IOP PUBLISHING SMART MATERIALS AND STRUCTURES

Smart Mater. Struct. 20 (2011) 105025 (11pp) doi:10.1088/0964-1726/20/10/105025

On-line structural damage localizationand quantification using wireless sensorsTing-Yu Hsu1, Shieh-Kung Huang1, Kung-Chung Lu2,Chin-Hsiung Loh2, Yang Wang3 and Jerome Peter Lynch4

1 National Center for Research on Earthquake Engineering, No. 200, Section 3, XinHai Road,Taipei 106, Taiwan2 Department of Civil Engineering, National Taiwan University, Taipei 106, Taiwan3 School of Civil and Environment Engineering, Georgia Institute of Technology, 790 AtlanticDrive, Atlanta, GA 30332-0355, USA4 Department of Civil and Environmental Engineering, University of Michigan,2328 G G Brown, Ann Arbor, MI 48109-2125, USA

E-mail: dysheu@ncree.narl.org.tw (T-Y Hsu)

Received 28 March 2011, in final form 6 July 2011Published 13 September 2011Online at stacks.iop.org/SMS/20/105025

AbstractIn this paper, a wireless sensing system is designed to realize on-line damage localization andquantification of a structure using a frequency response function change method (FRFCM).Data interrogation algorithms are embedded in the computational core of the wireless sensingunits to extract the necessary structural features, i.e. the frequency spectrum segments aroundeigenfrequencies, automatically from measured structural response for the FRFCM. Instead ofthe raw time history of the structural response, the extracted compact structural features aretransmitted to the host computer. As a result, with less data transmitted from the wirelesssensors, the energy consumed by the wireless transmission is reduced. To validate theperformance of the proposed wireless sensing system, a six-story steel building with replaceablebracings in each story is instrumented with the wireless sensors for on-line damage detectionduring shaking table tests. The accuracy of the damage detection results using the wirelesssensing system is verified through comparison with the results calculated from data recorded ofa traditional wired monitoring system. The results demonstrate that, by taking advantage ofcollocated computing resources in wireless sensors, the proposed wireless sensing system canlocate and quantify damage with acceptable accuracy and moderate energy efficiency.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Since the mid-1990s, a number of research teams in bothacademia and industry have proposed an impressive arrayof wireless sensing unit prototypes to be implemented forstructural health monitoring [1]. The essential part of awireless sensing systems (WSS) is the wireless sensing unit(WSU) which generally consists of three or four functionalsubsystems: sensing interface, computational core, wirelesstransceiver and, for some, an actuation interface. A benefitof wireless structural monitoring systems is that they areinexpensive to install because extensive wiring is no longerrequired between sensors and a central data acquisition system.Furthermore, a wireless sensing network is not simply a

substitute for traditional tethered monitoring systems but alsoa decentralized architecture offering parallel processing ofmeasured data. The collocated computational power endowswireless sensing systems with great potential for the researchcommunity to discover.

Researchers have utilized the decentralized parallelcomputing resources in a WSS by employing local dataprocessing algorithms in the WSU for structural healthmonitoring purposes. By reducing the size of data to betransmitted, data communication, which is the most significantsource of power consumption of the wireless sensing units, canbe reduced. Therefore, minimizing the need to transfer timehistories of structural response data by programming wirelesssensing units to locally interrogate their data first seems to be

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Smart Mater. Struct. 20 (2011) 105025 T-Y Hsu et al

one of the appropriate solutions to improve the overall energyefficiency of the wireless structural monitoring system.

