damage detection in composite plates with embedded pzt transducers

8/14/2019 Damage Detection in Composite Plates With Embedded PZT Transducers

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Mechanical Systems

and

Signal ProcessingMechanical Systems and Signal Processing 22 (2008) 13271335

Damage detection in composite plates with

embedded PZT transducers

P. Kudelaa,,1, W. Ostachowicza,b, A. Zaka

aInstitute of Fluid Flow Machinery, Polish Academy of Sciences, ul. Fiszera 14, 80 952 Gdansk, PolandbFaculty of Navigation, Gdynia Maritime University, Al. Jana Pawa II 3, 81 345 Gdynia, Poland

Received 5 January 2007; received in revised form 16 July 2007; accepted 17 July 2007

Available online 2 August 2007

Abstract

This paper presents a concept of a structural health monitoring system based on PZT transducers. Taking advantage of

spectral element method simulations of A0 mode of the Lamb waves propagating in a multilayer composite plate have

been carried out. Based on obtained signals for a clock-like configuration of sensors, a damage detection algorithm has

been proposed. The results for the proposed algorithm have been presented in the form of damage maps. It can be

concluded that the clock-like sensor configuration is suitable for embedding in composite plates because information about

wave velocities at each angle can be included.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Crack detection; Signal processing; Composite plate

1. Introduction

As a human body, structures deteriorate or are damaged in a long-term use. The damage can be generated

by initial defects, fatigue, overloads, and impacts. In composite structures, the different damage modes

expected are: delamination, fibre breakage and matrix cracking. Damage and deterioration of structures

appear as a significant problem because they often cause catastrophic accidents. However, unlike a human

body, the health of structures cannot be self recovered. Therefore, periodic inspections are essential to ensure

the safe operation of structures [1].

Traditional nondestructive evaluation techniques such as: ultrasonic scan, eddy current method,

X radiography, acoustic emission and passive thermography are difficult to use in operation due to the sizeand weight of necessary devices. Moreover, operation must be interrupted, parts must be disassembled and re-

assembled for inspection, which is complex, expensive and time consuming. In opposite, a structural health

monitoring system is an attractive approach to solve problems that occur in degraded structures. Damage and

intensity of degradation are monitored in real time providing useful information for predicting the service life.

Such a system can improve not only safety and reliability but also can reduce maintenance costs.

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www.elsevier.com/locate/jnlabr/ymssp

0888-3270/$- see front matterr 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ymssp.2007.07.008

Corresponding author.

E-mail addresses: [email protected] (P. Kudela), [email protected] (W. Ostachowicz), [email protected] (A. Zak).1Supported by the Polish Ministry of Education and Science (Proj. No. N501 001 31/0103).
http://www.elsevier.com/locate/jnlabr/ymssphttp://dx.doi.org/10.1016/j.ymssp.2007.07.008mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.ymssp.2007.07.008http://www.elsevier.com/locate/jnlabr/ymssp


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The most popular sensors suitable for embedding in structures are fibre-optic sensors and piezoelectric

sensors. In the first case, sensing area is focused around fibres and the cost of a complete system depends on

the type of sensors and configuration of distributing and multiplexing techniques. In the second case, the

sensing area is reasonably, sensors can be placed in a network configuration (Fig. 1a) or connected in a small

circular group working similar to radar devices (Fig. 1b). Piezoelectric sensing systems are cheaper than the

systems based on fibre-optic sensors and are the subject of this paper.

2. Lamb wave modelling

Piezoelectric sensors use diagnostic signals that are generated by impact or actuators. Input signals usually

excite Lamb waves. In practical application only input signals that excite fundamental modes of Lamb waves

(A0 and S0) are considered, in order to simplify interpretation of signal responses. In this case a wave

dispersion appears as an important problem. That situation requires to chose an optimal operation point

corresponding to an excitation frequency. The most suitable cycle number and frequency for a Lamb mode

can be determined by the minimum resolvable distance (MRD) approach [2]:

MRD V0

dL

1

Vmin

1

Vmax

Tin

, (1)

where L and d are the wave propagation distance and plate thickness, V0, Vmin, Vmax are the group velocity at

the central frequency of the input wave-packet, minimum and maximum velocities in the wave packet to travel

through the distance of L, while Tin is the duration of the input signal. It has been found that the smaller a

MRD value the better the resolution and the more suitable the current frequency and cycle number. Modes S0

and A0 are usually observed to have very low MRD values.

