ROAD RESTRAINT SYSTEMS MONITORING WITH STEREOSCOPIC DIP-TECHNIQUE

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1 VOL. 0, NO. 4, AUGUST 05 ISSN Asan Rsarch Publshng Ntwork (ARPN). All rghts rsrvd. ROAD RESTRAINT SYSTEMS MONITORING WITH STEREOSCOPIC DIP-TECHNIQUE Marco Gurrr, and Raffal Mauro Dpartmnt of Cvl, Envronmntal and Mchancal Engnrng, Unvrsty of Trnto, Italy Euro-Mdtrranan Insttut of Scnc and Tchnology (IEMEST), Va Emrco Amar, Palrmo, Italy E-Mal: ABSTRACT Road rstrant systms (RRS) ar usd to protct vhcl occupants from dangrous roadsd lmnts such as rgd obstacls, slops, utlty pols, tc. Th crashs on a road rstrant systm damag ts structur and, thrfor, th functonal bhavoral; for ths rason s rqurd montorng th RRS nto thr opratonal condtons. Th rsarch addrsss th problm of th masurmnt of safty barrr (SB) dformatons by mans dgtal mag procssng tchnqu (DIP). Ths tchnqu s foundd on th analyss of hgh rsoluton photos/vdos, obtand by mans of 3D camra nstalld nto a data vhcl. Th DIP tchnqu has bn usd for valuatng th longtudnal safty barrrs dformatons. A cas study concrnng N W-bam guardrals nstalld along a rural road n Italy was xamnd. Th procdur has shown that th DIP tchnqu can b usd wth th am to montorng guardrals and, thrfor, to dntfy th cass n whch damagd SB must b rpard or rplacd. Kywords: road rstrant systms (RRS), w-bam guardral, dgtal mag procssng (DIP), stroscopc INTRODUCTION Road rstrant systms (RRS) - safty barrrs, crash cushons, trmnal of barrrs, transtons among dffrnt road rstrant systms, motorcyclst protcton dvcs - ar usd to protct vhcl occupants from dangrous roadsd lmnts such as rgd obstacls, slops, utlty pols and othr dangrous obstacls []. Safty barrrs (SB) ar currntly dsgnd for dffrnt prformanc lvls, whch ar st accordng to currnt CEN prformanc standards [] usng thr man crtra: vhcl contanmnt; mpact svrty to occupants; dformaton wdth of th barrr. In Europ, th safty barrrs ar classfd n th followng man typs: N, N, H, H, H3, H4a and H4b (cfr. Fgur-), as functon of th contanmnt Lvl (CL). It ndcats th barrr s strngth, by spcfyng th maxmum amount of kntc nrgy th barrr s abl to contan. Accordng to EN 37 [] thr ar thr dffrnt contanmnt lvls: T - low contanmnt lvl (T-T3), N - normal contanmnt lvl (N-N), and H hgh (H-H3) or vry hgh contanmnt lvl (H4a-H4b). Th valus of CL assocatd wth ach safty barrr typ ar shown n Tabl-. For ach of th prvous typs, a standard crash tst s assumd to b rprsntatv of ral accdnts (spd and angl of crash ar gvn by ln gud). Howvr, th cnmatc of ral accdnts rarly ar vry smlar to th mpact condtons as smulatd n th crash tst. For valuatng th njury rsk n th vnt of a motor vhcl crash tst, two dffrnt typ of crtra has bn dvlopd: Anthropomtrc tst dvc basd njury crtra (.. Abbrvatd Injury Scal (AIS), Had Injury Crtron (HIC)); Vhcl-basd njury crtra (Acclraton Svrty Indx (ASI), Thortcal Had Impact Vlocty (THIV), Post-mpact Had Dclraton (PHD)). Thr ar many rasons why vhcls lav th pavmnt and ncroach onto th roadsd, ncludng: drvr fatgu or nattnton, xcssv spd, drvng undr th nflunc of drugs or alcohol, crash avodanc, rbound off an ntal crash wthn th roadway, nvronmntal condton such as c, ran or poor vsblty, vhcl componnt falur. Roqu and Cardoso [] show that for prdctng roadsd crash frquncy (crashs on a roadway scton durng a prfxd tm prod) can b usd th Posson and th ngatv bnomal rgrsson count modls, as follows: Posson rgrsson P(y ) y! y () 5875