Since the end of the 1990s, researchers have been tryingto embed modal analysis and damage detection algorithms intowireless sensing units for damage detection purposes. Straserand Kiremidjian [2] were the first to embed civil structuralhealth monitoring algorithms in WSUs. The normalizedArias intensity, which is essentially determined by summingthe square of the structural acceleration measured over anearthquake event, is calculated within WSUs as a damageindicator for damage assessment. Damage existence andlocations of a structure can be assessed by the differenceof the energy profile between different floors of a buildingimmediately following an earthquake. Tanner et al [3] applya statistical process control (SPC) algorithm to detect theexistence of damage of a small bolted frame structure. Twoaccelerometers mounted across each joint of the structureare connected to a WSU. Preload of the bolt is released byvarying the input voltage to a piezoelectric actuator underneaththe head of the bolt. The cross-correlation coefficientsbetween the two measured acceleration time histories underthe vibration generated by an electromagnetic shaker areprocessed locally on a WSU. An alarm will be triggeredautomatically if an outlier is indicated. Caffrey et al[4] propose to detect damage of a structure by assessingchange in modal frequencies and signal energy containedin each corresponding mode. Fourier spectra of structuralacceleration time histories are calculated in each WSU. Afterthe modal frequencies and modal signal energy contributionsare determined in the WSUs, they are transmitted to thehost computer to perform damage assessment. The proposedapproach is verified by detecting the presence of damageof the IASC-ASCE Structural Health Monitoring BenchmarkStructure. Lynch et al [5] apply a two-tiered time-seriesdamage detection algorithm, the autoregressive (AR) andautoregressive model with exogenous inputs (ARX) predictionmodel, to automatically detect damage of a lumped-masslaboratory structure using a WSS. The coefficients of anAR model are calculated in the WSUs and transmitted tothe host computer. The residual error in the ARX modelof the measured data computed in the WSUs is used todetermine the presence of damage in the structure. The samedamage detection algorithm is later successfully applied todetect damage of nearly full-scale single-story reinforcement-concrete frames [6]. Gao et al [7] propose a distributedcomputing strategy using WSUs which apply a flexibility-based damage detection method to assess local health conditionof a truss structure. Adjacent WSUs are grouped together as acommunity via a hierarchical strategy. After the WSUs in eachgroup transmit raw time-history data to a group-head WSU,the flexibility matrix is constructed using modal parametersidentified by the natural excitation technique (NExT) andeigenvalue realization algorithm (ERA). Damage locatingvectors (DLV) are then computed in each community to detectdamage. Nagayama et al [8] later improve this strategyby introducing stochastic DLV which eliminates the need toestimate normalization constants. The improved method isverified through applying to a laboratory 3D truss structure.

Hackmann et al [9] try to localize damage of a structure basedon the damage location assurance criterion (DLAC) method.The DLAC method locates damage by comparing the identifiedmodal frequencies of each WSU to a frequency databasegenerated by simulation of different damage patterns of ananalytical model of the structure. The wireless sensors performfast Fourier transform (FFT), power spectrum analysis (PPA)and fractional polynomial curve fitting (FPCF) to determinemeasured frequencies. The proposed approach is verifiedby both a cantilever beam and a 3D truss structure withsingle damage location. Hackmann et al [10] later proposeanother approach which uses the angles-between-string-and-horizon flexibility-based method (ASHFM) and the axial strainflexibility-based method (ASFM) to detect damage of a beamstructure and an analytical truss structure, respectively. Afterthe modal frequencies are selected in WSUs using similaralgorithms of the previous paper, the spectrum data of theselected modal frequencies are transmitted to other WSUs.The cross-spectral density (CSD) matrices are calculatedand singular value decomposition (SVD) is performed onthe CSD matrices at each modal frequency to obtain modeshapes. Finally the modal frequencies and mode shapes aretransmitted to the host computer to assess damage. Wanget al [11] apply transmissibility function analysis to detectdamage locations of a 2D steel portal frame using mobileWSUs. The Fourier spectrum of the measured accelerationtime history is calculated in each WSU. The FFT results withinthe interested frequency range are transmitted to other WSUs.The damage indicators are determined by the transmissibilityfunction analysis in WSUs and then transmitted to the hostcomputer.

As described in Rytter [12], damage detection can beclassified as four levels:

• Level 1: determination that damage is present in thestructure.

• Level 2: determination of the geometric location of thedamage.

• Level 3: quantification of the severity of the damage.• Level 4: prediction of the remaining service life of the

structure.

The above-mentioned literature integrates damage de-tection algorithms with WSS to determine the existence ofdamage, i.e. level 1 damage detection, or the locations ofdamage, i.e. level 2 damage detection. There is no WSS whichintegrates damage detection algorithms and achieves level 3damage detection of a structure.

