research article damage detection and quantification using

Research ArticleDamage Detection and Quantification Using TransmissibilityCoherence Analysis

Yun-Lai Zhou1 E Figueiredo2 N Maia3 and R Perera1

1Department of Mechanical Engineering Technical University of Madrid Jose Gutierrez Abascal 2 28006 Madrid Spain2Faculdade de Engenharia da Universidade Lusofona Campo Grande 376 1749-024 Lisbon Portugal3LAETA IDMEC Instituto Superior Tecnico University of Lisbon Avenida Rovisco Pais 1049-001 Lisbon Portugal

Correspondence should be addressed to Yun-Lai Zhou yunlaizhoualumnosupmes and R Perera ricardopereraupmes

Received 23 November 2014 Revised 10 March 2015 Accepted 15 March 2015

Academic Editor Peng Chen

Copyright copy 2015 Yun-Lai Zhou et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A new transmissibility-based damage detection and quantification approach is proposed Based on the operational modal analysisthe transmissibility is extracted from system responses and transmissibility coherence is defined and analyzed Afterwards asensitive-damage indicator is defined in order to detect and identify the severity of damage and compared with an indicatordeveloped by other authors The proposed approach is validated on data from a physics-based numerical model as well asexperimental data from a three-story aluminum frame structure For both numerical simulation and experiment the results ofthe new indicator reveal a better performance than coherence measure proposed in Rizos et al 2008 Rizos et al 2002 Fassois andSakellariou 2007 especially when nonlinearity occurs which might be further used in real engineering The main contribution ofthis study is the construction of the relation between transmissibility coherence and frequency response function coherence andthe construction of an effective indicator based on the transmissibility modal assurance criteria for damage (especially for minornonlinearity) detection as well as quantification

1 Introduction

Structural health monitoring (SHM) has experienced a hugedevelopment from more than four decades ago since therehabilitation cost of oil pipes bridges tall buildings and soon rapidly increased In the last two decades a lot of SHMmethods have been developed based on both physics and datamodels For instance one systematic SHM solution for bridgemaintenance is presented in [1] where both kinds of modelsare combined to identify damage Other SHM solutions canbe found in [2 3]

For large and complex structures the use of accelerome-ters has made possible the development of vibration-basedmethods to analyze structures Modal testing is the mostcommon by carrying out the experimental modal analysis(EMA) of a structure some modal parameters such asfrequency mass and damping can be extracted and afrequency response function (FRF) can be obtained Thiswill make possible the construction of different damageindicators Modal testing is also conducted on structures

in real operational conditions within which the excitationwill be very difficult or even impossible to be measuredoperational modal analysis (OMA) uses the response signalsonly to extract the structural dynamic parameters in orderto assess the structural states In addition for long-termoperating structures like oil pipes turbines or bridgesstatistical methods are also developed for real-time onlineSHM systems

In real engineering motivated on solving the difficultyin capturing the excitation in the middle of 1980s trans-missibility (or direct transmissibility) was raised Instead ofconsidering the input and output signals of the structuralsystem transmissibility only pays attention to the outputsthat is it concentrates on the interrelation of two outputsof the structure in order to create a connection withthe structural dynamic characteristic Afterwards a lot ofresearchers developed it for parameter identification [4]damage detection as well as quantification [5] uncertaintyanalysis [6] and responseexcitation (ie force) reconstruc-tion [7] and so on In [4] relative mode shape is extracted

Hindawi Publishing CorporationShock and VibrationVolume 2015 Article ID 290714 16 pageshttpdxdoiorg1011552015290714

2 Shock and Vibration

from the transmissibility in the natural resonant frequencieswhich avoids the use of FRF in mode shape estimationIn [5] a method of taking advantage of response vectorassurance criterion (RVAC) [8] was proposed replacing theFRF by transmissibility function in the indicator RVACand detection and relative damage quantification indicator(DRQ) [9] which is the average value of RVAC along thefrequency domain The RVAC is a simplified form of FDACwhich was defined by Heylen et al [8] The key idea is to usethe sum of all coordinates FRF before and after damage of allloading conditions in the form of modal assurance criteria

However the detection of damage at an early stage is stilla very difficult and challenging task therefore the proposalof new indicators based on dynamic responses that maybe sensitive enough to minor damage is very important Inthis sense the coherence as a function dependent on thefrequency and able to analyze the spatial correlation betweentwo signals [10 11] might be potentially a good starting pointto develop sensitive damage indicators

The coherence function formally defined by Wiener[12 13] has been extensively studied and used especiallyafter the development of the Fourier transform in a lot ofresearch fields with extensions to the most modern waveletcoherence and partial directed coherence neurology mostlyin electroencephalography (EEG) studies [14ndash16] like EEGmicrostates detection in insight and calm meditation [14]Coherence is also used in skin blood oscillations analysis inhuman [17] nerve fiber layer thickness quantification [18]

In another aspect spatial coherencemeasure is also devel-oped for signal enhancement [19] by designing coherence-based post filters In recent years coherence function hasbeen used in mechanical engineering for damage identi-fication namely detection type and quantification [20ndash24] In [20] a coherence algorithm is proposed for damagetype recognition and damage localization for large flexiblestructures with a nine-bay truss example the key idea isto construct a connection between coherence and trans-fer function and the transfer function parameter changeis extracted for damage detection In [21] local temporalcoherence is developed and extended to time-varying processwith the basic coherence conception from the cross corre-lation defined in [25] and the corresponding peak value isdefined as peak coherence creating a connection with thetemperature and introduced damage change that is the peakcoherence for temperaturedamage change is somewhat afunction of time In addition the peak performs well in dis-tinguishing environmental change and damage In [22 23]coherence is integrated in the frequency domain and set as anindicator-coherence measure as a sensitive enough indicatorfor quantifying the skin damage and assessing restorationquality In [24] coherence measure based method as atime series method is developed for fault detection andidentification in vibrating structures

In this paper coherence analysis of transmissibility isperformed and from it an effective indicator for damageespecially nonlinearity is proposed and compared with thecoherence measure raised in [22] In order to test thefeasibility of the proposed approach numerical simulationof a laboratory structure is carried out and additionally

experimental measurements on a three-story aluminumstructure are used to check the applicability of the proposedindicator

2 Transmissibility Based Coherence

As described in [2] SHM is essentially a statistical patternrecognition problem It can be described as a four-stageprocess

(1) operational evaluation

(2) data acquisition Fusion and Cleansing

(3) feature extraction and information condensation

(4) statistical model development for feature discrimina-tion

As for vibration-based SHM the core idea is to find asensitive feature able to discriminate a damaged structurewhen compared to the baseline structure (healthy state)therefore the damage detection conclusion can be drawn outwith choosing a threshold of the change before and afterdamage considering the influence of operational variety Asdescribed in the introduction lots of approaches featuresand measurement methodologies have been used in the past[2 3 26 27]

21 Applicability of Coherence in Damage Detection As com-mented in the introduction coherence has been used inmanyapplications It is useful to examine the correlation betweentwo frequency signals in a similar way to the correlationcoefficient in frequency More details can be found in [28]

Coherence as a complex measure is estimated by divid-ing the square of the cross-spectral density between twosignals by the product of the autospectral densities of bothsignals Consequently it will be sensitive to both changes inpower and phase relationships in one of the two signals [29]

The magnitude-squared coherence for the bivariate timeseries enables us to identify significant frequency-domaincorrelation between the two time series [30] For the purposeof preventing obtaining an estimate of magnitude-squaredcoherence to be identically 1 for all frequencies an averagedmagnitude-squared coherence estimator has to be used BothWelchrsquos overlapped segment averaging (WOSA) and multi-taper techniques are appropriate [30] In this study WOSAis utilized for the coherence estimate A detailed discussionof several seemingly disparate nonparametric magnitudesquared coherence estimation methods including Welchrsquosaveraged periodogram the minimum variance distortionlessresponse (MVDR) and the canonical correlation analysis(CCA) can be found in [31]

For SHM purposes the most important task is to finda structural feature sensitive to the occurrence of damageMethodologies involving coherence have been developedin the past decades [20ndash24 32] As proved in [22ndash24] acoherence based damage indicator can be used in damagedetection The premise behind this is that the coherence willdecrease as nonlinearity increases

Shock and Vibration 3

22 Transmissibility Considering a linear multiple-degree-of-freedom system the dynamic equilibrium equation can bewritten by thewell-known second order differential equation

119872 (119905) + 119862 (119905) + 119870119909 (119905) = 119891 (119905) (1)

where 119872 119862 and 119870 are the mass damping and stiffnessmatrices of the system respectively 119891(119905) is the input forcevector and 119909(119905) contains the responses of each degree-of-freedom of the system

Herein for a harmonic applied force at a given coordinatethe transmissibility between point 119894 and a reference point 119895can be defined as

119879(119894119895) =119883119894 (120596)

119883119895 (120596) (2)

where 119883119894 and 119883119895 are the complex amplitudes of the systemresponses 119909119894(119905) and 119909119895(119905) respectively and 120596 is the frequency[4]

In order to calculate the transmissibility no matter inreal engineering or experiment analysis apart from directextracting from the two responses it can be derived in severalways [5] for instance using the FRFs

119879(119894119895) =119883119894 (120596) 119865119897 (120596)

