Hierarchical PSD damage detection methods for smart sensor networks

Transcription

1 Herarchcal PSD damage detecton methods for smart sensor networks R.K. Gles & B.F. Spencer, Jr. Unversty of Illnos at Urbana-Champagn, USA ABSTRACT: Structural health montorng (SHM) wll transform the management and mantenance of cvl nfrastructure as avalable technology and methods contnue to mprove. Realzng the full potental of SHM requres the development of dense arrays of mult-scale sensors runnng robust and effcent programs. However, the scale of a densely nstrumented cvl nfrastructure wll generate vast amounts of data. Organzng the sensors n a herarchcal computng envronment wll store and process more data locally on each smartsensor. Ths organzaton wll greatly reduce the amount of data broadcast to a base staton or mult-hopped along the network, thereby reducng ts power consumpton. However, because herarchcal computng only shares data locally, damage detecton algorthms need to effectvely perform n the presence of ths constrant. Ths paper examnes a damage detecton algorthm that analyzes the changes n the structure s Power Spectral Densty (PSD) n a herarchcal, dstrbuted computng envronment. The method s model-ndependent, requrng only output measurement. The effect of group sze, sensor overlap, and frequency range are consdered usng numerc smulaton. The results show that lmtatons exst for these varables to mantan the functonalty of the damage detecton algorthm. Nevertheless, when the herarchcal dstrbuton properly addresses these lmtatons, the proposed algorthm s effectve n accurately detectng damage. Keywords: herarchcal computng, smart sensor, damage detecton. INTRODUCTION Structural health montorng (SHM) systems nclude networks of sensors used to montor the condton, and thus the safety, of structures. Once bult, cvl nfrastructure mmedately begns to age and deterorate due to ts constant exposure to the elements. Systems of manual nspectons exst to ensure the publc safety; but, they are costly n terms of human and fnancal captal and ther effectveness s dependent on the skll and thoroughness of the nspector. Installng a SHM system could mprove the effcency of the nspecton process, ncrease the accuracy of the evaluaton, and thus mprove the safety levels of the structure (Sohn et al. 3, Doeblng et al. 996). The effectveness of an nstalled SHM system depends on the type of sensor network nstalled, the computatonal model employed, and the damage detecton algorthm mplemented. Ideally, a SHM system would consst of denselydstrbuted, mult-scale sensors performng varous algorthms to verfy and refne the dentfcaton, localzaton, and quantfcaton of damage. However, the scale of cvl nfrastructure poses many challenges n developng the deal SHM system. Two general categores of sensor networks exst: wred and wreless. A brdge nstrumented wth a wred network would requre consderable lengths of cable to provde power to and communcate wth the sensors. A wreless network elmnates the long cable lengths but has a lmted power supply. Both wred and wreless networks have reled on a tradtonal computng paradgm where nether data storage nor calculaton occurs at the sensor locaton; rather, the sensors transmt the data back to a base staton for storage and computaton. For small-scale deployments, ths strategy s suffcent. However, a largescale dense network would be unweldy wth such a centralzed approach. An alternatve s a smart sensor network where each sensor has an on-board mcroprocessor and a wreless communcaton lnk. A smart sensor network can provde advantages n data aggregaton, computaton, and transmttance, as well as provdng a more fault-tolerant approach to SHM. Ths new approach s not wthout problems. A prncpal task s to develop effectve algorthms that functon wthn the dstrbuted computng envronment of smart sensor networks. A smart algorthm

2 requres that damage detecton occur herarchcally where only lmted, local nformaton s avalable and the computaton can occur on the sensors themselves (Gao et al. 6, Nagayama et al. 6). Ths paper presents numercal smulatons that explore a model-ndependent, herarchcal, dstrbuted-computng, damage-detecton algorthm. Expermental varatons n group sze, multple damage locatons, group overlap, and frequency content are consdered to examne the lmts of each factor on the effectveness of the proposed algorthm. DAMAGE DETECTION USING POWER SPECTRAL DENSITY METHODS. Power Spectral Densty Methods The proposed approach s an extenson of the work of Beskhyroun et al. (4, 5) that examned the changes n the Power Spectral Densty (PSD) of the structure nduced by damage (Beskhyroun et al. 5a,b 6). For completeness, ths secton summarzes ths work. The theory behnd the PSD damage detecton algorthms holds that changes n the operatonal mode shapes, or changes n ther curvatures, correspond to changes n the structure due to damage. Beskhyroun et al. (5a, 6) presented two varatons on the PSD methods. Both the