CLUSTERING OF ACOUSTIC EMISSION SIGNALS FOR FRACTURE ...framcos.org/FraMCoS-10/Full-Papers/235554.pdf · AE source localisation and characterisation are important to assess a structure

10th International Conference on Fracture Mechanics of Concrete and Concrete StructuresFraMCoS-X

G. Pijaudier-Cabot, P. Grassl and C. La Borderie (Eds)

CLUSTERING OF ACOUSTIC EMISSION SIGNALS FOR FRACTUREMONITORING DURING ACCELERATED CORROSION OF REINFORCED

CONCRETE PRISMS

CHARLOTTE VAN STEEN∗, MARTINE WEVERS† AND ELS VERSTRYNGE ‡

∗Department of Civil Engineering, KU LeuvenLeuven, Belgium

e-mail: [email protected]

†Department of Materials Engineering, KU LeuvenLeuven, Belgium


‡Department of Civil Engineering, KU LeuvenLeuven, Belgium


Key words: Reinforcement corrosion, Acoustic Emission, Signal Analysis, Fracture, Localisation,Clustering

Abstract. Corrosion of the reinforcement is one of the major deterioration mechanisms in existingreinforced concrete (RC) structures causing considerable costs for maintenance and repair. The devel-opment of reliable tools to localise and characterise such damage is essential to assess the structuralcapacity. This paper investigates the use of the acoustic emission (AE) technique during an accel-erated corrosion process of reinforced concrete prisms. AE monitoring was performed continuouslyduring the corrosion process using six sensors to allow localisation of the AE events in 3D. A samplewith and without a stirrup was tested. An AE testing and post-processing protocol was developedand will be discussed in this paper. A signal-based clustering algorithm was developed to distinguishdifferent AE sources from each other. Results show that damage could be localised correctly in bothsamples. Different types of signals could be distinguished by the clustering algorithm. This was com-pared with crack width measurements, time of arrival, location and RA-AF analysis. It was concludedthat mainly concrete cracking was recorded and localised by AE sensing in both samples.

1 INTRODUCTION

One of the deterioration mechanisms that se-riously threatens the durability of our existingreinforced concrete (RC) structures is corro-sion. Due to either carbonation and/or chlo-rides, steel is consumed and turned into expan-sive corrosion products. These products causeinternal tensile stresses in the concrete and willeventually cause cracking and spalling.

The most common inspection method on-site

is visual inspection where the damage is as-sessed on the surface by taking pictures, ham-mer tapping and crack width measurements.This method provides insight in the cause andextent of the damage, however, only damageon the surface can be detected. Electrochem-ical techniques are also widely used, unfortu-nately they are dependent on climatic condi-tions and might lack to provide precise infor-mation [1][2]. This urges the need for the de-

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grassl

Typewritten Text

https://doi.org/10.21012/FC10.23554

https://doi.org/10.21012/FC10.235554

Charlotte Van Steen, Martine Wevers and Els Verstrynge

velopment of other techniques. Acoustic emis-sion (AE) technique is very promising as it cancapture the corrosion process itself, but also theprogress of concrete cracking by detecting thehigh-frequency elastic waves that are emitted bythe fracture process [3][4].

AE monitoring has been successfully appliedduring rebar corrosion in concrete and destruc-tive testing of corroded RC samples and com-ponents [5][6]. In the literature, AE analysisis mainly performed based on AE parameterswhich are a set of extracted features that de-scribe the signal. For corrosion monitoring, itallows to distinguish different stages during theprocess such as the initiation (before cracking)and propagation (after cracking) stage [7]. Un-fortunately this approach is dependent on a userdefined threshold which makes it hard to com-pare the results when having different setups.

Signal-based analysis can alter this as it takesinto account the underlying modal structure ofan AE signal. It can allow to distinguish differ-ent damage processes leading to a more reliableinterpretation of the different damage mecha-nisms. It would give the end user the abil-ity to tell which source mechanism is presentand whether maintenance or repair is necessary.However, this approach poses some challengesas the transfer function of a signal is influencedby many aspects such as the couplant, sensorand system, but also the propagation path ofthe signal. It has been applied successfully incomposites and in fibre reinforced concrete tomake a distinction between fibre pull-out, ma-trix cracking and fibre failure [8][9], but hasnot been performed so far on corrosion in re-inforced concrete.