119883119895 (120596) 119865119897 (120596)=

119867(119894119897) (120596)

119867(119895119897) (120596) (3)

where 119897 is the excitation point and119867 represents the FRF Notethat herein the transmissibility is a norm that estimates thestructural dynamic responses

23 Transmissibility Coherence Given the structural systemdescribed above with one single excitation the FRF of points119894 to 119897 can be calculated by two forms in estimation that is

1198671 (120596) =119878(119894119897) (120596)

119878(119897119897) (120596)

1198672 (120596) =119878(119894119894) (120596)

119878(119897119894) (120596)

(4)

where 119878 represents the auto- and cross-spectrum for thetwo points Correspondingly the coherence function (ormagnitude squared coherence function) is indicated as [3334]

1205742=1198671 (120596)

1198672 (120596)=119878(119894119897) (120596)

119878(119897119897) (120596)

119878(119897119894) (120596)

119878(119894119894) (120596)

=119878(119894119897) (120596)

119878(119894119894) (120596)

119878lowast(119894119897) (120596)

119878(119897119897) (120596)=

1003816100381610038161003816119878(119894119897) (120596)1003816100381610038161003816

2

119878(119894119894) (120596) 119878(119897119897) (120596)

(5)

By analogy with (5) the transmissibility coherence (TC)can be defined from (3) as follows

1205742

TC =

1198791(119894119895) (120596)

1198792(119894119895) (120596)=

1198671(119894119897) (120596) 1198671(119895119897) (120596)

1198672(119894119897) (120596) 1198672(119895119897) (120596)

=1198671(119894119897) (120596)

1198672(119894119897) (120596)

1198672(119895119897) (120596)

1198671(119895119897) (120596)=

1205742(119894119897)

1205742(119895119897)

(6)

Herein above all transmissibility coherence means themagnitude squared coherence secondly from the equationabove one can see that the TC can be calculated directlyfrom the coherence of corresponding FRFs which gives away for estimating the transmissibility coherence in labo-ratory experiments analysis Thirdly note that herein theTC as an estimation indicator for transmissibility that iscoherence for two outputs is an indicator revealing thecoherencecorrelation between two outputs with consideringthe excitation point

On the other hand if direct transmissibility is directlyestimated using two outputs that is not taking the FRFs intoaccount referring to the conception of coherence [12 13 34]TC can be also derived solely by using the auto- and cross-spectrum of the two responses signals

1198791(119894119895) =119883119894 (120596)

119883119895 (120596)

119883119895 (120596)

119883119895 (120596)=

119878(119894119895) (120596)

119878(119895119895) (120596)

1198792(119894119895) =119883119894 (120596)

119883119895 (120596)

119883119894 (120596)

119883119894 (120596)=

119878(119894119894) (120596)

119878(119895119894) (120596)

(7)

From (7) TC will be exp as

1205742

TC =

1198791(119894119895) (120596)

1198792(119894119895) (120596)=

119878(119894119895) (120596) 119878(119895119895) (120596)

119878(119894119894) (120596) 119878(119895119894) (120596)

=

119878(119894119895) (120596) 119878(119895119894) (120596)

119878(119895119895) (120596) 119878(119894119894) (120596)=

10038161003816100381610038161003816119878(119894119895) (120596)

10038161003816100381610038161003816

2

119878(119894119894) (120596) 119878(119895119895) (120596)

(8)

Fourier transform in (8) gives the frequency distributionof TC For the TC estimation Welch method [35] andminimum variance distortionless response (MVDR) [36]method are commonly used

As the coherence is a squared magnitude TC is higherthan zero Comparing (6) and (8) one can observe that TCcan be estimated in two ways from the coherence of FRF likein (6) and from direct estimation as described in (8) Similarto FRF coherence the first function of TC is for checkingwhether the experiment is well conducted And basically TCreveals the coherence of two outputs that is it indicates theinterrelation of the dynamic characteristics of two outputsTherefore it is assumed that when the damage occurs in astructure TC as a sensitive indicator will change comparedto the baseline of the structural system and so it might beused to detect structural damage

3 Damage Identification Based on TC

31 Damage Indicators By using a similar approach to [22ndash24] a TC damage indicator is defined here based on theaccumulation of TC along frequency domain as follows

ATC = int

119891max

119891min

TC119889119891 (9)

where the interval [119891min 119891max] is the frequency bandwidthof interest for our problem As TC gt 0 then ATC gt 0


y5

y4

y3

y2

m4

c4

k4m3

c3

k3m2

c2

k2m1

c1

k1

y1F (excitation)

(a)

0 10 20

minus50

0

50

Time (s)

Exci

tatio

n fo

rce (

N)

(b)

Figure 1 (a) Shear-building model of a three-story structure (b) The excitation force

Compared to the coherence measure in [22] the basic ideais the same being the main difference that ATC is computedfrom the coherence between two output responses instead ofexcitation-response

Additionally another indicator has been defined basedon the MAC criterion [37ndash40] For its application a vectoris defined grouping the values of TC for each spectrum lineConsidering the same dimension for each TC set a trans-missibility modal assurance criterion (TMAC) is defined asfollows

TMAC

=

100381610038161003816100381610038161003816((TC (119908))

119889)119879(TC (119908))

119906100381610038161003816100381610038161003816

2

(((TC (119908))119889)119879(TC (119908))

119889) (((TC (119908))

119906)119879(TC (119908))

119906)

(10)

where ( )119889 means the vector under damage scenario ( )119906

means the vector under healthy condition and ( )119879means thetransposed form of the vector

Theoretically speaking for each damage scenarioTMAC isin [0 1] If the TMAC is ldquo1rdquo the structure is totallyundamaged if the TMAC is very close to ldquo1rdquo it means that thestructure is confidently undamaged and when the TMACvalue decreases it means that damage or deterioration isoccurring in the structure as the TMAC gets close to ldquo0rdquoit means that the damage severity increased Finally if theTMAC is ldquo0rdquo the structure is severely damaged

In conclusion two different damage indicators based onTC have been proposed to detect structural damage Thedamage quantification indicators ATC and TMAC intendto extract a global indicator which might be monotonicallyrelated to the structural damage Basically the indicatorincreases as the severity of damage or nonlinearity increases

Due to this fundamental idea the ATC performs by accumu-lating all the coherence value to eachmeasurement of damagescenarios which will reveal the whole interrelation of the twooutputs The TMAC performs using the assurance criterionprincipals

32 Damage Identification Scheme Damage identificationscheme will be conducted as follows

Step 1 (response measurement) In this step the vibrationdynamic responses of the studied structure will be captured

Step 2 (transmissibility extraction) In this step transmissi-bility will be estimated via (3)

Step 3 (coherence estimation) Coherence will be estimatedand we determine whether the experiment is well conductedif not Step 1 will be redone for a new measurement

Step 4 (damage feature calculation) Regarding the estimatedcoherence from Step 3 damage sensitive features are calcu-lated and analyzed for detecting the potential damage

4 Numerical Simulation

41 Model Description For the purpose of evaluating the fea-sibility of the proposed approach a physics-based numericalmodel is developed The test structure is modeled as four-lumped masses at the floors including the base that slides onrails as shown in Figure 1(a) The excitation point is at thebase as shown in Figure 1(a) the responses (ldquo1199101rdquo ldquo1199102rdquo ldquo1199103rdquoldquo1199104rdquo and ldquo1199105rdquo) are measured at each floor Figure 1(b) showsa sample from a random excitation [40]

In this case damage is introduced by increasing themass at the base and first floor as well as stiffness reduc-tion at the columns as listed in Table 1 Random noise is


20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

3) (

dB)

D0D1

D5D6

(a)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

3) (

dB)

D0wD1w

D5wD6w

(b)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

2) (

dB)

D0D1

D5D6

(c)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

2) (

dB)

D0wD1w

D5wD6w

(d)

Figure 2 119879 (5 3) and 119879 (5 2) for damage scenarios D0 D1 D5 and D6 (a) without random noise (b) with 5 random noise (c) withoutrandom noise and (d) with 5 random noise

introduced to the system for comparison in analysis The875 reduction in stiffness was chosen in order to beconsistent with the experimental procedure developed in[40]

42 Transmissibility TC and FRF Coherence Comparison

421 Transmissibility and TC Comparison Considering thepersonal experience in transmissibility work one can choosetransmissibility between different nodes however resultsmight be quite different And therefore to choose trans-missibility is a difficult mission which will greatly influencethe potential results Here in this study of the simplestructure all the transmissibilities can be plotted and later

analyzed however not all the transmissibilities will performvery well Some representative transmissibilities and relatedindicators are analyzed in this study according to the engineerexperience Figures 2(a) and 2(b) show the transmissibilitybetween nodes 5 and 3 and 5 and 2 119879 (5 3) and 119879 (5 2)for damage scenarios D0 D1 D5 and D6 without and with5 random noise respectively From all Figures 2(a)ndash2(d)little difference between D0 and D1 can be observed whichsuggests that ldquoadding 12 Kg to the baserdquo has very small effectto the dynamic responses FromFigures 2(a) and 2(c) one canobserve small differences in the second half of the frequencydomain and two peak shifts can be found in the first half ofthe frequency domain which might be used for predictingdamage