2 VOL. 0, NO. 4, AUGUST 05 ISSN Asan Rsarch Publshng Ntwork (ARPN). All rghts rsrvd. Whr P(y ) s th probablty of y crashs occurrng on hghway lmnt durng tm prod j and λ s th xpctd valu of y, X E(y ) () P(C w v / E sc csc W h cot P(L j w v ) (/ 580) [L P(L W cos W P(L j C)] h B) A) (5) For a roadway scton n tm prod j, β s th vctor of paramtrs to b stmatd and X s a vctor of xplanatory varabls dscrbng roadway scton gomtrc charactrstcs, nvronmntal charactrstcs and othr rlvant roadsd faturs that may affct crash frquncy, such as traffc. Ngatv bnomal modl Th ngatv bnomal modl s drvd by rwrtng Posson paramtr for ach obsrvaton n a gvn tm ntrval j as [3]: (X ) (3) Th probablty of an mpact on th safty barrr P(C/E) can b obtand by mans q. (6): P(C / E) P(E w v w v / E) (C / E Whr P(C/E) s th probablty of a crash C gvn an ncroachmnt E. P(C w v / E) s th probablty of an ncroachmnt wth a gvn vhcl typ w, spd v, angl θ, and vhcl orntaton ψ. L h, L, A, W, B, j, C ar th gomtrc paramtrs usd to dscrb th ncroachmnt path [4, 5]. w v w v ) (6) whr xp( ) s a random rror trm that follows a Gamma probablty dstrbuton wth man and varanc. Ths addton allows th varanc to dffr from th man as statd blow: VAR[y ] E[y ] ( E[y ]) E[y ] E[y ] (4) Th natonal and local road authorts tak lmtd fundng for addrssng guardrals nd for nw nstallatons and for chang xstng damag barrrs or sub-standards guardrals. Gnrally, for good allocatons of th fundng, cost-ffctvnss analyss (CEA) ar carrd out. CEA ar basd on th valuaton of roadsd safty mprovmnts usng ncroachmnt probablty modls and accdnt-data. Th prncpal am s to maxmz th total lngth of hazardous st protcton for gvn montary budgt. For ths propos Roadsd Safty Analyss Program softwar (RSAP) can b usd [4]. Th annual crash probablty can b stmatd accordng to th Coopr study [5]. In addton, ths study s mplmntd n th RSAP [4, 5]. RASP s basd on th assumpton that crash frquncy s proportonal to ncroachmnt frquncy, whch s a functon of th hghway typ or functonal class and avrag daly traffc (Fgur-). w w Th probablty P(C v / E v ) that a vhcl (of sz w, ncroachng wth a gvn spd v, angl θ, and orntaton ψ) s wthn th hazard nvlop and ncroachng far nough to mpact th hazard s gvn by th followng rlaton [4]: Safty Barrr N Safty Barrr H (typ ) Safty Barrr H Safty Barrr H3 Fgur-. Safty barrrs typs. Safty Barrr H (typ ) Safty Barrr H4 5876

