Keywords

1 Introduction

Structural health monitoring (SHM) of any in-service structure is of prime interest to sustain its serviceability throughout its design life. Acoustic Emission (AE) technique is an emerging technique which is gaining popularity for SHM. SHM using AE technique involves identification and localisation of structural damages/defects, which is in-fact AE sources. Structural defects e.g. generation of cracks, growth of crack, yielding, failure of bonds, fibre failure etc. act as AE sources. AE sources emit transient elastic stress waves, which are recorded by sensors mounted on the surface of the structure. AE source localisation method can be one, two or three dimensional (Eaton et al. 2012). One dimensional location gives linear distance of AE source from sensor; in two-dimensional location the localisation is done in a two-dimensional plane, whereas in three-dimension, depth of the source is also considered. The standard approach of AE source location, which is known as ‘time of arrival (TOA)’ method, depends upon the arrival time measurement in an array of sensors. The arrival time is determined by ‘first threshold crossing’, which is defined as reaching a certain user defined voltage value. This method introduces errors in accuracy of localisations due to various reasons such as attenuation of signal, dispersive nature of media, inhomogeneity of media etc. (Eaton et al. 2012). In this regard, wavelet transform (WT), which is a powerful signal processing tool, is used by some researchers towards more efficient AE source localisation method.

The WT of AE response shows the distribution of energy as a function of frequency and time. Researchers, previously, used WT on AE signals to discriminate and locate the AE sources for beams and plates. Suzuki et al. (1996) applied WT to AE signals to classify signal types from GFRP specimens. Jeong and Jang (2000) used WT analysis of AE signal to localise the AE source using 4 sensors. Jeong (2001) investigated dispersion behaviour of CFRP laminates. Hamstad et al. (2002b) showed that the maximum energy content of a WT scalogram at a given frequency can be utilised to measure the arrival time of predominant Lamb mode. Based on this approach, the authors previously studied on the AE source localisation using WT on plates of different thicknesses (Sengupta et al. 2020). Jiao et al. (2004) used the same approach to identify the arrival time of fundamental Lamb modes. Wang et al. (2017) utilised WT analysis of AE waves to introduce a novel type of sensors.

However, this approach is very effective for large plates and becomes less reliable in the presence of nearby boundaries, which is the case of small plate-like strictures, due to edge reflections. The AE transient signals reflect from the edge/boundary of the structural components and mixes with the signals generated due to the original AE source. Hamstad et al. (2002b) studied this problem in small plates by comparing AE signals in 1000 mm × 1000 mm large plate and 480 mm × 25.4 mm small coupon specimen using numerical analysis. However, only a few tens of microseconds of the acquired signal contains the relevant AE features and is enough to identify the fundamental Lamb modes and their arrivals. Signals due to edge reflections reaches the sensors, preferably, after the original signal. Keeping this in mind, applying the WT by varying signal time length may increase the efficiency of the localisation method.

In the present study, the applicability of the WT based AE source localisation method is checked on geometrically small plates. The AE responses are obtained using laboratory experiments. Firstly, the localisation method is tested on a large thin aluminium plate and results are observed. Then, one small thin aluminium plate is used in laboratory experiment to obtain AE signals. Responses are then analysed with WT and localisation technique is applied to locate the AE source. The localisation results are analysed and effectiveness of WT localisation method on small plates is investigated.

2 Methodology

2.1 WT Localisation Method

The AE source localisation method is based on the investigations by Hamstad et al. (2002b).

WT allows the user to plot signal frequency spectra as a function of time. WT diagram gives the spectra of WT coefficients with time and frequency axes. The method proceeds with selecting a frequency for an energetic mode. The maximum energetic mode is selected by finding maximum WT coefficient from the WT diagram. One frequency component in the signal can be extracted from the amplitude of the envelope of WT (Jiao et al. 2004):

$$\left|{WT}_{u}\left(x,t\right)\right|= \sqrt{2a}\left|{\widehat{\psi }}_{g}\left(a{\omega }_{c}\right)\right|{[1+\mathrm{cos}(2\Delta kx- 2\Delta \omega b)]}^{1/2}$$
(1)

where, \(\left|{WT}_{u}\left(x,t\right)\right|\) is the magnitude of WT, \(x\) is the signal, \({\widehat{\psi }}_{g}\left(\omega \right)\) is the Fourier transform of the basic wavelet, the parameters a and b stand for scale and shift of the basic wavelet, k is the wavenumber corresponding to frequency ω (Jingpin et al. 2008).

