Online Damage Detection for Theme Park Rides

Transcription

1 Onlne Damage Detecton for Theme Park Rdes Hoon Sohn, Gordon Thompson, Amy N. Robertson, Gyuhae Park and Charles R. Farrar Engneerng Scences and Applcatons Dvson Weapon Response Group Los Alamos Natonal Laboratory Los Alamos, NM ABSTRACT In ths study, an onlne montorng system has been developed for amusement park rdes. A specfc type of damage nvestgated s the delamnaton between an nner alumnum wheel and an outer polymer layer of a roller coaster rde whle the vehcle s on a ral. A unque combnaton of tme seres analyss and statstcal pattern recognton technques s developed to automate the montorng process. Frst, a tme predcton model called an auto-regressve and auto-regressve wth eogenous nputs (AR-ARX) model s constructed from measured vbraton sgnals. Then, a damage classfer based on outler analyss s constructed for onlne delamnaton detecton. Data from a real-world theme park rde n Orlando, Florda are analyzed to demonstrate the effectveness of the proposed approach. INTRODUCTION Currently every rde n theme parks must go through rgorous vsual nspecton on a daly bass to make sure t s as safe as possble before t opens every mornng. Snce 980 there have been over 470 amusements rde deaths n the Unted States, although most of these deaths are related to rders not followng safety procedures ( However, the recent accdent on Bg Thunder Mountan n Dsneyland, Calforna rases questons about the safety of theme parks n general. The accdent occurred at the Dsney Anahem Theme Park on September 5th, 003, after the locomotve sped through an uphll tunnel, the cars were separated from the locomotve and the locomotve deraled. Ths accdent left one person dead and 0 other people njured ( It seems that daly nspecton mght not be enough to prevent catastrophc dsasters and the amusement park rdes need to be contnuously montored. Ideally, the damage detecton should be contnuous and automated, requrng mnmum human nterventon only when damage has occurred. The man objectve of ths study s to develop an onlne montorng system for a specfc roller coast rde, as seen n Fgure that can be nstalled on the rals of theme park rdes and montor ncpent damage durng ts normal operaton. The specfcs of the roller coaster are not dsclosed at ths pont because of a nondsclosure agreement wth our ndustral partner. Our customer dentfes that the man falure mode of the rde system s the delamnaton between an nner alumnum wheel and an outer polymer layer of the roller coaster vehcle. However, because a sensng system cannot be easly nstalled on the movng wheels, a compromse s made to nstall the sensng system at one pont of the ral track. Ths ssue of the sensor placement lmtaton makes damage dentfcaton more challengng for ths applcaton. In ths paper, a structural health montorng system based on tme seres analyss and outler analyss has been developed and appled to data recorded from feld testng of roller coaster rdes n Orlando, Florda. Damage detecton methods based on wavelet analyss has been also appled to these data and the results are presented n another paper [8]. Ths paper s organzed as follows: Frst, the test confguraton of the roller coaster rdes and data recorded from the test are descrbed. Second, a bref descrpton of AR-ARX tme seres analyss, prncpal component analyss and outler analyss s gven. Then, the epermental results based on the proposed structural health montorng process are presented. Fnally ths paper concludes wth fndngs of ths study and recommendatons for future testng. ROLLER COASTER TEST CONFIGURATION The data presented here were recorded from actual roller coasters at a theme park n Orlando, Florda on July 9-0, 003 [see Fgure ]. It was then provded to LANL staff for damage detecton analyss. Followng the rde closng around 0 pm on July 9, 003, sensors and a data recorder were nstalled at one poston of the roller coaster track. The locaton of the sensng system s shown n Fgure. Data were subsequently acqured durng

