Impact Damage Detection in Composites using Nonlinear Vibro-Acoustic Wave Modulations and Cointegration Analysis

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1 11th Euroean Conference on Non-Destructive esting (ECND 214), October 6-1, 214, Prague, Czech Reublic More Info at Oen Access Database Imact Damage Detection in Comosites using Nonlinear Vibro-Acoustic Wave Modulations and Cointegration Analysis Phong B. DAO 1, Wieslaw J. SASZEWSKI 1, Andrzej KLEPKA 1, Francesco AYMERICH 2 1 Deartment of Robotics and Mechatronics, AGH University of Science and echnology, Al. Mickiewicza 3, 3-59 Krakow, Poland. Phone: , Fax: ; hongdao@agh.edu.l, w.j.staszewski@agh.edu.l, kleka@agh.edu.l 2 Deartment of Mechanical, Chemical and Materials Engineering, University of Cagliari, Piazza d Armi, 9123 Cagliari, Italy; francesco.aymerich@dimcm.unica.it Abstract his aer resents an alication of nonlinear acoustics for imact damage detection in comosite laminates. he method is based on nonlinear vibro-acoustic wave modulations. he concet of stationarity of time series is emloyed for the analysis of vibro-acoustic data. Analysis of stationary statistical characteristics of vibroacoustic resonses after the cointegration rocess (i.e. cointegration residuals) are used for damage detection. he method is demonstrated using two comosite lates. One of the lates is intact whereas the other late is damaged after the low-velocity imact with the 3.9 J energy. Both comosite lates are instrumented with surface-bonded, low-rofile iezoceramic transducers that are used for high-frequency ultrasonic excitation. Low-frequency modal excitation is alied using an electromagnetic shaker. Scanning laser vibrometry is used for non-contact measurements of vibro-acoustic resonses. he method is validated using vibro-acoustic data catured for several frequencies of low-frequency excitation corresonding to different vibration modes. he exerimental results show that the method can accurately detect imact damage for all data sets investigated. Keywords: Structural damage detection, comosites, nonlinear acoustics, variable oerational conditions, nonstationarity, cointegration analysis 1. Introduction Recent years have shown many interests in nonlinear acoustic methods that are used for structural damage detection. Various aroaches based on ultrasonic wavefield and vibroacoustic wave interactions have been develoed, as illustrated in [1 5]. he vibro-acoustic wave modulation technique is based on nonlinear interactions of high-frequency ultrasonic wave and low-frequency modal (or vibration) excitation introduced to a monitored structure simultaneously. However, it is well known that modulation intensity, often used for damage detection, strongly deends on amlitude of the low-frequency modal excitation associated with different vibration modes. Previous investigations [4,5] showed that different vibration modes can lead to different damage detection sensitivity. In addition, once this frequency is selected, damage detection results cannot be comared with similar results for other frequencies. Hence, comensation for this effect is imortant to develo methods that are sensitive only to damage but insensitive (or indeendent) to oerational conditions. Various aroaches were develoed to deal with the undesired effect of environmental and oerational variability in data used for damage detection, as discussed in [6]. With resect to nonlinear acoustics, a ossible solution is that, instead of directly analysing and interreting data, one can first aly an aroriate signal rocessing technique on vibroacoustic data (i.e. data normalisation) and then analyse and interret the damage-sensitive features obtained. he cointegration aroach develoed originally in the field of econometrics [7] has been recently roosed as a new methodology for dealing with the roblem of oerational/environmental variability in Process Engineering [8] and Structural Health Monitoring (SHM) [9 12]. he major idea used in these investigations is based on the concet of stationarity. Monitored variables are cointegrated to create a stationary residual whose stationarity reresents intact condition. hen any dearture from stationarity