In this paper, the authors propose to integrate thefrequency response function change method (FRFCM) [13]with WSS to not only detect the presence and location ofdamage but also estimate the extent of damage, i.e. level 3damage detection. This is contributed by the advantage ofthe FRFCM where enough equations to assess locations andthe extent of damage of a structure can be acquired by usingfrequency response functions (FRFs) at a few frequencies.To calculate FRFs, one only needs the frequency spectrumsegments calculated from measurement in each sensing nodesusing the FFT algorithm. Without transmitting the whole time

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Figure 1. Functional diagram detailing the hardware design of thewireless sensing unit.

history, only a short array composed of selected frequencyspectrum segments is transmitted between the wireless sensingnetworks. The frequency spectrum segments can be selectedat the frequencies close to the eigenfrequencies of the systemsince the signal-to-noise ratio of these Fourier spectra ismuch higher than others. The proposed decentralized strategywhich integrates the FRFCM with WSS is accomplished andthen validated via a scaled six-story steel building structureon a shaking table. Potential energy efficiency gained bythe proposed decentralized strategy is discussed. Furthermodification of hardware for the purpose of minimizing energyconsumption of WSUs is beyond the research scope of thisstudy.

2. Implementation of the FRFCM on WSS

2.1. Wireless sensing units

The academic prototype of a WSU developed by Wang [14] isemployed here to realize the on-line level 3 damage detection.This prototype has been successfully applied to both structuralhealth monitoring [15] and structural control [16, 17]. Figure 1shows the overall hardware design of the WSU prototypewith an optional off-board auxiliary module for conditioninganalog sensor signals. The key parameters of the prototypewireless sensing unit are summarized in table 1. The mainWSU (shown in the top part of figure 1) consists of threefunctional modules: sensor signal digitization, computationalcore and wireless communication. The sensing interfaceconverts analog sensor signals on multiple channels into 16-bit digital formats. The digital data is then transferred to thecomputational core by a high-speed serial peripheral interface(SPI) port. Abundant external memory (128 kB) is associatedwith the computational core for local data storage and analysis.The Maxstream 24XStream wireless modem, operating on the2.4 GHz wireless band is used for peer-to-peer communicationbetween WSUs and between WSUs and the host computer.The auxiliary sensor signal conditioning module (shown in thebottom part of figure 1) is designed to assist in adjusting analogsensor signals prior to digitization.

Table 1. Key performance parameters of the wireless sensing unit.

Design parameter Specification

Computing coreMicrocontroller 8-bit RISCa architecture, up to

16MIPSb throughput at 16 MHzFlash memory 128 kBInternal SRAMc 4 kBExternal SRAM 128 kBEEPROMd 4 kBPower consumption 30 mA active, 55 μA standby

Wireless transmissionOperating frequency ISM 2.4000–2.4835 GHzData transfer rate 19.2 kbpsCommunication range Up to 180 m indoor, 5 km at

line-of-sightPower consumption 150 mA transmitting, 80 mA

receiving, 26 μA standby

Sensing interfaceSampling precision and rate 16 bit, up to 100 kHzAnalog sensor channels 4

a RISC: reduced instruction set computer.b MIPS: million instructions per second.c SRAM: static random access memory.d EEPROM: electrically erasable programmable read-only memory.

2.2. The frequency response function change method

The frequency response function change method (FRFCM)derived from the equation of motion of a shear buildingsubjected to a ground motion both before and after damageis capable of detecting the location and extent of damage [13].The damage identification equation of the FRFCM is presentedas

τd(ω)�κ = (−ω2M + iωC1 + K)(Td(ω) − T(ω)) (1)

where M, C1 and K denote the n × n mass, damping andstiffness matrices, respectively; T(ω) and Td(ω) denote thefrequency response function matrix between the input groundacceleration vector and the response displacement vector forthe intact and damaged system, respectively; �κ denotes thevariation of story stiffness of a shear building as

�κ = [ �k1 �k2 · · · �kn ]T (2)

and τd(ω) denotes the matrix composed of components inTd(ω) as

τd(ω)

=

⎡⎢⎢⎢⎢⎢⎣

Td1(ω) Td1(ω) − Td2(ω)

0 Td2(ω) − Td1(ω). . .

. . .

00

. . .

Td(n−1)(ω) − Td(n−2)(ω) Td(n−1)(ω) − Tdn(ω)

0 Tdn(ω) − Td(n−1)(ω)

⎤⎥⎥⎥⎥⎦

(3)

where Tdp(ω) presents the pth component in Td(ω).