An effective development of damage detection systems which utilize guided waves must be supported by

numerical simulations. Wave propagation and scattering that appears in composite plates can be modelled by

taking advantage of spectral element method [3]. Spectral elements are versatile and can be applied to domains

of complex boundaries. Moreover, selection of suitable base functions and numerical integration points enable

equations uncoupling and crucial reduction of calculation time. Also convergence is very fast comparing with

the classical FEM.

3. Numerical calculations

3.1. Influence of composite material parameters on wave propagation

Parameters of composite materials strongly influence on the velocity of propagating waves. Waves in

composite plates propagate in each direction with different velocities. That can be plotted in the polar

coordinates as presented in Fig. 2. It can be seen that numerical model gives little slower wave front than the

wave front calculated using a simply analytical procedure given in [4].

Also the shape of the wave front changes with the frequency. For this reason a right choice of an optimal

excitation frequency should minimize dispersion (MRD value) and should give the most circular wave front.

Fortunately, the frequency range which gives a flat group velocity curve (Fig. 3) gives the most circular wave

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Fig. 1. Configuration of sensors: (a) a distributed sensor array, and (b) a clock-like sensor array.

P. Kudela et al. / Mechanical Systems and Signal Processing 22 (2008) 132713351328


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front. It should be noticed that dispersion curves presented in Fig. 3 are obtained from a mathematical model

of the composite plate based on Mindlins plate theory. This theory gives a good approximation of A0 mode

of the Lamb waves (cw curve in Fig. 3) only below cut off frequencies. A1 and A2 mode of the Lamb waves are

approximated very roughly (ca and cb curves in Fig. 3, which correspond to rotational degrees of freedom).

If a composite material contains more fibres then waves propagate at higher velocities. Also the shape of the

group velocity surface changes with the volume fraction of the fibres. The group velocity depends also on the

orientation angle of the reinforcing fibres. Theoretical and numerical calculations for a single layer graphite-

epoxy composite plate with a constant volume fraction of the fibres show that the front of the propagating

wave is preserved, while an ellipse shaped elongation is rotated according to the fibre orientation angle [4].

3.2. Multilayer composite plate with crack

A plate under consideration (Fig. 4) has the following dimensions: length 500 mm, width 500 mm, and

thickness 2 mm. The excitation source is a 105.7 kHz sinusoidal signal modulated by Hanning window of five

cycles. This frequency corresponds to the maximum group velocity of A0 mode of the Lamb waves (vide

Fig. 2). It is assumed that the plate consists of four graphite-epoxy layers. A volume fraction of the reinforcing

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s08

500

1000

1500

210

60

240

90

270

120

300

150

330

180 0

100 kHz

30 kHz

20 kHz

100 kHz simul.

Fig. 2. Group velocity surfaces calculated analytically compared with velocities estimated from a simulation (cross markers) by spectral

element method.

Frequency [kHz]

Groupvelocity[km/s]

ccc

0 100 200 300 400 500 6000

1

2

3

4

5

105.7

kHz

~343kHz

Fig. 3. Dispersion curves for a 452 composite plate of 2 mm thick obtained from a mathematical model.

P. Kudela et al. / Mechanical Systems and Signal Processing 22 (2008) 13271335 1329


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fibres in each layer is 50%. The ply stacking sequence of the plate is 452. The total time of analysis has been

assumed 0.7 ms, which is enough for propagating wave to travel from excitation point to the boundaries of the

plate and back. The excitation point is located at the center of a clock-like array of sensors and the remaining

points in Fig. 4 indicate sensors.

Based on the assumptions described above, numerical simulations of A0 mode of the Lamb waves have

been carried out in the case of undamaged and damaged plate. This problem is solved by the use of spectral

element method. A grid of 30 30 100-node spectral plate elements has been used. It gives roughly 220 000degrees of freedom and about seven nodes per wavelength. The total simulation time has been divided into

15 000 time steps. Such parameters assure stability of the method.

Two damage scenarios have been investigated. In the first case only crack no. 2 is present. In the second case

crack nos. 1 and 2 are present in the plate as presented in Fig. 4. Left tip of the crack no. 1 has coordinates

(300 mm, 83.3 mm) and length is 16.6 mm. Left tip of the crack no. 2 has coordinates (233 mm, 300 mm) and

the length 16.6 mm. The cracks have been introduced by separations appropriate element nodes.