20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0D1

D5D6

(a)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0wD1w

D5wD6w

(b)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0D1

D5D6

(c)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0wD1w

D5wD6w

(d)

Figure 3 TC (5 3) and TC (5 2) for damage scenarios D0 D1 D5 and D6 (a) without random noise (b) with 5 random noise (c) withoutrandom noise and (d) with 5 random noise

Table 1 Damage scenario

Damage scenario Case descriptionD0 Baseline (undamaged condition)D1 Add mass 12 kg at the baseD2 Add mass 12 kg at the first floorD3 50 stiffness reduction in 1198962

D4 875 stiffness reduction in 1198962





In Figures 2(b) and 2(d) it is clear that the random noiseintroduced some influence into the transmissibility espe-cially visible in the high frequency domain (gt80Hz) whichis heavily affected by the noise Furthermore comparingFigures 2(c) and 2(d) it can be observed that the peak value ofD6w at 40Hz was reduced by the random noise effect whichmight add challenge in the process of damage detection

Figures 3(a) 3(b) 3(c) and 3(d) plot the transmissibilitycoherence TC (5 3) and TC (5 2) for damage scenariosD0 D1 D5 and D6 without and with 5 random noiserespectively The TC (5 3) and TC (5 2) overlap in all thefrequencies to the case without random noise and overlapin most of the frequencies to the case with 5 randomnoise between D0 and D1 This confirms the conclusion in


FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(c)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(d)Figure 4 FRF coherence (5 1) and FRF coherence (3 1) for damage scenarios D0 D1 D5 and D6 (a) without random noise (b) with 5random noise (c) without random noise and (d) with 5 random noise

the aforementioned discussion in 119879 (5 3) and 119879 (5 2) thatldquoadding 12 Kg to the baserdquo contributes little to the dynamicresponses

FromFigures 3(a) and 3(c) one can find that TC (5 2) hastwo peaks for each scenario while TC (5 3) only has one peakfor D5 and D6 while it has two peaks for D0 and D1 Thenfrom D0 to D5 and D6 the peaks shift toward left side thatis the corresponding frequencies decrease The same patterncan be observed in Figures 3(b) and 3(d) when the data aresmearedwith noise As TC is for estimating the two outputs ofa structural system change will be introduced to the dynamicoutputs when damage occurs which will later cause effect toTC like frequency shift And therefore from this aspect TCmight be used to detect damage

From Figures 3(b) and 3(d) another phenomenon canbe observed as noise influences a lot the TC this might be

used to check whether the experiment is well conductedwhich shares the same function of FRF coherence in realengineering but hasmore potentiality as excitation not alwayscan bemeasured If the experiment is well conducted withoutbeing highly influenced by the environmental variety likenoise then nonlinearity occurrence or novelty existencemight be taken into account

422 TC and FRFCoherence Comparison For the purpose ofcomparing with TC discussed above and due to the reasonthat TC is for two outputs and FRF coherence is for theone input and one output herein some representative FRFcoherences are selected according to the engineer experienceFigures 4(a) 4(b) 4(c) and 4(d) show the FRF coherence(5 1) and FRF coherence (3 1) without and with 5 randomnoise respectively


TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)

Figure 5 TC (3 2) for damage scenarios D0 D5 and D6 (a) without noise and (b) with 5 random noise

To themass influence fromFigures 4(a) and 4(c) one canfind that the difference betweenD0 andD1 is very little whichconfirms the analysis before in 119879 and TC

To the stiffness reduction influence to the without-noisecases that is in Figures 4(a) and 4(c) it can be also found thatpeak frequency shifts fromD0 to D5 and D6 that is the peakfrequency difference before and after damage is clear whichsuggests that it might be used as damage-sensitive feature Onthe other hand in the case with random noise Figures 4(b)and 4(d) show that the differences are apparently higher forthe FRF coherence (5 1) than FRF coherence (3 1) Thus itindicates that if the FRF coherence is not well chosen then itmight be hard to detect damage

Additionally one can also notice that noise highly affectsthe coherence in the high frequency domain which inputshigher power of noise in that frequency domain In realsituations the result presented in Figures 4(b) and 4(d)suggests that the experiment is badly conducted and it shouldbe reconducted as normally 09 is the threshold for coherenceanalysis And if in the frequency band of interest lots of valuesare lower than 09 it means that the experiment might bewrongly done or badly influenced by noise If the experimentis well conducted it might mean that nonlinearity occurs ornovelty happens This conclusion is similar to the discussionof TC aforementioned

With regard to Figure 4(d) and from Figure 5 one canfind that if theTC is notwell chosen it will be also challengingin detecting with the frequency shift like in Figures 5(a)and 5(b) This also confirms the same idea of FRF coherencediscussed above

Finally from the discussion above one might concludethe following

(a) The comparison between Figures 3 and 4 indicatesthat both the FRF coherence and the TC have theability to unveil differences when damage is presentin the structure if they are well chosen

(b) ldquoAdding 12 Kgrdquo to the base did quite little influenceto the dynamic responses according to the 119879 TC andFRF coherence analysis

(c) For both TC and FRF coherence peak shifts mightbe used for detecting damage as the TC (5 3) andTC (5 2) and FRF coherence (5 1) perform well indifferentiating the damage cases from the baselineHowever if TC and FRF coherence are not wellchosen it will be challenging in detecting damage viathe peak frequency shift

(d) As TC has the same ability as FRF coherence inchecking whether the experiment is well conductedthen its output-only characteristic might be consid-ered better than FRF coherence in the data acquisitionaspect as the excitation in real engineering is notalways possible to be measured

43 Damage Identification Procedure For the indicatorsdescribed in Section 31 herein Table 2 summarizes the ATC(5 3) from damage scenarios D0 to D8 without and with 5random noise

For the case with addingmass to the base or the first floorfrom Table 2 from D0 to D1 and D2 it can be observed thatATC (5 3) decreases as the mass is added into the base anddecreases continually as the mass is moved from the base tothe first floor in all the cases without noise and with randomnoise

For the case of stiffness reduction from Table 2 one canobserve that ATC (5 3) does not hold the same rule fromD4 to D8 to all the integration types values more than ldquo1rdquoexist that is it will be challenging in drawing out a conclusionfor detecting damage or it is hard to find a clear rule forpredicting damage This means that ATC might not work inlinear part The discussion about ATC in nonlinearity partwill be addressed in the later experiment result discussion


Table 2 ATC (5 3) for damage scenarios D0 to D8

Damage scenarioATC (5 3)

[0 80] (Hz) [20 80] (Hz) [40 80] (Hz) [40 140] (Hz)Noise free 5 noise Noise free 5 noise Noise free 5 noise Noise free 5 noise

D0 10000 10000 10000 10000 10000 10000 10000 10000D1 09989 09802 10000 09807 09994 09627 09998 09491D2 09990 09613 09993 09643 09986 09474 09995 09322D3 09927 09204 09995 09026 09976 08334 09993 08192D4 10159 07384 10081 07091 10058 05854 10026 05798D5 09739 09287 10149 09431 10027 08124 10010 07998D6 09888 07313 10134 07024 09975 06208 09959 06172D7 09716 09274 10052 09255 09989 08487 09998 08373D8 09959 08350 10102 08248 10069 06853 10030 06872

D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 3

)

Without noiseWith 5 noise

(a)


D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 2

)

(b)

Figure 6 (a) TMAC (5 3) for damage scenarios D0ndashD8 (b) TMAC (5 2) for damage scenarios D0ndashD8

Finally TMAC (5 3) and TMAC (5 2) are plotted inFigures 6(a) and 6(b) respectively For the mass adding typefrom D0 to D1 and D2 one can observe that in both TMAC(5 3) and TMAC (5 2) the TMAC varies insignificantlywhich need to be identified by graphical amplification Forthe stiffness reduction type the TMAC (5 3) and TMAC (52) vary clearly for each column stiffness reduction like fromD3 to D4 fromD5 to D6 and fromD7 to D8 respectively Inconclusion these observations suggest that TMAC might beused for relative damage quantification

5 Experimental Verification

For testing the applicability of the proposed methodologyin complex structures a three-story building structure [41]testing data from the Los Alamos National Laboratory isused As shown in Figure 7 for each floor four aluminumcolumns (177times25times06 cm3) are connected with the top andbottom aluminumplates (305times305times25 cm3)The structureperforms as a four-degree-of-freedom (DOF) system Bolt

joints are used to assemble each connection between columnsand plates In addition the structure slides on rails that allowmovement only in the 119909-direction A center column (150 times25times25 cm3) is suspended from the top floorThis column isused as a source of damage that induces nonlinear behaviorwhen it contacts a bumper mounted on the next floor Theposition of the bumper can be adjusted to vary the extent ofimpacting that occurs during a particular excitation level

An electrodynamic shaker provides a lateral excitationto the base floor along the centerline of the structure Thestructure and shaker are mounted together on an aluminumbase plate (762 times 305 times 25 cm3) and the entire system restson rigid foam The foam is intended to minimize extraneoussources of unmeasured excitation from being introducedthrough the base of the system A load cell (Channel 1)was attached at the end of a stinger to measure the inputforce from the shaker to the structure Four accelerometers(Channels 2ndash5) with nominal sensitivities of 1000mVg wereattached at the centerline of each floor on the opposite sidefrom the excitation source to measure the system response


