research article structural damage detection by power...

14
Research Article Structural Damage Detection by Power Spectral Density Estimation Using Output-Only Measurement Eun-Taik Lee 1 and Hee-Chang Eun 2 1 Department of Architectural Engineering, Chung-Ang University, Seoul 06794, Republic of Korea 2 Department of Architectural Engineering, Kangwon National University, Chuncheon 24341, Republic of Korea Correspondence should be addressed to Hee-Chang Eun; [email protected] Received 25 June 2015; Revised 25 October 2015; Accepted 26 October 2015 Academic Editor: Mohammad Elahinia Copyright © 2016 E.-T. Lee and H.-C. Eun. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Most damage detection methods have difficulty in detecting damage using only measurement data due to the existence of external noise. It is necessary to reduce the noise effect to obtain accurate information and to detect damage by the output-only measurement without baseline data at intact state and input data. is work imported the power spectral density estimation (PSE) of a signal to reduce the noise effect. By estimating the PSE to characterize the frequency content of the signal, this study proposes a damage detection method to trace the damage by the curvature of the PSE. Two numerical applications examine the applicability of the proposed method depending on a window function, frequency resolution, and the number of overlapping data in the PSE method. e knowledge obtained from the numerical applications leads to a series of experiments that substantiate the potential of the proposed method. 1. Introduction Early detection of defects in civil structures is a critical process in assisting structural maintenance and management plans. With a robust damage detection methodology, it becomes possible to fix the structure during the early stages of damage. e existing damage detection methods are performed using measurement data in the time-domain or frequency- domain. e time-domain methods usually go through stochastic processes. Cattarius and Inman [1] provided a non- destructive time-domain approach to examining structural damage using time histories of the vibration response of the structure. Majumder and Manohar [2] developed a time- domain approach to detecting damage in bridge structures by analyzing the combined system of the bridge and vehicle. Sandesh and Shankar [3] presented a time-domain damage detection scheme based on a substructure system identifica- tion method using Genetic Algorithms and Particle Swarm Optimization to filter out the updated parameters. Lu and Gao [4] presented a time series model for the diagnosis of structural damage considering a damage sensitive feature without input excitation. Many damage detection methods require information about the baseline data and the input data. However, the data collection is not always practical because they cannot be readily obtained. Output-only methods use only the vibration response signals and may be classified into nonparametric methods based on corresponding time series representations and parametric methods based on scalar or vector parametric time series representations. Yao and Pakzad [5] presented an autoregressive method with exogenous input modeling for measurements and investigated an application to detect dam- age in a space truss structure. Power spectral density (PSD), defined as the squared value of the signal, describes the power of a signal or time series distributed over different frequen- cies. e PSD is the Fourier transform of the autocorrelation function, which provides the transformation from the time- domain to the frequency-domain. By estimating the PSD localized in bandwidth regions near resonance, Liberatore and Carman [6] presented a method of structural damage identification. Beskhyroun et al. [7] proposed a damage Hindawi Publishing Corporation Shock and Vibration Volume 2016, Article ID 8761249, 13 pages http://dx.doi.org/10.1155/2016/8761249

Upload: others

Post on 01-Apr-2020

9 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

Research ArticleStructural Damage Detection by Power Spectral DensityEstimation Using Output-Only Measurement

Eun-Taik Lee1 and Hee-Chang Eun2

1Department of Architectural Engineering Chung-Ang University Seoul 06794 Republic of Korea2Department of Architectural Engineering Kangwon National University Chuncheon 24341 Republic of Korea

Correspondence should be addressed to Hee-Chang Eun heechangkangwonackr

Received 25 June 2015 Revised 25 October 2015 Accepted 26 October 2015

Academic Editor Mohammad Elahinia

Copyright copy 2016 E-T Lee and H-C Eun This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Most damage detection methods have difficulty in detecting damage using only measurement data due to the existence of externalnoise It is necessary to reduce the noise effect to obtain accurate information and to detect damage by the output-onlymeasurementwithout baseline data at intact state and input data This work imported the power spectral density estimation (PSE) of a signal toreduce the noise effect By estimating the PSE to characterize the frequency content of the signal this study proposes a damagedetection method to trace the damage by the curvature of the PSE Two numerical applications examine the applicability of theproposed method depending on a window function frequency resolution and the number of overlapping data in the PSEmethodThe knowledge obtained from the numerical applications leads to a series of experiments that substantiate the potential of theproposed method

1 Introduction

Early detection of defects in civil structures is a criticalprocess in assisting structural maintenance and managementplans With a robust damage detection methodology itbecomes possible to fix the structure during the early stagesof damage

The existing damage detection methods are performedusing measurement data in the time-domain or frequency-domain The time-domain methods usually go throughstochastic processes Cattarius and Inman [1] provided a non-destructive time-domain approach to examining structuraldamage using time histories of the vibration response of thestructure Majumder and Manohar [2] developed a time-domain approach to detecting damage in bridge structuresby analyzing the combined system of the bridge and vehicleSandesh and Shankar [3] presented a time-domain damagedetection scheme based on a substructure system identifica-tion method using Genetic Algorithms and Particle SwarmOptimization to filter out the updated parameters Lu andGao [4] presented a time series model for the diagnosis of

structural damage considering a damage sensitive featurewithout input excitation

Many damage detection methods require informationabout the baseline data and the input data However thedata collection is not always practical because they cannot bereadily obtainedOutput-onlymethods use only the vibrationresponse signals and may be classified into nonparametricmethods based on corresponding time series representationsand parametricmethods based on scalar or vector parametrictime series representations Yao and Pakzad [5] presented anautoregressive method with exogenous input modeling formeasurements and investigated an application to detect dam-age in a space truss structure Power spectral density (PSD)defined as the squared value of the signal describes the powerof a signal or time series distributed over different frequen-cies The PSD is the Fourier transform of the autocorrelationfunction which provides the transformation from the time-domain to the frequency-domain By estimating the PSDlocalized in bandwidth regions near resonance Liberatoreand Carman [6] presented a method of structural damageidentification Beskhyroun et al [7] proposed a damage

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 8761249 13 pageshttpdxdoiorg10115520168761249

2 Shock and Vibration

identificationmethod to detect damage and its location basedon changes in the PSD curvature before and after damageBayissa and Haritos [8] presented a damage identificationmethod based on bending moment response PSD Zhouet al [9] provided a damage identification method basedon the PSD transmissibility using output-only responsemeasurements From the sensitivities of PSD with respect tothe structural damage parameters and finite element modelupdating Chen et al [10] presented a method to identifystructural damage Zheng et al [11] considered a structuraldamage detection method from the finite element modelwhich is updated using the measured PSD

PSE estimates the spectral density of a random signalfrom a sequence of time sampleThe techniquesmay be basedon time-domain or frequency-domain analysis Welch [12]provided a method for the application of the fast Fouriertransform (FFT) algorithm for the estimation of power spec-traTheWelchmethod is a nonparametricmethod includingthe periodogram with the advantage of possible implemen-tation using FFT The Welch method is used to find the PSDof a signal and to reduce the effect of noise Vamvoudakis-Stefanou et al [13] analyzed six well-known output-onlystatistical time series methods and compared the methodsthrough the detection and identification of various typesof damage Kopsaftopoulos and Fassois [14 15] investigatedthe potential and effectiveness of the statistical time seriesmethods through experiments on a laboratory aluminumtruss structure They assessed several scalar and vector sta-tistical time series methods for vibration based on structuralhealth monitoring Gupta et al [16] compared several typesof window functions and observed that the rectangular andHamming windows gave better results than the BartlettHamming and Blackman windows Zimin and Zimmerman[17] compared Time-Domain Periodogram Analysis (TDPA)with Frequency-Domain Periodogram Analysis (FDPA) forsynthetic signals and suggested that TDPA can be utilizedas an index to evaluate the existence of structural damageGiles and Spencer Jr [18] provided a damage detectionalgorithm using the changes in the PSD of a structurebetween undamaged and damaged systems and only outputthe measurement data Fang and Perera [19] introducedpower mode shape curvature and power flexibility and theyproposed the damage detection method using their variationbetween undamaged and damaged statesMasciotta et al [20]presented a spectrum-driven method to detect the damageusing a proper combination of the eigenparameters extractedfrom the PSD matrix

This work uses only the output data without the baselinedata unlike the existing methods to compare the differencein damage indices such as PSE mode shapes and flexibilitybetween the undamaged and damaged statesThere are dam-age detectionmethods that are very sensitive to external noiseso that the damage cannot be traced This study providesa damage detection method that utilizes the response datatransformed to the frequency-domain from the time-domainand the Welch method to find the PSE of a signal Damageis evaluated using the curvature of the PSE This workinvestigates the validity of the damage detection methoddepending on the rectangular Hamming Bartlett Hann

and Blackman windows with theWelch method overlappingof 40 and 50 and frequency resolution of 05Hz and10Hz Two numerical applications for detecting damage ina beam structure examine and compare the applicability ofthe proposedmethod depending on thewindow function thefrequency resolution and the number of overlapping dataThe knowledge obtained from the numerical applicationsleads to a series of experiments that substantiate the potentialof the proposed method

2 Damage Detection Scheme Based onthe Welch Method

TheWelchmethod divides the time series data into segmentscomputes a modified periodogram of each segment andaverages the PSE A portion of the data stream near theboundaries of the window function is ignored in the analysisand its situation can be improved by letting the segmentsoverlapThe PSD represents the strength of the variations as afunction of frequency The spectral density characterizes thefrequency content of the signal and its estimation detects anyperiodicities in the data by observing peaks at the frequenciescorresponding to these periodicities The PSE 119878

119909119909(119891) is the

discrete Fourier transform (DFT) of the autocorrelationestimate 119877

119909119909(119896) or

119878119909119909(119891) =

infin

sum

119896=minusinfin

119877119909119909(119896) 119890minus119894120596119896119879

(1)

where 119894 = radicminus1 This assumes that 119873 point data sequence119883(119899) is a discrete time random process with an autocor-relation function 119877

119909119909(119896) The number of overlapping data

window function and frequency resolution affect the PSE in(1) and are defined in the following

21 SampleOverlapping Dividing119883(119899) 0 le 119899 le 119873minus1 fromastationary second-order stochastic sequence into 119871 segmentsof119872 samples (119873 ge 119871119872) the data segment can be expressedas

1198831(119899) = 119883 (119899) 119899 = 0 1 2 119872 minus 1 (2)

Similarly

1198832(119899) = 119883 (119899 + 119863) 119899 = 0 1 2 119872 minus 1

119883119896(119899) = 119883 (119899 + (119896 minus 1)119863) 119896 = 0 1 2 119871 minus 1

(3)

where 119896119863 is the starting point for the 119896th sequence If119863 = 119872the segment does not overlap

Welchrsquos method to modify Bartlettrsquos method applies thewindow 119882(119899) directly to the data segment before com-puting the individual periodograms The 119871 modified orwindowed periodogram to form119883

1(119899)119882(119899) 119883

119896(119899)119882(119899)

119899 = 0 1 119872 minus 1 can be defined as

119896

119909119909(119891) =

1

119880119872[

119872minus1

sum

119899=0

119883119896(119899)119882 (119899) 119890

minus1198942120587119891119899

]

2

119896 = 0 1 119871 minus 1

(4)

Shock and Vibration 3

where 119894 = radicminus1 and 119880 is a normalization factor for the powerwritten as

119880 =1

119872

119872minus1

sum

119899=0

1198822

(119899) (5)

The Welch PSE 119878119908

119909119909(119891) is the average of modified peri-

odogram defined as

119878119908

119909119909(119891) =

1

119871

119871minus1

sum

119896=0

119896

119909119909(119891) (6)

And its expected value is given by

119864 [119878119908

119909119909(119891)] = 119878

119909119909(119891)119882 (119891) (7)

where

119878119909119909(119891) =

1

119873[119883 (119891)]

2

119882 (119891) =1

119880119872[

119872minus1

sum

119899=0

119882(119899) 119890minus1198942120587119891119899

]

(8)

The window functions 119882(119899) considered in this study are asfollows

22 Window Functions Rectangular window

119882(119899) =

1 |119899| lt119873 minus 1

2

0 otherwise(9)

Bartlett window

119882(119899) =

1 minus2 |119899|

119873 |119899| lt

119873 minus 1

2

0 otherwise(10)

Hann window

119882(119899) =

05 + 05 cos(2120587119899119873

) |119899| lt119873 minus 1

2

0 otherwise(11)

Hamming window

119882(119899) =

054 + 046 cos(2120587119899119873

) |119899| lt119873 minus 1

2

0 otherwise(12)

Blackman window

119882(119899)

=

042 minus 05 cos( 2120587119899

119873 minus 1) + 008 cos( 4120587119899

119873 minus 1) |119899| lt

119873 minus 1

2

0 otherwise

(13)

23 Frequency Resolution Frequency resolution is the dis-tance in Hz between two adjacent data points in DFT It isdefined as

Fr =119865119904

119873 (14)

where 119865119904denotes the sampling rate and 119873 is the number of

data From the relationship of the sampling rate and time119873 = 119865

119904119905 it can also be expressed by

Fr = 1

119905 (15)

This equation indicates that the frequency resolution isaffected by the prescribed time

The normalizing factor 119880 is required so that the PSE ofthe modified periodogram will be asymptotically unbiasedThe PSE is determined by the spectral resolution of eachsegment of length 119871 and it depends on the window functionto minimize the effect of leakage to better represent thefrequency spectrum of the data

This work considers the optimal PSE data correspondingto the frequency to display the maximum energy The curva-ture is utilized as an index to evaluate the damage becausethe beam is characterized by the flexural response Thedamage present in the region represents the abrupt variationin the curvature The curvature at each location 119897 119878119908

119909119909119897

10158401015840 isnumerically obtained by a central difference approximation

119878119908

119909119909119897

10158401015840

=119878119908

119909119909119897minus1minus 2119878119908

119909119909119897+ 119878119908

119909119909119897+1

ℎ2

119897 = 1 2 119873 minus 2

(16)

where ℎ is the distance between two successive nodes Thevalidity of the proposed method is illustrated by a numericalapplication and a beam test

3 Numerical Applications

A numerical application was performed to detect damageof a finite element model of a fixed-end beam as shown inFigure 1 The nodal points and the elements are numberedas shown in the figure A beam with a length of 1m ismodeled using 50 beam elements The beam has an elasticmodulus of 20times105MPa and a unit mass of 7860 kgm3Thebeamrsquos gross cross section is 75mm times 9mm and its damagesection is established as 75mm times 85mm The dampingmatrix is assumed as Rayleigh damping and is expressed bythe stiffness matrix and a proportional constant of 00001This application considers a beam with multiple damage atelements 19 and 41

4 Shock and Vibration

11

2 32 3

48 4949 50middot middot middot

50 20mm

Figure 1 A fixed-end beam structure model

0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1

Time (s)

minus02

minus04

minus06

minus08

minus1

Base

exci

tatio

n (m

ms2)

times10minus3

(a)

0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1

Time (s)

minus02

minus04

minus06

minus08

minus1

Base

exci

tatio

n (m

ms2)

times10minus3

(b)

Figure 2 Acceleration of external excitation at the left support (a) time step of 0001 sec (b) time step of 0002 sec

Assume the beam structure is subjected to the white noiseexcitation at the left support with a step size of 0001 secand 0002 sec for one second as shown in Figure 2 Thedynamic responses in the time-domain are simulated bysolving the dynamic equation of the finite element modelsubject to the excitation and the response data of the samelength as the input force are collected We assume thatthe information about the excitation is unknown for thisnumerical application

The dynamic responses of the practical system are con-taminated by external noise In this study the measuredresponse data are simulated by adding a series of randomnumbers to the calculated displacement responses Thedisplacements 119906