3 VOL. 0, NO. 4, AUGUST 05 ISSN Asan Rsarch Publshng Ntwork (ARPN). All rghts rsrvd. Tabl-. Contmnt lvl of safty barrrs. Safty barrr typ Contanmnt lvl (CL) [kj] N 44 N 8 H 7 H 88 H3 463 H4a 57 H4b 74 Th Had mpact powr (HIP) s usd as a crtron for valuatng th mld traumatc bran njury (MTBI), dfnd as a trauma nducd altraton n mntal status that may or may not nvolv loss of conscousnss [9]. Th HIP s usd to masur th chang n translatonal and n rotatonal kntc nrgy of th had [0,, ]: Powr P ma v I [kw] (8) Whr: m s th mass of th had; I s th rotatonal nrta, a s th lnar acclraton; v s th lnar vlocty; α s th angular acclraton, and ω s th angular vlocty. Whn th coffcnts ar st qual to th mass and approprat mass momnts of nrta for th human had, th xprsson bcoms: HIP 4,50a x a x dt 4,50a y a ydt 4,50a z a zdt (9) 0,06 dt 0,04 dt 0,0 dt x x y Th Fgur-3 shows th corrlaton btwn th probablty of concusson and th maxmum valu of th Powr Indx (HPI m) [0]. y z z Fgur-. Encroachmnt frquncy as functon of traffc volum (sourc [5]). Th man scalng procdurs usd to charactrz th svrty of njury and th probablty of dath from multpl njurs, ar th Abbrvatd njury scal (AIS) and th Injury svrty scor (ISS) [6]. For th crashs aganst th safty barrrs ar of ntrst th njury masurs concrns th had mpact du to th potntal svr consquncs. Th Had njury crtron (HIC) s computd as [7]: t,5 HIC max[ a(t)dt] (t t ) (7) t t t Fgur-3. Probablty of concusson as functon of th maxmum valu of th Powr Indx (sourc [6]). whr t and t ar arbtrary tms wthn th acclraton puls. Acclraton, a(t), s xprssd as a multpl of gravtatonal acclraton (g = 9,8 m/s ). Th Had njury crtron s usd, as xampl, to pass th tst of th Fdral Motor Vhcl Safty Standard (FMVSS 08) succssfully [8]. In USA, th automobl manufacturrs must dmonstrat, whn subjctd to a 30 mph frontal barrr mpact that a fully rstrand 50 th prcntl mal Anthropomorphc Tst Dvc (ATD) s xposd to HIC scors of lss than 700 and 000, valuatd ovr maxmum tm ntrvals of 5 ms and 36 ms, rspctvly [8]. Th crashs on th barrr damag ts structur and th functonal bhavoral (n fact th w-bam absorbs th kntc nrgy of th mpactng vhcl by mans of plastc dformatons) for ths rason s rqurd montorng th guardrals nto thr opratonal condtons [3, 4]. Imag procssng tchnqu offrs grat potntalts n hghway and n ralway ngnrng [5, 6, 7], so th tchnqu basd on dgtal mag analyss, (DIP) can b usd for valuaton th longtudnal barrrs dformatons n a prcs and quck way [8]. THEORY 5877

VOL. 0, NO. 4, AUGUST 05 ISSN 89-6608 006-05 Asan Rsarch Publshng Ntwork (ARPN). All rghts rsrvd. In th prsnt rsarch, w appld DIP tchnqu wth th stroscopc mthod.

Th photos hav bn takn wth a car spd btwn 0 to 30 km/h.