Absolute Dfference PSD (ADPSD) Method and the Curvature Dfference PSD (CDPSD) Method have the same ntal calculatons. The frst step s to calculate the PSD, G (f), va G ( f ) = E [ X ( f ) ] () T where X(f) s the Fourer transform of the measured acceleraton, f s frequency n Hertz, E[.] s the expected value operator, T s the measured record length, and s the sensor node number. Then, the methods normalze the PSD usng the sum of the squares of the PSD evaluated at each frequency P( f ) = G( f ) n = G ( f ) () where P(f) s the normalzed PSD and n s the number of nodes. Normalzng the PSD serves a dual purpose. Frst, t allows for the use of dfferent exctaton events n the analyss. Second, t equalzes the mportance of each mode shape by effectvely elmnatng the modal contrbuton factors. Ths normalzaton of the modal contrbutons suggests that the more modes shapes ncluded n the analyss, the more accurate the algorthm wll become.. Absolute Dfference PSD Method After normalzaton by Equaton, the ADPSD and the CDPSD have dvergent calculaton paths. The ADPSD mmedately determnes the change n the normalzed PSD, P (f), usng the undamaged normalzed PSD, P u (f), and the damaged normalzed PSD, P d (f), va u d Δ P ( f ) = P ( f ) P ( f ) (3) Thresholdng then elmnates all but the maxmum change n the normalzed PSD value for each frequency. Thus, the matrx MAX PP, representng the maxmum change n the normalzed PSDs, has a sngle non-zero value for each frequency but may have many non-zero values for each node, to wt ΔP MAX ( f ) Λ MAX MAX MAX ΔP ( f) Λ ΔP ( f 3) ΔP = (4) Μ Μ Ο Μ Λ Λ ΔP Λ C = (5) Μ Μ Ο Μ Λ where m s the frequency ndex. At the same tme as the thresholdng, a countng matrx, C P, s establshed by replacng each non-zero value n PP MAX wth a. These matrces are then summed for each node to create a vector wth length equal to the group sze. After computng the standard devaton for each vector, twce the respectve standard devaton s subtracted from each value to form a normalzed nodal damage qualty vector, Pˆ, and a normalzed nodal damage quantty vector, C ˆ, where all negatve values are elmnated va m Pˆ = ΔP Cˆ f f = f fm = C f = f MAX ΔP ( f ) σ ( f ) σ C P (6) (7) where f m s the last frequency n the PSD, σ P s the standard devaton of ΔPPMAX, and σ C s the standard devaton of C ΔP. The Accumulated Damage Index (ADI), D, s then computed by multplyng the nodal values of the Pˆ and C ˆ values together. D = Pˆ Cˆ (8).3 Curvature Dfference PSD Method After the normalzaton n Equaton, the CDPSD fts the normalzed PSD, P(f), to a seres of cubc splnes wth perodc end condtons for each frequency. Ths step allows the second dervatve of the PSD the curvature of the operatonal mode shapes to be determned. After computng the undamaged and damaged curvatures, they are used to compute PP (f), the change n the curvature of the normalzed PSD va

3 u d Δ P = P ( f ) P ( f ) (9) where PP u s the undamaged normalzed PSD curvature and P d P s the damaged normalzed PSD curvature. Before thresholdng, ΔPP (f) s normalzed as a sample populaton usng the mean and standard devaton of the sample, to wt ΔP ( f ) ΔP( f ) P ( f ) = () σ P ( f ) where P (f) s the renormalzed PSD curvature dfference matrx, ΔP( f ) s the mean of nodal values for each frequency, and σ P (f) s the standard devaton for each frequency. P (f) s then thresholded and counted by elmnatng all values that are less than a percentage, α, of the maxmum P (f) value, P max(f). A countng matrx, C(f), s also formed at ths pont as n Equaton 5 accordng to the followng crtera. f P ( f ) P < α max then P (f)= and C (f)= () f P ( f ) P α max then P (f)= P (f) and C (f)= () In ths paper, α was set to 57.5% to acheve sutable results. The P (f) and C(f) matrces are then summed for each nodal value to create vectors wth length equal to the group sze. f = m A P ( f ) (3) O f = f fm = C ( f ) (4) f = f Fnally, these values are multpled together at each node to produce the ADI matrx, D. D = A O (5).4 Proposed Algorthm Modfcatons to the PSD methods are necessary to accommodate the requrements of operatng n the dstrbuted computng envronment ntrnsc to fullscale smart sensor networks. Rather than the data collected by every sensor beng avalable for calculaton, the sensors arrange themselves n dataclusters such that a manager sensor wll execute algorthms usng only the data avalable wthn the clusters. When the unaltered PSD methods are appled to the data-clusters, the sgnfcant varaton n the magntudes of the ADI make t dffcult to determne whether damage or nose s responsble for the gven results. Normalzng the ADIs of both the ADPSD and CDPSD by dvdng each D from (6) and () by the respectve sum of D for the group wll elmnate the varatons n magntude. The normalzaton allows for the establshment of a unform set of crtera to be programmed nto the algorthm to detect damage even f group sze vares. The unform set of damage crtera mproves the robustness and fault tolerance of the smart sensor network