To apply AE sensing reliably on-site, bothAE source localisation and characterisation areimportant to assess a structure. In this pa-per, an AE testing and post-processing proto-col is presented in order to reach this goal. Anew signal-based clustering algorithm based oncross-correlation was developed by the authors

and proven to be applicable on small scale sam-ples [4]. In this paper, the clustering algorithmwill be upscaled to reinforced concrete prisms.

2 EXPERIMENTAL PROCEDURE2.1 Materials and specimen preparation

Two samples were compared in the currentinvestigation: (1) one sample with a rebar inthe center of the sample (sample A), and (2) asimilar sample also having a corroding stirrup(sample B) (figure 1). A ribbed rebar (BE400)with a nominal diameter of 14 mm was placedhorizontally in the center of the wooden mould(150x150x250 mm3) and was protruding fromboth sides in order to connect the power supplyfor the accelerated corrosion afterwards. For thesecond sample, a smooth stirrup with a nom-inal diameter of 6 mm was placed around themain rebar and was electrically connected to itwith a copper wire. The concrete compositionis shown in table 1. The average compressivestrength at 28 days, tested on cubes, was 55.04MPa with a deviation of 3.19 MPa and the aver-age flexural strength, tested on prisms, was 5.16MPa with a deviation of 0.63 MPa. After cur-ing for 28 days in a curing room (± 20◦C, ±95% RH), the specimens were fully immersedin a 5% sodium chloride solution for three days.Afterwards, the specimens were placed in theaccelerated corrosion setup (figure 2) in a cli-matised room (± 20◦C, ± 60% RH). The ac-celerated corrosion process and AE monitoringstarted at an age of 31 days.

Table 1: Concrete composition [kg/m3].

CEM I Sand Aggregates42.5N (0/5) (4:14)

350 620 1270

Water Chlorides W/C

164 7 0.46

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AE sensor Sample boundaries

PVC Bonded length

S1

S2

S5

S6

S3

S4

S1

S2

S5

S6

S3

S4

Sample A Sample B

250 mm

150 m

m

150 m

m

X

YZ

Figure 1: Sample layout and sensor arrangement for sample A and B.

Stirrup

Figure 2: Accelerated corrosion setup.

2.2 Accelerated corrosion process

An imposed direct current was used to ac-celerate the corrosion process in the laboratory.A constant current density of 100 µA/cm2 waschosen. The rebar acted as the anode and isthus connected to the positive side of the DCregulator. The negative side was connected tothe cathode which was a stainless steel plate.The specimen was partially immersed in a 5%sodium chloride solution to ensure electricalconnectivity and chloride ingress. The setup isshown in figure 2. Cracks were measured everyweek with a crack meter having an accuracy of

0.05 mm. The samples were corroded and AEwere monitored continuously for two months.

2.3 Acoustic emission (AE) monitoring

AE monitoring was performed during the ac-celerated corrosion process with six piezoelec-tric sensors with a flat frequency response be-tween 100-400 kHz. The six sensors were at-tached on the specimen surface with hot meltglue and connected to pre-amplifiers with afixed gain of 34 dB. The sensor arrangementand coordinates are shown in figure 1 and ta-ble 2 respectively. The pre-amplifiers were con-

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nected to a Vallen AMSY-6 acquisition sys-tem with six AE channels. AE parameters andwaveforms were stored on a PC and the VallenVisualAE software was used to visualise thedata in real time. Matlab was used for furtherprocessing. The first arrival time picking wasdone using a fixed threshold of 50 dB. This firstestimation of the time of arrival (TOA) tfirstwas used to discretise different signals and storethem afterwards. The stored signal had a totallength of 200 µs including 20 µs before tfirst.

Table 2: Sensor coordinates [mm].

Sensor X Y Z

S1 0 0 0S2 100 0 0S3 -25 -50 75S4 125 -25 75S5 -25 -25 -75S6 125 -50 -75

3 AE DATA POST-PROCESSING

Load AE waveforms in Matlab

Filter AE signals

SNR AIC-graph

Localisation of AE signals

Estimation of location error

Clustering of AE signals

error

Characterisation of AE signals

location, TOA, crack measurements

Filter AE signals

within sample

based on clusters in comparison with

new TOA with AIC picker

Figure 3: Flowchart of AE post-processing protocol.

