Design of a Wireless Active Sensing Unit for Structural Health Monitoring

Transcription

1 Source: SPIE 11th Annul Interntionl Symposium on Smrt Structures nd Mterils, Sn Diego, CA, USA, Mrch 14-18, 2004 Design of Wireless Active Sensing Unit for Structurl Helth Monitoring Jerome P. Lynch*, Arvind Sundrrjn b, Kincho H. Lw b, Hoon Sohn c nd Chrles R. Frrr c Dept. of Civil nd Environmentl Engineering, University of Michign, Ann Arbor, MI b Dept. of Civil nd Environmentl Engineering, Stnford University, Stnford, CA c Engineering Sciences nd Applictions, Los Almos Ntionl Lbortory, Los Almos, NM ABSTRACT Mny cdemic nd commercil reserchers re exploring the design nd deployment of wireless sensors tht cn be used for structurl monitoring. The concept of intelligent wireless sensors cn be further extended to include ctution cpbilities. In this study, the design of wireless sensing unit tht hs the cpbility to commnd ctive sensors nd ctutors is proposed for structurl monitoring pplictions. Active sensors re sensors tht cn input excittions into structurl system nd simultneously monitor the corresponding system s response. The computtionl core of the wireless ctive sensing unit is cpble of interrogting response dt in rel time nd cn be used to execute embedded dmge detection nlyses. With high-order vibrtion modes of structurl elements exhibiting greter sensitivity to dmge thn globl structurl modes, wireless ctive sensors cn ply mjor role in structurl helth monitoring system becuse they re cpble of exciting high-order modes. A computtionl frmework for nlyzing piezoelectric bsed ctive sensor signls for indictions of structurl dmge is proposed. For illustrtion, simple luminum plte with piezoelectric ctive sensors mounted to its surfce is used. Keywords: Wireless ctive sensors, structurl helth monitoring, sensing networks, ctive sensors 1. INTRODUCTION The poor stte of our ntionl infrstructure underscores the need for low-cost structurl monitoring systems tht cn trck the performnce of structures over their entire opertionl lives. Dt collected by permnently instlled monitoring systems cn offer opportunities to rpidly ssess the condition of structure s overll integrity nd llow structurl dmge to be repired when it occurs. Response mesurements could lso provide better understnding of structurl live lods nd structurl nonliner behvior under seismic lodings. In response to these needs, mny hve begun to experiment with new technologies such s wireless communictions, microelectromechnicl system (MEMS) sensors nd mobile computing to improve current structurl monitoring prctices. For exmple, reserchers re exploring the doption of wireless rdios for communiction of mesurement dt in structurl monitoring systems in order to reduce the high costs ssocited with the instlltion of wires between sensors nd centrlized dt repositories 1. Lynch et l. 2 hve extended this work to include embedded microcontrollers within wireless sensing unit prototype; embedded microcontrollers cn be loded with numericl lgorithms to loclly process nd interrogte mesurement dt directly t the sensor. This convergence of wireless communictions, embedded computing nd sensors is creting exciting opportunities to improve the functionl fetures of current wire-bsed monitoring systems, while simultneously reducing their costs. The dvntges of wireless structurl monitoring system hve recently been illustrted during forced vibrtion testing of the Almos Cnyon Bridge in southern New Mexico. During testing, the bridge ws instrumented with wireless sensing units nd MEMS ccelerometers to monitor the bridge s response to modl hmmer blows nd trffic lods. To benchmrk the performnce of the wireless monitoring system, commercil wire-bsed (tethered) monitoring system ws instlled in prllel. The vibrtion tests conducted on the Almos Cnyon Bridge hve reveled number of importnt findings 3 : 1) wireless sensing prototypes were cpble of collecting sensor dt with high precision, 2) bridge modl frequencies were ccurtely determined using fst Fourier trnsform (FFT) embedded in nd executed by the wireless sensing unit core, nd 3) the instlltion of the wireless monitoring system ws completed in pproximtely hlf the time required by the tethered wire-bsed system. *jerlynch@umich.edu; phone ; fx ;