2 can indicate that monitored rocesses, objects or structures are no longer oerating under normal condition. he work resented in [8, 9] shows that if some variables from a rocess under investigation are cointegrated, the stationary linear combinations of these variables during the cointegration rocess are urged of all common trends in the original data, leaving residuals equivalent to the long-run dynamic equilibriums of the rocess. his work has been extended to the concet of multile cointegration analysis in [1], which demonstrates a non-conventional aroach to cointegration for temerature effect comensation (i.e. data normalisation) and damage detection in Lamb wave based damage detection of aluminium structures. More recently this aroach has been used for multile temerature trend removal [11]. he cointegration used for damage detection has been also analysed in the context of fractal signal rocessing [12]. he current aer builds uon revious studies on the cointegration method for trend removal in SHM data. he major objective is to resent a new aroach based on cointegration for the removal of variable oerational conditions associated with low-frequency modal excitation in nonlinear vibro-acoustic wave modulations (i.e. data normalisation) such that imact damage detection in comosite laminates can be carried out reliably. Analysis of stationary statistical characteristics of vibro-acoustic resonses after the cointegration rocess (i.e. cointegration residuals) based on the augmented Dickey-Fuller (ADF) statistical test are used for damage detection. he structure of the aer is as follows. Section 2 briefly introduces the concet of cointegration analysis and the ADF statistical test. Section 3 resents a cointegration-based aroach to SHM used for damage detection. he nonlinear vibro-acoustic exerimental data used to illustrate the method are resented in Section 4. Damage detection results are resented in Section 5. Finally, the aer is concluded in Section Cointegration analysis A set of non-stationary time series, least) a vector stationary, i.e. ( 1, 2,, n ) t t ( 1t, y2t, y, y ) nt, are cointegrated if there exists (at such that it results in a linear combination of them that is 1 y1t 2 y2t n ynt (1) he stationary linear combination t is referred to as a cointegration residual or a longrun equilibrium relationshi between time series [13]. he vector is called a cointegrating vector. It is imortant to note that the work resented in this aer considers the action of creating the cointegration residual ( ut t ) as the action of rojecting the (nonstationary) time series Yt on the cointegrating vector. A non-stationary time series yi in Yt is integrated order d, denoted y i ~ I( d), if after differencing the series d times it becomes stationary. he number of differences required to achieve stationarity is called the order of integration. In essence, testing for cointegration is testing for the existence of stationary linear combinations among all elements of t [13]. Such tests have two imortant requirements. Firstly, any analysed time series must exhibit at least a common trend. Secondly, the analysed

3 time series must have the same degree of non-stationarity, i.e. they must be integrated of the same order. When there are only two variables in t, a two-ste residual-based test rocedure develoed in [7] can be used. his rocedure is based on regression techniques for determining if the vector is a cointegrating vector. he first ste is to form the cointegration residual ut t. he second ste is to erform a unit root test on ut to determine if it is a stationary time series. he Augmented Dickey-Fuller (ADF) test described in [14] is the most widely used unit root test in ractice. he ADF test checks the null hyothesis that a time series is a non-stationary tye series against the alternative hyothesis that it is a stationary tye series, assuming that the dynamics in the data have an Auto-Regressive Moving Average (ARMA) structure [13]. he ADF test is based on estimating the following regression formula y t D t t 1 j yt j t j 1 y (2) where D is a deterministic linear trend. In Equation (2), the t lagged difference terms or lag length ( ) are used for aroximating the ARMA structure of the errors. he j j y 1 t j value of the lag length is set to a value, so that the error t is a white noise rocess [13]. When t includes more than two variables, a sequential rocedure for determining the existence of cointegration develoed in [15] and known as the Johansen s cointegration method is widely used. his rocedure is a combination of cointegration and error correction models in a Vector Error Correction Model (VECM) that takes the form t Dt t 1 1 t 1 1 t 1 t (3) where and are ( n r) matrices with rank( ) rank( ) r and the first term on the righthand side i.e. D t contains deterministic terms (e.g. constant only or constant lus time trend). he stationary linear combinations ( urt t ) are referred to as the r cointegration residuals that are formed through rojecting the (non-stationary) time series Yt on the r cointegrating vectors. he non-deterministic art on the right hand side of Equation (3) i.e. 1 t 1 1 t 1 denotes the 1 lagged difference terms (or the lag length ) used for aroximating the VECM. he Johansen s cointegration method is used in this study for cointegration analysis. he method is a comlex sequential rocedure and therefore it is not resented in this aer. For more detailed descrition of the entire rocedure, otential readers are referred to [15]. 3. Cointegration-based aroach to SHM used for damage detection he method erformed involves two stages: 1. he stationarity-based aroach [16 18] is firstly alied to determine the otimal lag length(s); 2. he best statistically selected lag length(s) are then used for damage detection analysis.