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The only unknown in equation (1) is the vector �κ . Thesystem matrices of the intact system, i.e. mass matrix, dampingmatrix and stiffness matrix, and the FRFs both before andafter damage are required to solve equation (1). In order toobtain the well-estimated system matrices of the intact system,one can construct a finite element model of the structure andmodify it to acquire well-estimated system matrices by modelupdating techniques. Alternatively, the subspace identificationtechnique proposed by Xiao et al [18] is a very useful tool toobtain the well-estimated system matrices. Once the systemparameter matrix A and output matrix C have been obtained bythe subspace identification algorithm from the measured data,the system damping and stiffness matrices can be obtained foracceleration sensing as

[ K C1 ] = −MCR−1, R =[

CA−2

CA−1

]. (4)

For velocity sensing or displacement sensing, similar equationscan be utilized. This technique needs a reasonable system massmatrix which can be obtained from a finite element model ofthe system. It has been derived that, for obtaining the ratioof the story stiffness variation, it is not necessary for the massmatrix of a shear building structure to be known [19]. Thesystem matrices in this research are obtained by the subspaceidentification technique by assuming a diagonal mass matrix asdescribed in the following sections.

For a certain frequency ω j , there are 2n equations(separating real parts and imaginary parts) with n unknownsof the story stiffness variations. To reduce the error due tonoise in signals, it is suggested to use m different frequenciesaround each eigenfrequency and get 2n × m equations foreach eigenfrequency because the signal-to-noise ratios aroundstructural eigenfrequencies are higher. Also the predictedvariations of story stiffness are determined as weightedmeans of the results obtained using frequencies around eacheigenfrequency according to a results-similarity criterion. Theresults-similarity criterion weights the identified story stiffnessvariations obtained by each mode according to their similarityto the median value of each story as shown in the followingequations:

�κi =p∑

j=1

�κi j × wi j (5)

wi j = exp(−2(�κi j − �κi)2/(σi )

2) (6)

σi =√√√√

p∑j=1

(�κi j − �κi )2 (7)

where �κi represents the weighted identified stiffnessvariations of the i th story; �κi j represents the identifiedstiffness variations of the i th story using frequencies aroundmode j ; wi j represents the weighting determined by thesimilarity measurement result of each �κi j ; σ represents thestandard deviation between the identified stiffness variations�κi j and the median of identified stiffness variations �κi ;and p represents the number of identified modes. It hasbeen shown that more reliable results can be obtained withoutthe interference of numerical errors caused by measurementnoise [13].

2.3. Integrating WSS with the FRFCM

With the system matrices and also the FRFs of the intactsystem written in the host computer of a WSS, the restof the information needed for damage detection of themonitored structure is some segments of FRFs around thestructural eigenfrequencies. On the other hand, becauseeach wireless sensing unit is equipped with a computationcore which enables it to transform the measured time historyto the Fourier spectrum and also identify the possiblestructural eigenfrequencies, the segments of FRFs around thestructural eigenfrequencies can be calculated and transmittedautomatically to the host computer. Therefore, the FRFCM ischosen to be integrated with the WSS to realize on-line damagelocalization and quantification.

The on-line damage detection procedure and data broad-cast between the WSUs and the host computer are described asfollows. After the acceleration time history yi(t) is measuredin the i th WSU, the Fourier spectrum Yi (ω) is calculated byan embedded FFT algorithm. A set of p eigenfrequenciesof the structure in the i th WSU, ωi = [ωi1, ωi2, . . . , ωi p],is determined by an embedded peak-picking algorithm whichselects the peaks of the Fourier spectrum smoothed byan embedded smoothing algorithm. The frequency set ωi

selected in each WSU is then transmitted wirelessly tothe host computer. The most probable set of the systemeigenfrequencies ωsystem is decided by taking the median ofeach set of peaks in the host computer and then broadcast toall the n WSUs. The i th WSU then transmits a set of Fourierspectrum Yi(ωsystem) around the system eigenfrequencies backto the host computer. Note that the frequency set ωsystem