2 With embedded computing coupled with the sensor, lgorithms tht utomte the interrogtion of response dt cn be executed in rel-time. One set of lgorithms being considered for inclusion in wireless sensor is one tht would interrogte dt for indictions of structurl dmge. A mjority of the dmge detection methods previously considered for civil structures depend on chnges in the globl vibrtion chrcteristics of structurl systems for the identifiction of the existence, loction nd severity of dmge 4. The cost of wire-bsed monitoring systems tends to limit the number of sensors tht cn be economiclly instlled in structure. Globl vibrtion chrcteristics offer n ttrctive lterntive becuse they cn identify dmge using the smll number of sensors vilble without hving to be collocted in the vicinity of the dmge. Unfortuntely, the complexities of civil structures pose unique chllenges tht often render globl vibrtion-bsed dmge detection ineffective 5. First, ccurte mesurements of globl modl properties re difficult to obtin using experimentl response dt. In ddition, subtle chnges in modl properties re often msked by chnges originting from environmentl influences such s temperture nd humidity. Finlly, low-order modes (defined t low frequencies) re known to be less sensitive to subtle levels of structurl dmge. As the cost of wireless monitoring systems continue to decline, sensor networks defined by high nodl densities re now possible. Structurl monitoring systems with lrge number of sensor nodes cn mesure the globl response of the structure in ddition to the behvior of individul structurl elements. With high-order modl vibrtion chrcteristics of structurl elements more relible for dmge detection, monitoring key structurl elements cn represent n ttrctive nd effective monitoring strtegy 6. In ddition, dmge detection lgorithms focused on locl responses of the structure (e.g., vibrtions in bem) would not require the trnsfer of dt from mny wireless sensors thereby preserving the utonomy of the computtionlly self-sufficient wireless sensing unit. Otherwise, response time-histories of the globl system would need to be wirelessly communicted between sensor nodes resulting in rpid depletion of portble power sources, such s btteries. In recent yers, new sensing prdigm, termed ctive sensing, hs emerged nd hs been shown to be n effective tool for structurl helth monitoring. The vst mjority of sensors used in structurl engineering re pssive since they only mesure structurl responses to externl lods, which they hve no control over. In contrst, n ctive sensor cn excite structurl system nd record the structurl response tht it hs initited 7. An ttrctive feture of ctive sensors lies in the fct tht their excittions cn be precisely repeted. In recent yers, ctive sensing hs grown in populrity nd hs begun to be explored for detection of dmge in civil structurl systems; ctive sensors often excite structure in locl re with low energy excittions. With mny structurl elements (e.g. bems, columns, truss elements, joints) exhibiting sensitivity to dmge t high-order modl frequencies, ctive sensors cn conveniently excite structurl elements using high frequency bnded excittions. To dte, the mjority of ctive sensors investigted hve been bsed on the use of piezoelectric mterils to excite nd sense the structurl system. Prk et l. 6 hve illustrted the utility of mesuring the electricl impednce of piezoelectric elements mechniclly coupled to structure s surfce. Termed the electromechnicl impednce (EMI) method, dmge in the vicinity of the piezoelectric element cuses noticeble chnge in the rel component of the complex impednce of the coupled piezoelectric-structurl system. Their pproch hs been shown to successfully detect the onset of crcking in msonry structures nd bolt loosening in steel truss joints. Bhll nd Soh 8 find similr results when the EMI method ws pplied to reinforced concrete frme system. In nother technique, Wu nd Chng 9 hve employed piezoelectric rings mounted to steel reinforcement brs encsed in concrete elements to ccurtely detect debonding dmge. Their findings revel debonding of the reinforcement element cuses n increse in the mplitude envelopes of high-frequency sinusoidl signls trnsmitted cross the steel br from one piezoelectric pd to nother. All of these methods employ excittion signls defined by high frequency content well bove 1 khz. While high frequency signls re effective in exciting the high-order modes of structurl elements, they quickly ttenute in structurl mterils. As result of the sptil ttenution of the ctive sensor excittion, dmge detection performed using ctive sensors often focuses on loclized res ner the ctive sensor. This pper describes the rchitecturl design of wireless ctive sensing unit tht cn improve the functionlity of structurl helth monitoring systems. In prticulr, wireless sensors re enhnced with the bility to pply ctution forces into the structure. The wireless ctive sensing unit s high-speed ctution interfce is designed to fcilitte the use of ll types of ctive sensors nd structurl ctutors in monitoring system. So tht the high-order modes of structurl elements cn be illuminted, the ctution nd sensing interfces re both designed to hve high smpling rtes of 40 khz. After completion of the wireless ctive sensing unit, embedded softwre is written to operte the unit nd to interrogte mesurement dt. To showcse the cpbilities of the unit s computtionl core, softwre frmework tht