119903for describing the practical responses at

node 119903 can be calculated from the simulated noise-freedisplacements 1199060

119903 by the following equation

119906119903= 1199060

119903(1 + 120572120590

119903) (17)

where 120572 denotes the relative magnitude of the error and 120590119895is

a random number variant in the range [minus1 1] The measureddisplacement responses including the contaminated externalnoise are established by inserting 120572 = 3 into (17)

Most damage detection methods are sensitive to externalnoise contained in the measurement data The measurementdata sets collected from repeated numerical simulations areused to reduce the effect of the external noise For this

numerical application ten data sets were utilized Taking theFFT the ten displacement response data sets in the time-domain were transformed into responses in the frequency-domain Figure 3(a) represents the absolute amplitude curvesof the displacement responses in the frequency-domain aftertransforming 1000 displacement response data points at allnodes for one second with a time step of 0001 secondsThe first resonance frequency is located at approximately36Hzsample For the maximum values corresponding to allnodes in the neighborhood of 36Hzsample the curve toconnect them is exhibited in Figure 3(b) It is difficult to tracethe damage location from the plot Considering that the beamis a flexural member the flexural curvature is predicted by acentral difference method Figure 3(c) displays the curvaturecurves on ten data sets and abrupt changes in all cases arefound near nodes 19 and 41 including the damage The FFTdata set can be utilized to detect damage The concept isexpanded to the periodogram and PSE to detect damagebecause the PSE Welch method originated from the FFT

This work estimates the Welch PSE by dividing theresponse into eight segments in lengthThe numerical resultsare compared according to the following test parametersthe rectangular Hamming Bartlett Hann and Blackmanwindow functions sample overlaps of 40 and 50 andfrequency resolutions of 05Hz and 10Hz Figures 4(a)and 4(b) represent the PSE curves for 50 overlappingsamples between two adjacent segments of eight segments

Shock and Vibration 5

0 100 200 300 400 5000

02

04

06

08

1

14

Frequency (Hzsample)

abs(Y(f

))times10minus9

12

(a)

0

002

004

006

008

01

012

014

Max

(abs

(Y(f

)))

10 20 30 40 500Node number(b)

0 10 20 30 40 50Node number

Curv

atur

e of M

ax(a

bs(Y

(f))

)

15

1

05

0

minus05

minus1

minus15

minus2

times10minus11

(c)

Figure 3 Numerical results in the frequency-domain (a) FFT curves (b) maximum FFT curve corresponding to the first resonancefrequency and (c) its curvature curves

0 100 200 300 400 500Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus80

minus70

minus60

minus50

minus40

minus30

minus90

minus100

minus20

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus80

minus70

minus60

minus50

minus40

minus30

minus90

minus10

minus20

(b)

Figure 4 PSE curves (a) Fr = 10Hz (b) Fr = 05Hz

6 Shock and Vibration

Pow

erfr

eque

ncy

(dB

Hz)

minus155

minus160

minus165

minus170

minus175

minus1805 10 15 20 25 30 35 40 45 500

Node number(a)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(b)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(c)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(d)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(e)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(f)

Figure 5 PSE curve and its curvature under the condition of Fr = 05Hz (a) PSE curve (rectangular window 50 overlap) bymaximum PSEvalues around 36Hzsample (b) PSE curvature (rectangular window) (c) PSE curvature (Hamming window) (d) PSE curvature (Bartlettwindow) (e) PSE curvature (Hann window) and (f) PSE curvature (Blackman window)

Shock and Vibration 7

10 20 30 40Node number

Curv

atur

e of P

SE

50

40

005

0

minus005

minus01

minus015

minus02

minus025

minus03

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

5040

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

(b)

Figure 6 PSE curvature depending on the overlap (a) rectangular window (b) Hamming window

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus03

Fr = 05Hz

Fr = 10Hz

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

Fr = 05Hz

Fr = 10Hz

(b)

Figure 7 PSE curvature (a) rectangular window 50 overlap (b) Hamming window 50 overlap

with 1000 and 500 sampling record lengths respectively witha rectangular window The signal power is concentrated atapproximately 36Hzsample and the curves are character-ized by the frequency resolution

Figure 5 represents the PSE and the curvature curvesaccording to the window functions The curve in Figure 5(a)consists of the maximum PSE values at all nodes at approx-imately 36Hzsample and displays the maximum energy inthe PSE curves of Figure 4(a) which looks similar to thefundamental mode of the beam structure Figures 5(b)ndash5(f) display the curvature curves according to the windowfunctions on the ten data sets with the identical condition

of 50 overlap and Fr = 05Hz It is shown that the damageis located in the region representing the abrupt change inthe curvature All plots exhibit more abrupt changes in thecurvature at the damage location than in any other regionswhich indicate that the window functions introduced in thisstudy can be used to detect damage

Figure 6 compares the PSE curvatures of ten data setsdepending on the overlaps of 50 and 40under the same Fr= 05Hz using rectangular and Hamming windowsThe 50overlap leads to a larger change in the damage region than the40 overlap This indicates that more data overlap providesmore conservative results Figure 7 compares the applicability

8 Shock and Vibration

Damage

Damage

Damage

Beam 2

Beam 1

052m

115m

028m

085m

(a)

1 7 8 23 29 30 38 39

301 8 39 40Damage Damage

Beam 1

40 50mm

12mm100mm

middot middot middot middot middot middotmiddot middot middotmiddot middot middot

115m

(b)

1 4 5 12 13 19

131 5 20Damage

Beam 1

10mm

100mm

20 40mm

middot middot middot middot middot middot middot middot middot

052m

(c)

Figure 8 A crossed-beam structure (a) a beam structure (b) finite elements of beam 1 and (c) finite elements of beam 2

of damage detection by the PSE curvature depending onfrequency resolutions of 05Hz and 10Hz using rectangularandHamming windows In the plots the low frequency reso-lution leads to amore abrupt change in the curvature and thedamage region can be more explicitly found This numericalapplication demonstrates that the damage detection methodusing the data samples with 50 sample overlap and 05Hzfrequency resolution with the window functions consideredin this study is more effective

As another numerical application a crossed-beam struc-ture withmultiple damages in Figure 8 is considered to detectthe damage location Fixed-endbeam 1 is jointed onfixed-endbeam 2 The nodal points and the members are numberedas shown in the figure Assuming a Bernoulli-Euler planebeam element the beam finite elements are obtained bysubdividing the beam members longitudinally Beams 1 and2 are then modeled using 40 and 20 elements Each nodehas two DOFs of transverse displacement and slope Thetwo beams have an identical elastic modulus 119864 = 200GPaand a unit mass of 7860 kgm3 Undamaged beams 1 and2 are 2m and 08m in length and the cross sections are100 times 12mm and 100 times 10mm respectively Two damagesof beam 1 are located at elements 8 and 30 with the samecross section of 100 times 115mm and damage to beam 2 islocated at element 5 with a cross section of 100 times 9mm

This work assumes a Rayleigh damping of the stiffness matrixand a proportional constant of 00002 and assumes the beamstructure is subjected to the base excitation in Figure 2(b)Based on these variables this numerical application considersthe validity of the proposed method originating from thedisplacement responses contaminated by 3 external noisein (17)

Utilizing the 50 overlap samples of eight segments with500 sampling record lengths with a rectangular window thePSEs were extracted from the displacement responses inthe time-domain Figures 9(a) and 9(b) represent the PSEcurves of beams 1 and 2 transformed from the displacementresponses in the time-domain without the external noiserespectively The first resonance frequency of beams 1 and 2exists at the frequency of 16Hzsample The PSE curvaturesare estimated by the second-order difference method Takingthe maximum PSE values at the first resonance frequencyand calculating the curvatures the resulting curvature curvesare plotted as shown in Figures 9(c) and 9(d) It is observedthat the damaged elements correspond with the locations torepresent the abrupt curvature change except the joint nodesused to connect the two beams

Utilizing the numerically simulated data contaminatedby 3 external noise and taking the same process as theprevious case the PSE curves in Figures 10(a) and 10(b)

Shock and Vibration 9

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus140

(a)

0 50 100 150 200Frequency (Hzsample)

250

Pow

erfr

eque

ncy

(dB

Hz)

minus240

minus230

minus220

minus210

minus200

minus190

minus180

minus170

minus160

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0015

001

0005

0

minus0005

minus001

minus0015

Damage Damage

(c)

64 108 1412 16Node number

PSE

curv

atur

e

004

002

0

minus01

minus012

minus008

minus006

minus004

minus002

Damage

(d)

Figure 9 PSE and the curvature curves of noise-free structure (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

display more complicated relations than Figures 9(a) and9(b)The first resonance frequency of 16Hzsample coincideswith the PSE curve without the external noise The curvaturecurves represent the explicit curvature variations at elements8 and 30 of beam 1 in Figure 10(c) and element 5 of beam 2in Figure 10(d) It is observed that the proposed method canbe utilized in detecting beam structure damage despite theexistence of external noise

4 Beam Test

A beam test was performed to detect the damage of a simplysupported beam as shown in Figure 11 The gross crosssection of the beam is 119887 times 119905 = 100mm times 11mm and thenet length of the span between end supports is 1200mmThedamage is located at 350mm from the left support whichis between nodes 2 and 3 The damaged cross section was

established as 119887 times 119905 = 100mm times 8mmThe eight points mea-sured by accelerometers are numbered as shown in Figure 11The beam is excited by hitting an impact hammer withsupersoft tip on the support to collect response data withinthe low frequency range The experiment was conductedusing DYTRANmodel 3055B1 uniaxial accelerometers and aminiature transducer hammer (Bruel and Kjaer model 8204)for the excitation of the system The data acquisition systemwas a DEWETRON model DEWE-43 The accelerationresponse data in the time-domain were measured by theDEWETRON The input acceleration excited by the impacthammer was not measured

Figure 12(a) represents the acceleration responses in thetime-domain at all nodes for one second after hitting Figures12(b) and 12(c) display the FFT and PSE curves at allnodes in the frequency-domain to transform the accelera-tion responses The maximum energy is revealed at 171 Hz

10 Shock and Vibration

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus120

minus130

minus140

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0008

0006

0004

0002

0

minus0006

minus0004

minus0002

minus0008

minus001

minus0012

Damage

Damage

(c)

64 108 1412 16 18Node number

PSE

curv

atur

e

006

004

002

0

minus006

minus004

minus002

minus008

Damage

(d)

Figure 10 PSE and the curvature curves containing 3 noise (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

1 2 3 64 75

Rubber packing

8

Damage

SupportAccelerometer

Impact hammer1 2 3 64 75 8

Support

Impact hammer

7 150mm

350mm1200mm1400mm

75mm 75mm

(a)

Undamaged section

Damaged section

100mm

100mm

11mm

8mm3mm

(b)

(c)

Hammer tip = supersoft

(d)Figure 11 Test beam (a) plan view (b) section (c) photo of test beam and (d) impact hammer

Shock and Vibration 11

0 05 1 15 2Time (s)

minus0015

minus001

minus0005

0

0005

001

0015

Acce

lera

tion

resp

onse

(g)

(a)

0 50 100 150 200 2500

02

04

06

08

1

12

14

16

18

Frequency (Hz)

Abso

lute

val

ues o

f acc

eler

atio

n re

spon

ses

times10minus3

(b)

Pow

erfr

eque

ncy

(dB

Hz)

0 50Frequency (Hzsample)

100 150 200 250

minus60

minus65

minus70

minus75

minus80

minus85

(c)

1 2 3 4 5 87604

06

08

1

12

14

16

18

Node number

Max

(abs

olut

e val

ues o

f acc

eler

atio

n re

spon

ses)

times10minus3

(d)

2 3 4 5 76Node number

6

4

2

0

minus2

minus4

minus6

Curv

atur

e of m

axim

um v

alue

s

times10minus4

(e)

Figure 12 Continued

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 2: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

2 Shock and Vibration

identificationmethod to detect damage and its location basedon changes in the PSD curvature before and after damageBayissa and Haritos [8] presented a damage identificationmethod based on bending moment response PSD Zhouet al [9] provided a damage identification method basedon the PSD transmissibility using output-only responsemeasurements From the sensitivities of PSD with respect tothe structural damage parameters and finite element modelupdating Chen et al [10] presented a method to identifystructural damage Zheng et al [11] considered a structuraldamage detection method from the finite element modelwhich is updated using the measured PSD

PSE estimates the spectral density of a random signalfrom a sequence of time sampleThe techniquesmay be basedon time-domain or frequency-domain analysis Welch [12]provided a method for the application of the fast Fouriertransform (FFT) algorithm for the estimation of power spec-traTheWelchmethod is a nonparametricmethod includingthe periodogram with the advantage of possible implemen-tation using FFT The Welch method is used to find the PSDof a signal and to reduce the effect of noise Vamvoudakis-Stefanou et al [13] analyzed six well-known output-onlystatistical time series methods and compared the methodsthrough the detection and identification of various typesof damage Kopsaftopoulos and Fassois [14 15] investigatedthe potential and effectiveness of the statistical time seriesmethods through experiments on a laboratory aluminumtruss structure They assessed several scalar and vector sta-tistical time series methods for vibration based on structuralhealth monitoring Gupta et al [16] compared several typesof window functions and observed that the rectangular andHamming windows gave better results than the BartlettHamming and Blackman windows Zimin and Zimmerman[17] compared Time-Domain Periodogram Analysis (TDPA)with Frequency-Domain Periodogram Analysis (FDPA) forsynthetic signals and suggested that TDPA can be utilizedas an index to evaluate the existence of structural damageGiles and Spencer Jr [18] provided a damage detectionalgorithm using the changes in the PSD of a structurebetween undamaged and damaged systems and only outputthe measurement data Fang and Perera [19] introducedpower mode shape curvature and power flexibility and theyproposed the damage detection method using their variationbetween undamaged and damaged statesMasciotta et al [20]presented a spectrum-driven method to detect the damageusing a proper combination of the eigenparameters extractedfrom the PSD matrix

This work uses only the output data without the baselinedata unlike the existing methods to compare the differencein damage indices such as PSE mode shapes and flexibilitybetween the undamaged and damaged statesThere are dam-age detectionmethods that are very sensitive to external noiseso that the damage cannot be traced This study providesa damage detection method that utilizes the response datatransformed to the frequency-domain from the time-domainand the Welch method to find the PSE of a signal Damageis evaluated using the curvature of the PSE This workinvestigates the validity of the damage detection methoddepending on the rectangular Hamming Bartlett Hann

and Blackman windows with theWelch method overlappingof 40 and 50 and frequency resolution of 05Hz and10Hz Two numerical applications for detecting damage ina beam structure examine and compare the applicability ofthe proposedmethod depending on thewindow function thefrequency resolution and the number of overlapping dataThe knowledge obtained from the numerical applicationsleads to a series of experiments that substantiate the potentialof the proposed method

2 Damage Detection Scheme Based onthe Welch Method

TheWelchmethod divides the time series data into segmentscomputes a modified periodogram of each segment andaverages the PSE A portion of the data stream near theboundaries of the window function is ignored in the analysisand its situation can be improved by letting the segmentsoverlapThe PSD represents the strength of the variations as afunction of frequency The spectral density characterizes thefrequency content of the signal and its estimation detects anyperiodicities in the data by observing peaks at the frequenciescorresponding to these periodicities The PSE 119878

119909119909(119891) is the

discrete Fourier transform (DFT) of the autocorrelationestimate 119877

119909119909(119896) or

119878119909119909(119891) =

infin

sum

119896=minusinfin

119877119909119909(119896) 119890minus119894120596119896119879

(1)

where 119894 = radicminus1 This assumes that 119873 point data sequence119883(119899) is a discrete time random process with an autocor-relation function 119877

119909119909(119896) The number of overlapping data

window function and frequency resolution affect the PSE in(1) and are defined in the following