2 test operaton of the rde. As shown n Fgure, three accelerometers were nstalled on the left ral and three accelerometers and a photosensor were nstalled on the rght ral. Wlcoon 786A accelerometers and a Sony PC6A data recorder were used for the test. All data are sampled at,000 Hz, and the senstvty of all accelerometers s 00 mv/g. In addton, a mcrophone was nstalled on the rght ral and can be seen n Fgure 3. The photosensor shown n Fgure 3 was used to ndcate when the vehcle s over the sensng system. Once the data acquston system s trggered, the accelerometers and a mcrophone shown n Fgure and Fgure 3 are actvated to record acceleraton and acoustc sgnals. The data recorded consst of the followng tme sgnals. L: acceleraton n g s along the X-as of the accelerometer n the lateral drecton perpendcular to the left ral [Channel n Fgure (a)]. Ly: acceleraton n g s along the Y-as of the accelerometer n the vertcal drecton to the left ral [Channel n Fgure (a)]. Lz: acceleraton n g s along the Z-as of the accelerometer n the lateral drecton parallel to the left ral [Channel 3 n Fgure (a)]. R: acceleraton n g s along the X-as of the accelerometer n the lateral drecton perpendcular to the left ral [Channel 4 n Fgure (b)]. Ry: acceleraton n g s along the Y-as of the accelerometer n the vertcal drecton to the left ral [Channel 5 n Fgure (b)]. Rz: acceleraton n g s along the Z-as of the accelerometer n the lateral drecton parallel to the left ral [Channel 6 n Fgure (b)]. Photosensor: the voltage from the photosensor. A postve pulse ndcates a passng tran. Acoustc sgnals pcked up by the dynamc mcrophone. Ffty data sets were subsequently acqured from three dfferent vehcles (trans 3, 4 and 6 n Table ) wth varyng speeds, mass loadng and damage condtons, as lsted n Table. Each data set contans a tme sgnal from one complete run of a tran over the sensng system. Because the majorty of the data n each sgnal corresponds to tmes when the tran was far away from the sensors, the sgnals were trmmed. By nspectng the photosensor sgnal, the sgnals were trmmed to nclude only the sectons where the tran was over the sensng system. All of the trmmed sgnals are 70,00 data ponts long. Roller coaster vehcle A sde-gude wheel A sde-gude wheel (a) A roller coaster vehcle and a test wheel (b) a zoomed left rear sde-gude wheel Fgure : A roller coaster vehcle and a test wheel For damage cases, the left rear sde-gude wheel of tran 3, as shown n Fgure, was replaced wth several damaged wheels, as shown n Fgure 4. The frst wheel from the left n Fgure 4 s an ntact normal wheel, and the second wheel n Fgure 4 has a lght colored spot delamnaton. The fully delamnated wheel, whch s the thrd wheel from the left n Fgure 4, s specally manufactured by coatng the alumnum wheel wth the polymer layer wthout puttng any epoy between them. Contrary to our epectaton, the polymer layer dd not come off from the alumnum wheel even after several test runs. The fnal damage case was smulated by completely removng the polymer layer from the alumnum wheel. Fve data sets were recorded from tran 3 wth the normal wheel (data set #: 3, 6, 9, and 5), two data sets wth the partally delamnated wheel (data set #: 9 and ), addtonal two data set wth the fully delamnated wheel (data set #: 37 and 40), and one data set wth only the bare alumnum wheel (data set #: 48), respectvely. All data from trans 4 and 6 were recorded wth the normal wheel.