4 VOL. 0, NO. 4, AUGUST 05 ISSN Asan Rsarch Publshng Ntwork (ARPN). All rghts rsrvd. In th prsnt rsarch, w appld DIP tchnqu wth th stroscopc mthod. Th acquston systm usd for th datast of our xprmnts conssts nto a 3D- Camra (Samsung NX 300 camra systm, quppd wth a 45mm f/.8, D/3D lnt) that was nstalld nto a data vhcl by mans a tlscopc arm. Th photos hav bn takn wth a car spd btwn 0 to 30 km/h. Du to th rlatv spd btwn objcts (guardrals) and data vhcl, th planar surfac undr prspctv projcton can b dscrbd as a scond ordr functon of mag coordnats nvolvng ght ndpndnt paramtrs. Thrfor, th mag moton nducd by a rgdly movng objct can b obtand as n [9, 0,, ]: u (x) A(x)t B(x) (0) Z(x) Whr Z(x) s th dstanc from th camra of th pont whos mag poston s x = (x, y), and f 0 x A (x) () 0 f y B(x) (f (xy) / f x ) / f (f x ) / f y (xy) / f x () Th A and th B matrcs dpnd only on th mag postons and th focal lngth f of th camra. Also, t s th translaton vctor and th angular vlocty vctor. Substtutng nto q. (0) th q. () and q. () w obtan: T u(x) [A(x)t] [r(t) K] B(x) (3) P ~ nw C [I 0] G C [R T] (6) Whr: f k f k 0 u 0 v u C v 0 (7) Whl R and T ar rspctvly th translaton vctor and th rotaton vctor drvd from th prlmnary calbraton procdur. T r T R r (8) T r3 t T t (9) t 3 Matrx C ncods th ntrnsc paramtrs (f, k u, k v,u 0, v 0) of th vdo camra, on th othr hand matrx G ~ ncods th xtrnsc paramtrs (R and T [8]). Th Pnw rprsnts th Prspctv Projcton Matrx (PPM) whch rgulats th projcton of spac ponts (rfrrd to th systm-world) onto th mag plan. In th cas undr xamnaton (cfr. nxt scton), downstram of th rctfcaton procdur, th two prspctv transformd mags hav bn dtrmnd and th mag pars gnratng th 3D hav bn rctfd. Ths flow fld s quadratc n (x) and can b wrttn as: u (x) a a x a y a x a xy (4) v(x) a (5) 4 a 5x a 6y a 7xy a 8y Whr th 8 coffcnts a, =,,3 8 ar functons of th moton paramtrs t, and th surfac paramtrs K. Snc ths 8-paramtr form s rathr wllknown [3, 4, 5, 6] w omt ts dtals. In th cas of Stroscopy (basd on th analyss of mags comng from two vdo camras locatd at a crtan dstanc btwn ach othr, calld basln) th most gnral form of th prspctv projcton matrx can b wrttn as follows: Fgur-4. Lft and rght barrr mags rctfd 5878

5 VOL. 0, NO. 4, AUGUST 05 ISSN Asan Rsarch Publshng Ntwork (ARPN). All rghts rsrvd. Fgur-5. Bnary mag (Canny algorthm []) Fgur-7. Stro systm. Fgur-6. Bnary mag wthout dscontnuty As prvously mntond, th straght ln connctng th optcal cntrs O L and O R of th two vdo camras s calld basln. By mans of a smpl gomtrcal analyss of Fgur-7, dpth Z s dducd as nvrsly proportonal to th dsparty X L X R. Th stro-trangulaton (cfr. Fgur-8) s th mthodology whch allows to valuat th 3D pont plac n th spac startng from th pxl coordnats of ts projctons onto th rtnal snsor plans. Gvn th prspctv projcton matrcs, whch rgulat th projcton of a coordnat pont w (s Fgur- 8) onto th two mag plans, and gvn th homognous pxl coordnats of ts projctons, th w poston can b obtand by ntrsctng optcal rays assocatd to th plans. Th followng rlatons gv th poston of a gnrc pont n th spac-world: w c (A n R ) w c (A n R n n ) m ~ m ~ n n (0) Whr A n and R n ar th nw matrcs rsultng from th rctfcaton and th coordnats and ar th nw w projctons onto th rtnal plans aftr th rctfyng transformatons and th compnsaton for radal and tangntal dstortons. Th coordnats of a gnrc pont n th world, can b dnotd as follows []: Fgur-8. Axonomtrc projcton of th conjugat ponts n th stroscopc trangulaton procss. Th man problm to b facd n th 3D constructon s th corrspondnc that s th sarch for th projcton of th sam physcal pont onto both mags (matchng pont sarch). Ths problm s handld wth global or local mthods. Th corrct and rapd corrspondnc stmaton s mathmatcally and computatonally complx. Th man dffcults whch may lad to an rronous assocaton of two non-corrspondng ponts ar du to: occlusons, dstortons, dffrnt camra paramtrs, spcular rflctons, snsor nos. Th possblty of dtctng an objct dstanc s xtrmly mportant n ths rsarch. Indd, only a trdmnsonal analyss of th safty barrr domnon n ts ral form and dmnson may lad to nfrncs about ts functonal ffcncy stat. Th smplst cas of 3D sarch occurs n prsnc of a canoncal stro systm, that s whn th corrspondng mags hav no dstortons and ar prfctly coplanar and algnd by pxl ln, wth prfctly paralll axs, concdng focal lngths and so calbratd man ponts cl and c R that ar at th sam pxl coordnats n both mags. Such an array, calld fronto-paralll, s shown n Fgur-7 [7]. x w lft y () z x w rght y () z w w lft w rght (3) CASE STUSY AND RESULTS Th DIP tchnqu has bn appld for valuaton th damag of W- bam N guardral (cfr. Fgur- and Fgur-4) nstalld along on rural road n Italy (road SS 7 bs n Scly). Th transvrsal and vrtcal dstortons of guardrals hav bn carrd out by mans of th 3D analyss. Th Fgurs 0-5 show th dagrams of guardrals dformaton for thr sctons of th road SS 7 bs (sctons n., and 3) obtand wth th projcton of th 3D modl of th longtudnal barrr (s Fgur-4 and Fgur-9) onto th plan (XY) and (XZ). Th longtudnal 5879