21 SampleOverlapping Dividing119883(119899) 0 le 119899 le 119873minus1 fromastationary second-order stochastic sequence into 119871 segmentsof119872 samples (119873 ge 119871119872) the data segment can be expressedas

1198831(119899) = 119883 (119899) 119899 = 0 1 2 119872 minus 1 (2)

Similarly

1198832(119899) = 119883 (119899 + 119863) 119899 = 0 1 2 119872 minus 1

119883119896(119899) = 119883 (119899 + (119896 minus 1)119863) 119896 = 0 1 2 119871 minus 1

(3)

where 119896119863 is the starting point for the 119896th sequence If119863 = 119872the segment does not overlap

Welchrsquos method to modify Bartlettrsquos method applies thewindow 119882(119899) directly to the data segment before com-puting the individual periodograms The 119871 modified orwindowed periodogram to form119883

1(119899)119882(119899) 119883

119896(119899)119882(119899)

119899 = 0 1 119872 minus 1 can be defined as

119896

119909119909(119891) =

1

119880119872[

119872minus1

sum

119899=0

119883119896(119899)119882 (119899) 119890

minus1198942120587119891119899

]

2

119896 = 0 1 119871 minus 1

(4)

Shock and Vibration 3

where 119894 = radicminus1 and 119880 is a normalization factor for the powerwritten as

119880 =1

119872

119872minus1

sum

119899=0

1198822

(119899) (5)

The Welch PSE 119878119908

119909119909(119891) is the average of modified peri-

odogram defined as

119878119908

119909119909(119891) =

1

119871

119871minus1

sum

119896=0

119896

119909119909(119891) (6)

And its expected value is given by

119864 [119878119908

119909119909(119891)] = 119878

119909119909(119891)119882 (119891) (7)

where

119878119909119909(119891) =

1

119873[119883 (119891)]

2

119882 (119891) =1

119880119872[

119872minus1

sum

119899=0

119882(119899) 119890minus1198942120587119891119899

]

(8)

The window functions 119882(119899) considered in this study are asfollows

22 Window Functions Rectangular window

119882(119899) =

1 |119899| lt119873 minus 1

2

0 otherwise(9)

Bartlett window

119882(119899) =

1 minus2 |119899|

119873 |119899| lt

119873 minus 1

2

0 otherwise(10)

Hann window

119882(119899) =

05 + 05 cos(2120587119899119873

) |119899| lt119873 minus 1

2

0 otherwise(11)

Hamming window

119882(119899) =

054 + 046 cos(2120587119899119873

) |119899| lt119873 minus 1

2

0 otherwise(12)

Blackman window

119882(119899)

=

042 minus 05 cos( 2120587119899

119873 minus 1) + 008 cos( 4120587119899

119873 minus 1) |119899| lt

119873 minus 1

2

0 otherwise

(13)

23 Frequency Resolution Frequency resolution is the dis-tance in Hz between two adjacent data points in DFT It isdefined as

Fr =119865119904

119873 (14)

where 119865119904denotes the sampling rate and 119873 is the number of

data From the relationship of the sampling rate and time119873 = 119865

119904119905 it can also be expressed by

Fr = 1

119905 (15)

This equation indicates that the frequency resolution isaffected by the prescribed time

The normalizing factor 119880 is required so that the PSE ofthe modified periodogram will be asymptotically unbiasedThe PSE is determined by the spectral resolution of eachsegment of length 119871 and it depends on the window functionto minimize the effect of leakage to better represent thefrequency spectrum of the data

This work considers the optimal PSE data correspondingto the frequency to display the maximum energy The curva-ture is utilized as an index to evaluate the damage becausethe beam is characterized by the flexural response Thedamage present in the region represents the abrupt variationin the curvature The curvature at each location 119897 119878119908

119909119909119897

10158401015840 isnumerically obtained by a central difference approximation

119878119908

119909119909119897

10158401015840

=119878119908

119909119909119897minus1minus 2119878119908

119909119909119897+ 119878119908

119909119909119897+1

ℎ2

119897 = 1 2 119873 minus 2

(16)

where ℎ is the distance between two successive nodes Thevalidity of the proposed method is illustrated by a numericalapplication and a beam test

3 Numerical Applications

A numerical application was performed to detect damageof a finite element model of a fixed-end beam as shown inFigure 1 The nodal points and the elements are numberedas shown in the figure A beam with a length of 1m ismodeled using 50 beam elements The beam has an elasticmodulus of 20times105MPa and a unit mass of 7860 kgm3Thebeamrsquos gross cross section is 75mm times 9mm and its damagesection is established as 75mm times 85mm The dampingmatrix is assumed as Rayleigh damping and is expressed bythe stiffness matrix and a proportional constant of 00001This application considers a beam with multiple damage atelements 19 and 41

4 Shock and Vibration

11

2 32 3

48 4949 50middot middot middot

50 20mm

Figure 1 A fixed-end beam structure model

0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1

Time (s)

minus02

minus04

minus06

minus08

minus1

Base

exci

tatio

n (m

ms2)

times10minus3

(a)

0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1

Time (s)

minus02

minus04

minus06

minus08

minus1

Base

exci

tatio

n (m

ms2)

times10minus3

(b)

Figure 2 Acceleration of external excitation at the left support (a) time step of 0001 sec (b) time step of 0002 sec

Assume the beam structure is subjected to the white noiseexcitation at the left support with a step size of 0001 secand 0002 sec for one second as shown in Figure 2 Thedynamic responses in the time-domain are simulated bysolving the dynamic equation of the finite element modelsubject to the excitation and the response data of the samelength as the input force are collected We assume thatthe information about the excitation is unknown for thisnumerical application

The dynamic responses of the practical system are con-taminated by external noise In this study the measuredresponse data are simulated by adding a series of randomnumbers to the calculated displacement responses Thedisplacements 119906

119903for describing the practical responses at

node 119903 can be calculated from the simulated noise-freedisplacements 1199060

119903 by the following equation

119906119903= 1199060

119903(1 + 120572120590

119903) (17)

where 120572 denotes the relative magnitude of the error and 120590119895is

a random number variant in the range [minus1 1] The measureddisplacement responses including the contaminated externalnoise are established by inserting 120572 = 3 into (17)

Most damage detection methods are sensitive to externalnoise contained in the measurement data The measurementdata sets collected from repeated numerical simulations areused to reduce the effect of the external noise For this

numerical application ten data sets were utilized Taking theFFT the ten displacement response data sets in the time-domain were transformed into responses in the frequency-domain Figure 3(a) represents the absolute amplitude curvesof the displacement responses in the frequency-domain aftertransforming 1000 displacement response data points at allnodes for one second with a time step of 0001 secondsThe first resonance frequency is located at approximately36Hzsample For the maximum values corresponding to allnodes in the neighborhood of 36Hzsample the curve toconnect them is exhibited in Figure 3(b) It is difficult to tracethe damage location from the plot Considering that the beamis a flexural member the flexural curvature is predicted by acentral difference method Figure 3(c) displays the curvaturecurves on ten data sets and abrupt changes in all cases arefound near nodes 19 and 41 including the damage The FFTdata set can be utilized to detect damage The concept isexpanded to the periodogram and PSE to detect damagebecause the PSE Welch method originated from the FFT

This work estimates the Welch PSE by dividing theresponse into eight segments in lengthThe numerical resultsare compared according to the following test parametersthe rectangular Hamming Bartlett Hann and Blackmanwindow functions sample overlaps of 40 and 50 andfrequency resolutions of 05Hz and 10Hz Figures 4(a)and 4(b) represent the PSE curves for 50 overlappingsamples between two adjacent segments of eight segments

Shock and Vibration 5

0 100 200 300 400 5000

02

04

06

08

1

14

Frequency (Hzsample)

abs(Y(f

))times10minus9

12

(a)

0

002

004

006

008

01

012

014

Max

(abs

(Y(f

)))

10 20 30 40 500Node number(b)

0 10 20 30 40 50Node number

Curv

atur

e of M

ax(a

bs(Y

(f))

)

15

1

05

0

minus05

minus1

minus15

minus2

times10minus11

(c)

Figure 3 Numerical results in the frequency-domain (a) FFT curves (b) maximum FFT curve corresponding to the first resonancefrequency and (c) its curvature curves

0 100 200 300 400 500Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus80

minus70

minus60

minus50

minus40

minus30

minus90

minus100

minus20

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus80

minus70

minus60

minus50

minus40

minus30

minus90

minus10

minus20

(b)

Figure 4 PSE curves (a) Fr = 10Hz (b) Fr = 05Hz

6 Shock and Vibration

Pow

erfr

eque

ncy

(dB

Hz)

minus155

minus160

minus165

minus170

minus175

minus1805 10 15 20 25 30 35 40 45 500

Node number(a)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(b)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(c)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(d)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(e)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(f)

Figure 5 PSE curve and its curvature under the condition of Fr = 05Hz (a) PSE curve (rectangular window 50 overlap) bymaximum PSEvalues around 36Hzsample (b) PSE curvature (rectangular window) (c) PSE curvature (Hamming window) (d) PSE curvature (Bartlettwindow) (e) PSE curvature (Hann window) and (f) PSE curvature (Blackman window)

Shock and Vibration 7

10 20 30 40Node number

Curv

atur

e of P

SE

50

40

005

0

minus005

minus01

minus015

minus02

minus025

minus03

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

5040

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

(b)

Figure 6 PSE curvature depending on the overlap (a) rectangular window (b) Hamming window

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus03

Fr = 05Hz

Fr = 10Hz

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

Fr = 05Hz

Fr = 10Hz

(b)

Figure 7 PSE curvature (a) rectangular window 50 overlap (b) Hamming window 50 overlap

with 1000 and 500 sampling record lengths respectively witha rectangular window The signal power is concentrated atapproximately 36Hzsample and the curves are character-ized by the frequency resolution

Figure 5 represents the PSE and the curvature curvesaccording to the window functions The curve in Figure 5(a)consists of the maximum PSE values at all nodes at approx-imately 36Hzsample and displays the maximum energy inthe PSE curves of Figure 4(a) which looks similar to thefundamental mode of the beam structure Figures 5(b)ndash5(f) display the curvature curves according to the windowfunctions on the ten data sets with the identical condition

of 50 overlap and Fr = 05Hz It is shown that the damageis located in the region representing the abrupt change inthe curvature All plots exhibit more abrupt changes in thecurvature at the damage location than in any other regionswhich indicate that the window functions introduced in thisstudy can be used to detect damage

Figure 6 compares the PSE curvatures of ten data setsdepending on the overlaps of 50 and 40under the same Fr= 05Hz using rectangular and Hamming windowsThe 50overlap leads to a larger change in the damage region than the40 overlap This indicates that more data overlap providesmore conservative results Figure 7 compares the applicability

8 Shock and Vibration

Damage

Damage

Damage

Beam 2

Beam 1

052m

115m

028m

085m

(a)

1 7 8 23 29 30 38 39

301 8 39 40Damage Damage

Beam 1

40 50mm

12mm100mm

middot middot middot middot middot middotmiddot middot middotmiddot middot middot

115m

(b)

1 4 5 12 13 19

131 5 20Damage

Beam 1

10mm

100mm

20 40mm

middot middot middot middot middot middot middot middot middot

052m

(c)

Figure 8 A crossed-beam structure (a) a beam structure (b) finite elements of beam 1 and (c) finite elements of beam 2

of damage detection by the PSE curvature depending onfrequency resolutions of 05Hz and 10Hz using rectangularandHamming windows In the plots the low frequency reso-lution leads to amore abrupt change in the curvature and thedamage region can be more explicitly found This numericalapplication demonstrates that the damage detection methodusing the data samples with 50 sample overlap and 05Hzfrequency resolution with the window functions consideredin this study is more effective

As another numerical application a crossed-beam struc-ture withmultiple damages in Figure 8 is considered to detectthe damage location Fixed-endbeam 1 is jointed onfixed-endbeam 2 The nodal points and the members are numberedas shown in the figure Assuming a Bernoulli-Euler planebeam element the beam finite elements are obtained bysubdividing the beam members longitudinally Beams 1 and2 are then modeled using 40 and 20 elements Each nodehas two DOFs of transverse displacement and slope Thetwo beams have an identical elastic modulus 119864 = 200GPaand a unit mass of 7860 kgm3 Undamaged beams 1 and2 are 2m and 08m in length and the cross sections are100 times 12mm and 100 times 10mm respectively Two damagesof beam 1 are located at elements 8 and 30 with the samecross section of 100 times 115mm and damage to beam 2 islocated at element 5 with a cross section of 100 times 9mm

This work assumes a Rayleigh damping of the stiffness matrixand a proportional constant of 00002 and assumes the beamstructure is subjected to the base excitation in Figure 2(b)Based on these variables this numerical application considersthe validity of the proposed method originating from thedisplacement responses contaminated by 3 external noisein (17)

Utilizing the 50 overlap samples of eight segments with500 sampling record lengths with a rectangular window thePSEs were extracted from the displacement responses inthe time-domain Figures 9(a) and 9(b) represent the PSEcurves of beams 1 and 2 transformed from the displacementresponses in the time-domain without the external noiserespectively The first resonance frequency of beams 1 and 2exists at the frequency of 16Hzsample The PSE curvaturesare estimated by the second-order difference method Takingthe maximum PSE values at the first resonance frequencyand calculating the curvatures the resulting curvature curvesare plotted as shown in Figures 9(c) and 9(d) It is observedthat the damaged elements correspond with the locations torepresent the abrupt curvature change except the joint nodesused to connect the two beams

Utilizing the numerically simulated data contaminatedby 3 external noise and taking the same process as theprevious case the PSE curves in Figures 10(a) and 10(b)

Shock and Vibration 9

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus140

(a)

0 50 100 150 200Frequency (Hzsample)

250

Pow

erfr

eque

ncy

(dB

Hz)

minus240

minus230

minus220

minus210

minus200

minus190

minus180

minus170

minus160

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0015

001

0005

0

minus0005

minus001

minus0015

Damage Damage

(c)

64 108 1412 16Node number

PSE

curv

atur

e

004

002

0

minus01

minus012

minus008

minus006

minus004

minus002

Damage

(d)

Figure 9 PSE and the curvature curves of noise-free structure (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

display more complicated relations than Figures 9(a) and9(b)The first resonance frequency of 16Hzsample coincideswith the PSE curve without the external noise The curvaturecurves represent the explicit curvature variations at elements8 and 30 of beam 1 in Figure 10(c) and element 5 of beam 2in Figure 10(d) It is observed that the proposed method canbe utilized in detecting beam structure damage despite theexistence of external noise

4 Beam Test

A beam test was performed to detect the damage of a simplysupported beam as shown in Figure 11 The gross crosssection of the beam is 119887 times 119905 = 100mm times 11mm and thenet length of the span between end supports is 1200mmThedamage is located at 350mm from the left support whichis between nodes 2 and 3 The damaged cross section was

established as 119887 times 119905 = 100mm times 8mmThe eight points mea-sured by accelerometers are numbered as shown in Figure 11The beam is excited by hitting an impact hammer withsupersoft tip on the support to collect response data withinthe low frequency range The experiment was conductedusing DYTRANmodel 3055B1 uniaxial accelerometers and aminiature transducer hammer (Bruel and Kjaer model 8204)for the excitation of the system The data acquisition systemwas a DEWETRON model DEWE-43 The accelerationresponse data in the time-domain were measured by theDEWETRON The input acceleration excited by the impacthammer was not measured

Figure 12(a) represents the acceleration responses in thetime-domain at all nodes for one second after hitting Figures12(b) and 12(c) display the FFT and PSE curves at allnodes in the frequency-domain to transform the accelera-tion responses The maximum energy is revealed at 171 Hz

10 Shock and Vibration

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus120

minus130

minus140

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0008

0006

0004

0002

0

minus0006

minus0004

minus0002

minus0008

minus001

minus0012

Damage

Damage

(c)