by allowng truly dynamc assgnment or reassgnment of clusters f the system detects a sensor falure. However, the normalzaton process also elmnates the ablty of the method to determne the magntude of the damage. ADPSD damage ndcaton has one condton: D max >. where D max s the maxmum value excludng the D at the end nodes CDPSD damage ndcaton must satsfy the followng two condtons: D ma >.5/n where n s the length of the group D ma <.5/n where n s the length of the group and D end s ether end node. Note that the crtera exclude the cluster s end nodes from the calculatons because the end nodes return false postves for damage. These false postves are remnants of the clusterng process and ts affect on the normalzaton constants and dfferent vrtual boundary condtons for the group because of the splne curve fttng n the CDPSD method. Usng the ADPSD and CDPSD n sequence creates a combned algorthm more robust n locatng structural damage than ether component. Both ndvdual methods must yeld postve damage dentfcaton results for the algorthm as a whole to return a postve damage result. Usng the methods n sequence to form a sngle algorthm takes advantage of the unque characterstcs and abltes of each ndvdual procedure. The ADPSD requres less calculaton, and therefore power consumpton, because t does not requre splne fttng and dfferentaton. Its less ntensve damage detecton calculatons allow the node to return to a lower power state, wthout performng the CDPSD, f the method detects no damage. The ADPSD s very senstve to damage and though at tmes yelds false postves, ndcatng damage s present when none exsts, t does not yeld false negatves that would ndcate the dangerous stuaton where no damage s detected when damage exsts. The senstvty of the ADPSD to the presence of damage comes at the expense of ts ablty to locate effectvely the damage locaton. The ADPSD often gves a sngular strong damage ndcaton on one sensor when the damage s located between two sensors that should both experence the effects of damage. Therefore, to both confrm and better locate the damage between two sensors, once the ADPSD has ndcated ts presence, the smartsensor wll perform the more calculaton ntensve CDPSD. Usng the CDPSD on ts own s not advsable because of ts calculaton ntensty and ts propensty for ndcatng damage when no damage s present n the herarchcal envronment due to splne fttng resduals. The fnal step n the algorthm s to combne the results of the two PSD methods nto a fnal damage ndcator and locator. To do so, the two normalzed ADIs from both algorthms are average to form a

4 Combned ADI. Throughout the algorthm, the cluster heads perform the calculatons locally wthout needng to communcate wth sensors outsde the desgnated group. However, once the algorthm detects damage, the cluster heads can communcate wth adjonng and overlappng clusters heads to confrm the presence and locaton of the damage. If they confrm each other s results, they only need to transmt a message as small as a sngle bt ndcatng damage and two bytes contanng the numbers of the affected nodes to the base staton. Transmttng nformaton to addtonal nodes and base statons only when damage s present mproves the power effcency of the network wthout sacrfcng confdence n the reported results. 3 NUMERIC EXAMPLES 3. Mathematcal Model A MATLAB fnte element model of a planar truss served to analyze the proposed algorthm. As llustrated n Fgure, the truss contans 53 frame elements arranged n fourteen bays wth a centerlne axs of symmetry and smple supports. Appled vertcally at node 7, a band lmted whte nose served as exctaton to smulate ambent vbraton. In generatng ths whte nose, a dfferent seed began the random generaton sequence to smulate acceleraton records taken at two dstnct tmes under dfferent ambent exctaton for the damaged and undamaged case. The smulaton recorded the vertcal acceleraton at the 5 sensor locatons shown n Fgure. The analyss used two cutoff frequences, 9 Hz and 5 Hz, wth approprate samplng rates and flters to prevent alasng. The calculatons used 4 FFT ponts. 3. Investgated Damage Cases Examnng the effects of cluster sze, node overlap, and frequency content on the performance of the proposed algorthm requred the analyss of several damage cases. Reducng the cross-sectonal area of desgnated members n the MATLAB model served to smulate damage n the truss structure. For llustratve purposes, ths paper presents only cases that smulate only a 5% reducton n cross-sectonal area of members 9 and 33 as shown n Fgure. For each damage case presented, the cluster sze and node overlap between the clusters of the groupngs were vared. For each case, the algorthm was performed Table. Investgated Damage Cases Case No. of Groups Sze Overlap I 5 II III 4 3 Fgure : 4-Bay Planar Truss usng cutoff frequences of both 9 Hz and 5 Hz to examne the ncluson of hgher modes n the calculatons. In the damage cases, the groups are numbered from left to rght, nclude the ndcated number of sensors, and overlap the ndcated number of sequental sensors from the prevous group. Table lsts all damage cases presented n ths paper. 