horizontal force output data block Hankel matrix transfer function complex frequency response function impedance matrix

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1 AMBENT VBRATON Nomnclatur 1 NOMENCLATURE a a acclraton, coffcnt dmnsonlss corrcton factor A, B, C, D dscrt-tm stat sac modl b coffcnt c damng, stffnss C constant valu, damng matrx d damtr d dyn d stat D D k E E f f F G ( τ ) dynamc dformaton statc dformaton damng accordng to Lhr artal damags lmnt wht nos trm at tm nstant k xctd valu orator, Young modulus bndng stffnss frquncy n Hz nrtal forc forc nxt stat-outut covaranc matrx, shar modulus ht unt-muls rsons functon H H rf horzontal forc outut data block Hankl matrx H ( f ) transfr functon H ( j ) comlx frquncy rsons functon ( j ) magnary unt, ndcs momnt of nrta mdanc matrx j comlx numbr, magnary unt, ndcs J snstvty matrx J θ k k 1, k 2 0 Jacoban matrx gallong crtron aramtr, ndcs, numbr nlargmnt factors alman gan, stffnss matrx stffnss matrx ntal lmnt stffnss matrx udatd lmnt stffnss matrx

2 2 AMBENT VBRATON Nomnclatur u B 1 l L L max m m M M dr n n n N unchangd lmnt stffnss matrx vbraton coffcnt rgardng DN 1054 / ÖNORM S9010 convntonal r-strssd mono-block concrt slrs cabl lngth, numbr of oututs slcton matrx that slcts th rfrncs from th oututs maxmum san of th structur ndcs, mass r unt, slo, structural mass mass r unt mass matrx, numbr basc dsgn momnt ndcs numbr of udatd lmnts numbr of fatgu rlvant loadng cycls, numbr of occurrng loadng cycls allowabl numbr of cycls, cabl forc, numbr N ( x, θ ) global damag functon O ff P P d rf P q ( ) obsrvablty matrx of ordr ndcs, load multlcaton factors ffctv load forward stat covaranc matrx dsgn valu of th load on th slr rojcton of th row sac of th futur oututs nto th row sac of th ast rfrncs ndcs qk z quadratc modl functon Q, R, S rocss and masurmnt nos covaranc matrcs Q 0 statc load r damng, ndcs, numbr of rfrncs r rsdual vctor r f r s R frquncy rsdual vctor mod sha rsdual vctor covaranc matrx R R(t) S S c t t T u k covaranc matrx of th nnovatons k xctaton vctor staton of BRMOS rcordr masurd from a column of th mddl san Scruton numbr tm sha aramtrs kntc nrgy, tm rod nut at tm nstant k

3 AMBENT VBRATON Nomnclatur 3 u masurd u ral U(t) U v v k V V krt w w k W masurd valu masurabl valu dslacmnt vctor otntal nrgy dslacmnt, vlocty masurmnt nos du to snsor naccuracy vrtcal forc crtcal wnd sd dslacmnt rocss nos du to dsturbancs and modlng naccuracs wghtng matrx W( j ) dslacmnt n frquncy-doman x x x k x Trggr X X ˆ y k rf 0 1 gomtrcal coordnats dscrt masurng valu stat at tm nstant k trggr valu varabl alman fltr stat squnc outut at tm nstant k rf Y, Y Hankl matrx of ast rfrnc oututs Yf, Y 2 1 Hankl matrx of all futur oututs Y(t) ( ) modal coordnat z j θ analytcal modal quantty z Z n (t) masurd quantty n-th modal coordnat β rato dynamc ncrmnt for uncrtants n th contact slrs ballast bd d load dstrbuton factor dynamc ncrmnt for damng ffcts v artal safty factor (covrs uncrtants n th contact slrs ballast bd) rgular dynamc ncrmnt (covrs sd ffcts) ral numbr absolut absolut masurmnt rror q ronckr dlta ral rlatv masurmnt rror () t Drac dlta functon σ crtan strss rang-lvl

4 4 AMBENT VBRATON Nomnclatur σ D constant amltud fatgu lmt σ L cut-off lmt ζ θ λ φ ( x) damng coffcnt otmzaton varabl charactrstc root, gnvalu dynamc amlfcaton factor φ n n-th mod sha functon ξ ρ σ τ ψ D damng rato, rlatd bndng stffnss dnsty normal strss tm nstant of ald muls mod sha natural crcular frquncy, ral numbr damd natural crcular frquncy natural crcular frquncy natural crcular gnfrquncy loadng crcular frquncy [] matrx, vctor ( ) T transos ( j ) frquncy-doman varabl ( s) sac-doman varabl ( t) tm-doman varabl ( x, t) varabl ovr lac and tm h homognous soluton max maxmum valu mn mnmum valu artcular soluton,x frst drvatv wth rsct to th lac,xx scond drvatv wth rsct to th lac g frst drvatv wth rsct to th tm vlocty scond drvatv wth rsct to th tm acclraton ground acclraton xrmntal valu vctor matrx dt () dtrmnant

5 AMBENT VBRATON Nomnclatur 5 x () xonntal f () functon F () functon ln () natural logarthm L {} Lalac transform ADTV ANPSD APSD AVD AVM CQC DFT FEM FFT FR LSCE MAC MDOF MSS RDT RMS RS95 SDOF Avrag Daly Traffc Volum Avragd Normalzd Powr Sctral Dnsty Avragd Powr Sctral Dnsty Ambnt Vbraton Drvatvs Ambnt Vbraton Mthod Comlt Quadratc Combnaton Dscrt Fourr Transformaton Fnt Elmnt Mthod Fast Fourr Transformaton Fatgu Rlvanc Last Squars Comlx Exonntal Modal Assuranc Crtra Mult Dgr Of Frdom Mass-Srng-Systm Random Dcrmnt Tchnqu Root Man Squar nw fram slrs Sngl Dgr Of Frdom SLD Sylodyn SLS Sylomr SRSS SS SS - DATA SVD Squar Root of th Sum of th Squars Stochastc Subsac dntfcaton DATA-drvn Stochastc Subsac dntfcaton Sngular Valu Dcomoston