64 108 1412 16 18Node number

PSE

curv

atur

e

006

004

002

0

minus006

minus004

minus002

minus008

Damage

(d)

Figure 10 PSE and the curvature curves containing 3 noise (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

1 2 3 64 75

Rubber packing

8

Damage

SupportAccelerometer

Impact hammer1 2 3 64 75 8

Support

Impact hammer

7 150mm

350mm1200mm1400mm

75mm 75mm

(a)

Undamaged section

Damaged section

100mm

100mm

11mm

8mm3mm

(b)

(c)

Hammer tip = supersoft

(d)Figure 11 Test beam (a) plan view (b) section (c) photo of test beam and (d) impact hammer

Shock and Vibration 11

0 05 1 15 2Time (s)

minus0015

minus001

minus0005

0

0005

001

0015

Acce

lera

tion

resp

onse

(g)

(a)

0 50 100 150 200 2500

02

04

06

08

1

12

14

16

18

Frequency (Hz)

Abso

lute

val

ues o

f acc

eler

atio

n re

spon

ses

times10minus3

(b)

Pow

erfr

eque

ncy

(dB

Hz)

0 50Frequency (Hzsample)

100 150 200 250

minus60

minus65

minus70

minus75

minus80

minus85

(c)

1 2 3 4 5 87604

06

08

1

12

14

16

18

Node number

Max

(abs

olut

e val

ues o

f acc

eler

atio

n re

spon

ses)

times10minus3

(d)

2 3 4 5 76Node number

6

4

2

0

minus2

minus4

minus6

Curv

atur

e of m

axim

um v

alue

s

times10minus4

(e)

Figure 12 Continued

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 3: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

Shock and Vibration 3

where 119894 = radicminus1 and 119880 is a normalization factor for the powerwritten as

119880 =1

119872

119872minus1

sum

119899=0

1198822

(119899) (5)

The Welch PSE 119878119908

119909119909(119891) is the average of modified peri-

odogram defined as

119878119908

119909119909(119891) =

1

119871

119871minus1

sum

119896=0

119896

119909119909(119891) (6)

And its expected value is given by

119864 [119878119908

119909119909(119891)] = 119878

119909119909(119891)119882 (119891) (7)

where

119878119909119909(119891) =

1

119873[119883 (119891)]

2

119882 (119891) =1

119880119872[

119872minus1

sum

119899=0

119882(119899) 119890minus1198942120587119891119899

]

(8)

The window functions 119882(119899) considered in this study are asfollows

22 Window Functions Rectangular window

119882(119899) =

1 |119899| lt119873 minus 1

2

0 otherwise(9)

Bartlett window

119882(119899) =

1 minus2 |119899|

119873 |119899| lt

119873 minus 1

2

0 otherwise(10)

Hann window

119882(119899) =

05 + 05 cos(2120587119899119873

) |119899| lt119873 minus 1

2

0 otherwise(11)

Hamming window

119882(119899) =

054 + 046 cos(2120587119899119873

) |119899| lt119873 minus 1

2

0 otherwise(12)

Blackman window

119882(119899)

=

042 minus 05 cos( 2120587119899

119873 minus 1) + 008 cos( 4120587119899

119873 minus 1) |119899| lt

119873 minus 1

2

0 otherwise

(13)

23 Frequency Resolution Frequency resolution is the dis-tance in Hz between two adjacent data points in DFT It isdefined as

Fr =119865119904

119873 (14)

where 119865119904denotes the sampling rate and 119873 is the number of

data From the relationship of the sampling rate and time119873 = 119865

119904119905 it can also be expressed by

Fr = 1

119905 (15)

This equation indicates that the frequency resolution isaffected by the prescribed time

The normalizing factor 119880 is required so that the PSE ofthe modified periodogram will be asymptotically unbiasedThe PSE is determined by the spectral resolution of eachsegment of length 119871 and it depends on the window functionto minimize the effect of leakage to better represent thefrequency spectrum of the data

This work considers the optimal PSE data correspondingto the frequency to display the maximum energy The curva-ture is utilized as an index to evaluate the damage becausethe beam is characterized by the flexural response Thedamage present in the region represents the abrupt variationin the curvature The curvature at each location 119897 119878119908

119909119909119897

10158401015840 isnumerically obtained by a central difference approximation

119878119908

119909119909119897

10158401015840

=119878119908

119909119909119897minus1minus 2119878119908

119909119909119897+ 119878119908

119909119909119897+1

ℎ2

119897 = 1 2 119873 minus 2

(16)

where ℎ is the distance between two successive nodes Thevalidity of the proposed method is illustrated by a numericalapplication and a beam test

3 Numerical Applications

A numerical application was performed to detect damageof a finite element model of a fixed-end beam as shown inFigure 1 The nodal points and the elements are numberedas shown in the figure A beam with a length of 1m ismodeled using 50 beam elements The beam has an elasticmodulus of 20times105MPa and a unit mass of 7860 kgm3Thebeamrsquos gross cross section is 75mm times 9mm and its damagesection is established as 75mm times 85mm The dampingmatrix is assumed as Rayleigh damping and is expressed bythe stiffness matrix and a proportional constant of 00001This application considers a beam with multiple damage atelements 19 and 41

4 Shock and Vibration

11

2 32 3

48 4949 50middot middot middot

50 20mm

Figure 1 A fixed-end beam structure model

0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1

Time (s)

minus02

minus04

minus06

minus08

minus1

Base

exci

tatio

n (m

ms2)

times10minus3

(a)

0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1

Time (s)

minus02

minus04

minus06

minus08

minus1

Base

exci

tatio

n (m

ms2)

times10minus3

(b)

Figure 2 Acceleration of external excitation at the left support (a) time step of 0001 sec (b) time step of 0002 sec

Assume the beam structure is subjected to the white noiseexcitation at the left support with a step size of 0001 secand 0002 sec for one second as shown in Figure 2 Thedynamic responses in the time-domain are simulated bysolving the dynamic equation of the finite element modelsubject to the excitation and the response data of the samelength as the input force are collected We assume thatthe information about the excitation is unknown for thisnumerical application

The dynamic responses of the practical system are con-taminated by external noise In this study the measuredresponse data are simulated by adding a series of randomnumbers to the calculated displacement responses Thedisplacements 119906

119903for describing the practical responses at

node 119903 can be calculated from the simulated noise-freedisplacements 1199060

119903 by the following equation

119906119903= 1199060

119903(1 + 120572120590

119903) (17)

where 120572 denotes the relative magnitude of the error and 120590119895is

a random number variant in the range [minus1 1] The measureddisplacement responses including the contaminated externalnoise are established by inserting 120572 = 3 into (17)

Most damage detection methods are sensitive to externalnoise contained in the measurement data The measurementdata sets collected from repeated numerical simulations areused to reduce the effect of the external noise For this

numerical application ten data sets were utilized Taking theFFT the ten displacement response data sets in the time-domain were transformed into responses in the frequency-domain Figure 3(a) represents the absolute amplitude curvesof the displacement responses in the frequency-domain aftertransforming 1000 displacement response data points at allnodes for one second with a time step of 0001 secondsThe first resonance frequency is located at approximately36Hzsample For the maximum values corresponding to allnodes in the neighborhood of 36Hzsample the curve toconnect them is exhibited in Figure 3(b) It is difficult to tracethe damage location from the plot Considering that the beamis a flexural member the flexural curvature is predicted by acentral difference method Figure 3(c) displays the curvaturecurves on ten data sets and abrupt changes in all cases arefound near nodes 19 and 41 including the damage The FFTdata set can be utilized to detect damage The concept isexpanded to the periodogram and PSE to detect damagebecause the PSE Welch method originated from the FFT

This work estimates the Welch PSE by dividing theresponse into eight segments in lengthThe numerical resultsare compared according to the following test parametersthe rectangular Hamming Bartlett Hann and Blackmanwindow functions sample overlaps of 40 and 50 andfrequency resolutions of 05Hz and 10Hz Figures 4(a)and 4(b) represent the PSE curves for 50 overlappingsamples between two adjacent segments of eight segments

Shock and Vibration 5

0 100 200 300 400 5000

02

04

06

08

1

14

Frequency (Hzsample)

abs(Y(f

))times10minus9

12

(a)

0

002

004

006

008

01

012

014

Max

(abs

(Y(f

)))

10 20 30 40 500Node number(b)

0 10 20 30 40 50Node number

Curv

atur

e of M

ax(a

bs(Y

(f))

)

15

1

05

0

minus05

minus1

minus15

minus2

times10minus11

(c)

Figure 3 Numerical results in the frequency-domain (a) FFT curves (b) maximum FFT curve corresponding to the first resonancefrequency and (c) its curvature curves

0 100 200 300 400 500Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus80

minus70

minus60

minus50

minus40

minus30

minus90

minus100

minus20

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus80

minus70

minus60

minus50

minus40

minus30

minus90

minus10

minus20

(b)

Figure 4 PSE curves (a) Fr = 10Hz (b) Fr = 05Hz

6 Shock and Vibration

Pow

erfr

eque

ncy

(dB

Hz)

minus155

minus160

minus165

minus170

minus175

minus1805 10 15 20 25 30 35 40 45 500

Node number(a)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(b)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(c)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(d)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(e)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(f)

Figure 5 PSE curve and its curvature under the condition of Fr = 05Hz (a) PSE curve (rectangular window 50 overlap) bymaximum PSEvalues around 36Hzsample (b) PSE curvature (rectangular window) (c) PSE curvature (Hamming window) (d) PSE curvature (Bartlettwindow) (e) PSE curvature (Hann window) and (f) PSE curvature (Blackman window)

Shock and Vibration 7

10 20 30 40Node number

Curv

atur

e of P

SE

50

40

005

0

minus005

minus01

minus015

minus02

minus025

minus03

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

5040

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

(b)

Figure 6 PSE curvature depending on the overlap (a) rectangular window (b) Hamming window

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus03

Fr = 05Hz

Fr = 10Hz

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

Fr = 05Hz

Fr = 10Hz

(b)

Figure 7 PSE curvature (a) rectangular window 50 overlap (b) Hamming window 50 overlap

with 1000 and 500 sampling record lengths respectively witha rectangular window The signal power is concentrated atapproximately 36Hzsample and the curves are character-ized by the frequency resolution

Figure 5 represents the PSE and the curvature curvesaccording to the window functions The curve in Figure 5(a)consists of the maximum PSE values at all nodes at approx-imately 36Hzsample and displays the maximum energy inthe PSE curves of Figure 4(a) which looks similar to thefundamental mode of the beam structure Figures 5(b)ndash5(f) display the curvature curves according to the windowfunctions on the ten data sets with the identical condition

of 50 overlap and Fr = 05Hz It is shown that the damageis located in the region representing the abrupt change inthe curvature All plots exhibit more abrupt changes in thecurvature at the damage location than in any other regionswhich indicate that the window functions introduced in thisstudy can be used to detect damage

Figure 6 compares the PSE curvatures of ten data setsdepending on the overlaps of 50 and 40under the same Fr= 05Hz using rectangular and Hamming windowsThe 50overlap leads to a larger change in the damage region than the40 overlap This indicates that more data overlap providesmore conservative results Figure 7 compares the applicability

8 Shock and Vibration

Damage

Damage

Damage

Beam 2

Beam 1

052m

115m

028m

085m

(a)

1 7 8 23 29 30 38 39

301 8 39 40Damage Damage

Beam 1

40 50mm

12mm100mm

middot middot middot middot middot middotmiddot middot middotmiddot middot middot

115m

(b)

1 4 5 12 13 19

131 5 20Damage

Beam 1

10mm

100mm

20 40mm

middot middot middot middot middot middot middot middot middot

052m

(c)

Figure 8 A crossed-beam structure (a) a beam structure (b) finite elements of beam 1 and (c) finite elements of beam 2

of damage detection by the PSE curvature depending onfrequency resolutions of 05Hz and 10Hz using rectangularandHamming windows In the plots the low frequency reso-lution leads to amore abrupt change in the curvature and thedamage region can be more explicitly found This numericalapplication demonstrates that the damage detection methodusing the data samples with 50 sample overlap and 05Hzfrequency resolution with the window functions consideredin this study is more effective

As another numerical application a crossed-beam struc-ture withmultiple damages in Figure 8 is considered to detectthe damage location Fixed-endbeam 1 is jointed onfixed-endbeam 2 The nodal points and the members are numberedas shown in the figure Assuming a Bernoulli-Euler planebeam element the beam finite elements are obtained bysubdividing the beam members longitudinally Beams 1 and2 are then modeled using 40 and 20 elements Each nodehas two DOFs of transverse displacement and slope Thetwo beams have an identical elastic modulus 119864 = 200GPaand a unit mass of 7860 kgm3 Undamaged beams 1 and2 are 2m and 08m in length and the cross sections are100 times 12mm and 100 times 10mm respectively Two damagesof beam 1 are located at elements 8 and 30 with the samecross section of 100 times 115mm and damage to beam 2 islocated at element 5 with a cross section of 100 times 9mm

This work assumes a Rayleigh damping of the stiffness matrixand a proportional constant of 00002 and assumes the beamstructure is subjected to the base excitation in Figure 2(b)Based on these variables this numerical application considersthe validity of the proposed method originating from thedisplacement responses contaminated by 3 external noisein (17)

Utilizing the 50 overlap samples of eight segments with500 sampling record lengths with a rectangular window thePSEs were extracted from the displacement responses inthe time-domain Figures 9(a) and 9(b) represent the PSEcurves of beams 1 and 2 transformed from the displacementresponses in the time-domain without the external noiserespectively The first resonance frequency of beams 1 and 2exists at the frequency of 16Hzsample The PSE curvaturesare estimated by the second-order difference method Takingthe maximum PSE values at the first resonance frequencyand calculating the curvatures the resulting curvature curvesare plotted as shown in Figures 9(c) and 9(d) It is observedthat the damaged elements correspond with the locations torepresent the abrupt curvature change except the joint nodesused to connect the two beams

Utilizing the numerically simulated data contaminatedby 3 external noise and taking the same process as theprevious case the PSE curves in Figures 10(a) and 10(b)

Shock and Vibration 9

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus140

(a)

0 50 100 150 200Frequency (Hzsample)

250

Pow

erfr

eque

ncy

(dB

Hz)

minus240

minus230

minus220

minus210

minus200

minus190

minus180

minus170

minus160

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0015

001

0005

0

minus0005

minus001

minus0015

Damage Damage

(c)

64 108 1412 16Node number

PSE

curv

atur

e

004

002

0

minus01

minus012

minus008

minus006

minus004

minus002

Damage

(d)

Figure 9 PSE and the curvature curves of noise-free structure (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

display more complicated relations than Figures 9(a) and9(b)The first resonance frequency of 16Hzsample coincideswith the PSE curve without the external noise The curvaturecurves represent the explicit curvature variations at elements8 and 30 of beam 1 in Figure 10(c) and element 5 of beam 2in Figure 10(d) It is observed that the proposed method canbe utilized in detecting beam structure damage despite theexistence of external noise

4 Beam Test

A beam test was performed to detect the damage of a simplysupported beam as shown in Figure 11 The gross crosssection of the beam is 119887 times 119905 = 100mm times 11mm and thenet length of the span between end supports is 1200mmThedamage is located at 350mm from the left support whichis between nodes 2 and 3 The damaged cross section was

established as 119887 times 119905 = 100mm times 8mmThe eight points mea-sured by accelerometers are numbered as shown in Figure 11The beam is excited by hitting an impact hammer withsupersoft tip on the support to collect response data withinthe low frequency range The experiment was conductedusing DYTRANmodel 3055B1 uniaxial accelerometers and aminiature transducer hammer (Bruel and Kjaer model 8204)for the excitation of the system The data acquisition systemwas a DEWETRON model DEWE-43 The accelerationresponse data in the time-domain were measured by theDEWETRON The input acceleration excited by the impacthammer was not measured