4 3.1 Otimal lag length selection In this stage, the SHM data reresenting undamaged condition are used to establish the otimal value(s) of lag length. he algorithm roosed in [16 18] for otimal lag length selection in cointegration analysis used for damage detection can be described using four major stes: Ste 1: Determine the min and max values. It is clear that min 1 is the minimum value of lag length that can be used in cointegration analysis. he maximum lag length value max can be calculated using the following equation [19]. 1 4 N max 12 (4) 1 where the square brackets denote the integer art of the result, and samles. Equation (4) guarantees that max N is the number of data grows with the number of data samles used. Ste 2: Cointegration analysis. After the min and max values are established, N sets of SHM data reresenting undamaged condition are cointegrated using the Johansen s cointegration rocedure. his results in N 1 linearly indeendent cointegrating vectors. hese vectors are then used to roduce N 1 cointegration residuals by erforming the socalled on rojection. his rojection means that data reresenting the undamaged condition are rojected on the cointegrating vectors obtained from data reresenting the undamaged condition. he entire analysis is erformed for all lag length values 1,2,3,...,, leading to a ( N 1) matrix of cointegration residuals. max Ste 3: AD test. ADF t-statitics are calculated for all cointegartion residuals (i.e. ( N 1) max matrix of cointegration residuals) and lag length values. As a result, N 1 ADF t-statistics are obtained for each value of lag length. Ste 4: Averaged ADF t-statistics calculation. An averaged value of ADF t-statistics is calculated for each lag length 1,2,3,..., max. he most negative value from all averaged ADF t-statistics indicates the otimal value of lag length that roduces the most stationary residuals obtained for the. he assumtion is that the selected lag length is the otimal value, leading to the best results when cointegration analysis is used for damage detection in the next stage. 3.2 Damage detection analysis In this stage, damage detection analysis is erformed using cointegration analysis and ADF statistical test with the otimal lag length value(s) found and other randomly chosen lag lengths, for comarison. his analysis involves the analysed data on analysed data rojection. his rojection means that data reresenting damage conditions are rojected on the cointegrating vectors obtained from data reresenting damage conditions. he damage detection rocedure that is used can be described using the sequence of the following stes SHM data Cointegration analysis ADF statistical tests ADF t-statistics. In other words, after the cointegration analysis is used, the ADF test is alied to cointegration residuals and then ADF t-statistics are calculated. he resulting statistics are then used for damage detection to searate data reresenting damaged and undamaged conditions. max

5 4. Nonlinear vibro-acoustic data Nonlinear vibro-acoustic data used in this aer come from a series of exerimental tests described in [5]. hese tests were erformed for two comosite lates, i.e. one intact (or undamaged) and one with a delamination ositioned centrally. he secimens were manufactured from carbon/eoxy (Seal HS16/REM) unidirectional rereg layers. he stacking sequence of the laminate was [3/93]s. he average laminate thickness was equal to 2 mm. Nonlinear acoustic tests were erformed for both, i.e. the undamaged and damaged comosite lates. Low-rofile iezoceramic transducers were surface-bonded to the lates using two-comonent eoxy adhesive. Exerimental modal analysis was erformed to select resonance frequencies for low-frequency vibration/modal excitation. he frequency corresond to vibration mode were used as monoharmonic low-frequency excitation. wo iezoceramic transducers were used to excite the structure; PI ceramics PIC155 for highfrequency excitation and NOLIAC CMAP4 for low-frequency excitation. A Polytec PSV-4 laser vibrometer was used for non-contact measurements of vibration resonses. he excitation signals were generated and amlified using PAQ-G amlifier. he frequency of the high-frequency ultrasonic excitation was equal to 6 khz with amlitude level equal to 25. [V]. One of the ten selected resonance frequencies i.e. 77, 178, 25, 314, 37, 477, 498, 545, 744 or 92 Hz was used for low-frequency vibration/modal excitation. For each vibration mode, thirteen different amlitude levels (. [V], 1. [V], 2. [V],, 1. [V], 11. [V]) were used in the nonlinear vibro-acoustic tests. Figure 1 gives examles of nonlinear vibro-acoustic resonses for the undamaged and damaged comosite lates excited with two different resonance frequencies. In this aer, we analysed the nonlinear vibro-acoustic data obtained from low-frequency modal excitation using the same frequency but with different amlitude levels. In other words, single variable oerational condition (i.e. a variety of amlitude levels associated with lowfrequency excitation) was considered in this case. x 1-3 (a) x 1-3 (b) 5 5 Amlitude [-] Amlitude [-] Data samles x 1 6 x 1-3 (c) Data samles x 1 6 x 1-3 (d) 5 5 Amlitude [-] Amlitude [-] Data samles x Data samles x 1 6 Figure 1. Examles of nonlinear vibro-acoustic resonses for low-frequency modal excitation using the same amlitude level (6. [V]) but with two different frequencies: (a,b) 2 nd vibration mode 178 Hz; (c,d) 9 th vibration mode 744 Hz. Left column shows the data for the undamaged comosite late whereas the right column gives the data for the damaged late.