3 Note that damage was ntroduced only to tran 3, and addtonal mass loadng was ntroduced to tran 3 by addng rock dummes on the vehcle (as ndcated by the full loadng condton n Table ). In addton, at any gven tme pont, there was only one test vehcle on the track. Two dfferent levels of the rde speeds ( hgh and normal ) are eperenced by the rde, but no quanttatve nformaton regardng the absolute speed of the tran was provded at ths pont. (a) Installaton of accelerometers on left ral (b) Installaton of accelerometers and photosensor on rght ral Fgure : Locaton of s accelerometers and one photosensor Table : A lst of collected test data sets ID # Tme Tran Loadng Speed Wheel ID # Tme Tran Loadng Speed Wheel 3:5 4 Empty Normal 6 :05 4 Empty Hgh 3:53 6 Empty Normal 7 :06 6 Empty Hgh 3 3:54 3 Full Hgh New 8 :08 4 Empty Normal 4 3:54 4 Empty Normal 9 :0 6 Empty Normal 5 3:55 6 Empty Normal 30 : 4 Empty Normal 6 3:56 3 Full Hgh New 3 : 6 Empty Normal 7 3:57 4 Empty Normal 3 :3 4 Empty Normal 8 3:58 6 Empty Normal 33 :4 6 Empty Normal 9 0:00 3 Full Hgh New 34 :6 4 Empty Normal 0 0:0 4 Empty Normal 35 :9 6 Empty Normal 0:0 6 Empty Normal 36 :0 4 Empty Normal 0:03 3 Full Normal New 37 : 3 Full Hgh Fully Delamnated 3 0:05 4 Empty Normal 38 : 6 Empty Normal 4 0:06 6 Empty Normal 39 :3 4 Empty Normal 5 0:07 3 Full Normal New 40 :5 3 Full Hgh Fully Delamnated 6 0:08 4 Empty Normal 4 :6 6 Empty Normal 7 0:09 6 Empty Normal 4 :7 4 Empty Normal 8 0:35 4 Empty Hgh 43 :30 6 Empty Normal 9 0:38 3 Full Hgh Spot-delamnated 44 :3 4 Empty Normal 0 0:4 4 Empty Hgh 45 :37 6 Empty Normal 0:46 3 Full Hgh Spot-delamnated 46 :40 4 Empty Normal 0:48 4 Empty Hgh 47 :4 6 Empty Normal 3 0:50 6 Empty Hgh 48 :4 3 Full Hgh Bare Alumnum 4 0:5 4 Empty Normal 49 :43 4 Empty Normal 5 :04 6 Empty Hgh 50 :44 6 Empty Normal

4 Data recorder Mcrophone Fgure 3: Data acquston system and mcrophone used n the test Fgure 4: Damage condtons of the left rear sde-gude wheel AR-ARX TIME SERIES ANALYSIS In ths study, a tme predcton model combnng an auto-regressve (AR) process and an auto-regressve wth eogenous nputs (ARX) process s employed to compute nput features for the outler analyss descrbed n the subsequent sesson. Frst, all tme sgnals are standardzed pror to fttng an AR model such that; µ ˆ = () σ where ˆ s the standardzed sgnal, µ and σ are the mean and standard devaton of, respectvely. Ths standardzaton procedure s appled to all sgnals employed n ths study. (However, for smplcty, s used to denote ˆ hereafter.) For a gven tme sgnal (t), an AR model wth r auto-regressve terms s constructed. An AR( r ) model can be wrtten as []: r ( t) = φ j ( t j) + e ( t) () j= The AR order can be normally set based on a partal auto-correlaton analyss descrbed n []. For the constructon of a two-stage predcton model proposed n ths study, t s assumed that the error between the measurement and the predcton obtaned by the AR model [ e (t) n Equaton ()] s manly caused by the unknown eternal nput []. Based on ths assumpton, an ARX model s employed to reconstruct the nput/output relatonshp between e (t) and (t) ; a = ( t) = α ( t ) + β e ( t j) + ε ( t) b j= where ε (t) s the predcton error after fttng the ARX model to e (t) and (t) par. Note that ths AR-ARX modelng s smlar to a lnear appromaton method of an Auto-Regressve Movng-Average (ARMA) model presented n [3] and references theren. Ljung [3] suggests keepng the sum of a and b smaller than r ( a + b r ). Although the a and b values of the ARX model are set rather arbtrarly n ths study, smlar results are obtaned for dfferent combnatons of a and b values as long as the sum of a and b s kept smaller than r. Ether the α and β j coeffcents of the ARX model or the predcton error term are used as nput parameters for the followng prncpal component analyss (PCA) or outler analyss. PRINCIPAL COMPONENT ANALYSIS PCA s a classcal method of multvarate statstcs, and ts theory and use are documented n many tetbooks from that feld [4]. Only the brefest descrpton wll be gven here. Gven N samples of data n p -dmensons (,,, p ), PCA seeks to project the data nto a new p -dmensonal set of Cartesan coordnates ( z, z,, z p ) by a lnear transformaton. The goal of PCA s to conduct data reducton n such a way that ths lnear combnaton of the orgnal varables contan as much of the total varance as possble when projected nto the j (3)