Figure 12(a) represents the acceleration responses in thetime-domain at all nodes for one second after hitting Figures12(b) and 12(c) display the FFT and PSE curves at allnodes in the frequency-domain to transform the accelera-tion responses The maximum energy is revealed at 171 Hz

10 Shock and Vibration

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus120

minus130

minus140

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0008

0006

0004

0002

0

minus0006

minus0004

minus0002

minus0008

minus001

minus0012

Damage

Damage

(c)

64 108 1412 16 18Node number

PSE

curv

atur

e

006

004

002

0

minus006

minus004

minus002

minus008

Damage

(d)

Figure 10 PSE and the curvature curves containing 3 noise (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

1 2 3 64 75

Rubber packing

8

Damage

SupportAccelerometer

Impact hammer1 2 3 64 75 8

Support

Impact hammer

7 150mm

350mm1200mm1400mm

75mm 75mm

(a)

Undamaged section

Damaged section

100mm

100mm

11mm

8mm3mm

(b)

(c)

Hammer tip = supersoft

(d)Figure 11 Test beam (a) plan view (b) section (c) photo of test beam and (d) impact hammer

Shock and Vibration 11

0 05 1 15 2Time (s)

minus0015

minus001

minus0005

0

0005

001

0015

Acce

lera

tion

resp

onse

(g)

(a)

0 50 100 150 200 2500

02

04

06

08

1

12

14

16

18

Frequency (Hz)

Abso

lute

val

ues o

f acc

eler

atio

n re

spon

ses

times10minus3

(b)

Pow

erfr

eque

ncy

(dB

Hz)

0 50Frequency (Hzsample)

100 150 200 250

minus60

minus65

minus70

minus75

minus80

minus85

(c)

1 2 3 4 5 87604

06

08

1

12

14

16

18

Node number

Max

(abs

olut

e val

ues o

f acc

eler

atio

n re

spon

ses)

times10minus3

(d)

2 3 4 5 76Node number

6

4

2

0

minus2

minus4

minus6

Curv

atur

e of m

axim

um v

alue

s

times10minus4

(e)

Figure 12 Continued

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 4: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

4 Shock and Vibration

11

2 32 3

48 4949 50middot middot middot

50 20mm

Figure 1 A fixed-end beam structure model

0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1

Time (s)

minus02

minus04

minus06

minus08

minus1

Base

exci

tatio

n (m

ms2)

times10minus3

(a)

0 01 02 03 04 05 06 07 08 09 1

0

02

04

06

08

1

Time (s)

minus02

minus04

minus06

minus08

minus1

Base

exci

tatio

n (m

ms2)

times10minus3

(b)

Figure 2 Acceleration of external excitation at the left support (a) time step of 0001 sec (b) time step of 0002 sec

Assume the beam structure is subjected to the white noiseexcitation at the left support with a step size of 0001 secand 0002 sec for one second as shown in Figure 2 Thedynamic responses in the time-domain are simulated bysolving the dynamic equation of the finite element modelsubject to the excitation and the response data of the samelength as the input force are collected We assume thatthe information about the excitation is unknown for thisnumerical application

The dynamic responses of the practical system are con-taminated by external noise In this study the measuredresponse data are simulated by adding a series of randomnumbers to the calculated displacement responses Thedisplacements 119906

119903for describing the practical responses at

node 119903 can be calculated from the simulated noise-freedisplacements 1199060

119903 by the following equation

119906119903= 1199060

119903(1 + 120572120590

119903) (17)

where 120572 denotes the relative magnitude of the error and 120590119895is

a random number variant in the range [minus1 1] The measureddisplacement responses including the contaminated externalnoise are established by inserting 120572 = 3 into (17)

Most damage detection methods are sensitive to externalnoise contained in the measurement data The measurementdata sets collected from repeated numerical simulations areused to reduce the effect of the external noise For this

numerical application ten data sets were utilized Taking theFFT the ten displacement response data sets in the time-domain were transformed into responses in the frequency-domain Figure 3(a) represents the absolute amplitude curvesof the displacement responses in the frequency-domain aftertransforming 1000 displacement response data points at allnodes for one second with a time step of 0001 secondsThe first resonance frequency is located at approximately36Hzsample For the maximum values corresponding to allnodes in the neighborhood of 36Hzsample the curve toconnect them is exhibited in Figure 3(b) It is difficult to tracethe damage location from the plot Considering that the beamis a flexural member the flexural curvature is predicted by acentral difference method Figure 3(c) displays the curvaturecurves on ten data sets and abrupt changes in all cases arefound near nodes 19 and 41 including the damage The FFTdata set can be utilized to detect damage The concept isexpanded to the periodogram and PSE to detect damagebecause the PSE Welch method originated from the FFT

This work estimates the Welch PSE by dividing theresponse into eight segments in lengthThe numerical resultsare compared according to the following test parametersthe rectangular Hamming Bartlett Hann and Blackmanwindow functions sample overlaps of 40 and 50 andfrequency resolutions of 05Hz and 10Hz Figures 4(a)and 4(b) represent the PSE curves for 50 overlappingsamples between two adjacent segments of eight segments

Shock and Vibration 5

0 100 200 300 400 5000

02

04

06

08

1

14

Frequency (Hzsample)

abs(Y(f

))times10minus9

12

(a)

0

002

004

006

008

01

012

014

Max

(abs

(Y(f

)))

10 20 30 40 500Node number(b)

0 10 20 30 40 50Node number

Curv

atur

e of M

ax(a

bs(Y

(f))

)

15

1

05

0

minus05

minus1

minus15

minus2

times10minus11

(c)

Figure 3 Numerical results in the frequency-domain (a) FFT curves (b) maximum FFT curve corresponding to the first resonancefrequency and (c) its curvature curves

0 100 200 300 400 500Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus80

minus70

minus60

minus50

minus40

minus30

minus90

minus100

minus20

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus80

minus70

minus60

minus50

minus40

minus30

minus90

minus10

minus20

(b)

Figure 4 PSE curves (a) Fr = 10Hz (b) Fr = 05Hz

6 Shock and Vibration

Pow

erfr

eque

ncy

(dB

Hz)

minus155

minus160

minus165

minus170

minus175

minus1805 10 15 20 25 30 35 40 45 500

Node number(a)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(b)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(c)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(d)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(e)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(f)

Figure 5 PSE curve and its curvature under the condition of Fr = 05Hz (a) PSE curve (rectangular window 50 overlap) bymaximum PSEvalues around 36Hzsample (b) PSE curvature (rectangular window) (c) PSE curvature (Hamming window) (d) PSE curvature (Bartlettwindow) (e) PSE curvature (Hann window) and (f) PSE curvature (Blackman window)

Shock and Vibration 7

10 20 30 40Node number

Curv

atur

e of P

SE

50

40

005

0

minus005

minus01

minus015

minus02

minus025

minus03

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

5040

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

(b)

Figure 6 PSE curvature depending on the overlap (a) rectangular window (b) Hamming window

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus03

Fr = 05Hz

Fr = 10Hz

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

Fr = 05Hz

Fr = 10Hz

(b)

Figure 7 PSE curvature (a) rectangular window 50 overlap (b) Hamming window 50 overlap

with 1000 and 500 sampling record lengths respectively witha rectangular window The signal power is concentrated atapproximately 36Hzsample and the curves are character-ized by the frequency resolution

Figure 5 represents the PSE and the curvature curvesaccording to the window functions The curve in Figure 5(a)consists of the maximum PSE values at all nodes at approx-imately 36Hzsample and displays the maximum energy inthe PSE curves of Figure 4(a) which looks similar to thefundamental mode of the beam structure Figures 5(b)ndash5(f) display the curvature curves according to the windowfunctions on the ten data sets with the identical condition

of 50 overlap and Fr = 05Hz It is shown that the damageis located in the region representing the abrupt change inthe curvature All plots exhibit more abrupt changes in thecurvature at the damage location than in any other regionswhich indicate that the window functions introduced in thisstudy can be used to detect damage

Figure 6 compares the PSE curvatures of ten data setsdepending on the overlaps of 50 and 40under the same Fr= 05Hz using rectangular and Hamming windowsThe 50overlap leads to a larger change in the damage region than the40 overlap This indicates that more data overlap providesmore conservative results Figure 7 compares the applicability

8 Shock and Vibration

Damage

Damage

Damage

Beam 2

Beam 1

052m

115m

028m

085m

(a)

1 7 8 23 29 30 38 39

301 8 39 40Damage Damage

Beam 1

40 50mm

12mm100mm

middot middot middot middot middot middotmiddot middot middotmiddot middot middot

115m

(b)

1 4 5 12 13 19

131 5 20Damage

Beam 1

10mm

100mm

20 40mm

middot middot middot middot middot middot middot middot middot

052m

(c)

Figure 8 A crossed-beam structure (a) a beam structure (b) finite elements of beam 1 and (c) finite elements of beam 2

of damage detection by the PSE curvature depending onfrequency resolutions of 05Hz and 10Hz using rectangularandHamming windows In the plots the low frequency reso-lution leads to amore abrupt change in the curvature and thedamage region can be more explicitly found This numericalapplication demonstrates that the damage detection methodusing the data samples with 50 sample overlap and 05Hzfrequency resolution with the window functions consideredin this study is more effective

As another numerical application a crossed-beam struc-ture withmultiple damages in Figure 8 is considered to detectthe damage location Fixed-endbeam 1 is jointed onfixed-endbeam 2 The nodal points and the members are numberedas shown in the figure Assuming a Bernoulli-Euler planebeam element the beam finite elements are obtained bysubdividing the beam members longitudinally Beams 1 and2 are then modeled using 40 and 20 elements Each nodehas two DOFs of transverse displacement and slope Thetwo beams have an identical elastic modulus 119864 = 200GPaand a unit mass of 7860 kgm3 Undamaged beams 1 and2 are 2m and 08m in length and the cross sections are100 times 12mm and 100 times 10mm respectively Two damagesof beam 1 are located at elements 8 and 30 with the samecross section of 100 times 115mm and damage to beam 2 islocated at element 5 with a cross section of 100 times 9mm

This work assumes a Rayleigh damping of the stiffness matrixand a proportional constant of 00002 and assumes the beamstructure is subjected to the base excitation in Figure 2(b)Based on these variables this numerical application considersthe validity of the proposed method originating from thedisplacement responses contaminated by 3 external noisein (17)

Utilizing the 50 overlap samples of eight segments with500 sampling record lengths with a rectangular window thePSEs were extracted from the displacement responses inthe time-domain Figures 9(a) and 9(b) represent the PSEcurves of beams 1 and 2 transformed from the displacementresponses in the time-domain without the external noiserespectively The first resonance frequency of beams 1 and 2exists at the frequency of 16Hzsample The PSE curvaturesare estimated by the second-order difference method Takingthe maximum PSE values at the first resonance frequencyand calculating the curvatures the resulting curvature curvesare plotted as shown in Figures 9(c) and 9(d) It is observedthat the damaged elements correspond with the locations torepresent the abrupt curvature change except the joint nodesused to connect the two beams

Utilizing the numerically simulated data contaminatedby 3 external noise and taking the same process as theprevious case the PSE curves in Figures 10(a) and 10(b)

Shock and Vibration 9

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus140

(a)

0 50 100 150 200Frequency (Hzsample)

250

Pow

erfr

eque

ncy

(dB

Hz)

minus240

minus230

minus220

minus210

minus200

minus190

minus180

minus170

minus160

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0015

001

0005

0

minus0005

minus001

minus0015

Damage Damage

(c)

64 108 1412 16Node number

PSE

curv

atur

e

004

002

0

minus01

minus012

minus008

minus006

minus004

minus002

Damage

(d)

Figure 9 PSE and the curvature curves of noise-free structure (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

display more complicated relations than Figures 9(a) and9(b)The first resonance frequency of 16Hzsample coincideswith the PSE curve without the external noise The curvaturecurves represent the explicit curvature variations at elements8 and 30 of beam 1 in Figure 10(c) and element 5 of beam 2in Figure 10(d) It is observed that the proposed method canbe utilized in detecting beam structure damage despite theexistence of external noise

4 Beam Test

A beam test was performed to detect the damage of a simplysupported beam as shown in Figure 11 The gross crosssection of the beam is 119887 times 119905 = 100mm times 11mm and thenet length of the span between end supports is 1200mmThedamage is located at 350mm from the left support whichis between nodes 2 and 3 The damaged cross section was

established as 119887 times 119905 = 100mm times 8mmThe eight points mea-sured by accelerometers are numbered as shown in Figure 11The beam is excited by hitting an impact hammer withsupersoft tip on the support to collect response data withinthe low frequency range The experiment was conductedusing DYTRANmodel 3055B1 uniaxial accelerometers and aminiature transducer hammer (Bruel and Kjaer model 8204)for the excitation of the system The data acquisition systemwas a DEWETRON model DEWE-43 The accelerationresponse data in the time-domain were measured by theDEWETRON The input acceleration excited by the impacthammer was not measured

Figure 12(a) represents the acceleration responses in thetime-domain at all nodes for one second after hitting Figures12(b) and 12(c) display the FFT and PSE curves at allnodes in the frequency-domain to transform the accelera-tion responses The maximum energy is revealed at 171 Hz

10 Shock and Vibration

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus120

minus130

minus140

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0008

0006

0004

0002

0

minus0006

minus0004

minus0002

minus0008

minus001

minus0012

Damage

Damage

(c)

64 108 1412 16 18Node number

PSE

curv

atur

e

006

004

002

0

minus006

minus004

minus002

minus008

Damage

(d)

Figure 10 PSE and the curvature curves containing 3 noise (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

1 2 3 64 75

Rubber packing

8

Damage

SupportAccelerometer

Impact hammer1 2 3 64 75 8

Support

Impact hammer

7 150mm

350mm1200mm1400mm

75mm 75mm

(a)

Undamaged section

Damaged section

100mm

100mm

11mm

8mm3mm

(b)

(c)

Hammer tip = supersoft

(d)Figure 11 Test beam (a) plan view (b) section (c) photo of test beam and (d) impact hammer

Shock and Vibration 11

0 05 1 15 2Time (s)

minus0015

minus001

minus0005

0

0005

001

0015

Acce

lera

tion

resp

onse

(g)

(a)

0 50 100 150 200 2500

02

04

06

08

1

12

14

16

18

Frequency (Hz)

Abso

lute

val

ues o

f acc

eler

atio

n re

spon

ses

times10minus3

(b)

Pow

erfr

eque

ncy

(dB

Hz)

0 50Frequency (Hzsample)

100 150 200 250

minus60

minus65

minus70

minus75

minus80

minus85

(c)

1 2 3 4 5 87604

06

08

1

12

14

16

18

Node number

Max

(abs

olut

e val

ues o

f acc

eler

atio

n re

spon

ses)

times10minus3

(d)

2 3 4 5 76Node number

6

4

2

0

minus2

minus4

minus6

Curv

atur

e of m

axim

um v

alue

s

times10minus4

(e)

Figure 12 Continued

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 5: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

Shock and Vibration 5

0 100 200 300 400 5000

02

04

06

08

1

14

Frequency (Hzsample)

abs(Y(f

))times10minus9

12

(a)

0

002

004

006

008

01

012

014

Max

(abs

(Y(f

)))

10 20 30 40 500Node number(b)

0 10 20 30 40 50Node number

Curv

atur

e of M

ax(a

bs(Y

(f))

)

15

1

05

0

minus05

minus1

minus15

minus2

times10minus11

(c)

Figure 3 Numerical results in the frequency-domain (a) FFT curves (b) maximum FFT curve corresponding to the first resonancefrequency and (c) its curvature curves

0 100 200 300 400 500Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus80

minus70

minus60

minus50

minus40

minus30

minus90

minus100

minus20

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus80

minus70

minus60

minus50

minus40

minus30

minus90

minus10

minus20

(b)