177

177

177

3rd floor

2nd floor

1st floor

BumperColumn

Base

A

A

B

B

C

C

D

D

1 1

2 2

3 3

x

z

y

1745Load cell

(Channel 1)

Load cell(Channel 1)

Baseplate

Shaker

Accelerometer (Channel 5)





305

305

Direction of shakingXZ

Y

Figure 7 Schematic representation of the three-story building structure (all dimensions are in cm)

Table 3 Structural state condition

Label State condition Case descriptionState 1 Undamaged Baseline conditionState 2 Undamaged Added mass (12 Kg) at the baseState 3 Undamaged Added mass (12 Kg) at the first floorState 4 Undamaged Stiffness reduction in column 1BDState 5 Undamaged Stiffness reduction in columns 1AD and 1BDState 6 Undamaged Stiffness reduction in column 2BDState 7 Undamaged Stiffness reduction in columns 2AD and 2 BDState 8 Undamaged Stiffness reduction in column 3BDState 9 Undamaged Stiffness reduction in columns 3 AD and 3 BDState 10 Damaged Gap (02mm)State 11 Damaged Gap (015mm)State 12 Damaged Gap (013mm)State 13 Damaged Gap (010mm)State 14 Damaged Gap (005mm)State 15 Damaged Gap (02mm) and mass (12 Kg) at the baseState 16 Damaged Gap (02mm) and mass (12 Kg) on the 1st floorState 17 Damaged Gap (01mm) and mass (12 Kg) on the 1st floor

Force and acceleration time-series from 17 different struc-tural state conditions were collected as given in Table 3 Forinstance ldquoState 4rdquo is described as ldquostiffness reduction incolumn 1BDrdquo which means that there was an 875 stiffness

reduction (corresponding to a 50 reduction in the columnthickness) in the column located between the base and firstfloor at the intersection of planes B andD For each structuralstate condition data were acquired from 50 separate tests


20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)

T (5

3) (

dB)

State number 1State number 2


(a)

T (5

2) (

dB)

20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)



(b)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1

TC (5

3)

(c)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1TC

(5 2

)

(d)Figure 8 (a) 119879 (5 3) (b) 119879 (5 2) (c) TC (5 3) and (d) TC (5 2) of measurement 1 of State numbers 1 2 6 and 7

For each test the data correspond to a set of five timeseries measured with the input force transducer and the fouraccelerometers

The structural state conditions can be categorized intofour main groups The first group is the baseline conditionThe baseline condition is the reference structural state and islabeled ldquoState 1rdquo in Table 3 The bumper and the suspendedcolumn are included in the baseline condition but the spac-ing between them was maintained in such a way that therewere no impacts during the excitation The second groupincludes the states with simulated operational and environ-mental variability Such variability often manifests itself inchanges in the stiffness or mass distribution of the structureIn order to simulate such operational and environmentalcondition changes tests were performed with different mass-loading and stiffness conditions (State numbers 2ndash9) Themass changes consisted of adding 12 kg (approximately 19

of the total mass of each floor) to the base and first floor Thestiffness changes were introduced by reducing the stiffnessof one or more of the columns by 875 This process wasexecuted by replacing the corresponded column with onethat had half the cross-sectional thickness in the direction ofshaking

Those changes were designed to introduce variabilityin the fundamental natural frequency up to approximately7 from the baseline condition which is within the rangenormally observed in real-world structures More detailsabout the test structure as well as data sets can be found inFigueiredo et al [40 41]


511 Transmissibility and TC Comparison In order to showthe advantage of TC over transmissibility a comparison


Table 4 The comparison of transmissibility TC and FRF coherence in peak change

State Indicator Frequency shift (Hz) Amplitude valuePeak 1 119868 ()lowast Peak 2 119868 ()lowast Peak 1 119868 ()lowast Peak 2 119868 ()lowast

1119879 (5 2)

4754 mdash 6992 mdash 5018 mdash 2895 mdash6 4715 minus082 6547 minus636 4658 minus717 2762 minus4597 4625 minus271 6042 minus1359 4742 minus550 2894 minus0031

TC (5 2)4758 mdash 7008 mdash 054 mdash 018 mdash

6 4707 minus107 6555 minus646 036 minus3333 021 0177 4625 minus280 6063 minus1348 026 minus5185 052 188891

FRFC (5 1)5488 mdash 7188 mdash 083 mdash 080 mdash

6 5496 015 6719 minus652 076 minus843 086 757 5469 minus035 6215 minus1354 078 minus602 089 1125lowastIncrease from the baseline ldquoState 1rdquo

between TC and transmissibility is proposed herein Severalrepresentative TC and 119879 have been chosen and studiedaccording to the engineering experienceThe extracted trans-missibility 119879 (5 3) 119879 (5 2) and transmissibility coherenceTC (5 3) TC (5 2) under State numbers 2 6 and 7 alongwith baseline (State 1) are shown in Figure 8 which werecalculated using the Welch based methods with Hanningwindow

From Figures 8(a) 8(b) 8(c) and 8(d) one can observethe following

(a) As mass 12 Kg was added into the base little changein both 119879 and TC can be observed

(b) As damage happens the peaks of 119879 (5 2) 119879 (5 3) aswell as TC (5 2) TC (5 3) shift to the left directionthat is the corresponding frequencies decrease whichconfirm the simulation results described before Thisobservation suggests that the peak frequency shift canbe used for detecting damage Herein one needs tobear in mind that the T or TC should be well chosen

(c) Apparently 119879 (5 2) performs better than 119879 (5 3)in differentiating the difference in damage The sameconclusion can be drawn with TC where TC (5 2) isbetter than TC (5 3) in distinguishing the differencein damage

(d) Apart from this one can observe that during theexperiment the noise has a very small influence asthe coherence is close to value ldquo1rdquo in most parts Thisalso can be found in the transmissibility as 119879 (5 3)and 119879 (5 2) lines are very smooth This observationon the TC is very important which suggests that itcan be used for checking whether the experiment iswell conducted

512 FRF Coherence and TC Comparison In modal analysisespecially in experimental modal analysis the excitation isacquired during the experiment process and the FRF is a veryimportant estimator for analyzing the structural dynamicscharacteristics Herein the FRF coherence (5 1) is plotted inFigure 9 for the same state conditions as in the last subsection

From Figure 9 one can also find the peak shifts between[60 80]Hz Additionally comparing Figure 9 with TC (5 3)

0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)



Figure 9 FRF coherence (5 1) of measurement 1 of State numbers1 2 6 and 7

in Figure 8(c) and TC (5 2) in Figure 8(d) it can be observedthat TC (5 2) performs better than FRF coherence (5 1) indifferentiating differences in damage as the peaks of TC (52) are more pronounced However if only concerning peakfrequency shift FRF coherence (5 1) performs better than TC(5 3) in Figure 8(c)Therefore one can conclude that bothTCand FRF coherence might be used for detecting damage viathe peak frequency shift

In order to better indicate the damage detection abilityof transmissibility TC and FRF coherence Table 4 showsthe peak amplitude decrease and frequency shifts of the twoobvious peaks in transmissibility TC and FRF coherenceFromTable 4 one can find from119879 (5 2) TC (5 2) and FRFC(5 1) that all can performwell in damage detection with peakfrequency shift and amplitude change However the secondpeak frequency change is higher than the first one while thefirst peak amplitude changes more than the second one withexception of TC (5 2) in State 7

Note that in real engineering especially in operationalmodal analysis normally the excitation cannot be measured


0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)

0 100 200 300 400Measurement number

0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)

Figure 10 (a) ATC (5 3) (b) ATC (5 2) (c) TMAC (5 3) and (d) TMAC (5 2) for State numbers 1 to 9

Thus the FRF would be impossible to be used for modalanalysis Therefore the TC will perform in its perfectway as transmissibility is only depending on the structuralresponses as well as TC

52 Damage Identification Analysis in Linear Part Damagedetection plays a vital role in real-time SHM As shownin Figures 8(c) and 8(d) TC might be used for detectingdamage Herein ATC (5 3) and ATC (5 2) as well as TMAC(5 3) and TMAC (5 2) are shown in Figures 10(a) 10(b)10(c) and 10(d) respectively for 50 measurements from eachof the nine state conditions (State numbers 1 to 9) with 450measurements in total

From a general perspective one can observe that in bothcases ATC (ATC (5 2) ATC (5 3)) and TMAC (TMAC (5 2)andTMAC(5 3)) the variability is relatively small comparingwith the reference value of unit which suggests that these twoindicators do not perform very well in detecting damage

In Figures 10(a) and 10(b) for the mass type damage thatis from D0 to D1 and D2 ATC (5 3) and ATC (5 2) increasewhen mass is added into the base structure and when themass is moved into the first floor both ATC (5 3) and ATC(5 2) decrease In this case it would be hard to draw outa conclusion of mass influence into the indicator ATC Forstiffness reduction type damage it is difficult to predict thepresence of damage since ATC (5 2) of State 5 is higherthan the ones from the baseline State 1 However in thecase of ATC (5 3) one might draw a conclusion that ATC(5 3) can be used for detecting damage related to stiffnessreduction as to all the measurements from State numbers 4ndash9 the corresponding ATC (5 3) are lower than the baselineAnother aspect is that ATC (5 3) might be also used torelatively quantify the damage as it varies proportionally toeach state One can also observe that for each state the valuesof 50 measurements vary not too much which suggests thatthe experiment is conducted in a good condition