3 Multi- Chnnel Sensor Interfce Anlog Actutor 0-5V -5 to 5V Multi-Chnnel Anlog-Digitl Converter (ADC) 10-bit Resolution Actution Interfce Circuit 32-bit Microcontroller Floting Point Hrdwre Motorol PowerPC MPC555 Externl SRAM (512 KBytes) Hitchi SRAM 900 MHz Wireless Modem MxStrem XCite Fig. 1 Architecturl design of the wireless ctive sensing unit supports the utonomous execution of dmge detection nlyses is presented. An luminum plte ctively sensed by piezoelectric pds is employed to illustrte the performnce of the wireless ctive sensing unit s hrdwre nd softwre. 2. DESIGN OF A MULTI-FUNCTIONAL WIRELESS ACTIVE SENSING UNIT To monitor the helth of key elements within civil structures, the design of wireless ctive sensing unit bsed on lowcost off-the-shelf components is proposed. The rchitecturl design of the unit cn be divided into four functionl subsystems (sensor interfce, ctution interfce, computtionl core nd wireless communiction chnnel) whose interoperbility is described by Fig. 1. The computtionl core is the most importnt element of the unit design since it will be responsible for the overll opertion of the unit, will control the ctution, sensing nd wireless interfces nd must execute embedded lgorithms tht interrogte mesurement dt. 2.1 PowerPC-Bsed Computtionl Core The computtionl core is designed to support the utonomous opertion of the wireless ctive sensing unit. Some of the key roles the computtionl core will ply include opertion of sensing nd ctution interfces, mngement of mesurement dt, execution of embedded nlysis procedures nd control of the flow of informtion through the wireless modem. With embedded system microcontrollers well suited to ddress the tsks of the computtionl core, the Motorol PowerPC MPC555 microcontroller, with n internl 32-bit rchitecture, is chosen for the design of the wireless ctive sensing unit 10. The Motorol MPC555 opertes t clock frequencies s high s 40 MHz nd internlly integrtes floting-point rithmetic unit for single-cycle floting point clcultions. The high speed of the processor will be especilly useful if ctive sensors with high frequency opertionl rnges re connected to the unit. Coupled with this fst processor is 448 Kbytes of internl red-only memory (ROM) where firmwre will be stored for unit opertion nd execution of embedded dt processing lgorithms. The MPC555 lso hs 26 Kbytes of internl rndom ccess memory (RAM) tht could be used to store temporry dt generted by executing progrms running from ROM. Since the size of the internl RAM bnk is too smll for storing sensor mesurements, n externl sttic RAM (SRAM) integrted circuit (IC) is dded to the unit design to provide dditionl memory for dt storge. The current prototype uses the Hitchi HM628512B SRAM IC, providing 512 Kbytes of memory storge 2.2 Sensing Interfce for Anlog Sensors For digitiztion of mesurement dt from structurl sensors, the MPC555 internl nlog-to-digitl converter (ADC) will be employed. The 10-bit ADC cn ccommodte 32 simultneous sensing chnnels with smpling rtes s high s 100 khz. Additionl conversion resolutions cn be gined by employing over smpling techniques or through the use of low-noise mplifiction circuits. To mnge the sensing interfce in rel-time, the MPC555 interrupt service routines re utilized to ensure dt is red on strict timing schedule. Unfortuntely, inherent ltencies incurred by servicing the interrupts reduce the mximum ADC smpling rte to speeds of 40 khz. 2.3 Actution Interfce for Active Sensors nd Structurl Actutors An ctution interfce is responsible for providing commnd signls to brod rnge of ctive sensors or ctutors instlled within structurl system. A digitl-to-nlog converter (DAC) tht converts digitl commnd signls