Figure 4 PSE curves (a) Fr = 10Hz (b) Fr = 05Hz

6 Shock and Vibration

Pow

erfr

eque

ncy

(dB

Hz)

minus155

minus160

minus165

minus170

minus175

minus1805 10 15 20 25 30 35 40 45 500

Node number(a)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(b)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(c)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(d)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(e)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(f)

Figure 5 PSE curve and its curvature under the condition of Fr = 05Hz (a) PSE curve (rectangular window 50 overlap) bymaximum PSEvalues around 36Hzsample (b) PSE curvature (rectangular window) (c) PSE curvature (Hamming window) (d) PSE curvature (Bartlettwindow) (e) PSE curvature (Hann window) and (f) PSE curvature (Blackman window)

Shock and Vibration 7

10 20 30 40Node number

Curv

atur

e of P

SE

50

40

005

0

minus005

minus01

minus015

minus02

minus025

minus03

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

5040

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

(b)

Figure 6 PSE curvature depending on the overlap (a) rectangular window (b) Hamming window

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus03

Fr = 05Hz

Fr = 10Hz

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

Fr = 05Hz

Fr = 10Hz

(b)

Figure 7 PSE curvature (a) rectangular window 50 overlap (b) Hamming window 50 overlap

with 1000 and 500 sampling record lengths respectively witha rectangular window The signal power is concentrated atapproximately 36Hzsample and the curves are character-ized by the frequency resolution

Figure 5 represents the PSE and the curvature curvesaccording to the window functions The curve in Figure 5(a)consists of the maximum PSE values at all nodes at approx-imately 36Hzsample and displays the maximum energy inthe PSE curves of Figure 4(a) which looks similar to thefundamental mode of the beam structure Figures 5(b)ndash5(f) display the curvature curves according to the windowfunctions on the ten data sets with the identical condition

of 50 overlap and Fr = 05Hz It is shown that the damageis located in the region representing the abrupt change inthe curvature All plots exhibit more abrupt changes in thecurvature at the damage location than in any other regionswhich indicate that the window functions introduced in thisstudy can be used to detect damage

Figure 6 compares the PSE curvatures of ten data setsdepending on the overlaps of 50 and 40under the same Fr= 05Hz using rectangular and Hamming windowsThe 50overlap leads to a larger change in the damage region than the40 overlap This indicates that more data overlap providesmore conservative results Figure 7 compares the applicability

8 Shock and Vibration

Damage

Damage

Damage

Beam 2

Beam 1

052m

115m

028m

085m

(a)

1 7 8 23 29 30 38 39

301 8 39 40Damage Damage

Beam 1

40 50mm

12mm100mm

middot middot middot middot middot middotmiddot middot middotmiddot middot middot

115m

(b)

1 4 5 12 13 19

131 5 20Damage

Beam 1

10mm

100mm

20 40mm

middot middot middot middot middot middot middot middot middot

052m

(c)

Figure 8 A crossed-beam structure (a) a beam structure (b) finite elements of beam 1 and (c) finite elements of beam 2

of damage detection by the PSE curvature depending onfrequency resolutions of 05Hz and 10Hz using rectangularandHamming windows In the plots the low frequency reso-lution leads to amore abrupt change in the curvature and thedamage region can be more explicitly found This numericalapplication demonstrates that the damage detection methodusing the data samples with 50 sample overlap and 05Hzfrequency resolution with the window functions consideredin this study is more effective

As another numerical application a crossed-beam struc-ture withmultiple damages in Figure 8 is considered to detectthe damage location Fixed-endbeam 1 is jointed onfixed-endbeam 2 The nodal points and the members are numberedas shown in the figure Assuming a Bernoulli-Euler planebeam element the beam finite elements are obtained bysubdividing the beam members longitudinally Beams 1 and2 are then modeled using 40 and 20 elements Each nodehas two DOFs of transverse displacement and slope Thetwo beams have an identical elastic modulus 119864 = 200GPaand a unit mass of 7860 kgm3 Undamaged beams 1 and2 are 2m and 08m in length and the cross sections are100 times 12mm and 100 times 10mm respectively Two damagesof beam 1 are located at elements 8 and 30 with the samecross section of 100 times 115mm and damage to beam 2 islocated at element 5 with a cross section of 100 times 9mm

This work assumes a Rayleigh damping of the stiffness matrixand a proportional constant of 00002 and assumes the beamstructure is subjected to the base excitation in Figure 2(b)Based on these variables this numerical application considersthe validity of the proposed method originating from thedisplacement responses contaminated by 3 external noisein (17)

Utilizing the 50 overlap samples of eight segments with500 sampling record lengths with a rectangular window thePSEs were extracted from the displacement responses inthe time-domain Figures 9(a) and 9(b) represent the PSEcurves of beams 1 and 2 transformed from the displacementresponses in the time-domain without the external noiserespectively The first resonance frequency of beams 1 and 2exists at the frequency of 16Hzsample The PSE curvaturesare estimated by the second-order difference method Takingthe maximum PSE values at the first resonance frequencyand calculating the curvatures the resulting curvature curvesare plotted as shown in Figures 9(c) and 9(d) It is observedthat the damaged elements correspond with the locations torepresent the abrupt curvature change except the joint nodesused to connect the two beams

Utilizing the numerically simulated data contaminatedby 3 external noise and taking the same process as theprevious case the PSE curves in Figures 10(a) and 10(b)

Shock and Vibration 9

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus140

(a)

0 50 100 150 200Frequency (Hzsample)

250

Pow

erfr

eque

ncy

(dB

Hz)

minus240

minus230

minus220

minus210

minus200

minus190

minus180

minus170

minus160

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0015

001

0005

0

minus0005

minus001

minus0015

Damage Damage

(c)

64 108 1412 16Node number

PSE

curv

atur

e

004

002

0

minus01

minus012

minus008

minus006

minus004

minus002

Damage

(d)

Figure 9 PSE and the curvature curves of noise-free structure (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

display more complicated relations than Figures 9(a) and9(b)The first resonance frequency of 16Hzsample coincideswith the PSE curve without the external noise The curvaturecurves represent the explicit curvature variations at elements8 and 30 of beam 1 in Figure 10(c) and element 5 of beam 2in Figure 10(d) It is observed that the proposed method canbe utilized in detecting beam structure damage despite theexistence of external noise

4 Beam Test

A beam test was performed to detect the damage of a simplysupported beam as shown in Figure 11 The gross crosssection of the beam is 119887 times 119905 = 100mm times 11mm and thenet length of the span between end supports is 1200mmThedamage is located at 350mm from the left support whichis between nodes 2 and 3 The damaged cross section was

established as 119887 times 119905 = 100mm times 8mmThe eight points mea-sured by accelerometers are numbered as shown in Figure 11The beam is excited by hitting an impact hammer withsupersoft tip on the support to collect response data withinthe low frequency range The experiment was conductedusing DYTRANmodel 3055B1 uniaxial accelerometers and aminiature transducer hammer (Bruel and Kjaer model 8204)for the excitation of the system The data acquisition systemwas a DEWETRON model DEWE-43 The accelerationresponse data in the time-domain were measured by theDEWETRON The input acceleration excited by the impacthammer was not measured

Figure 12(a) represents the acceleration responses in thetime-domain at all nodes for one second after hitting Figures12(b) and 12(c) display the FFT and PSE curves at allnodes in the frequency-domain to transform the accelera-tion responses The maximum energy is revealed at 171 Hz

10 Shock and Vibration

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus120

minus130

minus140

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0008

0006

0004

0002

0

minus0006

minus0004

minus0002

minus0008

minus001

minus0012

Damage

Damage

(c)

64 108 1412 16 18Node number

PSE

curv

atur

e

006

004

002

0

minus006

minus004

minus002

minus008

Damage

(d)

Figure 10 PSE and the curvature curves containing 3 noise (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

1 2 3 64 75

Rubber packing

8

Damage

SupportAccelerometer

Impact hammer1 2 3 64 75 8

Support

Impact hammer

7 150mm

350mm1200mm1400mm

75mm 75mm

(a)

Undamaged section

Damaged section

100mm

100mm

11mm

8mm3mm

(b)

(c)

Hammer tip = supersoft

(d)Figure 11 Test beam (a) plan view (b) section (c) photo of test beam and (d) impact hammer

Shock and Vibration 11

0 05 1 15 2Time (s)

minus0015

minus001

minus0005

0

0005

001

0015

Acce

lera

tion

resp

onse

(g)

(a)

0 50 100 150 200 2500

02

04

06

08

1

12

14

16

18

Frequency (Hz)

Abso

lute

val

ues o

f acc

eler

atio

n re

spon

ses

times10minus3

(b)

Pow

erfr

eque

ncy

(dB

Hz)

0 50Frequency (Hzsample)

100 150 200 250

minus60

minus65

minus70

minus75

minus80

minus85

(c)

1 2 3 4 5 87604

06

08

1

12

14

16

18

Node number

Max

(abs

olut

e val

ues o

f acc

eler

atio

n re

spon

ses)

times10minus3

(d)

2 3 4 5 76Node number

6

4

2

0

minus2

minus4

minus6

Curv

atur

e of m

axim

um v

alue

s

times10minus4

(e)

Figure 12 Continued

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 6: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

6 Shock and Vibration

Pow

erfr

eque

ncy

(dB

Hz)

minus155

minus160

minus165

minus170

minus175

minus1805 10 15 20 25 30 35 40 45 500

Node number(a)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(b)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(c)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(d)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(e)

0 10 20 30 40 50Node number

PSE

curv

atur

e

05

0

minus05

minus1

minus15

minus2

minus25

minus3

(f)

Figure 5 PSE curve and its curvature under the condition of Fr = 05Hz (a) PSE curve (rectangular window 50 overlap) bymaximum PSEvalues around 36Hzsample (b) PSE curvature (rectangular window) (c) PSE curvature (Hamming window) (d) PSE curvature (Bartlettwindow) (e) PSE curvature (Hann window) and (f) PSE curvature (Blackman window)

Shock and Vibration 7

10 20 30 40Node number

Curv

atur

e of P

SE

50

40

005

0

minus005

minus01

minus015

minus02

minus025

minus03

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

5040

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

(b)

Figure 6 PSE curvature depending on the overlap (a) rectangular window (b) Hamming window

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus03

Fr = 05Hz

Fr = 10Hz

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

Fr = 05Hz

Fr = 10Hz

(b)

Figure 7 PSE curvature (a) rectangular window 50 overlap (b) Hamming window 50 overlap

with 1000 and 500 sampling record lengths respectively witha rectangular window The signal power is concentrated atapproximately 36Hzsample and the curves are character-ized by the frequency resolution

Figure 5 represents the PSE and the curvature curvesaccording to the window functions The curve in Figure 5(a)consists of the maximum PSE values at all nodes at approx-imately 36Hzsample and displays the maximum energy inthe PSE curves of Figure 4(a) which looks similar to thefundamental mode of the beam structure Figures 5(b)ndash5(f) display the curvature curves according to the windowfunctions on the ten data sets with the identical condition

of 50 overlap and Fr = 05Hz It is shown that the damageis located in the region representing the abrupt change inthe curvature All plots exhibit more abrupt changes in thecurvature at the damage location than in any other regionswhich indicate that the window functions introduced in thisstudy can be used to detect damage

Figure 6 compares the PSE curvatures of ten data setsdepending on the overlaps of 50 and 40under the same Fr= 05Hz using rectangular and Hamming windowsThe 50overlap leads to a larger change in the damage region than the40 overlap This indicates that more data overlap providesmore conservative results Figure 7 compares the applicability

8 Shock and Vibration

Damage

Damage

Damage

Beam 2

Beam 1

052m

115m

028m

085m

(a)

1 7 8 23 29 30 38 39

301 8 39 40Damage Damage

Beam 1

40 50mm

12mm100mm

middot middot middot middot middot middotmiddot middot middotmiddot middot middot

115m

(b)

1 4 5 12 13 19

131 5 20Damage

Beam 1

10mm

100mm

20 40mm

middot middot middot middot middot middot middot middot middot

052m

(c)

Figure 8 A crossed-beam structure (a) a beam structure (b) finite elements of beam 1 and (c) finite elements of beam 2

of damage detection by the PSE curvature depending onfrequency resolutions of 05Hz and 10Hz using rectangularandHamming windows In the plots the low frequency reso-lution leads to amore abrupt change in the curvature and thedamage region can be more explicitly found This numericalapplication demonstrates that the damage detection methodusing the data samples with 50 sample overlap and 05Hzfrequency resolution with the window functions consideredin this study is more effective

As another numerical application a crossed-beam struc-ture withmultiple damages in Figure 8 is considered to detectthe damage location Fixed-endbeam 1 is jointed onfixed-endbeam 2 The nodal points and the members are numberedas shown in the figure Assuming a Bernoulli-Euler planebeam element the beam finite elements are obtained bysubdividing the beam members longitudinally Beams 1 and2 are then modeled using 40 and 20 elements Each nodehas two DOFs of transverse displacement and slope Thetwo beams have an identical elastic modulus 119864 = 200GPaand a unit mass of 7860 kgm3 Undamaged beams 1 and2 are 2m and 08m in length and the cross sections are100 times 12mm and 100 times 10mm respectively Two damagesof beam 1 are located at elements 8 and 30 with the samecross section of 100 times 115mm and damage to beam 2 islocated at element 5 with a cross section of 100 times 9mm

This work assumes a Rayleigh damping of the stiffness matrixand a proportional constant of 00002 and assumes the beamstructure is subjected to the base excitation in Figure 2(b)Based on these variables this numerical application considersthe validity of the proposed method originating from thedisplacement responses contaminated by 3 external noisein (17)

Utilizing the 50 overlap samples of eight segments with500 sampling record lengths with a rectangular window thePSEs were extracted from the displacement responses inthe time-domain Figures 9(a) and 9(b) represent the PSEcurves of beams 1 and 2 transformed from the displacementresponses in the time-domain without the external noiserespectively The first resonance frequency of beams 1 and 2exists at the frequency of 16Hzsample The PSE curvaturesare estimated by the second-order difference method Takingthe maximum PSE values at the first resonance frequencyand calculating the curvatures the resulting curvature curvesare plotted as shown in Figures 9(c) and 9(d) It is observedthat the damaged elements correspond with the locations torepresent the abrupt curvature change except the joint nodesused to connect the two beams

Utilizing the numerically simulated data contaminatedby 3 external noise and taking the same process as theprevious case the PSE curves in Figures 10(a) and 10(b)

Shock and Vibration 9

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus140

(a)

0 50 100 150 200Frequency (Hzsample)

250

Pow

erfr

eque

ncy

(dB

Hz)

minus240

minus230

minus220

minus210

minus200

minus190

minus180

minus170

minus160

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0015

001

0005

0

minus0005

minus001

minus0015

Damage Damage

(c)

64 108 1412 16Node number

PSE

curv

atur

e

004

002

0

minus01

minus012

minus008

minus006

minus004

minus002

Damage

(d)

Figure 9 PSE and the curvature curves of noise-free structure (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

display more complicated relations than Figures 9(a) and9(b)The first resonance frequency of 16Hzsample coincideswith the PSE curve without the external noise The curvaturecurves represent the explicit curvature variations at elements8 and 30 of beam 1 in Figure 10(c) and element 5 of beam 2in Figure 10(d) It is observed that the proposed method canbe utilized in detecting beam structure damage despite theexistence of external noise

4 Beam Test

A beam test was performed to detect the damage of a simplysupported beam as shown in Figure 11 The gross crosssection of the beam is 119887 times 119905 = 100mm times 11mm and thenet length of the span between end supports is 1200mmThedamage is located at 350mm from the left support whichis between nodes 2 and 3 The damaged cross section was

established as 119887 times 119905 = 100mm times 8mmThe eight points mea-sured by accelerometers are numbered as shown in Figure 11The beam is excited by hitting an impact hammer withsupersoft tip on the support to collect response data withinthe low frequency range The experiment was conductedusing DYTRANmodel 3055B1 uniaxial accelerometers and aminiature transducer hammer (Bruel and Kjaer model 8204)for the excitation of the system The data acquisition systemwas a DEWETRON model DEWE-43 The accelerationresponse data in the time-domain were measured by theDEWETRON The input acceleration excited by the impacthammer was not measured