0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)

Linear partNonlinear part

(a)

0 100 200 300 400 500 600 700 800Measurement number

05055

06065

07075

08085

09095

1

TMAC

(5 2

) Linear partNonlinear part

(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3

) Linear part Nonlinear part

(d)

Figure 11 (a) ATC (5 2) (b) TMAC (5 2) (c) ATC (5 3) and (d) TMAC (5 3) for State numbers 1 to 17

In Figures 10(c) and 10(d) for the mass adding damagetype it is clear that from State 1 to State 3 the TMAC (53) and TMAC (5 2) decreased as the mass 12 Kg was addedinto the base in State 2 and later moved to first floor in State3 For stiffness reduction from State numbers 4 to 9 onecan find that both TMAC (5 3) and TMAC (5 2) decreaseas the stiffness reduction increased from State numbers 4 to5 from State numbers 6 to 7 and from State numbers 8 to 9respectively In Figure 10(c) one can also observe that TMAC(5 3) decreased clearly as the stiffness reduction changedfrom the first story to the second story and from second storyto third story Comparing State numbers 6 and 8 one can seesome decrease occurring in TMAC (5 3) For TMAC (5 2) inFigure 10(d) it can be found that the TMAC (5 2) decreasesfrom State numbers 4 to 5 from State numbers 6 to 7 andfrom State numbers 8 to 9 meaning that the TMAC (5 2)can relatively quantify the damage for each story ComparingFigures 10(c) and 10(d) one might conclude that TMAC canbe used for relatively quantifying damage Note that this alsoconfirms the same conclusion drawn out in the simulationsection analysis

53 Damage Identification Analysis in Nonlinear Part Inorder to show the capacity of the proposed approach to detectnonlinear behaviours related to damage Figure 11 shows theATC (5 2) and TMAC (5 2) as well as ATC (5 3) and TMAC(5 3) respectively for all 17 states From the figure one canclearly find that both damage-sensitive indicators ATC andTMAC perform much better in the nonlinear part (State

numbers 10ndash17 451ndash900) than in linear one (State numbers1ndash9 1ndash450) In the nonlinear part one can see clearly thateach state has been identified as outliers that is the ATC andTMAC successfully detect and identify the damage states

6 Conclusions

This study illustrated the coherence between two outputsand newly defined TC that is transmissibility coherenceit built the relation between the TC and the traditionalFRF coherence in modal analysis following the constructionof a damage-sensitive indicator using the modal assurancecriterion for detecting and relatively quantifying structuraldamage

The TC has an important advantage over the FRF coher-ence as the former does not need to know the input excitationto the system which might be an important feature for real-world applicationsThe TC can be used for checking whetherthe experiment is well conducted as it gives indications aboutthe presence of noise in the system It may also be usedfor detecting damage using the frequency shift as damageindicator Additionally the proposed ATC might be usedfor detecting damage especially in nonlinear analysis it wasdemonstrated that in nonlinear damage quantification itperforms well In addition the TC and related indicators aresensitive to environment variety like noise which might beused for monitoring the operational conditions

The TMAC can be used to relatively quantify the damageThe results of both the simulated frame and three-story frame


structure reveal the well performance in damage detectionand quantification both in linear and in nonlinear part inthe linear part all the damage scenarios were successfullydetected and relatively well quantified it was also demon-strated that in the nonlinear part the approach performsmuch better than in linear part

It is important to note that the proposed approachonly requires minimum two-sensor data acquisition in thestructural system for detecting and relatively quantifying thestructural damage Therefore it shows promising future inreal time SHM

Finally for cases simulation and experiment the wellperformance in detecting and quantifying the damage showsgreat promising future in real engineering usage

Conflict of Interests

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

Acknowledgments

Thewriters acknowledge the support for the work reported inthis paper from the Spanish Ministry of Economy and Com-petitiveness (Project no BIA2013-46944-C2-1-P) Financialsupport for the CSC research fellowship given to Yun-LaiZhou is also acknowledged The coauthor N Maia wouldlike to acknowledge the support of the Portuguese ScienceFoundation FCT through IDMEC under LAETA

References

[1] E Figueiredo I Moldovan and M B Marques Condition As-sessment of Bridges Past Present and Future A ComplementaryApproach Universidade Catolica Editora 2013

[2] H Sohn C R Farrar F M Hemez D D Shunk D W Stine-mates and B R Nadler A Review of Structural Health Monitor-ing Literature 1996ndash2001 Los Alamos National Laboratory LosAlamos NM USA 2003

[3] D Montalvao N M M Maia and A M R Ribeiro ldquoA reviewof vibration-based structural health monitoring with specialemphasis on composite materialsrdquo Shock and Vibration Digestvol 38 no 4 pp 295ndash324 2006

[4] WWeijtjens G De Sitter C Devriendt and P Guillaume ldquoRel-ative scaling of mode shapes using transmissibility functionsrdquoMechanical Systems and Signal Processing vol 40 no 1 pp 269ndash277 2013

[5] N M M Maia R A B Almeida A P V Urgueira and RP C Sampaio ldquoDamage detection and quantification usingtransmissibilityrdquoMechanical Systems and Signal Processing vol25 no 7 pp 2475ndash2483 2011

[6] Z Mao and M Todd ldquoA model for quantifying uncertaintyin the estimation of noise-contaminated measurements oftransmissibilityrdquoMechanical Systems and Signal Processing vol28 pp 470ndash481 2012

[7] Y E Lage N M M Maia and M M Neves ldquoForce magnitudereconstruction using the force transmissibility conceptrdquo Shockand Vibration vol 2014 Article ID 905912 9 pages 2014

[8] W Heylen S Lammens and P Sas Modal Analysis Theoryand Testing section A6 KU Leuven-PMA Brussels Belgium1998

[9] R P C Sampaio and N M M Maia ldquoStrategies for an efficientindicator of structural damagerdquoMechanical Systems and SignalProcessing vol 23 no 6 pp 1855ndash1869 2009

[10] A S Gevins ldquoOverview of computer analysisrdquo in Handbookof Electroencephalography and Clinical Neurophysiology A SGevins and A Remond Eds vol 1 pp 31ndash83 Elsevier NewYork NY USA 1987

[11] M A Guevara I Lorenzo C Arce J Ramos and M Corsi-Cabrera ldquoInter- and intrahemispheric EEG correlation duringsleep and wakefulnessrdquo Sleep vol 18 no 4 pp 257ndash265 1995

[12] T L Paez ldquoThe history of random vibrations through 1958rdquoMechanical Systems and Signal Processing vol 20 no 8 pp1783ndash1818 2006

[13] E A Robinson ldquoA historical perspective of spectrum estima-tionrdquo Proceedings of the IEEE vol 70 no 9 pp 885ndash907 1982

[14] J Kopal O Vysata J Burian M Schatz A Prochazka and MValis ldquoComplex continuous wavelet coherence for EEGmicros-tates detection in insight and calm meditationrdquo Consciousnessand Cognition vol 30 pp 13ndash23 2014

[15] R Srinivasan W R Winter J Ding and P L Nunez ldquoEEG andMEG coherence measures of functional connectivity at distinctspatial scales of neocortical dynamicsrdquo Journal of NeuroscienceMethods vol 166 no 1 pp 41ndash52 2007

[16] V Sakkalis and M Zervakis ldquoLinear and nonlinear synchro-nization analysis and visualization during altered states ofconsciousnessrdquo in Recent Advances in Biomedical Engineeringchapter 25 pp 493ndash517 InTech 2009

[17] A V Tankanag A A Grinevich T V Kirilina G V Kras-nikov G M Piskunova and N K Chemeris ldquoWavelet phasecoherence analysis of the skin blood flowoscillations in humanrdquoMicrovascular Research vol 95 pp 53ndash59 2014

[18] J S Schuman M R Hee C A Puliafito et al ldquoQuantificationof nerve fiber layer thickness in normal and glaucomatous eyesusing optical coherence tomography a pilot studyrdquo Archives ofOphthalmology vol 113 no 5 pp 586ndash596 1995

[19] J-S Hu and M-T Lee ldquoMulti-channel post-filtering based onspatial coherence measurerdquo Signal Processing vol 105 pp 338ndash349 2014

[20] J-S Lew ldquoUsing transfer function parameter changes fordamage detection of structuresrdquo AIAA Journal vol 33 no 11pp 2189ndash2193 1995

[21] J E Michaels and T E Michaels ldquoDetection of structuraldamage from the local temporal coherence of diffuse ultrasonicsignalsrdquo IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control vol 52 no 10 pp 1769ndash1782 2005

[22] DD Rizos S D Fassois Z PMarioli-Riga andAN KaranikaldquoVibration-based skin damage statistical detection and restora-tion assessment in a stiffened aircraft panelrdquoMechanical Systemsand Signal Processing vol 22 no 2 pp 315ndash337 2008