Certain results of numerical simulations are presented in Fig. 5. Reflections from the cracks can be clearly

visible.

4. Damage detection algorithm

For the purpose of damage detection based on the signals registered by the considered clock-like manner

sensor array a simple detection algorithm has been proposed and developed, and founded on the ideas

presented in [57].

The proposed damage detection algorithm makes use of the assumption that the excitation signal and

signals reflected from damage have matching features. If this is true the idea is to search all signals registered

for signals reflected from damage and subsequently to compare the features of these signals with the features

of the excitation signal. The excitation signal has a finite length (Fig. 6) and thus can be thought of as

surrounded by a virtual time window. This time window can be arbitrarily placed on each of the registered

signals resulting in a certain time shift, which is equivalent to a distance required for the propagating signal to

travel from the excitation point (the central transmitter) to a point Pof coordinates x and y (possible damage

location) and then back to an appropriate sensors. Based on the part of the registered signal matching the

extent of the time window a certain measure of the match between the signals can be built and associated with

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200

500

500

200

12

3

6

9

sensor array

100

Fig. 4. Geometry of a composite plate with two cracks.



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the coordinates x and y. In the case when the registered signal, within the considered time window, is free of

the signal reflected from damage the value of this measure is very low and close to zero. On the other hand

when the registered signal carries on some information about the signal reflected from the damage the value of

the measure is much higher. A special damage influence map can be built by application of this procedure to

all points of the plate and by summation of the obtained results.

For the signal registered by the kth sensor it can be written that:

ST STt0; t0 Dt; SR;k SR;kt0 Dt; t0 Dt

; k 1; . . . ; 12, (2)

where t0 is the beginning time of the time window, Dt is the width of the time window and Dt is the signal time

shift (Fig. 6). The two time signals ST and SR;k obtained in this way have the same width Dt. The signal time

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Fig. 5. Snapshots of the propagating waves in a graphite-epoxy composite plate with one crack (left) and with two cracks (right) obtained

from simulation. (a,b) Time 0.07ms; (c,d) time 0.12 ms; (e,f) time 0.16 ms; (g,h) time 0.21 ms.



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shift Dt may be expressed in terms of the distance between point P and the signal propagation group

velocity V as

Dtx;y d0P

V0P

dPk

VPk

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2 y2

pV0P

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix xk

2 y yk2

qVPk

, (3)

where d0P and dPk represent the distances between the central transmitter and point P and between point P

and kth sensor, respectively. It should be noticed that in composite materials the group velocity depends on

the direction of propagation (vide Fig. 2). For this reason the values of the group velocities V0P and VPk are

not equal and are different for each point Pin opposite to an isotropic case. Based on the time signals ST and

SRk the measure of the match between the two signals can be build and associated with the point P of

coordinates x and y as

ekx;y

Zt0Dtt0

STtFtGx;ySRkt dt, (4)

where Ft is a windowing function (such as Gauss, Hann, Hamming, etc.), while Gx;y is a function taking

into account the attenuation of the reflected signal amplitude:

Gx;y ea d0PdPk, (5)

where a is the attenuation coefficient. The total measure of the match between the signals obtained from all

receiving sensors can be build as follows:

E X

k

ZS

ekx;y dS %X

k

Xi;j

ekxi;yj,

k 1; . . . ; 12; i 1; . . . ; N; j 1; . . . ; M, 6

where Sis the surface of the plate and Nand Mrepresent the total number of nodes iand jlocated on the plate

surface.

4.1. Example of damage detection

The damage detection algorithm described in the previous section has been tested based on the results from

numerical simulations. The algorithm has been applied to signals registered by 12 sensors with random noise

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12

3

6

9

sensor array

P(x,y) P(x,y)

V( )

dPk

d0P

t*t

Fig. 6. The idea of a damage identification algorithm in a composite plate.