4 generted by the MPC555 into nlog representtions cceptble for commnding the ctutors is t the core of the ctution interfce. The Texs Instruments DAC7624 ccepts 12-bit digitl smples in prllel nd outputs zero-orderhold (ZOH) nlog signl from 0 to 2.5 V on four selectble chnnels 11. Using only one chnnel of the DAC, the settling time ssocited with ech conversion is 10 µsec (100 khz smpling rte). To improve the voltge rnge of the DAC, the DAC output signl is connected to the input of n instrumenttion mplifier tht cn rnge shift nd mplify the signl. An Anlog Devices AD620 mplifier is chosen to shift the DAC output to zero men (from 1.25 V) nd to mplify the signl by 4. This results in completed ctution interfce cpble of outputting commnd voltges from -5 to +5 V. Similr to the sensing interfce, embedded firmwre written to service the ctution interfce in rel-time will reduce the speed of the ctution interfce to 40 khz. 2.4 Spred Spectrum Wireless Communictions The use of wireless communictions will immeditely llevite some of the burdens of instlling nd mintining cbles in structure. However, to be n effective substitute for cbles, wireless rdios chosen for integrtion with the wireless ctive sensing unit must be low-cost, fr reching nd highly relible. Previous wireless sensing unit designs hve employed wireless modems such s the Proxim ProxLink nd Proxim RngeLAN2 rdio modems 2. While both Proxim rdios cn propgte over 300 m in unobstructed open spce, they consume over 150 ma of electricl current when trnsmitting nd receiving dt. To improve the power consumption chrcteristics of the wireless ctive sensing unit, new wireless rdio is considered for integrtion; in prticulr, the MxStrem XCite rdio is chosen. The XCite communictes on the unregulted 900 MHz rdio bnd nd cn communicte with over-the-ir dt rtes of 38,400 bits per second. The open spce communiction rnge of the rdio is 300 m but is only pproximtely 90 m when used in the interior of structures 12. In contrst to the Proxim modems, the XCite rdio only consumes 55 ma when trnsmitting dt nd 35 ma when receiving dt. Use of the XCite rdios reduce by t lest one third the power consumption demnds of the Proxim rdios without scrificing the distnce the rdios cn communicte. When the rdios utilize the wireless chnnel, frequency hopping spred spectrum encoding is employed ensuring the rdio chnnel is highly relible nd resilient to nrrow-bnd interference. 2.4 Prototype Fbriction To construct finl prototype, stcked circuit bord pproch is tken to the construction of the wireless ctive sensing unit. Bord stcking will llow the unit form fctor to be minimized nd will mke future upgrdes to the hrdwre esier to complete. First, the Motorol MPC555 is purchsed s smll strter development kit from Axiom (PB-555) where the microcontroller is mounted on smll-footprint (9 cm by 9 cm) printed circuit bord (PCB). The output pins of the MPC555 re provided s heder rows on the development kit bord. The heder rows of the Axiom bord will be conveniently used to mount custom mde printed circuit bords on top. To house the ctution interfce circuit nd the externl SRAM IC, PCB is designed nd fbricted. This circuit bord hs the sme dimensions s the MPC circuit bord. The MxStrem wireless rdios re purchsed from the mnufcturer on their own circuit bord (4 cm by 7 cm) nd re plced s third lyer over the ctution interfce circuit bord. Shown in Fig. 2 is the completed printed circuit bord stck (3 circuit bords) ssembled s single wireless ctive sensing unit. The finl dimensions of the fully ssembled wireless ctive sensing unit re 9 cm by 9 cm in re nd 4 cm in height. The cost of constructing the prototype, including the cost of the wireless modem, is pproximtely $250. However, the cost nd form fctor cn both be substntilly reduced if the wireless ctive sensing unit is commercilly mnufctured. 2.5 Power Sources nd Anticipted Opertionl Life In relistic field deployments, btteries re likely power source for the wireless ctive sensing unit. Wireless ctive sensing units embedded in infrstructure systems cn often be in difficult to rech loctions mking bttery replcement dunting tsk. The power demnds of wireless sensors nd the ssocited life expectncies of bttery pcks re importnt constrints to consider in the design of the finl unit. Previous wireless sensing unit designs hve selected low-power integrted circuit elements to minimize the overll power demnd of the ssembled unit. Locl dt interrogtion t the wireless sensor hs lso been identified s mechnism by which considerble bttery power cn be preserved 13. The wireless ctive sensing unit proposed in this study does not minimize the totl power consumption demnd becuse ttinment of high-frequency ctution interfce presented sufficient technicl chllenges. However, future itertions on the design of the wireless ctive sensing would ttempt to minimize power consumption through the selection of low-power components or through the design of two microcontroller computtionl core 2.