In order to assign possible damage sources tothe recorded AE signals, comparison with theirsource location can be helpful. Intensive filter-ing was needed in order to only keep the signalsthat will allow an accurate localisation. A post-processing protocol was developed and imple-mented in Matlab. The workflow is shown infigure 3.

3.1 Arrival time pickingA more exact TOA was determined using the

Akaike Information Criterion (AIC) [10][11],as expressed in equation 3.1:

AIC(tw) = tw· log10(var(Rw(1, tw))) + · · ·· · · (Tw − tw − 1) · · ·· · · · log10(var(Rw(tw + 1, Tw))),

The signal Rw is divided into two sectionsat a point tw. Point tw ranges from 1 to Tw,with Tw the non-dimensional length of the timewindow. The term var(Rw(1, tw)) is the vari-ance function of all samples from 1 to tw andvar(Rw(tw + 1, Tw)) is the variance function ofall samples from point tw + 1 to Tw. The ab-solute minimum of all values indicates the newonset time tAIC .

Only the signals of which the TOA could bedetermined accurately were used for localisa-tion. Two criteria were applied to estimate theaccuracy. These criteria were presented by Gol-lob [12] and adapted in the current paper. Thefirst criterion is based on the signal-to-noise ra-tio (SNR) which gives the ratio of the signalpower S to the noise power N. S was definedas the maximum amplitude of the entire signal.N was defined as the maximum amplitude of thefirst 10 µs of the signal. Based on the recordedsignals, SNR was set to 10. If the ratio waslarger than 10, the difference between the ac-tual signal and noise level was large enough andthe signals were kept for further analysis. Thesecond criterion enhances the shape of the AIC-value graph. The actual TOA was estimatedaccurately if tAIC coincided with the first lowpoint (local minimum) of the AIC-value graph.If this was not the case, the time difference be-tween this first low point and tAIC was checked.

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It was found that if the time difference was lessthan 7 µs, or if the time difference was largerthan 7 µs but the slope between the first lowpoint and tAIC was smaller than -25, the estima-tion with AIC was still found to be reasonablyaccurate. If none of the criteria were fulfilled,the signal was excluded from the analysis.

3.2 Localisation of AE eventsFor AE source localisation in 3D, Geiger’s

method was implemented in Matlab. Geiger’smethod is an iterative approach that computesthe best approximation of the source locationbased on a least-squares approach [12][13]. Atleast four sensors are needed to solve the equa-tions. In this paper, an homogeneous velocitymodel was used and a straight propagation pathbetween source and sensor is assumed. The ar-rival time ta,i at the ith sensor can be written asfollows:

ta,i = t0 + · · ·

· · · 1vp

√(xi − x0)2 + (yi − y0)2 + (zi − z0)2

(1)

with x0, y0 and z0 are the coordinates of an AEsource, t0 is the onset time or origin time ofthe source, xi, yi and zi are the coordinates ofthe ith sensor, and vp is the wave velocity. Thewave velocity was determined during calibra-tion and set to 3950 mm/ms for sample A and3980 mm/ms for sample B. A trial hypocenter(x0, y0, z0, t0) is needed as a first guess. Themiddle of the specimen was chosen as a firstsource location. The problem is overdeterminedwhen there are more than four arrival times. Foreach sensor i there will be residuals γi betweenthe observed TOA tao and calculated TOA tac:

γi = tao − tac (2)

These residuals will be minimised by calculat-ing and applying correction factors (δx, δy, δz,and δt) in order that the calculated arrival timesbest match the observed arrival times. Theresiduals can also be written as:

γi =∂fi∂x

δx+∂fi∂y

δy +∂fi∂z

δz +∂fi∂tδt (3)

where fi is the right side of eq. 1. or in matrixnotation:

γ = Aδcorr (4)

where A is the matrix of partial derivativesand δcorr the correction vector. For four sen-sors, one unique solution exists. For more thanfour sensors, the problem is overdefined and thecorrection vector is calculated by the Moore-Penrose inverse to compute the least squares so-lution:

δcorr = (ATA)−1ATγ (5)