4 ANALYSIS AND RESULTS 4. Case I Test Case I examned the functonalty of the proposed algorthm n the standard non-herarchcal computng scenaro. Ths case uses all the sensors, and therefore all the nformaton avalable, n a sngle group. However, beyond just the proof of concept, t shows the proposed algorthm s ablty to detect multple damage stes wthn a group. Fgures and 3 show that usng cutoffs of both 9 Hz and 5 Hz the method can detect the multple damage stes on the structure and wthn the group. In readng these fgures, the three graphs represent the output of the ADPSD, CDPSD, and Combned ADI from top to bottom respectvely. The Combned ADI Case I - 9Hz - Group One Fgure. Case I Group 9 Hz Case I - 5Hz - Group One Fgure 3. Case I Group 5 Hz

5 s the actual result of the proposed algorthm, but the ADPSD and CDPSD are ncluded for llustratve purposes. Comparng the results of the algorthm at the dfferent cutoff frequences n Fgures and 3 shows the nfluence of the hgher modes n the algorthm s effectveness. The hgher frequences tend to have a greater nfluence on the algorthm because the changes n the hgher operatonal modes are more dramatc and therefore survve the thresholdng methods n greater number. However, when more frequences are ncluded the changes n operatonal mode shapes caused by the damage begn to occur less locally and the damage ndcators to spread around the damage locaton. Ths result ndcates that when selectng a samplng rate and cutoff frequency, attenton to whch modes are ncluded s mportant. Ths ssue does not make the method model dependent, as an updated and accurate model s stll not necessary for ts functonalty. However, havng a smple model to help determne a sutable cutoff frequency can mprove ts effcacy. 4. Case II Ths computatonal scenaro dvdes the sensors nto three groups of seven sensors each wth three sensors overlappng the groups. Ths separates the damaged locatons from each other and places t on the boundary of two groups. The method successfully locates the damage when the damage locaton s not located on the edge of the group. Ths s true for both cutoffs, though the dffuson of the damage ndcator away from the damage locaton at the 5 Hz cutoff s greater than n Case I. Fgure 4 showng Group of the 9 Hz cutoff serves as the llustratve example of the method s success. Damage s successfully located between sensor 9 and. Fgure 4 also llustrates how the CDPSD serves as a check to the ADPSD. By tself, the ADPSD n Fgure 4 ndcates damage only at sensor 9. Ths result could ndcate that the vertcal member above sensor 9 n damaged. However, ths damage scenaro would stll affect the neghborng sensors due the stress dstrbutons and asymmetry of the truss. Together, the CDPSD and ADPSD detected damage and properly located the bay n whch t occurs. However, Fgure 5 shows the falngs of usng the CDPSD on ts own n a herarchcal envronment. When damage s located at the end of the group, the methods, even when used together as proposed, have dffculty detectng t. Fgure 5 shows that the ADPSD ndcates no damage at all because the end nodes, where the damage s located, are elmnated from the analyss. The elmnaton s necessary because the ends always nclude a large amount of ndcated damage due to the vrtual cut n the truss and the change n boundary condton assumptons for each group s operatonal mode shapes. As such, Case II - 9Hz - Group Two Fgure 4. Case II Group 9 Hz NO DAMAGE Case II - 5Hz - Group Three NO DAMAGE Fgure 5. Case II Group 3 5 Hz these values are set to zero n the graphs for easer readablty. The CDPSD stll detects damage at sensors 9 and but the false postves have ncreased to a sgnfcant level to cloud the actual damage locaton. The algorthm ndcates no damage n Fgure 5 even though damage s techncally present because of ths problem wth the end nodes. To overcome ths defcency, the cluster assgnments need to ensure they mantan an overlap of three, as a mnmum. Dong so wll ensure that damage wll stll be properly ndcated n the structure as a whole. 4.3 Case III Case III llustrates what happens when the group szes are too small for proper normalzaton of the PSD and subsequent splne fttng to determne the dervatves. In the deal case, where damage s located between the two center nodes of the four node group, the proposed algorthm properly ndcates the damage. However, when damage s located at the edges, ether the method ndcates no damage as shown n Fgure 5 of Case II or t ndcates damage n the wrong bay as llustrated n Fgure 6. As stated above, ths can be rectfed by havng a mnmum overlap. However, the small group sze also produced a large number of false postves n bays n whch no damage was present n any form. Fgure 7 shows an example of ths worrsome stuaton. Ths group s far from ether damage locaton, yet t falsely ndcates damage between sensors 3 and 4.