5 Wireless Modem Actution Bord PowerPC Bord Fig. 2. Three printed circuit bord stck ssembled s single wireless ctive sensing unit prototype Tble 1. Opertion Power Schedule of the Prototype Wireless Active Sensor Unit Component Reference Voltge (V) Electricl Current (ma) Opertionl Power (mw) Microprocessor MPC555 PowerPC Actution Interfce: DAC Converter Amplifier Piezoelectric Actutors -5 to 5 0 to 5 0 to 25 Wireless Modem: MxStrem XCite Rdio To ssess the totl mount of power required by the fully ssembled wireless ctive sensing unit prototype, electricl currents re mesured throughout the circuit. Tble 1 summrizes the mesured electricl currents nd the respective power consumed. To serve s n exmple of typicl ctive sensor tht could be interfced to the unit, the power required to commnd piezoelectric ctutor is mesured. The power expended in operting piezoelectric element is function of the commnd voltge pplied. Considering the mximum commnd (+5 V) tht cn be given to piezoelectric element by the unit, the worse cse power consumption of the ctutor is determined to be 25 mw. Bsed on the current drw of the unit s electricl components, if lithium bttery pck with high energy density is considered s portble power source, continuous opertionl life spn of pproximtely 20 hours is expected 14. Using seprte bttery pck, pproximtely 28 hours of continuous bttery life cn be expected for the wireless modem. In the field, duty cycle usge of the wireless ctive sensing units cn extend the life expectncy of the bttery pcks. For exmple, if 0.1% duty usge cycle is employed (i.e. 90 seconds of usge every dy), the nticipted life expectncy of the bttery pcks is on the order of 2 yers. 3. PERFORMANCE VALIDATION OF A WIRELESS ACTIVE SENSING UNIT To vlidte the performnce of the fbricted wireless ctive sensing unit design, cm thick luminum plte, roughly 28.6 cm long nd 6.8 cm wide, will be used. Mounted to the surfce of the sme side of the luminum plte re two 1.43 cm squre piezoelectric pds seprted by 18.9 cm. One pd is to be used s n ctutor for the emission of coustic surfce wves long the br s length. The second pd will be used s sensor to mesure the coustic wves received. A picture of the luminum plte nd mounted piezoelectric pds is presented in Fig. 3. The two piezoelectric

6 Fig. 3. Cntilevered luminum br with piezoelectric pds mounted to the top surfce INPUT SIGNAL Input Piezoelectric Pd T(z) Totl Dynmic System, H(z) Structurl Element S(z) Output Piezoelectric Pd R(z) OUTPUT SIGNAL Fig. 4. Segmenttion of the experimentl luminum br setup into distinct dynmic subsystems pds will be simultneously ctuted nd sensed using single wireless ctive sensing unit. In effect, the wireless ctive sensing unit closes n ctive sensing feedbck loop between the two piezoelectric pds. The br is cntilevered cm over the edge of tble surfce to which one end of the luminum br is clmped. The trnsmitting pd will remin on the side of the tble while the receiving pd will be on the cntilevered end of the br. A series of excittions, s commnded by the wireless ctive sensing unit core, re emitted by the trnsmitting piezoelectric pd into the luminum element. The coustic wve produced trnsverses the br s length nd is observed by the receiving piezoelectric pd. Employing two piezoelectric elements on single structurl element ims t obtining the complete input-output behvior of the structurl element system. Driving the ctution nd sensing interfces t their mximum speeds of 40 khz, the response modes of the luminum plte below the Nyquist frequency (20 khz) will be illuminted by the input excittions pplied to the system. In the luminum plte setup, the totl dynmic system cn be segmented into three dynmic elements: the two piezoelectric pds nd the luminum br s shown in Fig. 4. Assuming ech element to be liner nd time invrint (LTI), ech cn be chrcterized by liner trnsfer functions in both the continuous nd discrete-time complex domins (s- nd z-domins respectively). In the discrete-time domin, the trnsfer function of the input piezoelectric, structurl element nd output piezoelectric re denoted s T(z), S(z) nd R(z), respectively. The totl dynmic system trnsfer function, H(z), cn be chrcterized from the input voltge signl pplied to the trnsmitting piezoelectric pd nd the output signl from the receiving pd. In the complex z-domin, the discrete-time convolution sum is simply the multipliction of the individul trnsfer functions: H ( z) = T ( z) S( z) R( z) (1) To chrcterize the trnsfer function describing the input-output behvior of the luminum plte, white noise input signl is pplied by the trnsmitting piezoelectric pd. White noise is convenient excittion source becuse its power spectrl density is constnt cross the frequency bnd of interest nd will excite ll of the element vibrtion modes below the Nyquist frequency (20 khz). To ccurtely determine the vibrtion chrcteristics of the luminum plte, the presence of smll levels of electricl nd therml noise in the sensing nd ctution interfces must be ccounted for. Difficult to theoreticlly model, the noise cn be ccounted for by pplying lrge set of excittion sources. System prmeters (e.g. modl frequencies) clculted from the input-output system signls cn then be verged cross the signl smpling set to eliminte vribility due to noise. In totl, twenty white noise input excittions re pplied to the luminum plte with vrying levels of signl energy. All of the white noise signls re chosen to hve zero men but