The trial solution is updated at the beginning ofeach iteration step by adding the correction fac-tor from the previous iteration:

xk+1o = xko + δx,

yk+1o = yko + δy,

yk+1o = zko + δz,

tk+1o = tko + δt

Two criteria were set to stop the iterative pro-cess. The first stopping criterion is based onthe size of the correction vector. The correc-tion vector δcorr includes both spatial and timecomponents which makes it difficult to calcu-late its size as it contains different units [13].Therefore, the correction vector δd was deter-mined only based on the spatial components:

δd =√δx2 + δy2 + δz2 (6)

The correction vector should be smaller than achosen tolerance ε. When δd goes to zero, it isa sign of convergency. Therefore the toleranceε was chosen to be 0.02. The maximum amountof iterations was set to 50.

To visualise an estimation of the localisationaccuracy, error ellipsoids can be used. There-fore, the covariance matrix C should be calcu-lated:

C = σ2d(A

TA)−1 (7)

where σ2d is the data variance. Only spatial er-

rors are of interest. C is thus a 3x3 matrix hav-ing the variances of the source parameters in di-rection of the three coordinates on its diagonal.

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From the eigenvalues λi of C, the length of thesemi-axis can be determined. The eigenvectorsvi will describe the orientation. The semi-axesli for a 68%-ellipsoid are described as:

li =√

3.53λi (8)

The data variance σd is usually unknown. How-ever, it is possible to estimate this based on theresiduals by:

σ2d =

∑i=1

γTi γi

m− q(9)

with m the observed arrival times and q theunknown source parameters which is 4 in thiscase (x, y, z, t). However it is reported bySchechinger [14] that this gives an overestima-tion of the error. Therefore, σ2

d is substituted bys with following equation:

s =

∑i=1

γTi γi

m(10)

3.3 Agglomerative hierarchical clusteringbased on cross-correlation

In Van Steen et al. [4], a signal-based clus-tering algorithm is elaborated that can be usedto characterise different AE signals that orig-inate during the corrosion test. Clustering isthe process in which a set of objects or pointsare grouped into categories or clusters accord-ing to a virtual distance measure. Similar pointsin the same cluster will have a small distanceto each other while points in different clustersare dissimilar and thus are at a large distancefrom one another. In signal-processing, nor-malised cross-correlation can be used as a mea-sure of similarity of two signals. For continuousfunctions f(t) and g(t), the normalised cross-correlation is defined as:

Rfg(t) =Rfg(t)√

Rff (0)Rgg(0)(11)

where

Rfg(t) = (f ? g)(t) =

∫ +∞

−∞f(τ)g(t+ τ)dτ

(12)

Rff (0) =

∫ +∞

−∞f(τ)2dτ (13)

Rgg(0) =

∫ +∞

−∞g(τ)2dτ (14)

A correlation coefficient cc(f, g) between 0and 1 can be defined as the maximum of the ab-solute value of all points (Eq. 15). The value 1means that the two signals are identical whereas0 means that they are not similar at all.

cc(f, g) = max(abs(Rfg(t))) (15)

Dissimilarity can be used as a virtual dis-tance measure to cluster AE signals. The dis-tance or dissimilarity d(f, g) can be defined as1 minus the correlation coefficient cc(f, g). Ac-cording to this definition, the more similar twosignals are, the shorter their distance will be.The distance approaches 0 as correlation goesto 1. Each signal forms a separate cluster at thestart. These one-signal-clusters are then com-bined into larger clusters based on their close-ness. Two clusters with the shortest distance,i.e. smallest dissimilarity, are merged first. Thedistance between this newly formed cluster andthe other existing clusters needs to be calcu-lated first. The calculation of this inter-clusterdistance or cophenetic distance can be executedin different ways, among which single (nearestneighbour), complete (furthest neighbour), andaverage linkage are most commonly used. Av-erage linkage is used in this paper as single link-age can produce chain-shape clusters and com-plete linkage is more sensitive to outliers.

4 RESULTS AND DISCUSSION

Absorption

Drying upper part

Cement hydration

Corrosion

Micro-Cracking

Macro-Cracking

Salt crystallisation

probability to be recorded by AE

test duration

High Low

Figure 4: Possible AE sources.