6 The false postve results from the mnmal dfferences n the small group beng amplfed through the normalzaton processes. Increasng the group sze ensures that the normalzaton does not amplfy the small changes due to dfferent exctaton records when damage s not present n the group. Havng a mnmum group sze of fve elmnates the presence of the type of false postve shown n Fgure 7. The proposed algorthm does not report any false postves, even when no damage s present anywhere, as long as the group sze s above the mnmum of fve. 5 CONCLUSIONS Case III - 9Hz - Group Three Fgure 6. Case III Group 3 9 Hz Case III - 5Hz - Group Twelve Fgure 7. Case III Group 5 Hz The methods ntroduced by Beskhyroun et al. (4, 5) have been extended to mprove ther performance and to facltate mplementaton n the dstrbuted computng envronment ntrnsc to a smart sensor network. Through numercal examples, the modfed approach has been shown effectve n damage detecton and locaton when lmtatons of node overlap, cluster sze, cutoff frequency are properly observed. The mnmum overlap of three sensors and mnmum group sze of fve are exactly that mnmums. In full-scale cvl nfrastructure, the envsoned smart sensor network would consst of thousands of sensors deployed along ts length and heght. A network of only fve sensors would not provde suffcent nformaton to make an educated assessment of the structure s functonalty. However, any software that controls the clusterng of the nodes must observe these mnmums n order to mantan the accuracy and effcency of the entre network. Beng aware of the lmtatons of the damage detecton method used n the herarchcal envronment greatly mproves the fault tolerance of the smart sensor network. Whle consstng of thousands of nodes, smart sensor networks wll also be mult-scale. Ths mples that the networks wll use varous damage detecton algorthms usng dfferent nput data to evaluate the structure s status. The proposed PSD method, though lackng nformaton on the severty of damage, serves as a computatonally and energy effcent method to detect and locate the damage. Implementng other methods usng addtonal data, ncreased data sharng, or more ntense calculatons could then supplement the ntal damage report. Further analytcal and physcal experments are underway to expand the results presented heretofore. 6 ACKNOWLEDGEMENTS The authors gratefully acknowledge Natonal Scence Foundaton s support under grants CMS 3-4 and CMS 6-433, Dr. S.C. Lu, Program Manager. The frst author also acknowledges support by NSF s Graduate Research Fellowshp Program. REFERENCES Beskhyroun S, Oshma T, Mkam S. 4. Structural Health Montorng of Brdges Based on Vbraton Measurements. Internatonal Workshop on Modern Scence and Technology, Ktam, Japan, September -3, 4 Beskhyroun S, Oshma T, Mkam S, Yamazak T. 5. A Numercal Analyss of Structural Damage Detecton Usng Changes n the Curvature of Power Spectral De Journal of Structural Engneerng. Japan. 5A Beskhyroun S, Oshma T, Mkam S, Tsubota Y. 6. Structural Damage Identfcaton Algorthm Based on Changes n Power Spectral Densty. Journal of Appled Mechancs. Japan. 8 Doeblng SW, Farrar CR, Prme MB, Shevtz DW Damage Identfcaton and Health Montorng of Structural and Mechancal Systems from Changes n ther Vbraton Characterstcs: a Lterature Revew. Los Alamos Natonal Laboratory Report LA-37-MS. Gao Y, Spencer BF Jr, Ruz-Sandoval M. 6. Dstrbuted Computng Strategy for Structural Health Montorng. Structural Control and Health Montorng. 3: Nagayama T, Rce JA, Spencer BF, Jr. 6 Effcacy of Intel s Imote Wreless Sensor Platform for Structural Health Montorng Applcatons. Proceedngs of the Asa-Pacfc Workshop on Structural Health Montorng. Sohn H, Farrar CR, Hermez FM, Shunk DD, Stnemates DW, Nadler BR. 3 A Revew of Structural Health Montorng Lterature: Los Alamos Natonal Laboratory Report LA-3976-MS.