7 4 Input White Noise with Men = 0 V nd STD = 1.0 V 2 V Output Signl of Receiving Pd 4 V t (sec) Fig. 5. (Top) white noise excittion with 1.0 V stndrd devition; (bottom) mesured response of the luminum plte their stndrd devition re vried between 0.3 V to 1.2 V. The response of the luminum plte, s mesured by the second piezoelectric pd, to n input white noise excittion with 1.0 V stndrd devition is shown in Fig EMBEDDED SOFTWARE FOR LOCAL DAMAGE DETECTION With mple mounts of memory nd computtionl power integrted in the wireless ctive sensing unit design, inputoutput time history dt of n ctively sensed structurl element cn be nlyzed in ner rel-time for the detection of dmge. A novel dmge detection methodology recently proposed by Lynch 15 to monitor the helth of structurl elements tht re excited by ctive sensors is considered for inclusion in the core of the wireless ctive sensing unit. The dmge detection methodology is cpble of detecting dmge using the loction of system identifiction model poles. As dmge is incurred in the structurl element, subsequent chnges in the frequency nd dmping rtio of high-order vibrtion modes will cuse migrtion of the trnsfer function poles (roots) in the discrete-time complex plne. Using the poles s fetures, liner clssifiction boundries re clculted tht ttempt to seprte the poles of n unknown (dmged or undmged) structurl stte from those of the undmged structure. The qulity of the decision boundry, s mesured by the number of misclssifictions, provides mesure of the sttisticl seprbility of trnsfer function poles tht correspond to the unknown nd undmged structurl element; pole clusters seprble indicte the structurl element is dmged. This method hs been shown to be powerful tool for detecting the presence of structurl dmge s well s providing n estimte of its severity in elements ctively sensed using piezoelectric pds. With trnsfer function poles serving s the key feture of the method, the poles re determined from n uto-regressive with exogenous inputs (ARX) time-series model clculted using the input-output behvior of the structurl element. Fig. 6 summrizes the steps tken by the computtionl core in utonomously executing this novel dmge detection procedure. The steps corresponding to the ARX model will be described in more detil. 3.1 Embedment of ARX Time-Series Models Softwre is written for the PowerPC microcontroller tht will clculte n ARX time-series model bsed on the inputoutput response of the ctively sensed luminum plte element. Mny numericl methods re vilble for determintion of n ARX time series model, but lest-squres estimtion hs been selected in this study. Defining the input to the system t the discrete time-step k by the vrible k), nd the output, y(k), n ARX time-series model cn be written 16 : y( k) + 1 y( k 1) + L n y( k n ) = b1u ( k 1) + Lbn k nb ) e( k) (2) + b

8 Apply Excittion nd Record Plte Acoustic Wves Clculte ARX System ID Model Determine Roots of Chrcteristic Eqution (Poles) Liner Clssifiction of Trnfer Function Poles If Poles Seprble Wirelessly Report Dmge Acoustic Wve Aluminum Plte Fig. 6. Embedded dmge detection methodology bsed on the migrtion of trnsfer function pole loctions where weights on observtions of the system output nd input re denoted s nd b, respectively. In totl, n coefficients re pplied to the outputs while n b coefficients re pplied to pst inputs of the dynmic system. In this study, the system input, u, corresponds to the voltge pplied to the first piezoelectric pd while the output, y, is the voltge mesured from the second piezoelectric pd. In most cses, the ARX time-series model clculted will not precisely fit the mesurement dt resulting in model error denoted s e(k). To clculte the coefficients of the ARX model, lest squres estimtion pproch is tken to find the optiml ARX coefficients tht minimize qudrtic cost function of the model error time-history vector, e: 1 T J = e e (3) 2 With Eqution (2) holding true for ll observtions of y(k) from k = n to N, mtrix representtion of the ARX model, A, relting vector of the coefficients of the model, c, to the time-history output, y, cn be ssembled: y( n + 1) y( n ) y n ( + 2) y n y ( + 1) = = M y( N) y( N 1) L L O L y(1) y(2) M y( N n ) n ) n + 1) M N 1) L L O L 1 n nb + 1) M n n b + 2) n = Ac M b N n b ) M bn b M 1 (4) To ccurtely determine the coefficients of n ARX model, mny more response smples re collected thn the number of coefficients (N >> n b + n ). In this cse the mesurement mtrix, A, will be over-determined nd full rnk. To find the ARX model coefficients, the lest-squre solution of Eqution (4) is given by: T 1 T ( A A) A y c = (5) Subroutines for embedment in the wireless sensing unit core re written in C, high-level progrmming lnguge. These subroutines re intended to clculte the lest squre solution to Eqution (4). Singulr vlue decomposition is employed in the solution to ensure its ccurcy while recursive btch lgorithm for the finl solution is tken to preserve spce in memory ARX Model Size Selection To ccurtely model the input-output response time-histories using n ARX model, the size of the ARX model needs to be chosen priori. Size refers to the number of coefficients required to minimize the prediction error of the model. When fitting ARX models to system response dt, the size of the model will dictte its predictive qulities. Generlly, s sizes grow, model prediction errors will reduce. However, models too lrge re not necessrily better becuse they will over fit the mesurement dt; over fitting refers to the model cpturing the behvior of signl noise in ddition to the system s physicl behvior. To ssist in selecting suitble ARX model size tht only chrcterizes structurl behvior, two pirs of input-output time-history records re needed: the first is designted for clcultion of the model nd the second to verify the model prediction error. Using the first pir of input-output dt, ARX model coefficients re