contains not only the system eigenfrequencies ωsystem but alsoten adjacent frequencies around them. After the host computerreceives the selected frequency spectrum segments from all theWSUs, the FRF segments are estimated by dividing the cross-power spectrum between the structural response and inputexcitation by the auto-power spectrum of the input excitation.With the system matrices and FRFs of the structure in thereference state written in the host computer, the variations ofstory stiffness matrices �κ can be calculated using these FRFsegments by equation (1) and equations (5)–(7). Since thenecessary information for FRFCM to detect damage of thestructure could be accessed automatically right after a groundexcitation, e.g. a train passing or an earthquake, on-line dam-age detection could be achieved. A graphical representationof the implementation of the FRFCM on a wireless sensingsystem can be found in figure 2. In order to realize theintegration of the FRFCM and the WSS, the state machinewhich controls operating, computing and communicating ofthe WSUs was designed and coded. The FFT, peak-picking andsmoothing algorithms, described more explicitly in section 3.2,were also coded and embedded in the WSUs.

3. Experimental validation

3.1. Experimental set-up

A 1/4-scale six-story steel building structure (figure 3) wasemployed here to perform experimental validation of the

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Figure 2. Implementation of the FRFCM on a wireless sensing system.

proposed wireless on-line damage detection operation scheme.As shown in figure 3, the six-story 1/4-scale structureconsisted of a single bay with 1.0 m × 1.5 m floor area withuniformly a 1.0 m story height. The size of the columnand beam was 150 mm × 25 mm (rectangular section) and50 mm × 50 mm (L section), respectively. The beam–floorconnection was welded, and the floor–beam connection andthe floor–column connection were bolted. The dead load wassimulated by lead-block units fixed on the steel plate of eachfloor, and the total mass of each floor of the target structurewas 862.85 kg, except that the mass of the roof floor was803.98 kg. The stiffness of the bracing system was controlledby a small connecting plate (called ‘CP’) whose size was100 mm × 10 mm with clear height 196 mm (figure 4).

To imitate damage of the structure, the connecting platesof some of the stories were removed. Because the connectionof the connecting plates was designed as bolted, the bending

shape of the plate should be between double curvature andsingle curvature. The story stiffness reduction ratios after theconnecting plate was removed assuming the behavior of theplates as double curvature or single curvature were calculated.The mean value of these two values was −37.3% and waschosen as a reference value to check with the experimentalresults.

In order to investigate the feasibility of the proposedwireless sensing system, a total of four different damagecases (see table 2) under El Centro earthquake excitation inthe X direction were studied. Case W1 was the baselinetest and no damage was introduced. Case W2 was anotherbaseline test to see if the FRFCM may give false alarms.Case W3 and case W4 simulated the single and multipledamages, respectively, by removing the connecting platesin the designated stories. The peak ground acceleration iscontrolled as less than 0.05g because larger excitation may

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(a) (b)

Figure 3. A 1/4-scale six-story steel building structure: (a) an overview and (b) plane views.

Figure 4. Close view of the bolting connection of the connectingplates.

loosen the bolted connecting plates, which makes the extentof damage unpredictable. Note also that in real applicationswhere structural behavior under strong earthquakes maybecome nonlinear, only the response at the end of the wholetime history should be used to estimate the damage.

For the wired measurement system of the shaking tablefacility, Setra141-A accelerometers with an acceleration rangeof ±4g and a noise floor of 0.4mg were employed. MultiplePacific Instrument Series PI660-6000 data acquisition chassis

Table 2. Cases of experimental study (‘CP’ represents theconnecting plates; ‘R’ represents removal of connecting plates).

Case number

Story number W1 W2 W3 W4

6 CP CP CP CP5 CP CP CP CP4 CP CP CP CP3 CP CP CP R2 CP CP CP CP1 CP CP R R

are used in the wired system. The wireless sensing unitwas instrumented with the ‘Tokyo Sokushin Servo VelocitySeismometer’ type VSE-15A which was placed in each storyincluding the ground floor. The wireless sensing systemsconsists of seven wireless sensing units and seven VSE-15Asensors. A typical set-up of wireless sensing units and sensorsas well as associated power supply devices and antennas isshown in figure 5. The VSE-15A was switched to accelerationmode in order to compare the wireless-measured accelerationdata to the one measured by the data acquisition system of theshaking table facility. The analog output voltage of the VSE-15A sensor was −10–10 V, which was offset to 0–5 V by theauxiliary sensor signal conditioning module. The sampling rateof both the wired and wireless system was 200 Hz.