[23] DD Rizos S D Fassois Z PMarioli-Riga andAN KaranikaldquoStatistical skin damage detection and restoration assessmentfor aircraft panels via vibration testingrdquo in Proceedings of the 1stEuropean Workshop on Structural Health Monitoring pp 1211ndash1218 Paris France 2002

[24] S D Fassois and J S Sakellariou ldquoTime-series methodsfor fault detection and identification in vibrating structuresrdquoPhilosophical Transactions of the Royal Society of London SeriesAMathematical Physical and Engineering Sciences vol 365 no1851 pp 411ndash448 2007


[25] G R Cooper and C D McGillem Probabilistic Methods ofSignal and System Analysis Holt Rinehart and Winston NewYork NY USA 1971

[26] E Figueiredo L Radu KWorden andC R Farrar ldquoA Bayesianapproach based on a Markov-chain Monte Carlo methodfor damage detection under unknown sources of variabilityrdquoEngineering Structures vol 80 pp 1ndash10 2014

[27] E Figueiredo G Park C R Farrar K Worden and J Fi-gueiras ldquoMachine learning algorithms for damage detectionunder operational and environmental variabilityrdquo InternationalJournal of Structural Health Monitoring vol 10 no 6 pp 559ndash572 2011

[28] M B Priestley Spectral Analysis and Time Series AcademicPress New York NY USA 1981

[29] V Sakkalis and M Zervakis ldquoLinear and nonlinear synchro-nization analysis and visualization during altered states ofconsciousnessrdquo in Recent Advances in Biomedical EngineeringG R Naik Ed chapter 25 InTech 2009

[30] httpesmathworkscomhelpsignalugcross-spectrum-and-magnitude-squared-coherencehtml

[31] C Zheng M Zhou and X Li ldquoOn the relationship of non-parametric methods for coherence function estimationrdquo SignalProcessing vol 88 no 11 pp 2863ndash2867 2008

[32] C J Schallhorn Localization of vibration-based damage detec-tion method in structural applications [MS thesis] Universityof Iowa 2012

[33] N M M Maia and J M M SilvaTheoretical and ExperimentalModal Analysis vol 8 of Mechanical Engineering ResearchStudies Engineering Dynamics Research Studies Press 2003

[34] R Bortel and P Sovka ldquoStatistical evaluation of coherenceestimated from optimally beamformed signalsrdquo Computers inBiology and Medicine vol 43 no 9 pp 1286ndash1262 2013

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

[36] J Capon ldquoHigh resolution frequency-wavenumber spectrumanalysisrdquo Proceedings of the IEEE vol 57 no 8 pp 1408ndash14181969

[37] R J Allemang and D L Brown ldquoA correlation coefficient formodal vector analysisrdquo in Proceedings of the 1st InternationalModal Analysis Conference amp Exhibit pp 110ndash116 1982

[38] R Pascual J C Golinval and M Razeto ldquoFrequency domaincorrelation technique for model correlation and updatingrdquo inProceedings of the 15th International Modal Analysis Conference(IMAC rsquo97) pp 587ndash592 February 1997

[39] W Heylen and P Avitabile ldquoCorrelation considerationsmdashpart5 (degree of freedom correlation techniques)rdquo in Proceedings ofthe 16th International Modal Analysis Conference pp 207ndash214February 1998

[40] E Figueiredo G Park J Figueiras C Farrar and K WordenldquoStructural health monitoring algorithm comparisons usingstandard data setsrdquo Los Alamos National Laboratory ReportLA-14393 Los Alamos National Laboratory 2009

[41] httpinstitutelanlgoveistructural-health-monitoringtest-structures-applications

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Submit your manuscripts athttpwwwhindawicom

VLSI Design



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Civil EngineeringAdvances in

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



from the transmissibility in the natural resonant frequencieswhich avoids the use of FRF in mode shape estimationIn [5] a method of taking advantage of response vectorassurance criterion (RVAC) [8] was proposed replacing theFRF by transmissibility function in the indicator RVACand detection and relative damage quantification indicator(DRQ) [9] which is the average value of RVAC along thefrequency domain The RVAC is a simplified form of FDACwhich was defined by Heylen et al [8] The key idea is to usethe sum of all coordinates FRF before and after damage of allloading conditions in the form of modal assurance criteria

However the detection of damage at an early stage is stilla very difficult and challenging task therefore the proposalof new indicators based on dynamic responses that maybe sensitive enough to minor damage is very important Inthis sense the coherence as a function dependent on thefrequency and able to analyze the spatial correlation betweentwo signals [10 11] might be potentially a good starting pointto develop sensitive damage indicators

The coherence function formally defined by Wiener[12 13] has been extensively studied and used especiallyafter the development of the Fourier transform in a lot ofresearch fields with extensions to the most modern waveletcoherence and partial directed coherence neurology mostlyin electroencephalography (EEG) studies [14ndash16] like EEGmicrostates detection in insight and calm meditation [14]Coherence is also used in skin blood oscillations analysis inhuman [17] nerve fiber layer thickness quantification [18]

In another aspect spatial coherencemeasure is also devel-oped for signal enhancement [19] by designing coherence-based post filters In recent years coherence function hasbeen used in mechanical engineering for damage identi-fication namely detection type and quantification [20ndash24] In [20] a coherence algorithm is proposed for damagetype recognition and damage localization for large flexiblestructures with a nine-bay truss example the key idea isto construct a connection between coherence and trans-fer function and the transfer function parameter changeis extracted for damage detection In [21] local temporalcoherence is developed and extended to time-varying processwith the basic coherence conception from the cross corre-lation defined in [25] and the corresponding peak value isdefined as peak coherence creating a connection with thetemperature and introduced damage change that is the peakcoherence for temperaturedamage change is somewhat afunction of time In addition the peak performs well in dis-tinguishing environmental change and damage In [22 23]coherence is integrated in the frequency domain and set as anindicator-coherence measure as a sensitive enough indicatorfor quantifying the skin damage and assessing restorationquality In [24] coherence measure based method as atime series method is developed for fault detection andidentification in vibrating structures

In this paper coherence analysis of transmissibility isperformed and from it an effective indicator for damageespecially nonlinearity is proposed and compared with thecoherence measure raised in [22] In order to test thefeasibility of the proposed approach numerical simulationof a laboratory structure is carried out and additionally

experimental measurements on a three-story aluminumstructure are used to check the applicability of the proposedindicator

2 Transmissibility Based Coherence

As described in [2] SHM is essentially a statistical patternrecognition problem It can be described as a four-stageprocess

(1) operational evaluation

(2) data acquisition Fusion and Cleansing

(3) feature extraction and information condensation

(4) statistical model development for feature discrimina-tion

As for vibration-based SHM the core idea is to find asensitive feature able to discriminate a damaged structurewhen compared to the baseline structure (healthy state)therefore the damage detection conclusion can be drawn outwith choosing a threshold of the change before and afterdamage considering the influence of operational variety Asdescribed in the introduction lots of approaches featuresand measurement methodologies have been used in the past[2 3 26 27]

21 Applicability of Coherence in Damage Detection As com-mented in the introduction coherence has been used inmanyapplications It is useful to examine the correlation betweentwo frequency signals in a similar way to the correlationcoefficient in frequency More details can be found in [28]

Coherence as a complex measure is estimated by divid-ing the square of the cross-spectral density between twosignals by the product of the autospectral densities of bothsignals Consequently it will be sensitive to both changes inpower and phase relationships in one of the two signals [29]

The magnitude-squared coherence for the bivariate timeseries enables us to identify significant frequency-domaincorrelation between the two time series [30] For the purposeof preventing obtaining an estimate of magnitude-squaredcoherence to be identically 1 for all frequencies an averagedmagnitude-squared coherence estimator has to be used BothWelchrsquos overlapped segment averaging (WOSA) and multi-taper techniques are appropriate [30] In this study WOSAis utilized for the coherence estimate A detailed discussionof several seemingly disparate nonparametric magnitudesquared coherence estimation methods including Welchrsquosaveraged periodogram the minimum variance distortionlessresponse (MVDR) and the canonical correlation analysis(CCA) can be found in [31]

For SHM purposes the most important task is to finda structural feature sensitive to the occurrence of damageMethodologies involving coherence have been developedin the past decades [20ndash24 32] As proved in [22ndash24] acoherence based damage indicator can be used in damagedetection The premise behind this is that the coherence willdecrease as nonlinearity increases



119872 (119905) + 119862 (119905) + 119870119909 (119905) = 119891 (119905) (1)



119879(119894119895) =119883119894 (120596)

119883119895 (120596) (2)



119879(119894119895) =119883119894 (120596) 119865119897 (120596)

119883119895 (120596) 119865119897 (120596)=

119867(119894119897) (120596)

119867(119895119897) (120596) (3)



1198671 (120596) =119878(119894119897) (120596)

119878(119897119897) (120596)

1198672 (120596) =119878(119894119894) (120596)

119878(119897119894) (120596)

(4)


1205742=1198671 (120596)

1198672 (120596)=119878(119894119897) (120596)

119878(119897119897) (120596)

119878(119897119894) (120596)

119878(119894119894) (120596)

=119878(119894119897) (120596)

119878(119894119894) (120596)

119878lowast(119894119897) (120596)

119878(119897119897) (120596)=

1003816100381610038161003816119878(119894119897) (120596)1003816100381610038161003816