9 Model Prediction Error Verifiction Dt Set clculted for vrious model sizes. Once the model is determined, its predictive error is clculted using the trining s well s the vlidtion dt sets. The vector norm of the model s prediction error is resonble sclr quntity tht cn be used to quntify the model s qulity with smller norms indicting better fit to the input-output dt. At first, when the model size begins to increse, the norm of the prediction error of the ARX model using both sets of input-output dt will rpidly decrese. This indictes the lrger models re cpturing the structurl system s dynmics more completely. As the model size continues to grow, improvements in the model prediction error will occur t n incresingly slower rte. At one point, lrger models will strt to include signl noise; t this point, the prediction error of the second verifiction dt set will begin to increse. Fig. 7 summrizes the nticipted behvior of the ARX prediction error s function of the model size. The finl model size chosen should be sufficiently lrge to completely chrcterize the system without including signl noises in the model. For exmple, n cceptble ARX model size could be chosen from the region delineted in Fig. 7. To determine the idel ARX model size for the luminum plte element, the 0.3V input signl nd corresponding output response re chosen s the first dt set to which ARX models of vrious sizes will be fit. As the verifiction set, the input-output response dt from the 0.4V input signl is chosen. The selection of these two input-output dt sets ws rbitrry. Fig. 8 plots the ARX model prediction error for vrious model sizes. In ech of the six plots in Fig. 8, one model order (either n or n b ) is held constnt while the other is vried. Considering the prediction error of the ARX model s function of n (n b held fixed), we find the norm of the error decreses s expected. However, increses in the prediction error for the vlidtion dt set do not occur until lrge model orders in excess of n = 100 re considered. With only minor reduction in the model prediction error fter n = 21 nd the computtionl demnd of clculting the ARX coefficients incresing, the ARX model order, n = 21, is chosen. Considering the prediction error s function of n b, the error norm corresponding to the vlidtion dt set increses fter model order of n b = 4. As result, the finl ARX model order is chosen to be n = 21 nd n b = 4 nd is denoted s ARX(21,4). 3.3 ARX Model Trnsfer Function Poles After the ARX time-series model hs been found for set of input-output time-histories, the discrete-time trnsfer function of the system cn esily be derived. The Z-trnsform is employed to trnsfer the discrete-time time-series described by Eqution (2) into the complex z-domin: Z { y( k) + y( k 1) + L y( k n ) = b k 1) + Lb k n ) + e( k) } 1 Y ( z) + z n 1 1 Y ( z) + L Acceptble Model Orders n z ARX Model Size n 1 Clcultion Dt Set Fig. 7. Behvior of the ARX prediction error for the clcultion nd verifiction dt set s model order increse 1 Y ( z) = b z U ( z) + Lb 1 nb b nb z nb U ( z) + E( z) If the residul error, e(k), of the ARX time-series model is ignored, the trnsfer function of the dynmic liner system cn be written in the discrete-time complex domin, H(z): (6)

10 Norm Prediction Error Norm Prediction Error Norm Prediction Error ARX(,1) Clcultion Dt Vlidtion Dt ARX(,5) ARX(,10) Norm Prediction Error Norm Prediction Error Norm Prediction Error ARX(1,b) ARX(20,b) ARX(50,b) b Fig. 8. The ARX prediction error norm for chnges in the model order (The clcultion dt set corresponds to 0.3V white noise input nd the vlidtion dt set corresponds to 0.4V white noise excittion) 1 nb Y ( z) b1 z + Lbn z b H ( z) = = 1 n (7) U ( z) 1+ z + L z 1 n The denomintor of the trnsfer function is the chrcteristic eqution of the dynmic system nd encpsultes informtion on the frequency nd dmping rtio of ech vibrtion mode of the system. The roots of the chrcteristic eqution re termed the poles of the system nd uncouple the orthogonl set of modes. The frequency nd dmping rtio of the modes cn be found from the complex vlued pole (where T denotes the time step of the discrete-time signl): z = e 2 ξω n ± ωn 1 ξ j T (8) The migrtion of the trnsfer function poles will move s result of dmge; this migrtion is due to the structurl dmge influencing the frequency nd dmping rtios of some of the system vibrtion modes. To determine the roots of the chrcteristic eqution, numericl lgorithms bsed on Lguerre s formuls re being explored for doption 17.