The typical time history of the measured accelerationresponse of both the wireless system and wired system in caseW2 after zero mean are shown in the left part of figure 6. Ingeneral, the wireless-measured data had good agreement withthe wired-measured one. However, taking a close look at thedata as shown in the right part of figure 6, it is evident thatthe signal-to-noise ratio in the wireless-measured data is lower

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Figure 5. Close-up view of the wireless sensing units, power supplydevices, antennas and sensors.

than that in the wired-measured data, especially for the datameasured on the ground floor. Looking at the frequency spectraof the measured wired and wireless data as shown in figure 7,it is noted that the measured data on the ground floor is noisy,especially for the high frequency range. The extra noise in thewireless-measured data may contribute additional errors to thedamage detection results using FRFCM.

3.2. Embedded algorithms in the WSUs

The implementation of the FRFCM on WSS as described insection 3.1 requires the WSUs to equip with an FFT algorithm,

Figure 7. FFT results of wireless and wired sensor data.

a smoothing algorithm and a peak-picking algorithm. TheCooley–Tukey FFT algorithm was embedded in the WSUs.The algorithms for smoothing and peak-picking the Fourier

Figure 6. Measured time history of wireless and wired sensor data. Left: whole time history. Right: close-up view.

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Figure 8. Comparison among identified story stiffness variation ratio obtained by wireless on-line, wireless off-line and wired off-line.(a) Case W2, (b) case W3 and (c) case W4.

spectrum after taking the FFT of the measured data aredescribed here. The triangular smoothing with a weightingfunction was employed as

Y j =∑n

i=−n Y j+i × wi∑ni=−n wi

(8)

where wi = n + i + 1 if i � 0 and wi = i if i > 0; n denotesthe half-bandwidth of the weighting function; Y denotes theabsolute value of FFT results of the measured data; and Y j

denotes the absolute value of FFT results after smoothing. Thepeak of smoothed FFT results Y j was picked if Y j > Y j−1

and Y j+1 > Y j . For the measured data with a length of 4096points, the half-bandwidth of the weighting function n startedat 20 and increased by 10 per time if a wider bandwidth wererequired. The bandwidth stopped increasing if six peaks or lessthan six peaks were picked. For the six-story steel buildingstructure, only the FFT results below 20 Hz were smoothed.The smoothed FFT results below 0.2 Hz was eliminated toavoid abnormally large values caused by offset of the measureddata.

3.3. Damage detection results of FRFCM integrated withWSU

The methodology of the FRFCM requires the system matricesof the intact system and the FRFs both prior and posterior to anoccurrence of damage. In order to achieve on-line detectionof the stiffness variation ratio of each story by integratingFRFCM with the WSS, necessary information of the six-storysteel building structure in an intact state, i.e. the intact systemmatrices and the intact FRFs, needed to be written in the hostcomputer in advance. In this study, the mass matrix wasassumed diagonal with the lumped value of story mass asdescribed in section 3.1. The stiffness and damping matrices

of the structure in case W1 were identified from measured datausing the subspace identification technique with the diagonalmass matrix. The FRFs of the six-story steel building structurein case W1 and also the system matrices of the structureidentified using the measured data in case W1 were written inthe host computer in advance. For cases W2–W4, the adjacent11 FFT results around the six most probable eigenfrequenciescalculated by the WSUs were utilized to calculate FRFs rightafter the host computer received them from the WSUs. Withthe above-mentioned information ready, the variation of storystiffness can be calculated using equation (1) in the hostcomputer. Comparing to the story stiffness which can beestimated using the components in the identified stiffnessmatrix of the structure in the intact state, the story stiffnessvariation ratio can be estimated without establishing a finiteelement model of the structure.

The bars marked as ‘wireless on-line’ in figure 8 show thestiffness variation ratio of each story estimated on-line usingthe wireless-calculated FFT results transmitted from WSUs.For case W2 with no damage, no stiffness variations for everystory should be identified. For case W3 and case W4, thestiffness variation ratio of the stories with connecting platesremoved should be close to the reference value, while otherstories should have no stiffness variations. For all three cases,the damage locations are detected successfully with the errorof stiffness variation ratio less than 15%. In order to see ifthe error of stiffness variation ratio is mainly caused by theFFT algorithm embedded in the WSUs, the stiffness variationratio of each story estimated off-line using the FFT resultsof the wireless-measured time history calculated by the FFTalgorithm of the Matlab software in the host computer arealso plotted in figure 8 (marked as ‘wireless off-line’). Littleimprovement of the results is achieved if FFT results areobtained using the FFT algorithm in the Matlab software. Thisdemonstrates the robustness of the FFT algorithms embedded

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Table 3. WSS with embedded engineering analyses for damage detection.