5 reduced space. Consdered as a means of dmenson reducton, PCA works by dscardng those lnear combnatons of the data that contrbute least to the overall varance. The prncple coordnates are calculated as follows: gven data Σ s formed, = T [ p ], =,, N, the covarance matr where s a mean vector of s. Σ s decomposed as follows, N T Σ = ( )( ) (4) = T Σ = V Λ V (5) where Λ s a dagonal matr contanng the ranked egenvalues of Σ, and V s the matr contanng the correspondng egenvectors. (Sngular Value Decomposton can be used for ths step.) The transformaton to prncpal components s then, T z = V ( ) (6) Equaton (6) means that the coordnates z are the projecton of the orgnal onto the egenvectors of Σ. These egenvectors are called the prncpal components and the elements of z are called the scores. The new coordnates have the followng propertes: the z elements are uncorrelated, and the covarance matr of the z -coordnates s dag[ σ, σ,, σ p ]. Here σ σ σ p. Thus, z s the lnear combnaton of the orgnal s wth mamum varance σ, z s the lnear combnaton that eplans most of the remanng varance σ, and so on. It should be clear that f the p -coordnates are actually a lnear combnaton of q < p varables, the projectons onto the frst q prncpal components wll completely characterze the data, and the remanng p q projectons or scores wll be zero. In practce, because of measurement uncertanty, the scores wll all be non-zero and the user should select the number of sgnfcant components for retenton. Consdered as a means of dmenson reducton, PCA works by dscardng those lnear combnatons of the data that contrbute least to the overall varance. There are two man applcatons. Frst, the technque can provde an effectve means of feature etracton,.e. the salent nformaton n the data can be retaned whle reducng the dmenson. Second, the technque can provde an effectve means of vsualzng the data. If the reduced space has a dmenson of 3 or less, the reduced data can be plotted n a form that dsplays relatonshps between the ponts. In the reduced-dmensonal space, structure such as clusters may be vsualzed reflectng the dstrbuton of data n the orgnal hgher dmensons. OUTLIER ANALYSIS Outler analyss and removal has long been a concern of statstcans and the subject s found n a large volume of lterature [5]. A study of drect relevance to structural health and condton montorng can be found n [6]. As before, only the brefest survey s gven here for the sake of completeness. A dscordant outler n a data set s an observaton that s surprsngly dfferent from the rest of the data, and therefore s beleved to be generated by an alternatve mechansm. The dscordance of the canddate outler s a measure, whch may be compared aganst some objectve crteron. Ths measure allows the outler to be judged to be statstcally lkely or unlkely to have come from an assumed generatng model. For damage detecton purposes, the generatng model s smply the normal condton features of the machne or structure. The case of outler detecton n unvarate data s relatvely straghtforward n that outlers must `stck out' from one end or the other of the data set dstrbuton. There are numerous dscordance tests but one of the most common, and the one whose etenson to multvarate data wll be employed later, s based on devaton statstcs and gven by z = ξ ς (7) s where ς s the potental outler, and and s are the sample mean and standard devaton, respectvely. The latter two values may be calculated wth or wthout the potental outler n the sample dependng upon whether nclusve or eclusve measures are preferred. Ths dscordance value s then compared to some threshold value to determne f the observaton s an outler.