6 VOL. 0, NO. 4, AUGUST 05 ISSN Asan Rsarch Publshng Ntwork (ARPN). All rghts rsrvd. dstanc btwn th scton and and btwn th scton and 3 s qual to 5 m. For th guardral undr analyss, th maxmum transvrsal dformaton Y s 7, 8 cm, nstad th maxmum valu of vrtcal dformaton s 7, 5 cm. Fgur-. Dformaton on th plan XZ (scton ). Fgur-9. 3D Modl: dformd barrr n comparson wth th orgnal confguraton. Fgur-. Dformaton on th plan XY (scton ). Fgur-0. Dformaton on th plan XY (scton ). Fgur-3. Dformaton on th plan XZ (scton ). 5880

7 VOL. 0, NO. 4, AUGUST 05 ISSN Asan Rsarch Publshng Ntwork (ARPN). All rghts rsrvd. Fgur-4. Dformaton on th plan XY (scton 3). [] 007. Europan Commtt for Standardzaton, N 37- road rstrant systms-part. Tchncal Commtt CEN/TC 6, Brussls. [3] Karlafts Washngton M, Mannrng F.L. 0. Statstcal and Economtrc Mthods for Transportaton Data Analyss, Scond dton Chapman and Hall/CRC [4] 003. Roadsd Safty Analyss Program. Engnr s Manual. NCHRP REPORT 49, TRB, D.C. Fgur-5. Dformaton on th plan XZ (scton 3). CONCLUSIONS Th crashs on th road rstrant systms (RRS) (spcally th safty barrrs) can damag thr structurs. Th rsults of ths papr xplan th potntalty offrd by dgtal mag tchnqu (DIP) for th masurmnt of longtudnal safty barrrs (SB) dformatons, du to vhcls crashs. Wth th us of a 3D-Camra (Samsung NX 300 camra systm, quppd wth a 45mm f/.8 D/3D lnt), nstalld nto a data vhcl, hav bn don many xprmntal masurmnt of an N W-bam safty barrr along an Italan rural road (SS 7 bs n Scly, Italy). Th mags of th barrrs hav bn analyzd usng DIP tchnqu wth th stroscopy mthod. Th procdur dvlopd n th rsarch shows how th DIP mthod allows valuatng th transvrsal (XZ plan) and vrtcal dformatons (XZ plan) of th guardrals n a vry prcs and rapd way. So, wth th am to guarant rasonabl road safty lvls, th DIP tchnqu could b usd for montorng th longtudnal safty barrrs to dntfy th cass n whch barrrs must b rpard or rplacd wth nw SB. ACKNOWLEDGEMENTS Ths work was carrd out wthn th rsarch projct RE.S.E.T. Rt d laborator pr la Scurzza, Sostnbltà d Effcnza d Trasport dlla Rgon Sclana, whch s fundd from th PO-FESR Scla Ass IV, Obttvo opratvo 4.., Lna d ntrvnto 4...A. REFERENCES [] Roqu C, Cardoso J.L. 03. Obsrvatons on th rlatonshp btwn Europan standards for safty barrr mpact svrty and th dgr of njury sustand. IATSS Rsarch. 37: -9. [5] Coopr P Analyss of Roadsd Encroachmnts Sngl Vhcl Run-off-Road Accdnt Data Analyss for Fv Provncs. B. C. Rsarch, Vancouvr, Brtsh Columba, Canada. [6] Hays W. C., Erckson M. S., Powr E. D Fornsc Injury Bomchancs. Annu. Rv. Bomd. Eng. 9: [7] Klnbrgr M., Sun E., Eppngr R., Kuppa S., Saul R Dvlopmnt of mprovd njury crtra for th assssmnt of advancd automotv rstrant systms. NHTSA. Doc [8] 005. NHTSA. Fdral Motor Vhcl Safty Standards: Occupant crash protcton, FMVSS 57.08, Stand. No. 08, pp [9] 997. Qualty Stand. Subcomm. Practc paramtr: th managmnt of concusson n sports. Nurology. 48, [0] Nwman J. A., Shwchnko N., Wlbourn E. A Proposd Nw Bomchancal Had Injury Assssmnt Functon - Th Maxmum Powr Indx. 44 th Stapp Car Crash Confrnc Atlanta, Gorga. [] Schmtt K.U., Ndrr P., Musr M., Walz F. 00. Trauma Bomchancs, Accdntal Injury n Traffc and Sports. Thrd Edton. Sprngr. [] Shojaat M Corrlaton btwn njury rsk and mpact svrty ndx ASI. 3 rd Swss Transport Rsarch Confrnc, Ascona. [3] Martn J.-L., Mntsa-Eya C., Goubl C. 03. Longtrm analyss of th mpact of longtudnal barrrs on motorway safty. Accdnt Analyss and Prvnton. 59,