Performance attribute Reference [2] Reference [3] Reference [4] Reference [5] Reference [9]

WS prototype WiMMS Motes Wisden Dual-core prototypeby Lynch

Imote2

Damage detectionmethod

Normalized Ariasintensity

SPC Modal frequenciesand signal energy

AR–ARX DLAC

Embeddedengineering analysis

— Cross-correlationcoefficients

FFT AR, ARX residual FFT, PPA,FPCF

Data transmitted fromWSU

Time–energy profile Damage indicator Modal frequenciesand modal signalenergy

AR coefficients anddamage indicator

Modalfrequencies

Data reduction orderb 10−1 10−4 10−3 10−2 10−3

Damage detectionlevel

Level 2 Level 1 Level 1 Level 2 Level 2

Performance attribute Reference [8] Reference [10] Reference [11] This paper

WSU prototype Imote2 Imote2 Mobile sensingnode

Wireless sensorprototype by Wang

Damage detectionmethod

Stochastic DLV ASHFM/ASFM Transmissibilityfunction analysis

FRFCM

Embeddedengineering analysis

FFT, SVD, complexeigensolver, quicksort, complexmatrix inverse

FFT, PPA, FPCF,CSD, SVD

FFT FFT, smoothing, PP

Data transmitted fromWSU

Raw time history(partial sensors),damage indicator

Modal frequenciesand mode shapes

Fourier spectrum(interested rangea)and damageindicator

Modal frequenciesand Fourierspectrum (close tomodal frequencies)

Data reduction orderb 10−1 10−2 10−1 10−2

Damage detectionlevel

Level 2 Level 2 Level 2 Level 3

a Assuming 1/5 frequency range is interested.b Assuming two bytes for one raw data; four bytes for one engineering data (e.g. frequencies, FFT results, mode shapes, ARcoefficients, damage indicator).

in the WSUs. However, if the stiffness variation ratio of eachstory is estimated off-line using the FFT results of the ‘wired-measured’ time history, the results of damage localization andquantification improved a lot (marked as ‘wired off-line’ infigure 8). It was concluded that much less error is obtainedif wired-measured time-history data are used. The differencebetween wireless and wired data may be mainly contributedby the hardware difference including power supply devicesof sensors, type of sensors, data acquisition system, etc.Nevertheless, the feasibility of the proposed idea to achievelevel 3 damage detection by integrating the FRFCM with WSSis verified.

4. Potential energy efficiencies gained fromintegrating FRFCM with WSS

In order to illustrate the potential energy efficiencies of WSUsgained from integrating FRFC with WSS, both the energyconsumption of the traditional centralized strategy and theproposed decentralized strategy were measured off-line forten times respectively after the experiment. The latency ofcalculating and transmitting data of WSUs was obtained bycollecting time-stamp data from the WSUs. The current ofeach stage was measured by the National Instrument’s (NI)CompactRIO (cRIO) Control and Acquisition System withNI9227 current input module [20].

Since measurement of raw time-history data is necessaryfor both strategies, the energy consumption of this part isnot taken into account in this study. The calculated energyconsumption of the traditional centralized strategy, E1, onlyincludes the energy consumption for transmitting the rawtime history from the WSU back to the host computer. Thecalculated energy consumption of the proposed decentralizedstrategy, E2, includes the energy consumption for computingthe FFT, smoothing and peak-picking in WSUs as well as theenergy consumption for transmitting of calculated data. If E2

is less than E1, then there is an advantage of energy efficienciescontributed by the integration of FRFCM and WSS.