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up to 2% of the maximum amplitude of the signals. The plate has been divided into 200x200 nodes. The group

velocity of the propagation signal has been taken from the numerical simulations rather from the known

analytical formulas. The measure of the match between the two signals defined in Eq. (4) has been modified to

the form:

ektj jFfc

j % jDFTFtiSRktj i 1 dtj; i 1; . . . ; Nw, (7)

whereF is the linear interpolation of the amplitude corresponding to the carrier frequency fc of the excitation

signal ST, calculated using the signal registered by the kth sensor, the DFT denotes the discrete Fourier

transform, Fis the Hanning window, dt is the sampling interval, and Nw is the number of points in the virtual

window. Such definition causes that the damage detection algorithm can be classified as a time-frequency

method. Moreover, such a damage detection algorithm has excellent filtering properties. In all cases

investigated here the exact location of damage considered has been clearly indicated and marked for reference

purposes.

As a first damage influence maps have been built based on damage state signals (plate with cracks). It can be

seen that the reflections of the signal from the cracks (Figs. 7a and 8a) are obscured by the reflections from the

boundaries and the location of the cracks cannot be detected. However, boundary reflections can be removed

considering only the time of wave propagation from the central transmitter to the nearest boundary and backto the nearest sensor. In such a case the damage influence map gives a clear indication of the location of the

cracks (Figs. 7b and 8b). In the case of two cracks a damage influence map clearly indicates the position of

crack no. 1, which is located closer to the centre of the sensor array and the value of the damage influ-

ence amplitude is high, while reflections from crack no. 2 cause that the second maximum of the damage

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Fig. 7. Numerical results: damage influence maps for a plate with one crack (white mark). (a) Signals without a baseline; (b) Signals

without a baseline and with boundary reflections removed; (c) Signals with a baseline; (d) Signals with a baseline and with boundary

reflections removed.



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influence map indicate its location (Fig. 8b), but the value of damage influence amplitude is much smaller than

that for crack no. 1. Obviously, the front wave propagating parallel to the crack generates much more

scattered waves and for this reason identification of the position of crack no. 1 is easier.

Signals used by the algorithm can be related to the signals obtained for the plate with no damage. Such

differential signals carry all essential information about the presence of damage and can be very effectively

used (Figs. 7c and 8c). The location of a crack can be estimated with sufficient precision. The difference

between the maximum of the damage influence amplitude and the centre of the crack is less then 3 mm in the

case of one crack (Fig. 7d) and less than 10 mm in the case of two cracks (Fig. 8d).

Considering a clock-like PZT element as a moving monitoring tool, the dead zone presented in Fig. 4 could

be reduced and in a few stages a large area of a structure may be inspected. Another possibility is to cover the

area of a structure by few clock-like PZT elements and to monitor the structure online.

5. Conclusions

Spectral element method enables accurate modelling of the wave propagation phenomena in anisotropic

media with failures. In composite materials wave propagates in each direction with different velocity and this

information should be included in a damage detection algorithm. As a consequence of this property it is easier

to design a monitoring system with the clock-like PZT configuration than with a regular grid of sensors. The

proposed method of damage detection enables one to produce damage influence maps. Such maps show the

location and the severity of damage. The developed damage detection algorithm is universal and can be

applied to any sensor configuration.

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Fig. 8. Numerical results: damage influence maps for a plate with two cracks (white marks). (a) Signals without a baseline; (b) Signals

without a baseline and with boundary reflections removed; (c) Signals with a baseline; (d) Signals with a baseline and with boundary

reflections removed.



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References

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[3] A. Patera, A spectral element method for fluid dynamics: laminar flow in a channel expansion, Journal of Computational Physics 54

(1984) 468488.[4] P. Kudela, M. Krawczuk, W. Ostachowicz, M. Palacz, A. Zak, Wave propagation modelling in composite plates with damage, in:

Proceedings of the 3rd European Workshop on Structural Health Monitoring, 2006.

[5] V. Giurgiutiu, J. Bao, Embedded-ultrasonics structural radar for in situ structural health monitoring of thin-wall structures, Structural

Health Monitoring 3 (2) (2004) 121140.

[6] C. Wang, T. Rosej, F.-K. Chang, A synthetic time-reversal imaging method for structural health monitoring, Smart Materials and

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[7] P. Wilcox, Omni-directional guided wave transducer arrays for the rapid inspection of large areas of plate structures, IEEE

Transactions on Ultrasonics, Ferroelectric, and Frequency Control 50 (6) (2003) 699709.

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damage detection in composite plates with embedded pzt transducers

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