2

119878(119894119894) (120596) 119878(119897119897) (120596)

(5)


1205742

TC =

1198791(119894119895) (120596)

1198792(119894119895) (120596)=

1198671(119894119897) (120596) 1198671(119895119897) (120596)

1198672(119894119897) (120596) 1198672(119895119897) (120596)

=1198671(119894119897) (120596)

1198672(119894119897) (120596)

1198672(119895119897) (120596)

1198671(119895119897) (120596)=

1205742(119894119897)

1205742(119895119897)

(6)



1198791(119894119895) =119883119894 (120596)

119883119895 (120596)

119883119895 (120596)

119883119895 (120596)=

119878(119894119895) (120596)

119878(119895119895) (120596)

1198792(119894119895) =119883119894 (120596)

119883119895 (120596)

119883119894 (120596)

119883119894 (120596)=

119878(119894119894) (120596)

119878(119895119894) (120596)

(7)


1205742

TC =

1198791(119894119895) (120596)

1198792(119894119895) (120596)=

119878(119894119895) (120596) 119878(119895119895) (120596)

119878(119894119894) (120596) 119878(119895119894) (120596)

=

119878(119894119895) (120596) 119878(119895119894) (120596)

119878(119895119895) (120596) 119878(119894119894) (120596)=

10038161003816100381610038161003816119878(119894119895) (120596)

10038161003816100381610038161003816

2

119878(119894119894) (120596) 119878(119895119895) (120596)

(8)





ATC = int

119891max

119891min

TC119889119891 (9)



y5

y4

y3

y2

m4

c4

k4m3

c3

k3m2

c2

k2m1

c1

k1

y1F (excitation)

(a)

0 10 20

minus50

0

50

Time (s)

Exci

tatio

n fo

rce (

N)

(b)




TMAC

=

100381610038161003816100381610038161003816((TC (119908))

119889)119879(TC (119908))

119906100381610038161003816100381610038161003816

2

(((TC (119908))119889)119879(TC (119908))

119889) (((TC (119908))

119906)119879(TC (119908))

119906)

(10)















20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

3) (

dB)

D0D1

D5D6

(a)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

3) (

dB)

D0wD1w

D5wD6w

(b)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

2) (

dB)

D0D1

D5D6

(c)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

2) (

dB)

D0wD1w

D5wD6w

(d)







20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0D1

D5D6

(a)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0wD1w

D5wD6w

(b)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0D1

D5D6

(c)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0wD1w

D5wD6w

(d)












FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(c)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w








TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)


















D0 10000 10000 10000 10000 10000 10000 10000 10000D1 09989 09802 10000 09807 09994 09627 09998 09491D2 09990 09613 09993 09643 09986 09474 09995 09322D3 09927 09204 09995 09026 09976 08334 09993 08192D4 10159 07384 10081 07091 10058 05854 10026 05798D5 09739 09287 10149 09431 10027 08124 10010 07998D6 09888 07313 10134 07024 09975 06208 09959 06172D7 09716 09274 10052 09255 09989 08487 09998 08373D8 09959 08350 10102 08248 10069 06853 10030 06872

D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 3

)


(a)


D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 2

)

(b)








177

177

177

3rd floor

2nd floor

1st floor

BumperColumn

Base

A

A

B

B

C

C

D

D

1 1

2 2

3 3

x

z

y

1745Load cell

(Channel 1)


Baseplate

Shaker






305

305


Y







20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)

T (5

3) (

dB)



(a)

T (5

2) (

dB)

20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)



(b)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1

TC (5

3)

(c)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1TC

(5 2

)











1119879 (5 2)














0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)








0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119872 (119905) + 119862 (119905) + 119870119909 (119905) = 119891 (119905) (1)



119879(119894119895) =119883119894 (120596)

119883119895 (120596) (2)



119879(119894119895) =119883119894 (120596) 119865119897 (120596)

119883119895 (120596) 119865119897 (120596)=

119867(119894119897) (120596)

119867(119895119897) (120596) (3)



1198671 (120596) =119878(119894119897) (120596)

119878(119897119897) (120596)

1198672 (120596) =119878(119894119894) (120596)

119878(119897119894) (120596)

(4)


1205742=1198671 (120596)

1198672 (120596)=119878(119894119897) (120596)

119878(119897119897) (120596)

119878(119897119894) (120596)

119878(119894119894) (120596)

=119878(119894119897) (120596)

119878(119894119894) (120596)

119878lowast(119894119897) (120596)

119878(119897119897) (120596)=

1003816100381610038161003816119878(119894119897) (120596)1003816100381610038161003816

2

119878(119894119894) (120596) 119878(119897119897) (120596)

(5)


1205742

TC =

1198791(119894119895) (120596)

1198792(119894119895) (120596)=

1198671(119894119897) (120596) 1198671(119895119897) (120596)

1198672(119894119897) (120596) 1198672(119895119897) (120596)

=1198671(119894119897) (120596)

1198672(119894119897) (120596)

1198672(119895119897) (120596)

1198671(119895119897) (120596)=

1205742(119894119897)

1205742(119895119897)

(6)



1198791(119894119895) =119883119894 (120596)

119883119895 (120596)

119883119895 (120596)

119883119895 (120596)=

119878(119894119895) (120596)

119878(119895119895) (120596)

1198792(119894119895) =119883119894 (120596)

119883119895 (120596)

119883119894 (120596)

119883119894 (120596)=

119878(119894119894) (120596)

119878(119895119894) (120596)

(7)


1205742

TC =

1198791(119894119895) (120596)

1198792(119894119895) (120596)=

119878(119894119895) (120596) 119878(119895119895) (120596)

119878(119894119894) (120596) 119878(119895119894) (120596)

=

119878(119894119895) (120596) 119878(119895119894) (120596)

119878(119895119895) (120596) 119878(119894119894) (120596)=

10038161003816100381610038161003816119878(119894119895) (120596)

10038161003816100381610038161003816

2

119878(119894119894) (120596) 119878(119895119895) (120596)

(8)





ATC = int

119891max

119891min

TC119889119891 (9)



y5

y4

y3

y2

m4

c4

k4m3

c3

k3m2

c2

k2m1

c1

k1

y1F (excitation)

(a)

0 10 20

minus50

0

50

Time (s)

Exci

tatio

n fo

rce (

N)

(b)




TMAC

=

100381610038161003816100381610038161003816((TC (119908))

119889)119879(TC (119908))

119906100381610038161003816100381610038161003816

2

(((TC (119908))119889)119879(TC (119908))

119889) (((TC (119908))

119906)119879(TC (119908))

119906)

(10)















20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

3) (

dB)

D0D1

D5D6

(a)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

3) (

dB)

D0wD1w

D5wD6w

(b)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

2) (

dB)

D0D1

D5D6

(c)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

2) (

dB)

D0wD1w

D5wD6w

(d)







20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0D1

D5D6

(a)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0wD1w

D5wD6w

(b)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0D1

D5D6

(c)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0wD1w

D5wD6w

(d)












FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(c)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w








TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)


















D0 10000 10000 10000 10000 10000 10000 10000 10000D1 09989 09802 10000 09807 09994 09627 09998 09491D2 09990 09613 09993 09643 09986 09474 09995 09322D3 09927 09204 09995 09026 09976 08334 09993 08192D4 10159 07384 10081 07091 10058 05854 10026 05798D5 09739 09287 10149 09431 10027 08124 10010 07998D6 09888 07313 10134 07024 09975 06208 09959 06172D7 09716 09274 10052 09255 09989 08487 09998 08373D8 09959 08350 10102 08248 10069 06853 10030 06872

D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 3

)


(a)


D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 2

)

(b)








177

177

177

3rd floor

2nd floor

1st floor

BumperColumn

Base

A

A

B

B

C

C

D

D

1 1

2 2

3 3

x

z

y

1745Load cell

(Channel 1)


Baseplate

Shaker






305

305


Y







20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)

T (5

3) (

dB)



(a)

T (5

2) (

dB)

20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)



(b)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1

TC (5

3)

(c)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1TC

(5 2

)











1119879 (5 2)














0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)








0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










y5

y4

y3

y2

m4

c4

k4m3

c3

k3m2

c2

k2m1

c1

k1

y1F (excitation)

(a)

0 10 20

minus50

0

50

Time (s)

Exci

tatio

n fo

rce (

N)

(b)




TMAC

=

100381610038161003816100381610038161003816((TC (119908))

119889)119879(TC (119908))

119906100381610038161003816100381610038161003816

2

(((TC (119908))119889)119879(TC (119908))

119889) (((TC (119908))

119906)119879(TC (119908))

119906)

(10)















20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

3) (

dB)

D0D1

D5D6

(a)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

3) (

dB)

D0wD1w

D5wD6w

(b)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

2) (

dB)

D0D1

D5D6

(c)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

2) (

dB)

D0wD1w

D5wD6w

(d)







20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0D1

D5D6

(a)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0wD1w

D5wD6w

(b)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0D1

D5D6

(c)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0wD1w

D5wD6w

(d)












FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(c)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w








TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)


