With each data point requiring 2 bytes of memory, a 4096-point time-history record occupies 8192 bytes. The centralizedstrategy needs the WSU to transmit these data together withsome overheads to the host computer. This required thewireless module transmitting the raw time-history data for4.668 s on average. With an average current of 181.942 mAand internal voltage at 5 V, the energy consumption E1 fortransmitting the raw time history is equal to 4.299 J. Onthe other hand, the decentralized strategy incurred 22.234 son average for its computation stage which the centralizedstrategy did not need. With an average current of 24.473 mAand internal voltage at 5 V, the energy consumption forthe computation stage equaled 2.721 J. However, the dataaggregation greatly reduced the data to be transmitted from

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8192 to 540 bytes including 528 bytes of FFT results and12 bytes for the location of frequencies. This required thewireless module transmitting for 0.390 s on average andtherefore consumed 0.339 J of energy. As a result, the energyconsumption of the proposed decentralized strategy, E2, wasequal to 3.060 J, which is only 71.2% of E1. This illustratedthe advantage of energy efficiencies associated with FRFCMintegrated with WSS. Note that the data received by the hostcomputer using the proposed decentralized strategy are alreadythe required segments of the FFT results instead of the rawtime-history data.

Since in this case the computation of embedded algorithmsconsumed a lot of the energy for the proposed decentralizedstrategy, a low-power microcontroller with higher operationalrate can achieve even greater energy efficiency. Lynch et al[21] has already demonstrated the potential to greatly reducethe energy consumption of computing engineering analyseswithin a WSU by a two-microcontroller design. Besides alower-power controller in charge of the general operation ofa WSU, the additional microcontroller can be specially chosento execute embedded engineering analyses with little energyconsumption. The energy to calculate the FFT of 4096-pointdata is only about 1% of the energy to transmit the rawdata in their case. Alternatively, employing a single low-power microcontroller which can execute signal processingrequired by the embedded engineering analyses with highefficiency can replace two-microcontroller design and achieveeven higher system robustness. This demonstrates that carefuldesign of the hardware of a WSU can greatly improve energyefficiency gained by exploiting collocated computing resourcesof WSUs. In addition, customized hardware and powermanagement can further achieve optimized energy efficiencyof a WSU. The development of hardware in the future bringsan unlimited possibility to design a more energy-efficient WSUfor structural health monitoring purposes. In this study, onlythe potential energy efficiency gained by integrating FRFCMwith WSS is demonstrated. The design of a WSU to achievethe optimized energy efficiency is beyond the research scopeof this study.

5. Discussions and conclusions

A WSS for structural damage detection applications isdeveloped in this research. The WSS is integrated withthe FRFCM in order to achieve level 3 damage detectionand take advantage of collocated computing resources ofWSSs at the same time. A six-story steel building structureinstrumented with the developed WSUs is tested on a shakingtable to validate the proposed decentralized approach. Theexperimental results demonstrate that the proposed approachworks well for both single and multiple damage scenarios.The potential energy efficiency gained by the proposedapproach is illustrated using the experimental case studyas an example. Further energy efficiency of the proposeddecentralized strategy can be achieved by customized designof the hardware and energy management of WSUs.

For comparison, other approaches related to the sameidea which integrate damage detection algorithms with

wireless sensors and, at the same time, reduce overall powerconsumption by reducing the amount of data to be transmittedare compared with the proposed approach. The prototype ofWSUs, damage detection methods, damage detection levels,embedded engineering analysis algorithms and structuralfeatures transmitted from WSUs of these approaches aresummarized in table 3. Among them, it is evident that theproposed WSS is the only one which can achieve level 3damage detection. The accomplishment of performing on-linelevel 3 damage detection by integrating the FRCM and WSS isthe major contribution of this paper.

Because the major energy efficiency contributed by adecentralized strategy for WSUs depends on the reduction ofdata for transmitting, the reduction order of the transmitteddata using different approaches is estimated. The amountof data transmitted from WSUs using different approaches isestimated by assuming 4096 time-history length, 6 modes, 6DOFs and 30 AR coefficients for all cases. The reduction orderis then calculated by dividing these amounts by the one usingthe traditional centralized wireless approach. For example,if the raw time history is transmitted, the reduction ratio is100; if only six modal frequencies with floating number formatare transmitted, the reduction ratio is 10−3. The reductionorder of the data transmitted from the WSUs using differentapproaches is also listed in table 3. The reduction order of theproposed decentralized strategy is about 10−2, which allowsgreat potential for energy efficiency provided there is a lowenergy consumption of computation in WSUs.

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