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A list of possible sources that could havebeen be captured by the AE technique werelisted and the probability of their detection byAE sensing was estimated as shown in figure4. Dummy samples were tested to eliminatesome of these processes such as cement hy-dration (concrete block on a table) and absorp-tion/drying (concrete block in water). Somesignals were recorded due to absorption anddrying of the concrete block. However, thesewere mainly single hits for which the arrivaltime could not be picked accurately. These sig-nals would therefore be deleted automaticallywhen filtering the data.

4.1 Sample A: longitudinal reinforcement,no stirrup

AE localisation results without filtering andarrival time picking by AIC are shown in figure5. Localised events are very scattered and manyreflections can be noticed in the top part ofthe sample. Characterising the damage sourceswould be impossible.

Figure 6 shows the results after runningthrough the post-processing protocol, takinginto account the events that are localised by 4, 5or 6 channels and having an error of less than 20

mm in every direction of the error ellipsoid. No-tice that the events localised by 4 sensors do nothave an error ellipsoid as the solution is unique.

At the end of the experimental program, acrack could be noticed at the bottom side ofthe sample, perpendicular to the rebar. A smallamount of events is localised near the crack atthe bottom. The localisation results will be mostaccurate when the sensor array surrounds thearea of interest. Due to the corrosion setup, itwas necessary to place the sensors on top of thesample as it was impossible to attach the sen-sors in the salt solution. Therefore, this sensorlayout is not ideal to monitor the cracks that willbe formed at the bottom part of the sample. Thewave will be reflected and attenuated before itreaches one of the sensors. Also the rebar has abig influence on the propagation path to sensor1 and 2.

Also a crack at the side (surface where S5and S6 where mounted) could be seen. Thiscrack was parallel to the rebar and was localisedsuccesfully as visualised on figure 6.

AE events are also localised at the side of S3and S4. However, no crack could be seen on thissurface. It is possible that a crack was growing,but did not reach the surface yet.

S1 S2

S5

S3

S4

S6

S1

S2S4

S3

S5

S6

AE sensor sample boundariescrack on surface

PVC Bonded lengthAE event

Figure 5: Unfiltered localised events.

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S1 S2

S5

S3

S4

S6

S1

S2S5

S3

S4

S6

S1

S2S5

S6

S4

S3S1

S2

S5

S6S3

S4


PVC

Bonded lengthAE event

Localisation error

Figure 6: Localisation results of sample A with indication of the error ellipses and cracks that were visible on the samplesurface.

The results of the clustering algorithm areshown in figure 7. The threshold was set to0.7 as reported previously in Van Steen et al.[4] and verified by clustering signals from artifi-cial sources. Two clusters can be distinguished.The largest one (red, cluster 1) contains signalswith a peak frequency between 200 and 250kHz. The smallest cluster (green, cluster 2) con-tains only three signals having a peak frequencyaround 100 kHz.

Figure 7: Sample A: Dendrogram showing two differentclusters.

The signals of cluster 1 are recorded almostfrom the beginning of the test as shown in fig-ure 8. To investigate whether this process couldbe corrosion or concrete cracking, an RA-AFanalysis was carried out. The difference be-tween a shear crack and a tensile crack is de-fined through the RA value (Rise Time dividedby Amplitude) and average frequency (Countsdivided by Duration). For the latter, the samefrequency over the entire duration of the signalis assumed without performing a Fast FourierTransform (FFT). Higher frequencies and lowerRA-values are typically assigned to the tensilemode (cracking) whereas lower frequencies andhigher RA-values to the shear mode (in our casecorrosion, see [4][6]). As presented in figure 9,most signals are assigned to the tensile mode.Therefore it can be concluded that cluster 1 iscracking of the concrete cover. As only threesignals are assigned to cluster 2, it is hard to as-sign a damage source. Cluster 2 might be cor-rosion as this is typically a lower frequent sig-

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nal in comparison with concrete cracking [15].There may be two reasons why few signals arecaptured. On the one hand because of the largethickness of the concrete cover leading to thesignal being attenuated before it reaches thesensor. On the other hand because of the fre-quency range of the system and sensors whichwas between 95 kHz and 850 kHz and between100 and 400 kHz respectively.