D0 10000 10000 10000 10000 10000 10000 10000 10000D1 09989 09802 10000 09807 09994 09627 09998 09491D2 09990 09613 09993 09643 09986 09474 09995 09322D3 09927 09204 09995 09026 09976 08334 09993 08192D4 10159 07384 10081 07091 10058 05854 10026 05798D5 09739 09287 10149 09431 10027 08124 10010 07998D6 09888 07313 10134 07024 09975 06208 09959 06172D7 09716 09274 10052 09255 09989 08487 09998 08373D8 09959 08350 10102 08248 10069 06853 10030 06872

D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 3

)


(a)


D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 2

)

(b)








177

177

177

3rd floor

2nd floor

1st floor

BumperColumn

Base

A

A

B

B

C

C

D

D

1 1

2 2

3 3

x

z

y

1745Load cell

(Channel 1)


Baseplate

Shaker






305

305


Y







20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)

T (5

3) (

dB)



(a)

T (5

2) (

dB)

20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)



(b)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1

TC (5

3)

(c)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1TC

(5 2

)











1119879 (5 2)














0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)








0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

3) (

dB)

D0D1

D5D6

(a)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

3) (

dB)

D0wD1w

D5wD6w

(b)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

2) (

dB)

D0D1

D5D6

(c)

20 40 60 80 100 120 140

minus100

minus50

0

50

Frequency (Hz)

T (5

2) (

dB)

D0wD1w

D5wD6w

(d)







20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0D1

D5D6

(a)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0wD1w

D5wD6w

(b)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0D1

D5D6

(c)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0wD1w

D5wD6w

(d)












FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(c)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w








TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)


















D0 10000 10000 10000 10000 10000 10000 10000 10000D1 09989 09802 10000 09807 09994 09627 09998 09491D2 09990 09613 09993 09643 09986 09474 09995 09322D3 09927 09204 09995 09026 09976 08334 09993 08192D4 10159 07384 10081 07091 10058 05854 10026 05798D5 09739 09287 10149 09431 10027 08124 10010 07998D6 09888 07313 10134 07024 09975 06208 09959 06172D7 09716 09274 10052 09255 09989 08487 09998 08373D8 09959 08350 10102 08248 10069 06853 10030 06872

D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 3

)


(a)


D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 2

)

(b)








177

177

177

3rd floor

2nd floor

1st floor

BumperColumn

Base

A

A

B

B

C

C

D

D

1 1

2 2

3 3

x

z

y

1745Load cell

(Channel 1)


Baseplate

Shaker






305

305


Y







20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)

T (5

3) (

dB)



(a)

T (5

2) (

dB)

20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)



(b)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1

TC (5

3)

(c)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1TC

(5 2

)











1119879 (5 2)














0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)








0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0D1

D5D6

(a)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

3)

D0wD1w

D5wD6w

(b)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0D1

D5D6

(c)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

TC (5

2)

D0wD1w

D5wD6w

(d)












FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(c)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w








TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)


















D0 10000 10000 10000 10000 10000 10000 10000 10000D1 09989 09802 10000 09807 09994 09627 09998 09491D2 09990 09613 09993 09643 09986 09474 09995 09322D3 09927 09204 09995 09026 09976 08334 09993 08192D4 10159 07384 10081 07091 10058 05854 10026 05798D5 09739 09287 10149 09431 10027 08124 10010 07998D6 09888 07313 10134 07024 09975 06208 09959 06172D7 09716 09274 10052 09255 09989 08487 09998 08373D8 09959 08350 10102 08248 10069 06853 10030 06872

D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 3

)


(a)


D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 2

)

(b)








177

177

177

3rd floor

2nd floor

1st floor

BumperColumn

Base

A

A

B

B

C

C

D

D

1 1

2 2

3 3

x

z

y

1745Load cell

(Channel 1)


Baseplate

Shaker






305

305


Y







20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)

T (5

3) (

dB)



(a)

T (5

2) (

dB)

20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)



(b)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1

TC (5

3)

(c)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1TC

(5 2

)











1119879 (5 2)














0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)








0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(c)

FRF

cohe

renc

e (3

1)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w








TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)


















D0 10000 10000 10000 10000 10000 10000 10000 10000D1 09989 09802 10000 09807 09994 09627 09998 09491D2 09990 09613 09993 09643 09986 09474 09995 09322D3 09927 09204 09995 09026 09976 08334 09993 08192D4 10159 07384 10081 07091 10058 05854 10026 05798D5 09739 09287 10149 09431 10027 08124 10010 07998D6 09888 07313 10134 07024 09975 06208 09959 06172D7 09716 09274 10052 09255 09989 08487 09998 08373D8 09959 08350 10102 08248 10069 06853 10030 06872

D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 3

)


(a)


D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 2

)

(b)








177

177

177

3rd floor

2nd floor

1st floor

BumperColumn

Base

A

A

B

B

C

C

D

D

1 1

2 2

3 3

x

z

y

1745Load cell

(Channel 1)


Baseplate

Shaker






305

305


Y







20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)

T (5

3) (

dB)



(a)

T (5

2) (

dB)

20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)



(b)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1

TC (5

3)

(c)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1TC

(5 2

)











1119879 (5 2)














0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)








0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0D1

D5D6

(a)

TC (5

4)

20 40 60 80 100 120 1400

02

04

06

08

1

Frequency (Hz)

D0wD1w

D5wD6w

(b)


















D0 10000 10000 10000 10000 10000 10000 10000 10000D1 09989 09802 10000 09807 09994 09627 09998 09491D2 09990 09613 09993 09643 09986 09474 09995 09322D3 09927 09204 09995 09026 09976 08334 09993 08192D4 10159 07384 10081 07091 10058 05854 10026 05798D5 09739 09287 10149 09431 10027 08124 10010 07998D6 09888 07313 10134 07024 09975 06208 09959 06172D7 09716 09274 10052 09255 09989 08487 09998 08373D8 09959 08350 10102 08248 10069 06853 10030 06872

D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 3

)


(a)


D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 2

)

(b)








177

177

177

3rd floor

2nd floor

1st floor

BumperColumn

Base

A

A

B

B

C

C

D

D

1 1

2 2

3 3

x

z

y

1745Load cell

(Channel 1)


Baseplate

Shaker






305

305


Y







20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)

T (5

3) (

dB)



(a)

T (5

2) (

dB)

20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)



(b)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1

TC (5

3)

(c)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1TC

(5 2

)











1119879 (5 2)














0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)








0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













D0 10000 10000 10000 10000 10000 10000 10000 10000D1 09989 09802 10000 09807 09994 09627 09998 09491D2 09990 09613 09993 09643 09986 09474 09995 09322D3 09927 09204 09995 09026 09976 08334 09993 08192D4 10159 07384 10081 07091 10058 05854 10026 05798D5 09739 09287 10149 09431 10027 08124 10010 07998D6 09888 07313 10134 07024 09975 06208 09959 06172D7 09716 09274 10052 09255 09989 08487 09998 08373D8 09959 08350 10102 08248 10069 06853 10030 06872

D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 3

)


(a)


D0 D1 D2 D3 D4 D5 D6 D7 D80

02

04

06

08

1

Damage scenario

TMAC

(5 2

)

(b)








177

177

177

3rd floor

2nd floor

1st floor

BumperColumn

Base

A

A

B

B

C

C

D

D

1 1

2 2

3 3

x

z

y

1745Load cell

(Channel 1)


Baseplate

Shaker






305

305


Y







20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)

T (5

3) (

dB)



(a)

T (5

2) (

dB)

20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)



(b)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1

TC (5

3)

(c)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1TC

(5 2

)











1119879 (5 2)














0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)








0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










177

177

177

3rd floor

2nd floor

1st floor

BumperColumn

Base

A

A

B

B

C

C

D

D

1 1

2 2

3 3

x

z

y

1745Load cell

(Channel 1)


Baseplate

Shaker






305

305


Y







20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)

T (5

3) (

dB)



(a)

T (5

2) (

dB)

20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)



(b)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1

TC (5

3)

(c)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1TC

(5 2

)











1119879 (5 2)














0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)








0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)

T (5

3) (

dB)



(a)

T (5

2) (

dB)

20 40 60 80 100 120 140minus80

minus60

minus40

minus20

0

20

40

60

Frequency (Hz)



(b)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1

TC (5

3)

(c)

20 40 60 80 100 120 140Frequency (Hz)



0

02

04

06

08

1TC

(5 2

)











1119879 (5 2)














0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)








0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1119879 (5 2)














0

02

04

06

08

1

FRF

cohe

renc

e (5

1)

20 40 60 80 100 120 140Frequency (Hz)








0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 3

) (lo

g)

(a)

0 100 200 300 40009975

0998

09985

0999

09995

1

Measurement number

ATC

(5 2

) (lo

g)

(b)


0975

098

0985

099

0995

1

1005

TMAC

(5 3

)

(c)


0975

098

0985

099

0995

1

1005TM

AC (5

2)

(d)







0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 100 200 300 400 500 600 700 80009

091092093094095096097098099

1

Measurement number

ATC

(5 2

) (lo

g)


(a)


05055

06065

07075

08085

09095

1

TMAC

(5 2


(b)


09091092093094095096097098099

1

ATC

(5 3

) (lo

g)


(c)


05055

06065

07075

08085

09095

1

TMAC

(5 3


(d)





6 Conclusions










Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article damage detection and quantification using

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