6 In general, a multvarate data set consstng of n observatons n p varables may be represented as n ponts n p -dmensonal object space. It becomes clear that detecton of outlers n multvarate data s more dffcult than n the unvarate case due to the potental outler havng more room to hde. The dscordance test, whch s the multvarate equvalent of Equaton (7), s the Mahalanobs squared dstance measure gven by, T D ς = ( ξ ) s ( ξ ) (8) where ς s the potental outler vector, s the mean vector of the sample observatons and s the sample covarance matr. As wth the unvarate dscordance test, the mean and covarance may be nclusve or eclusve measures. In many practcal stuatons the outler s not known beforehand and so the test would necessarly be conducted nclusvely. In the case of on-lne damage detecton based on an unsupervsed learnng mode, the tranng phase of the damage detecton should be, however, performed beforehand wthout ncludng any potental outlers. Therefore, t s more sensble to calculate a value for the Mahalanobs squared dstance wthout ths observaton contamnatng the statstcs of the normal data. Whchever method s used, the Mahalanobs squared dstance of the potental outler s checked aganst a threshold value, as n the unvarate case, and ts status determned. Determnaton of the rejecton threshold s crtcal. However, the establshment of the threshold s not further dscussed here because not enough data sets were avalable to properly set the threshold value. Further dscusson on ths topc can be found n [5]. DAMAGE DIAGNOSIS In ths secton, damage detecton results based on the prevously descrbed AR-ARX model and outler analyss are presented. It should be noted that, out of s acceleraton channels shown n Fgure, the channel 4 sgnal, whch s the acceleraton measure n the lateral drecton perpendcular to the rght ral, produced the best dagnoss. Although further nvestgaton s needed, t s speculated at ths pont that the best performance of the channel 4 sgnal s attrbuted to the confguraton of the accelerometers. The accelerometer sensors are placed near the tal of the track s downhll run and there s a horzontal curve at the end of the hll, producng more centrfugal forces on the rght ral rather than on the left ral. Therefore, the left sde-gude wheel most lkely dd not make good contact wth the left ral, falng to fully transmt the loadng to the ral. Furthermore, because the polymer delamnaton s ntroduced on the sde-gude wheel as shown n Fgure (b), the channel 4 sensor, whch measures the accelerometer n the lateral drecton perpendcular to the ral, seems more nfluenced by damage than the sensors n the other drectons. Therefore, the results from channel 4 are manly presented n ths paper, unless t s eplctly stated otherwse. (a) Usng auto-regressve (AR) coeffcents (b) Usng movng-average (MA) coeffcents Fgure 5: Seperaton of data between Tran 3 and Trans 4 & 6 usng AR-ARX (4,,) model coeffcents Frst, an AR-ARX model wth r = 4, a = and b = [AR-ARX(4,,) model] s ft to each tme sgnal after resamplng one tme pont out of every fve ponts, resultng n an effectve samplng rate of,400 Hz (=,000Hz/5). The selecton of the AR-ARX model order requres several nvestgatons. In ths study, the best

7 AR-ARX model order s selected manly by comparng the standard devaton of the predcton errors. (Intutvely, a better tme predcton model wll produce a smaller standard devaton value of the predcton errors. However, another constrant s mposed on the model order selecton n ths study because of the curse of dmensonalty, whch s eplaned afterward.) Then, the AR and MA coeffcents of the ARX model are plotted separately n Fgure 5(a) and (b), respectvely. In Fgure 5(a), a clear separaton between the AR coeffcents from tran 3 and those of trans 4 and 6 are observed. Although a more thorough nvestgaton s requred, t seems that two dstnctve clusters n Fgure 5, one from tran 3, and the other from trans 4 and 6, s caused by dfferent mass loadng condtons between tran 3 and trans 4 and 6. Table ndcates that tran 3 was loaded wth rocks on the seats to smulate passenger loadng, whle trans 4 and 6 were tested wth the seats empty. A less obvous, but smlar concluson can be drawn from Fgure 5(b). In Fgure 6(a), PCA s performed on the AR coeffcents, projectng the orgnal AR coeffcent coordnate onto a two-dmensonal prncpal coordnate. Note that data only from undamaged cases are used for the computaton of prncpal components, because data from damage cases