6 5. Results and discussion Nonlinear vibro-acoustic data from comosite secimens described in Section 4 were used to illustrate the roosed method resented in Section 3. he analysis in this aer utilised twenty (i.e. N 2 ) nonlinear vibro-acoutic resonses for each damage condition. Initially, each resonse measurement consisted of N 5 data samles. he effect of using different numbers of data samles with resect to damage detection analysis was studied. 5.1 Otimal lag length selection he results obtained from the revious investigations in [16,18] have showed that the two lag length values 13 and 15 were determined as the otimal values. In order to confirm the findings, these two otimal lag lengths and two arbitrarily chosen lag lengths (i.e. 6 and 26 ) were selected for damage detection analysis. 5.2 Damage detection analysis Figure 2 resents some selected damage detection results calculated for the vibro-acoustic data obtained from exeriments with the first vibration mode (77 Hz). he results show that the average ADF t-statistics for the damaged comosite late are very well searated from the relevant t-statistics calculated for the undamaged late for almost nineteen cointegration residuals, when the lag lengths are equal to 13 and 15. As a result, the investigated imact damage can be detected. In contrast, when the lag lengths 6 and 26 are used, the average ADF t-statistics for both undamaged and damaged lates overla for the majority of cointegration residuals. Clearly, damage detection is not ossible in this case. he results have confirmed the roosed aroach and the otimal lag length selection results. (a) (b) 7 (c) 7 7 (d) 7 Figure 2. Damage detection based on nonlinear vibro-acoustic data obtained from exeriments with 1 st vibration mode. he average ADF t-statistics were calculated for the cointegration residuals reresenting two different damage conditions. he analysis was erformed for the lag lengths: (a) 13 ; (b) 15 ; (c) 6 ; (d) 26.

7 Next, damage detection analysis using different numbers of data samles was investigated. he nonlinear vibro-acoustic data reresenting the undamaged and damaged comosite lates and acquired from exeriments with the first vibration mode (77 Hz) for all thirteen different vibration amlitude levels were used in this analysis. he analysis was erformed for four different numbers of data samles: the initial value N 5 ; N 3; N 15 ; and the maximum value 64. he two otimal lag lengths (i.e. and 26 ) were used. 13 and 15 ) and two arbitrarily chosen lag lengths (i.e. 6 he results in Figure 3 for the otimal lag length 13 have showed that damage detection is ossible for all four different numbers of data samles investigated. It can be observed that when more data samles are used the ADF t-statistics for both damage conditions become more negative, or in other words, the relevant cointegration residuals become more stationary. One might conclude that the analysis using N 5 gives the best results because of clearer searation between ADF t-statistics of the undamaged and in Figure 3a. However, the searation amlitude is not really large; the maximum searation amlitude obtained for the 9 th cointegration residual equals in this case. Indeed, when more data samles are used the searation amlitude become much larger. For examles, the maximum searation amlitude equals in Figure 3b for the 19 th cointegration residual, equals in Figure 3c for the 17 th cointegration residual, and equals in Figure 3d for the 18 th cointegration residual. o make the comarison more clear, a new damage detection indicator (S) based on the average value of nineteen searation amlitudes between ADF t-statistics of the undamaged and was calculated for all nineteen cointegartion residuals. Figure 4 clearly shows that when more data samles are used the value of indicator S becomes larger. N (a) (c) (b) (d) Figure 3. Damage detection based on nonlinear vibro-acoustic data obtained from exeriments with 1 st vibration mode. he average ADF t-statistics were calculated for the cointegration residuals reresenting two different damage conditions. he analysis was erformed for the otimal lag length 13 for four different numbers of data samles: (a) N 5 ; (b) N 3 ; (c) N 15 ; (d) N 64.

