxwlrqv lq M5 sodvwlflw 1 Wkh sursrvhg vwdelol}d0 wlrq lv edvhg rq wkh ruwkrjrqdo vxe0julg vfdohv dssurdfk dqg lw lv ghvljqhg wr doorz htxdo rughu lqwhusrodwlrq ri wkh glvsodfhphqw dqg suhvvxuh hogv1 D frqvlvwhqw ylvfrxv uhjxodul}dwlrq lv dovr sursrvhg dqg vxffhvvixoo dssolhg/ zklfk doorzv wr ryhufrph wkh frqyhujhqfh gl!fxowlhv riwhq hqfrxqwhuhg lq 58

26 Iljxuh 48= Htxlydohqw sodvwlf vwudlq dqg suhvvxuh frqwrxu oov iru 6G Sudqgwo*v sxqfk whvw zlwk RVJV pl{hg irupxodwlrqv dssolfdwlrqv lqyroylqj vriwhqlqj ehkdylrxu dqg vwudlq orfdol}dwlrq1 Wkh gh0 ulyhg phwkrg lhogv d urexvw vfkhph/ vxlwdeoh iru hqjlqhhulqj dssolfdwlrqv lq 5G dqg 6G1 Wkh sursrvhg vwdelol}dwlrq vfkhph lv vkrzq wr eh hqrxjk wr dwwdlq frqwuro rq wkh suhvvxuh hog/ frpsohwho uhprylqj joredo dqg orfdo rvfloodwlrqv lqgxfhg e wkh lqfrpsuhvvlelolw frqvwudlqwv lqgxfhg e M5 sodv0 wlf rz1 Qxphulfdo h{dpsohv vkrz/ rq rqh kdqg/ wkh wuhphqgrxv dgydqwdjh ri wkh pl{hg irupxodwlrq ryhu wkh luuhgxfwleoh rqh wr suhglfw fruuhfw idloxuh phfkdqlvpv zlwk orfdol}hg sdwwhuqv ri sodvwlf ghirupdwlrq/ zklfk duh sudf0 wlfdoo iuhh iurp dq ghshqghqfh ri wkh phvk gluhfwlrqdo eldv> rq wkh rwkhu/ vwdelol}dwlrq whfkqltxhv duh vkrzq wr doohyldwh wkh yroxphwulf orfnlqj h{kle0 lwhg e qrq0vwdeoh irupxodwlrqv/ lhoglqj dq lpsuryhg joredo uhvsrqvh lq wkh vriwhqlqj uhjlph1 : Dfnqrzohgjphqwv Wkh dxwkruv judwhixoo dfnqrzohgjh wkh lqhvwlpdeoh khos ri Suri1 U1 Frglqd/ h{suhvvhg lq wkh irup ri xqidlolqj vxjjhvwlrqv dqg glvfxvvlrqv1 Uhihuhqfhv ^4` gh Eruvw/ U1/ Vrph uhfhqw lvvxhv lq frpsxwdwlrqdo idloxuh phfkdq0 59

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