are often unavalable durng the tranng process. That s, the tranng needs to be performed n an unsupervsed mode because t s etremely dffcult to ntentonally ntroduce damage to roller coater rdes n normal operaton. The projecton usng PCA produces much clearer separaton between tran 3 and trans 4 and 6 as shown n Fgure 6(a). A smlar result for the MA coeffcents s presented n Fgure 6(b). In the contet of outler analyss, t s desrable to classfy data sets only from damage cases (data set #: 9,, 30, 40, and 48) as outlers. However, as epected from Fgure 5 and Fgure 6, tran-to-tran (or mass loadng) varaton of the AR or MA coeffcents seems larger than the change of the AR or MA coeffcents caused by the polymer layer delamnaton. For nstance, because data sets from tran 3 devate sgnfcantly from the rest of data populaton from trans 4 and 6, many data sets from tran 3 appear as potental outlers regardless of ther actual damage condtons [see Fgure 5 and Fgure 6]. Ths observaton brngs our attenton to a data normalzaton process that dstngushes changes of features caused by damage from those caused by ambent operatonal and envronmental varatons of the system. It s clear that the data normalzaton ssue needs to be fully addressed before a robust montorng system can be mplemented. Collecton of addtonal data sets s beng planned to address the data normalzaton ssue. However, the dscusson hereafter has been lmted to data sets only from tran 3. (a) PCA of auto-regressve (AR) coeffcents (b) PCA of movng-average (MA) coeffcents Fgure 6: Seperaton of Tran 3 and Trans 4 & 6 data usng prncpal component analyss of AR-ARX (4,,) model coeffcents Net, the prevous PCA s revsted usng data sets only from tran 3. As before, data sets only from the undamaged cases (data set #: 3, 6, 9,, and 5) are used for the computaton of the prncpal components. The results of the modfed PCA usng the AR coeffcents are presented n Fgure 7(a), and the assocated outler analyss based on the projected AR coeffcents n Fgure 7(a) s shown n Fgure 7(b), respectvely. The dagnoss based on the AR coeffcents faled to successfully dentfy data sets from wheel delamnaton (data set #: 9,, 37, 40 and 48). It should be noted that although the sensors are nstrumented on the ral of the theme park rdes, we are manly nterested n detectng the polymer layer delamnaton n the wheel. In an ARX model, the AR coeffcents are related to the system poles and the MA coeffcents to the system zeros. In other words, the AR

8 coeffcents are more relevant to dynamc characterstcs of the ral system and the MA coeffcents are more closely related to the loadng to the ral. Therefore, t s presupposed that the wheel delamnaton wll have more effects on the loadng characterstcs of the ral system rather than the dynamc characterstcs of the ral tself, and the MA coeffcents wll be more senstve to the wheel delamnaton. Based on ths premse, the modfed PCA and outler analyss are repeated usng the MA coeffcents n Fgure 8. The dagnoss clearly manfests the delamnated wheels ecept the frst spot delamnaton case. It s possble that t takes some runs before the spot delamnaton grows to a pont where t can be detected. (a) Projecton of AR coeffcents on to the frst two prncpal component aes (b) Mahalanobs dstance meadure usng the projected AR coeffcents Fgure 7: Damage condtons of the left rear sde-gude wheel by performng PCA on AR coeffcents of AR- ARX(4,,) model (a) Projecton of MA coeffcents on to the frst two prncpal component aes (b) Mahalanobs dstance meadure usng the projected MA coeffcents Fgure 8: Damage condtons of the left rear sde-gude wheel by performng PCA on MA coeffcents of AR- ARX(4,,) model In Fgure 9, the same analyss s repeated by fttng an AR-ARX(7,8,9) model to each tme sgnal. Note that the multvarate outler analyss requres the estmaton of the sample covarance matr n Equaton (8). For p - dmensonal feature space, p ( p +) / number of varance components need to be computed for the multvarate outler analyss. Ths computaton of the covarance matr requres at least as many as p ( p +) / number of tranng data sets. Ths can be translated nto 45 [=(9 0)/] number of varance components for the covarance matr of the MA coeffcents of the AR-ARX(7,8,9) model, and a large number of tranng data sets are requred to compute the covarance matr. Ths problem s well known n statstcan communty as curse of dmensonalty [7]. The curse of dmensonalty was the man reason why a smpler AR-ARX model [AR-ARX(4,,)] was nvestgated frst. To avod ths problem, the MA coeffcents are projected onto the frst two prncpal components