Figure 10 shows the cumulative AE energyversus time in comparison with the crack mea-surements. The time frame where the cracksmust have reached the surface is indicated by agrey area. The moment at which internal crack-ing is initiated can typically be distinguishedby a sudden jump in the AE energy curve [16].Based on figure 10 this must have been aroundday 12. However, on figure 8 some low energyevents can alredy be noticed before day 12. Thismight be some initial micro-cracking.

Figure 8: Sample A: Events of different clusters versustime.

Figure 9: Sample A: Relationship between RA-value andAF of clustered events.

Figure 10: Sample A: Time history of AE energy in com-parison with average crack width.

4.2 Sample B: longitudinal reinforcementand stirrup

The same analysis was performed for sampleB. This sample already showed a small shrink-age crack at the beginning of the test. MostAE events are localised around the stirrup at theside where the crack was visible on the surface.This is shown in figure 11. Also for this sample,a large cluster (red, cluster 1) and smaller clus-ter (green, cluster 2) were distinguished by theclustering algorithm (figure 12). A third clus-ter (blue, cluster 3) can also be noticed. Againpeak frequencies range between 200 and 250kHz for cluster 1 and around 100 kHz for clus-ter 2. Cluster 3 only contains 2 signals havinga peak frequency around 180 kHz. A RA-AFanalysis was also carried out for sample B (fig-ure 13). As was the case for sample A, the sig-nals of sample B can mainly be assigned to thetensile mode meaning that cluster 1 is crack-ing of the concrete cover. Events are mainlyrecorded starting from day 20 (figure 8) whenthe crack started to grow (figure 15). Also forthis sample it is hard to assign a specific damagesource to cluster 2 and cluster 3 as few eventswere localised.

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S1 S2

S5

S3

S4

S6

S1

S2S5

S3

S4

S6

S1

S2S5

S6

S4

S3S1S2

S5S6

S3S4


PVC

Bonded lengthAE event

Localisation error

Figure 11: Localisation results of sample B with indication of the error ellipses and crack that was visible on the samplesurface.

Figure 12: Sample B: Dendrogram showing three differ-ent clusters.

Figure 13: Sample B: Relationship between RA-valueand AF of clustered events.

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Figure 14: Sample B: Events of different clusters versustime.

Figure 15: Sample B: Time history of AE energy in com-parison with average crack width.

4.3 AE post-processing protocol: evalua-tion

In this last section some important param-eters are discussed which could improve test-ing and analysis. First of all, the sensor lay-out is very important in order to be able accu-rately localise AE events. Due to the corrosionsetup, it was not possible to put the sensor ar-ray around the steel rebar. The sensors weretherefore placed as ideal as possible. The cur-rent layout has the disadvantage that the locali-sation errors of the events originating from thebottom part of the sample were too high or thatthey could not be localised at all (e.g. the crackat the bottom of sample A).Second, for this kind of AE analysis it is veryimportant that the length of the time window ofthe stored signal is long enough. Also the pre-trigger time is an important setting. A longerpre-trigger time than 20 µs might have been bet-ter in order to estimate the real arrival time for

more low-amplitude signals, originating fromthe corrosion itself.Third, the clustering algorithm was able to clus-ter different types of signals. However, manysignals were assigned to one cluster whereas forthe other clusters few signals were recorded. Abroadband sensor with a wider frequency rangemight help to overcome this. However, it waschosen in the current investigation to put thelower limit of the system to 95 kHz as manybackground noise was captured when this limitwas set to 25 or 50 kHz.

5 CONCLUSIONSIn this paper, an AE post-processing protocol

was presented as well as a clustering algorithmto distinguish different damage sources duringthe accelerated corrosion process of small RCprisms. Results show that the damage was lo-calised correctly for a sample with and with-out stirrup. Clustering and characterisation wasevaluated based on crack width measurements,time of arrival, and location. This was com-pared with an RA-AF analysis. It was foundthat mainly concrete cracking was recorded andlocalised. The AE post-processing protocol canbe of great value for on-site application of theAE technique. Therefore, this analysis will beupscaled to RC beams in further work .

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CLUSTERING OF ACOUSTIC EMISSION SIGNALS FOR FRACTURE ...framcos.org/FraMCoS-10/Full-Papers/235554.pdf · AE source localisation and characterisation are important to assess a structure