Figure 12(a) represents the acceleration responses in thetime-domain at all nodes for one second after hitting Figures12(b) and 12(c) display the FFT and PSE curves at allnodes in the frequency-domain to transform the accelera-tion responses The maximum energy is revealed at 171 Hz

10 Shock and Vibration

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus120

minus130

minus140

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0008

0006

0004

0002

0

minus0006

minus0004

minus0002

minus0008

minus001

minus0012

Damage

Damage

(c)

64 108 1412 16 18Node number

PSE

curv

atur

e

006

004

002

0

minus006

minus004

minus002

minus008

Damage

(d)

Figure 10 PSE and the curvature curves containing 3 noise (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

1 2 3 64 75

Rubber packing

8

Damage

SupportAccelerometer

Impact hammer1 2 3 64 75 8

Support

Impact hammer

7 150mm

350mm1200mm1400mm

75mm 75mm

(a)

Undamaged section

Damaged section

100mm

100mm

11mm

8mm3mm

(b)

(c)

Hammer tip = supersoft

(d)Figure 11 Test beam (a) plan view (b) section (c) photo of test beam and (d) impact hammer

Shock and Vibration 11

0 05 1 15 2Time (s)

minus0015

minus001

minus0005

0

0005

001

0015

Acce

lera

tion

resp

onse

(g)

(a)

0 50 100 150 200 2500

02

04

06

08

1

12

14

16

18

Frequency (Hz)

Abso

lute

val

ues o

f acc

eler

atio

n re

spon

ses

times10minus3

(b)

Pow

erfr

eque

ncy

(dB

Hz)

0 50Frequency (Hzsample)

100 150 200 250

minus60

minus65

minus70

minus75

minus80

minus85

(c)

1 2 3 4 5 87604

06

08

1

12

14

16

18

Node number

Max

(abs

olut

e val

ues o

f acc

eler

atio

n re

spon

ses)

times10minus3

(d)

2 3 4 5 76Node number

6

4

2

0

minus2

minus4

minus6

Curv

atur

e of m

axim

um v

alue

s

times10minus4

(e)

Figure 12 Continued

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 7: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

Shock and Vibration 7

10 20 30 40Node number

Curv

atur

e of P

SE

50

40

005

0

minus005

minus01

minus015

minus02

minus025

minus03

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

5040

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

(b)

Figure 6 PSE curvature depending on the overlap (a) rectangular window (b) Hamming window

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus03

Fr = 05Hz

Fr = 10Hz

(a)

10 20 30 40Node number

Curv

atur

e of P

SE

005

0

minus005

minus01

minus015

minus02

minus025

minus035

minus03

Fr = 05Hz

Fr = 10Hz

(b)

Figure 7 PSE curvature (a) rectangular window 50 overlap (b) Hamming window 50 overlap

with 1000 and 500 sampling record lengths respectively witha rectangular window The signal power is concentrated atapproximately 36Hzsample and the curves are character-ized by the frequency resolution

Figure 5 represents the PSE and the curvature curvesaccording to the window functions The curve in Figure 5(a)consists of the maximum PSE values at all nodes at approx-imately 36Hzsample and displays the maximum energy inthe PSE curves of Figure 4(a) which looks similar to thefundamental mode of the beam structure Figures 5(b)ndash5(f) display the curvature curves according to the windowfunctions on the ten data sets with the identical condition

of 50 overlap and Fr = 05Hz It is shown that the damageis located in the region representing the abrupt change inthe curvature All plots exhibit more abrupt changes in thecurvature at the damage location than in any other regionswhich indicate that the window functions introduced in thisstudy can be used to detect damage

Figure 6 compares the PSE curvatures of ten data setsdepending on the overlaps of 50 and 40under the same Fr= 05Hz using rectangular and Hamming windowsThe 50overlap leads to a larger change in the damage region than the40 overlap This indicates that more data overlap providesmore conservative results Figure 7 compares the applicability

8 Shock and Vibration

Damage

Damage

Damage

Beam 2

Beam 1

052m

115m

028m

085m

(a)

1 7 8 23 29 30 38 39

301 8 39 40Damage Damage

Beam 1

40 50mm

12mm100mm

middot middot middot middot middot middotmiddot middot middotmiddot middot middot

115m

(b)

1 4 5 12 13 19

131 5 20Damage

Beam 1

10mm

100mm

20 40mm

middot middot middot middot middot middot middot middot middot

052m

(c)

Figure 8 A crossed-beam structure (a) a beam structure (b) finite elements of beam 1 and (c) finite elements of beam 2

of damage detection by the PSE curvature depending onfrequency resolutions of 05Hz and 10Hz using rectangularandHamming windows In the plots the low frequency reso-lution leads to amore abrupt change in the curvature and thedamage region can be more explicitly found This numericalapplication demonstrates that the damage detection methodusing the data samples with 50 sample overlap and 05Hzfrequency resolution with the window functions consideredin this study is more effective

As another numerical application a crossed-beam struc-ture withmultiple damages in Figure 8 is considered to detectthe damage location Fixed-endbeam 1 is jointed onfixed-endbeam 2 The nodal points and the members are numberedas shown in the figure Assuming a Bernoulli-Euler planebeam element the beam finite elements are obtained bysubdividing the beam members longitudinally Beams 1 and2 are then modeled using 40 and 20 elements Each nodehas two DOFs of transverse displacement and slope Thetwo beams have an identical elastic modulus 119864 = 200GPaand a unit mass of 7860 kgm3 Undamaged beams 1 and2 are 2m and 08m in length and the cross sections are100 times 12mm and 100 times 10mm respectively Two damagesof beam 1 are located at elements 8 and 30 with the samecross section of 100 times 115mm and damage to beam 2 islocated at element 5 with a cross section of 100 times 9mm

This work assumes a Rayleigh damping of the stiffness matrixand a proportional constant of 00002 and assumes the beamstructure is subjected to the base excitation in Figure 2(b)Based on these variables this numerical application considersthe validity of the proposed method originating from thedisplacement responses contaminated by 3 external noisein (17)

Utilizing the 50 overlap samples of eight segments with500 sampling record lengths with a rectangular window thePSEs were extracted from the displacement responses inthe time-domain Figures 9(a) and 9(b) represent the PSEcurves of beams 1 and 2 transformed from the displacementresponses in the time-domain without the external noiserespectively The first resonance frequency of beams 1 and 2exists at the frequency of 16Hzsample The PSE curvaturesare estimated by the second-order difference method Takingthe maximum PSE values at the first resonance frequencyand calculating the curvatures the resulting curvature curvesare plotted as shown in Figures 9(c) and 9(d) It is observedthat the damaged elements correspond with the locations torepresent the abrupt curvature change except the joint nodesused to connect the two beams

Utilizing the numerically simulated data contaminatedby 3 external noise and taking the same process as theprevious case the PSE curves in Figures 10(a) and 10(b)

Shock and Vibration 9

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus140

(a)

0 50 100 150 200Frequency (Hzsample)

250

Pow

erfr

eque

ncy

(dB

Hz)

minus240

minus230

minus220

minus210

minus200

minus190

minus180

minus170

minus160

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0015

001

0005

0

minus0005

minus001

minus0015

Damage Damage

(c)

64 108 1412 16Node number

PSE

curv

atur

e

004

002

0

minus01

minus012

minus008

minus006

minus004

minus002

Damage

(d)

Figure 9 PSE and the curvature curves of noise-free structure (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

display more complicated relations than Figures 9(a) and9(b)The first resonance frequency of 16Hzsample coincideswith the PSE curve without the external noise The curvaturecurves represent the explicit curvature variations at elements8 and 30 of beam 1 in Figure 10(c) and element 5 of beam 2in Figure 10(d) It is observed that the proposed method canbe utilized in detecting beam structure damage despite theexistence of external noise

4 Beam Test

A beam test was performed to detect the damage of a simplysupported beam as shown in Figure 11 The gross crosssection of the beam is 119887 times 119905 = 100mm times 11mm and thenet length of the span between end supports is 1200mmThedamage is located at 350mm from the left support whichis between nodes 2 and 3 The damaged cross section was

established as 119887 times 119905 = 100mm times 8mmThe eight points mea-sured by accelerometers are numbered as shown in Figure 11The beam is excited by hitting an impact hammer withsupersoft tip on the support to collect response data withinthe low frequency range The experiment was conductedusing DYTRANmodel 3055B1 uniaxial accelerometers and aminiature transducer hammer (Bruel and Kjaer model 8204)for the excitation of the system The data acquisition systemwas a DEWETRON model DEWE-43 The accelerationresponse data in the time-domain were measured by theDEWETRON The input acceleration excited by the impacthammer was not measured

Figure 12(a) represents the acceleration responses in thetime-domain at all nodes for one second after hitting Figures12(b) and 12(c) display the FFT and PSE curves at allnodes in the frequency-domain to transform the accelera-tion responses The maximum energy is revealed at 171 Hz

10 Shock and Vibration

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus120

minus130

minus140

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0008

0006

0004

0002

0

minus0006

minus0004

minus0002

minus0008

minus001

minus0012

Damage

Damage

(c)

64 108 1412 16 18Node number

PSE

curv

atur

e

006

004

002

0

minus006

minus004

minus002

minus008

Damage

(d)

Figure 10 PSE and the curvature curves containing 3 noise (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

1 2 3 64 75

Rubber packing

8

Damage

SupportAccelerometer

Impact hammer1 2 3 64 75 8

Support

Impact hammer

7 150mm

350mm1200mm1400mm

75mm 75mm

(a)

Undamaged section

Damaged section

100mm

100mm

11mm

8mm3mm

(b)

(c)

Hammer tip = supersoft

(d)Figure 11 Test beam (a) plan view (b) section (c) photo of test beam and (d) impact hammer

Shock and Vibration 11

0 05 1 15 2Time (s)

minus0015

minus001

minus0005

0

0005

001

0015

Acce

lera

tion

resp

onse

(g)

(a)

0 50 100 150 200 2500

02

04

06

08

1

12

14

16

18

Frequency (Hz)

Abso

lute

val

ues o

f acc

eler

atio

n re

spon

ses

times10minus3

(b)

Pow

erfr

eque

ncy

(dB

Hz)

0 50Frequency (Hzsample)

100 150 200 250

minus60

minus65

minus70

minus75

minus80

minus85

(c)

1 2 3 4 5 87604

06

08

1

12

14

16

18

Node number

Max

(abs

olut

e val

ues o

f acc

eler

atio

n re

spon

ses)

times10minus3

(d)

2 3 4 5 76Node number

6

4

2

0

minus2

minus4

minus6

Curv

atur

e of m

axim

um v

alue

s

times10minus4

(e)

Figure 12 Continued

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 8: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

8 Shock and Vibration

Damage

Damage

Damage

Beam 2

Beam 1

052m

115m

028m

085m

(a)

1 7 8 23 29 30 38 39

301 8 39 40Damage Damage

Beam 1

40 50mm

12mm100mm

middot middot middot middot middot middotmiddot middot middotmiddot middot middot

115m

(b)

1 4 5 12 13 19

131 5 20Damage

Beam 1

10mm

100mm

20 40mm

middot middot middot middot middot middot middot middot middot

052m

(c)

Figure 8 A crossed-beam structure (a) a beam structure (b) finite elements of beam 1 and (c) finite elements of beam 2

of damage detection by the PSE curvature depending onfrequency resolutions of 05Hz and 10Hz using rectangularandHamming windows In the plots the low frequency reso-lution leads to amore abrupt change in the curvature and thedamage region can be more explicitly found This numericalapplication demonstrates that the damage detection methodusing the data samples with 50 sample overlap and 05Hzfrequency resolution with the window functions consideredin this study is more effective

As another numerical application a crossed-beam struc-ture withmultiple damages in Figure 8 is considered to detectthe damage location Fixed-endbeam 1 is jointed onfixed-endbeam 2 The nodal points and the members are numberedas shown in the figure Assuming a Bernoulli-Euler planebeam element the beam finite elements are obtained bysubdividing the beam members longitudinally Beams 1 and2 are then modeled using 40 and 20 elements Each nodehas two DOFs of transverse displacement and slope Thetwo beams have an identical elastic modulus 119864 = 200GPaand a unit mass of 7860 kgm3 Undamaged beams 1 and2 are 2m and 08m in length and the cross sections are100 times 12mm and 100 times 10mm respectively Two damagesof beam 1 are located at elements 8 and 30 with the samecross section of 100 times 115mm and damage to beam 2 islocated at element 5 with a cross section of 100 times 9mm

This work assumes a Rayleigh damping of the stiffness matrixand a proportional constant of 00002 and assumes the beamstructure is subjected to the base excitation in Figure 2(b)Based on these variables this numerical application considersthe validity of the proposed method originating from thedisplacement responses contaminated by 3 external noisein (17)

Utilizing the 50 overlap samples of eight segments with500 sampling record lengths with a rectangular window thePSEs were extracted from the displacement responses inthe time-domain Figures 9(a) and 9(b) represent the PSEcurves of beams 1 and 2 transformed from the displacementresponses in the time-domain without the external noiserespectively The first resonance frequency of beams 1 and 2exists at the frequency of 16Hzsample The PSE curvaturesare estimated by the second-order difference method Takingthe maximum PSE values at the first resonance frequencyand calculating the curvatures the resulting curvature curvesare plotted as shown in Figures 9(c) and 9(d) It is observedthat the damaged elements correspond with the locations torepresent the abrupt curvature change except the joint nodesused to connect the two beams

Utilizing the numerically simulated data contaminatedby 3 external noise and taking the same process as theprevious case the PSE curves in Figures 10(a) and 10(b)

Shock and Vibration 9

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus140

(a)

0 50 100 150 200Frequency (Hzsample)

250

Pow

erfr

eque

ncy

(dB

Hz)

minus240

minus230

minus220

minus210

minus200

minus190

minus180

minus170

minus160

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0015

001

0005

0

minus0005

minus001

minus0015

Damage Damage

(c)

64 108 1412 16Node number

PSE

curv

atur

e

004

002

0

minus01

minus012

minus008

minus006

minus004

minus002

Damage

(d)

Figure 9 PSE and the curvature curves of noise-free structure (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

display more complicated relations than Figures 9(a) and9(b)The first resonance frequency of 16Hzsample coincideswith the PSE curve without the external noise The curvaturecurves represent the explicit curvature variations at elements8 and 30 of beam 1 in Figure 10(c) and element 5 of beam 2in Figure 10(d) It is observed that the proposed method canbe utilized in detecting beam structure damage despite theexistence of external noise

4 Beam Test

A beam test was performed to detect the damage of a simplysupported beam as shown in Figure 11 The gross crosssection of the beam is 119887 times 119905 = 100mm times 11mm and thenet length of the span between end supports is 1200mmThedamage is located at 350mm from the left support whichis between nodes 2 and 3 The damaged cross section was

established as 119887 times 119905 = 100mm times 8mmThe eight points mea-sured by accelerometers are numbered as shown in Figure 11The beam is excited by hitting an impact hammer withsupersoft tip on the support to collect response data withinthe low frequency range The experiment was conductedusing DYTRANmodel 3055B1 uniaxial accelerometers and aminiature transducer hammer (Bruel and Kjaer model 8204)for the excitation of the system The data acquisition systemwas a DEWETRON model DEWE-43 The accelerationresponse data in the time-domain were measured by theDEWETRON The input acceleration excited by the impacthammer was not measured