8 55 5 N=64, S= Average searation amlitude (S) N=15, S= N=3, S= N=5, S= the number of data samles (N) x 1 5 Figure 4. Damage detection indicator was calculated from damage detection results in Figure 3. It is based on the average value of 19 searation amlitudes between ADF t-statistics of the undamaged and (a) (b) 26 (c) (d) Figure 5. Damage detection based on nonlinear vibro-acoustic data obtained from exeriments with 1 st vibration mode. he average ADF t-statistics were calculated for the cointegration residuals reresenting two different damage conditions. he analysis was erformed for the lag length 26 for four different numbers of data samles: (a) N 5 ; (b) N 3 ; (c) N 15 ; (d) N 64. Interestingly, in site of the fact that the four different numbers of data samles were also used for the case with the lag length 26 ; the damage detection results obtained in Figure 5 however did not exhibit much difference. ADF t-statistics for the undamaged and damaged

9 comosite lates are overlaed for almost all nineteen cointegartion residuals. here are some searations in ADF t-statistic results in Figure 5c and Figure 5d when 15 and N 64 were used, resectively; but these searations are not large enough to reliably detect the damage. his again confirms the imortance of the choice of lag length used in cointegration analysis and ADF test. N 6. Conclusions A cointegration-based aroach to SHM used for structural damage detection has been addressed in this aer. he method has been illustrated using nonlinear vibro-acoustic data from a delaminated comosite late exosed to different modal excitation. he aer investigated the case using the same frequency but with different amlitude levels. Analysis of stationary statistical characteristics of vibro-acoustic resonses after the cointegration rocess were used for damage detection. he results obtained in this aer confirm the findings from our revious studies in [16 18] that the choice of lag length to be used in cointegration analysis and ADF test lays an imortant role in damage detection analysis, i.e. damage detection was successful when the otimal values of lag length were used; in contrast, damage detection was not ossible for arbitrarily chosen lag lengths. In addition, when the otimal lag lengths were used, increasing the numbers of data samles emloyed in cointegration analysis and ADF test has imroved considerably the damage detection results. he work resented is a feasibility study. herefore, further research work is required to confirm all findings. Acknowledgement he work resented in this aer was suorted by funding from WELCOME research roject no. 21-3/2 sonsored by the Foundation for Polish Science (Innovative Economy, National Cohesion Programme, EU). References 1. F Aymerich and W J Staszewski, 'Imact Damage Detection in Comosite Laminates using Nonlinear Acoustics', Comosites Part A: Alied Science and Manufacturing, Vol 41, No 9, , Setember P Duffour, M Morbidini and P Cawley, 'A Study of he Vibro-Acoustic Modulation echnique for he Detection of Cracks in Metals', Journal of the Acoustical Society of America, Vol 119, No 3, , March Z Parsons and W J Staszewski, 'Nonlinear Acoustics with Low-rofile Piezoceramic Excitation for Crack Detection in Metallic Structures', Smart Materials and Structures, Vol 15, No 4, , August A Kleka, W J Staszewski, R B Jenal, M Szwedo, Uhl and J Iwaniec, 'Nonlinear Acoustics for Fatigue Crack Detection Exerimental Investigations of Vibro-Acoustic Wave Modulations', Structural Health Monitoring, Vol 11, No 2, , July 211.

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