8 VOL. 0, NO. 4, AUGUST 05 ISSN Asan Rsarch Publshng Ntwork (ARPN). All rghts rsrvd. [4] La Torr F., Domnchn L., Mocc M., Nocntn A., Morano S.G. 05. Evaluaton of th vhcl/safty barrr/sgn support ntracton by mans of FEM smulatons. Intrnatonal Journal of Crashworthnss. 0(): [7] Zhang Z Dtrmnng th ppolar gomtry and ts uncrtanty: A rvw. Intrnatonal Journal of Computr Vson. 7(): [5] Gurrr M., Corrr F., Parla G., Tcal D. 03. Estmaton of pollutant mssons from road traffc by mag procssng tchnqus: A cas study n a suburban ara. ARPN Journal of Engnrng and Appld Scncs. 8(8): [6] Gurrr M., Tcal D. 0. Dsgn standards for convrtng unusd ralway lns nto grnways. Procdngs of th Intrnatonal Confrnc on Sustanabl Dsgn and Constructon. 0, [7] Gurrr M., Parla G. 03. A nw hgh-ffcncy procdur for aggrgat gradaton dtrmnaton of th ralway ballast by mans mag rcognton mthod. Archvs of Cvl Engnrng. 59(4): [8] Gurrr M., Parla G., Corrr F. 03. A nw mthodology to stmat dformaton of longtudnal safty barrrs. ARPN Journal of Engnrng and Appld Scncs. 8(9): [9] Rchards J.A. 03. Rmot Snsng Dgtal Imag Analyss. Ffth Edton. [0] Frnandz-Malogn C. 03. Advancd Color Imag Procssng and Analyss. [] Mtch A., Aggarwal J.K. 04. Computr Vson Analyss of Imag Moton by Varatonal Mthods. [] Canny J A Computatonal Approach to Edg Dtcton. IEEE T Pattrn Anal. 8(6): [3] Horn B. K. P Robot Vson. MIT Prss, Cambrdg, MA. [4] Hartly R., Zssrman A Multpl Vw Gomtry n Computr Vson, nd dton. Cambrdg Unvrsty Prss. [5] Hartly R., Zssrman A Multpl Vw gomtry n Computr Vson. Cambrdg Unvrsty Prss. [6] Faugras O Thr-Dmntonal Computr Vson. MIT Prss, Cambrdg, MA

COMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP

ISAHP 00, Bal, Indonsa, August -9, 00 COMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP Chkako MIYAKE, Kkch OHSAWA, Masahro KITO, and Masaak SHINOHARA Dpartmnt of Mathmatcal Informaton Engnrng