Figure 12(a) represents the acceleration responses in thetime-domain at all nodes for one second after hitting Figures12(b) and 12(c) display the FFT and PSE curves at allnodes in the frequency-domain to transform the accelera-tion responses The maximum energy is revealed at 171 Hz

10 Shock and Vibration

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus120

minus130

minus140

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0008

0006

0004

0002

0

minus0006

minus0004

minus0002

minus0008

minus001

minus0012

Damage

Damage

(c)

64 108 1412 16 18Node number

PSE

curv

atur

e

006

004

002

0

minus006

minus004

minus002

minus008

Damage

(d)

Figure 10 PSE and the curvature curves containing 3 noise (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

1 2 3 64 75

Rubber packing

8

Damage

SupportAccelerometer

Impact hammer1 2 3 64 75 8

Support

Impact hammer

7 150mm

350mm1200mm1400mm

75mm 75mm

(a)

Undamaged section

Damaged section

100mm

100mm

11mm

8mm3mm

(b)

(c)

Hammer tip = supersoft

(d)Figure 11 Test beam (a) plan view (b) section (c) photo of test beam and (d) impact hammer

Shock and Vibration 11

0 05 1 15 2Time (s)

minus0015

minus001

minus0005

0

0005

001

0015

Acce

lera

tion

resp

onse

(g)

(a)

0 50 100 150 200 2500

02

04

06

08

1

12

14

16

18

Frequency (Hz)

Abso

lute

val

ues o

f acc

eler

atio

n re

spon

ses

times10minus3

(b)

Pow

erfr

eque

ncy

(dB

Hz)

0 50Frequency (Hzsample)

100 150 200 250

minus60

minus65

minus70

minus75

minus80

minus85

(c)

1 2 3 4 5 87604

06

08

1

12

14

16

18

Node number

Max

(abs

olut

e val

ues o

f acc

eler

atio

n re

spon

ses)

times10minus3

(d)

2 3 4 5 76Node number

6

4

2

0

minus2

minus4

minus6

Curv

atur

e of m

axim

um v

alue

s

times10minus4

(e)

Figure 12 Continued

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 9: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

Shock and Vibration 9

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus140

(a)

0 50 100 150 200Frequency (Hzsample)

250

Pow

erfr

eque

ncy

(dB

Hz)

minus240

minus230

minus220

minus210

minus200

minus190

minus180

minus170

minus160

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0015

001

0005

0

minus0005

minus001

minus0015

Damage Damage

(c)

64 108 1412 16Node number

PSE

curv

atur

e

004

002

0

minus01

minus012

minus008

minus006

minus004

minus002

Damage

(d)

Figure 9 PSE and the curvature curves of noise-free structure (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

display more complicated relations than Figures 9(a) and9(b)The first resonance frequency of 16Hzsample coincideswith the PSE curve without the external noise The curvaturecurves represent the explicit curvature variations at elements8 and 30 of beam 1 in Figure 10(c) and element 5 of beam 2in Figure 10(d) It is observed that the proposed method canbe utilized in detecting beam structure damage despite theexistence of external noise

4 Beam Test

A beam test was performed to detect the damage of a simplysupported beam as shown in Figure 11 The gross crosssection of the beam is 119887 times 119905 = 100mm times 11mm and thenet length of the span between end supports is 1200mmThedamage is located at 350mm from the left support whichis between nodes 2 and 3 The damaged cross section was

established as 119887 times 119905 = 100mm times 8mmThe eight points mea-sured by accelerometers are numbered as shown in Figure 11The beam is excited by hitting an impact hammer withsupersoft tip on the support to collect response data withinthe low frequency range The experiment was conductedusing DYTRANmodel 3055B1 uniaxial accelerometers and aminiature transducer hammer (Bruel and Kjaer model 8204)for the excitation of the system The data acquisition systemwas a DEWETRON model DEWE-43 The accelerationresponse data in the time-domain were measured by theDEWETRON The input acceleration excited by the impacthammer was not measured

Figure 12(a) represents the acceleration responses in thetime-domain at all nodes for one second after hitting Figures12(b) and 12(c) display the FFT and PSE curves at allnodes in the frequency-domain to transform the accelera-tion responses The maximum energy is revealed at 171 Hz

10 Shock and Vibration

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus120

minus130

minus140

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0008

0006

0004

0002

0

minus0006

minus0004

minus0002

minus0008

minus001

minus0012

Damage

Damage

(c)

64 108 1412 16 18Node number

PSE

curv

atur

e

006

004

002

0

minus006

minus004

minus002

minus008

Damage

(d)

Figure 10 PSE and the curvature curves containing 3 noise (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

1 2 3 64 75

Rubber packing

8

Damage

SupportAccelerometer

Impact hammer1 2 3 64 75 8

Support

Impact hammer

7 150mm

350mm1200mm1400mm

75mm 75mm

(a)

Undamaged section

Damaged section

100mm

100mm

11mm

8mm3mm

(b)

(c)

Hammer tip = supersoft

(d)Figure 11 Test beam (a) plan view (b) section (c) photo of test beam and (d) impact hammer

Shock and Vibration 11

0 05 1 15 2Time (s)

minus0015

minus001

minus0005

0

0005

001

0015

Acce

lera

tion

resp

onse

(g)

(a)

0 50 100 150 200 2500

02

04

06

08

1

12

14

16

18

Frequency (Hz)

Abso

lute

val

ues o

f acc

eler

atio

n re

spon

ses

times10minus3

(b)

Pow

erfr

eque

ncy

(dB

Hz)

0 50Frequency (Hzsample)

100 150 200 250

minus60

minus65

minus70

minus75

minus80

minus85

(c)

1 2 3 4 5 87604

06

08

1

12

14

16

18

Node number

Max

(abs

olut

e val

ues o

f acc

eler

atio

n re

spon

ses)

times10minus3

(d)

2 3 4 5 76Node number

6

4

2

0

minus2

minus4

minus6

Curv

atur

e of m

axim

um v

alue

s

times10minus4

(e)

Figure 12 Continued

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 10: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

10 Shock and Vibration

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus210

minus200

minus190

minus180

minus170

minus160

minus150

minus120

minus130

minus140

(a)

0 50 100 150 200 250Frequency (Hzsample)

Pow

erfr

eque

ncy

(dB

Hz)

minus220

minus210

minus200

minus190

minus180

minus170

minus160

minus150

(b)

0 105 2015 3025 35 40Node number

PSE

curv

atur

e

0008

0006

0004

0002

0

minus0006

minus0004

minus0002

minus0008

minus001

minus0012

Damage

Damage

(c)

64 108 1412 16 18Node number

PSE

curv

atur

e

006

004

002

0

minus006

minus004

minus002

minus008

Damage

(d)

Figure 10 PSE and the curvature curves containing 3 noise (a) PSE curves of beam 1 (b) PSE curves of beam 2 (c) PSE curvature of beam1 using the maximum PSEs at the first resonance frequency and (d) PSE curvature of beam 2 using the maximum PSEs at the first resonancefrequency

1 2 3 64 75

Rubber packing

8

Damage

SupportAccelerometer

Impact hammer1 2 3 64 75 8

Support

Impact hammer

7 150mm

350mm1200mm1400mm

75mm 75mm

(a)

Undamaged section

Damaged section

100mm

100mm

11mm

8mm3mm

(b)

(c)

Hammer tip = supersoft

(d)Figure 11 Test beam (a) plan view (b) section (c) photo of test beam and (d) impact hammer

Shock and Vibration 11

0 05 1 15 2Time (s)

minus0015

minus001

minus0005

0

0005

001

0015

Acce

lera

tion

resp

onse

(g)

(a)

0 50 100 150 200 2500

02

04

06

08

1

12

14

16

18

Frequency (Hz)

Abso

lute

val

ues o

f acc

eler

atio

n re

spon

ses

times10minus3

(b)

Pow

erfr

eque

ncy

(dB

Hz)

0 50Frequency (Hzsample)

100 150 200 250

minus60

minus65

minus70

minus75

minus80

minus85

(c)

1 2 3 4 5 87604

06

08

1

12

14

16

18

Node number

Max

(abs

olut

e val

ues o

f acc

eler

atio

n re

spon

ses)

times10minus3

(d)

2 3 4 5 76Node number

6

4

2

0

minus2

minus4

minus6

Curv

atur

e of m

axim

um v

alue

s

times10minus4

(e)

Figure 12 Continued

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 11: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

Shock and Vibration 11

0 05 1 15 2Time (s)

minus0015

minus001

minus0005

0

0005

001

0015

Acce

lera

tion

resp

onse

(g)

(a)

0 50 100 150 200 2500

02

04

06

08

1

12

14

16

18

Frequency (Hz)

Abso

lute

val

ues o

f acc

eler

atio

n re

spon

ses

times10minus3

(b)

Pow

erfr

eque

ncy

(dB

Hz)

0 50Frequency (Hzsample)

100 150 200 250

minus60

minus65

minus70

minus75

minus80

minus85

(c)

1 2 3 4 5 87604

06

08

1

12

14

16

18

Node number

Max

(abs

olut

e val

ues o

f acc

eler

atio

n re

spon

ses)

times10minus3

(d)

2 3 4 5 76Node number

6

4

2

0

minus2

minus4

minus6

Curv

atur

e of m

axim

um v

alue

s

times10minus4

(e)

Figure 12 Continued

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 12: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

12 Shock and Vibration

1 2 3 4 5 6 7 8Node number

Pow

erfr

eque

ncy

(dB

Hz)

minus60

minus62

minus64

minus66

minus70

minus68

minus72

(f)

2 3 4 5 6 7Node number

Curv

atur

e of p

ower

freq

uenc

y

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

minus7

(g)

Figure 12 Experimental results (a) acceleration responses in time-domain (b) absolute values of FFT in frequency-domain (c) PSE curves(d) maximum values of FFT nearby the first resonance frequency (e) their curvature (f) curve of maximum PSE and (g) its curvature

Figures 12(d) and 12(e) indicate the maximum values of FFTat all nodes corresponding to the first resonance frequencyand their curvature respectively Observing the abruptchange in the curve taken from themaximum absolute valuesof the FFT the damage can be detected by the response curveitself only unlike the results of the numerical applicationHowever the curvature curve more clearly indicates thedamage region near node 3 despite the existence of externalnoise Figures 12(f) and 12(g) represent the PSE curve andits curvature respectively using the data samples with 50sample overlap 055Hz frequency resolution and the rectan-gular window function The plots are similarly interpreted asthe results of using the FFT The numerical and beam testsindicate that the PSE curvature method can be effectivelyutilized for detecting damage without the baseline or otherinput data despite the existence of external noise

5 Conclusions

Practical damage detection was performed using output-only response data without baseline data from the intactstate and without other input data This study proposed adamage detection method to trace damage by the curvatureof the PSE using the Welch method to reduce the noiseeffect The validity of the proposed method was evaluatedaccording to the rectangular Hamming Bartlett Hannand Blackman window functions with the Welch methodoverlapping of 40 and 50 and frequency resolution of05Hz and 10Hz through a numerical application and abeam test The proposed method can be effectively utilizedfor detecting damagewithout the baseline or other input datadespite the existence of external noise

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported byBasic ScienceResearchProgramthrough the National Research Foundation of Korea (NRF)funded by the Ministry of Education (2013R1A1A2057431)

References

[1] J Cattarius and D J Inman ldquoTime domain analysis for damagedetection in smart structuresrdquo Mechanical Systems and SignalProcessing vol 11 no 3 pp 409ndash423 1997

[2] L Majumder and C S Manohar ldquoA time-domain approach fordamage detection in beam structures using vibration data witha moving oscillator as an excitation sourcerdquo Journal of Soundand Vibration vol 268 no 4 pp 699ndash716 2003

[3] S Sandesh and K Shankar ldquoDamage identification of a thinplate in the time-domain with substructuringmdashan applicationof inverse problemrdquo International Journal of Applied Science andEngineering vol 7 pp 79ndash93 2009

[4] Y Lu and F Gao ldquoA novel time-domain auto-regressive modelfor structural damage diagnosisrdquo Journal of Sound and Vibra-tion vol 283 no 3ndash5 pp 1031ndash1049 2005

[5] R Yao and S N Pakzad ldquoStructural damage detection usingmultivariate time series analysisrdquo in Proceedings of the SEMIMAC 30th Conference 2012

[6] S Liberatore andG P Carman ldquoPower spectral density analysisfor damage identification and locationrdquo Journal of Sound andVibration vol 274 no 3ndash5 pp 761ndash776 2004

[7] S Beskhyroun TOshima SMikami Y Tsubota andT TakedaldquoDamage identification of steel structures based on changes inthe curvature of power spectral densityrdquo in Proceedings of the2nd International Conference on Structural HealthMonitoring ofIntelligent Infrastructure Shenzhen China November 2005

[8] W L Bayissa and N Haritos ldquoDamage identification in plate-like structures using bending moment response power spectraldensityrdquo Structural Health Monitoring vol 6 no 1 pp 5ndash242007

[9] Y Zhou R Perera and E Sevillano ldquoDamage identificationfrom power spectrum density transmissibilityrdquo in Proceedings

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 13: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

Shock and Vibration 13

of the 6th European Workshop on Structural Health MonitoringDresden Germany July 2012

[10] W H Chen C Y Ding B Q He Z R Lu and J KLiu ldquoDamage identification based on power spectral densitysensitivity analysis of structural responsesrdquo Advanced MaterialsResearch vol 919-921 pp 45ndash50 2014

[11] Z D Zheng Z R Lu W H Chen and J K Liu ldquoStructuraldamage identification based on power spectral density sensitiv-ity analysis of dynamic responsesrdquo Computers amp Structures vol146 pp 176ndash184 2014

[12] P Welch ldquoThe use of fast Fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[13] K J Vamvoudakis-Stefanou J S Sakellarlou and S D FassoisldquoOutput-only statistical time series methods for structuralhealth monitoring a comparative studyrdquo in Proceedings ofthe 7th European Workshop on Structural Health Monitoring(EWSHM rsquo14) Nantes France July 2014

[14] F P Kopsaftopoulos and S D Fassois ldquoExperimental assessmenof vibration-based time series methods for structural healthmonitoringrdquo in Proceedings of the 4th European Workshop onStructural Health Monitoring Cracow Poland 2008

[15] F P Kopsaftopoulos and S D Fassois ldquoScalar and vector timeseries methods for vibration based damage diagnosis in a scaleaircraft skeleton structurerdquo Journal of Theoretical and AppliedMechanics vol 49 no 3 pp 727ndash756 2011

[16] H R Gupta S Batan and R Mehra ldquoPower spectrum estima-tion usingWelchmethod for variouswindow techniquesrdquo Inter-national Journal of Scientific Research EngineeringampTechnologyvol 2 no 6 pp 389ndash392 2013

[17] V D Zimin and D C Zimmerman ldquoStructural damagedetection using time domain periodogram analysisrdquo StructuralHealth Monitoring vol 8 no 2 pp 125ndash135 2009

[18] R K Giles and B F Spencer Jr ldquoHierarchical PSD damagedetection methods for smart sensor networksrdquo in Proceedingsof the World Forum on Smart Materials and Smart StructuresTechnology (SMSST rsquo07) Chongqing China May 2007

[19] S-E Fang and R Perera ldquoPower mode shapes for early damagedetection in linear structuresrdquo Journal of Sound and Vibrationvol 324 no 1-2 pp 40ndash56 2009

[20] M G Masciotta L F Ramos P B Lourenco M Vastaand G De Roeck ldquoA spectrum-driven damage identificationtechnique application and validation through the numericalsimulation of the Z24 Bridgerdquo Mechanical Systems and SignalProcessing 2015

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 14: Research Article Structural Damage Detection by Power ...downloads.hindawi.com/journals/sv/2016/8761249.pdf · Research Article Structural Damage Detection by Power Spectral Density

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of