11 5. CONCLUSIONS Mny innovtive technologies re being explored for use in structurl monitoring systems in order to reduce their instlltion costs nd enhnce their functionlity. This study hs explored the fesibility of including n ctution interfce within self-contined wireless sensing unit. Cpble of commnding structurl ctutors nd ctive sensors, the resulting wireless ctive sensing unit would be ble to enjoy direct interfce to the physicl system in which it is instlled. In prticulr, ctive sensors would be powerful tool to employ in structurl helth monitoring system becuse they cn imprt low-energy excittions into structurl elements tht illuminte their high-order response modes. Trcking high-order response modes for the detection of dmge is desirble becuse these modes re sensitive to the onset of dmge but re less sensitive to temperture vritions thn globl response modes. Furthermore, screening structure for dmge on n element by element bsis preserves the self-sufficiency of the wireless ctive sensing unit nd reduces the mount of wireless communictions needed to trnsfer dt thereby sving bttery power. To illustrte the performnce of prototype wireless ctive sensing unit, n luminum plte with two piezoelectric pds epoxy mounted to its surfce ws employed. White noise excittions re pplied to the plte by one pd while the unit simultneously records the response of the second piezoelectric pd. After collection of the system response, softwre embedded in the computtionl core ws utilized to clculte n ARX time-series model for the input-output mesurement dt. As prt of lrger dmge detection methodology tht identifies dmge from the migrtion of ARX trnsfer function poles, the stright-forwrd but non-trivil ARX softwre implementtion demonstrtes the possibility of developing self-ctuted wireless ctive sensing unit cpble of utonomously dignosing the helth of structures. ACKNOWLEDGEMENTS This reserch is prtilly funded by the Ntionl Science Foundtion under grnt number CMS Additionl support hs been provided by Los Almos Ntionl Lbortory, Contrct Number REFERENCES 1. E. G. Strser nd A. S. Kiremidjin. A modulr, wireless dmge monitoring system for structures. Report No. 128, John A. Blume Erthquke Engineering Center, Deprtment of Civil nd Environmentl Engineering, Stnford University, Stnford, CA, J. P. Lynch. Decentrliztion of wireless monitoring nd control technologies for smrt civil structures. Report No. 140, John A. Blume Erthquke Engineering Center, Deprtment of Civil nd Environmentl Engineering, Stnford University, Stnford, CA, J. P. Lynch, K. H. Lw, A. S. Kiremidjin, E. Crryer, C. R. Frrr, H. Sohn, D. Allen, B. Ndler nd J. Wit. Design nd performnce vlidtion of wireless sensing unit for structurl monitoring pplictions, Structurl Engineering nd Mechnics, Techno Press, 17(4), in press, S. W. Doebling, C. R. Frrr, M. B. Prime nd D. W. Shevitz. Dmge identifiction nd helth monitoring of structurl nd mechnicl systems from chnges in their vibrtion chrcteristics: literture review. Report No. LA MS, Los Almos Ntionl Lbortory, Los Almos, NM, J. L. Humr, A. Bgchi nd H. Xu. Chllenges in vibrtion-bsed structurl helth monitoring. Proceedings of the 1 st Interntionl Conference on Structurl Helth Monitoring nd Intelligent Infrstructure, Blkem Publishers, Tokyo, Jpn, pp , G. Prk, H. H. Cudney nd D. J. Inmn, Impednce-bsed helth monitoring of civil structurl components. Journl of Infrstructure Systems, ASCE, 6(3): R. R. Brooks nd S. S. Iyengr. Multi-sensor fusion. Prentice Hll, Upper Sddle River, NJ, S. Bhll nd C. K. Soh. Structurl impednce bsed dmge dignosis by piezo-trnsducers, Erthquke Engineering nd Structurl Dynmics, Wiley, 32(12): , F. Wu nd F. K. Chng, A built-in ctive sensing dignostic system for civil infrstructure systems, Proceedings of 8 th Interntionl Symposium on Smrt Structures nd Mterils, Sn Diego, CA, SPIE v. 4330, pp , Motorol Corp. Motorol PowerPC MPC555 user s mnul. Motorol Corportion, Phoenix, AZ, Texs Instruments. DAC7624: 12-bit qud voltge output digitl to nlog converter. Texs Instruments, Inc., Dlls, TX, MxStrem. XCite Advnced Progrmming nd Configurtion: Advnced Mnul. MxStrem, Inc., Lindon, UT, 2003.

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