9 and the multvarate outler analyss s performed based on ths reduced dmensonal space. Now the dmenson of the covarance matr becomes -by-. Then, only 3 varance components need to be estmated, and there are 5 tranng data sets (data set #: 3, 6, 9, and 5). In Fgure 9, the full delamnaton and bare alumnum cases are clearly classfed as damaged cases. (a) Projecton of MA coeffcents on to the frst two prncpal component aes (b) Mahalanobs dstance meadure usng the projected MA coeffcents Fgure 9: Damage detecton of the left rear sde-gude wheel by performng PCA on MA coeffcents of AR- ARX(7,8,9) model In Fgure 0, PCA and outler analyss are performed usng the predcton errors from s accelerometer channels. Frst, an ndvdual AR-ARX(7,8,9) model s ft to each tme sgnal, the predcton errors of each tme sgnal are computed by Equaton (3), and the standard devaton of the predcton errors s computed. Then, ths procedure s repeated for all s accelerometer channels, producng a s-dmensonal nput space for the subsequent PCA. Then, the standard devatons of the predcton errors from the s channels are projected onto the frst two prncpal components agan. The result s dsplayed n Fgure 0. The gradual departure of damaged cases from the central populaton of the baselne data sets s observed from the spot delamnaton to the bare alumnum wheel n Fgure 0(a). Fgure 0(b) provdes more quanttatve measure of outlers n terms of the Mahalanobs dstance. Although data sets whch ncluded spot delamnaton were not properly detected, the full delamnaton and bare alumnum cases were readly dentfed. (a) Projecton of predcton error standard devaton on to the frst two prncpal component aes (b) Mahalanobs dstance meadure usng the projected standard devaton of predcton errors Fgure 0: Damage detecton of the left rear sde-gude wheel by performng PCA on standard devaton of predcton errors from AR-ARX(7,8,9) model

10 CONCLUSION Ths paper apples tme seres based damage detecton methods to feld data collected from roller coast rdes at a theme park n Orlando, Florda. Damage of man nterest s the delamnaton of the outer polymer layer from the sde-gude alumnum wheel n the roller coaster vehcle. Results are presented that show the varablty of the undamaged data as well as the detecton of damage from the damaged data. Detecton of complete delamnaton, before the loss of the polymer coatng, s shown to be possble as well as detecton of bare alumnum wheels. It was shown that the varaton of acceleraton sgnals from one roller coaster vehcle to another was much larger than those epected from the wheel delamnaton n one vehcle, necesstatng an adopton of a proper data normalzaton procedure. However, the data normalzaton ssue s not fully addressed n ths study because of a lmted amount of data collected at ths pont. Further studes on the data normalzaton are warranted to make a technology transton of the proposed structural health montorng process to a broader spectrum of theme park rde systems. ACKNOWLEDGEMENT Fundng for ths project s provded by the Department of Energy through the nternal fundng programs at Los Alamos Natonal Laboratory known as Technology Maturaton Fund and Laboratory Drected Research and Development Fund. The authors acknowledge our ndustral partner for provdng epermental data from roller coaster rdes n Orlando, Florda. REFERENCES []. Bo, G. E. P., Jenkns, G. M., and Rensel, G. C., Tme Seres Analyss: Forecastng and Control, Thrd Edton, Prentce-Hall, Inc., New Jersey, 994. []. Sohn, H. and Farrar, C.R., Damage Dagnoss Usng Tme Seres Analyss of Vbraton Sgnals, Journal of Smart Materals and Structures, 0, pp , 00. [3]. Ljung, L, System Identfcaton: Theory for the User, Prentce Hall, Inc., New Jersey, 987. [4]. Sharma, S., Appled Multvarate Technques, John Wley and Son, 996. [5]. Barnett, V., and Lews T., Outlers n Statstcal Data, Thrd Edton, John Wley and Sons, Chchester, UK, 994. [6]. Worden, K., Manson, G., and Feller, N. J., Damage detecton usng outler analyss, Journal of Sound and Vbraton, 9, pp , 000. [7]. Slverman, B. W., Densty Estmaton for Statstcs and Data Analyss, Chapman and Hall, New York, 986. [8]. Robertson, A.N., Sohn, H., Farrar, C.R., Damage Detecton Usng Wavelet Transforms for Theme Park Rdes, Proceedngs of the nd Internatonal Modal Analyss Conference, Dearborn, MI, January 6-6, 004.