AGU-Vallen Wavelet program is used to perform WT of AE signals. This software is an open access software made especially for AE analysis at (see website https://www.vallen.de/). Gabor wavelet is used as the mother wavelet in this program. The maximum WT coefficient is identified in the obtained WT scalogram and corresponding frequency is determined. The arrival time of this energetic mode is also obtained from the spreadsheet supplied by the program. Group velocities of the Lamb modes also are calculated using AGU-Vallen Wavelet program. In this study, pencil lead break (PLB) is used as the simulated AE source. For this simulated source, the dominant mode shall be the anti-symmetric Lamb modes since PLB generates dominant flexural displacement. Furthermore, for thin plates, which is used in this study, fundamental Lamb modes are predominant. Therefore, it is expected that fundamental anti-symmetric Lamb mode must be the dominant mode in this study. Thereafter, the linear distance of PLB source from AE sensor is determined by multiplying the known group velocity of dominant Lamb mode and time of the maximum WT magnitude.

2.2 Experimental Setup

AE waves in a large aluminium plate and in a small aluminium plate are investigated experimentally as stated earlier in introduction section. AE waveforms are obtained using AE acquisition system. Micro II Express, made by Physical Acoustic Corporation, USA, is used for this purpose. To acquire the responses R15D sensors are used. R15D is resonant type sensor and has operable frequency range of 50–400 kHz. The signal leads from the sensor feeds into a differential pre-amplifier which amplifies and filters the response voltage output, and finally the response signal is acquired by digital AE data acquisition system. The digital AE system shows the response to the user using a user interface software. The sampling frequency is taken as 10 MHz and a total of 2048 samples are taken for each AE signal, which produces 204.8 μs of signal time length. Figure 1 shows the AE acquisition system with plate specimen.

Fig. 1.
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AE acquisition system with sensor and plate specimen.

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2.3 Simulated AE Source

Hsu-Nielsen source (Hsu and Breckenridge 1981), which is popularly known as pencil lead break (PLB), is used as the simulated AE source in experimental studies. PLB is applied to the surface of the specimen using a mechanical pencil with 0.5 mm HB lead. A guide ring is attached to the mechanical pencil to ensure contact angle of 45° and 3 mm free lead length is maintained for every application of PLB.

3 Results and Discussion

3.1 AE Source Localisation in Large Aluminium Plate

To verify the efficiency of WT localisation method, firstly, a large thin aluminium plate is studied experimentally. The dimension of plate is chosen as - 1000 mm × 600 mm × 1 mm. The material properties are given in Table 1. The dispersion relation for aluminium plate of 1 mm is shown in Fig. 2. It can be seen that only fundamental symmetric (S0) and anti-symmetric (A0) Lamb modes exist up to 1 MHz for 1 mm aluminium plate. However, as the simulated AE source is PLB on the surface of the plate and due to the reason that PLB generates predominant flexural mode, it is expected that group velocity curve of A0 mode will be needed for source localisation process using maximum energetic mode’s frequency.

Table 1. Isotropic aluminium plate material properties
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Fig. 2.
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Dispersion relation curve for aluminium plate of 1 mm thickness.

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The locations of AE sensor and PLBs are shown in Fig. 3. S is the location of the R15D sensor mounted on the surface of the plate and P1 and P2 are the PLB locations. The sensor and PLB location are taken far from the edge of the plate – near the centre, to minimise the edge reflection interference as much as possible (Fig. 3).

Fig. 3.
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Locations of sensor and PLB sources for laboratory experimental AE test on large aluminium plate.

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The signals obtained due to PLB at P1 and P2 are shown in Fig. 4, with WT diagrams. The WT localisation method is applied on obtained signals and results are tabulated in Table 2.

Fig. 4.
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Obtained AE signals on large aluminium plate and their corresponding WT scalograms due to PLB at – (a) P1 and (b) P2.

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Table 2. Source localisation results for large aluminium plate
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The localisation results can be said overall satisfactory with maximum error of 16% with respect to source to sensor distances, however, compared to overall plate dimension along the propagation of wave, which is 1000 mm, this error is tolerable.

3.2 AE Source Localisation in Small Aluminium Plate

The source localisation method is then tested for small plate. For experimental investigation on small plate, one isotropic small aluminium plate is chosen having same material properties as that of large plate (see Table 1). The dimension of the plate is chosen as - 250 mm × 150 mm × 1 mm. The dispersion relation remains same as thickness of the plate and material is same (see Fig. 2).

The locations of AE sensors and PLBs are shown in Fig. 5. S1 and S2 are the locations of two R15D sensors mounted on the surface of the plate and P1, P2, and P3 are the PLB locations. The geometry of the plate is chosen in a way that edge reflection must interfere in the obtained signals.

Fig. 5.
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Locations of sensors and PLB sources for laboratory experimental AE test on small aluminium plate.

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Fig. 6.
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Typical WT diagram for S2P2 (sensor at S2, PLB at P2) with superimposed dispersion curves – (a) for 200 µs and (b) for 100 µs.

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Firstly, a typical WT diagram, for S2P2, with superimposed dispersion curves are shown in Fig. 6. WT diagram is shown for 200 µs and for 100 µs. From the figure it is obvious that edge reflections are responsible for multiple energetic zones in the WT diagram for 200 µs (Fig. 6(a)), while fundamental anti-symmetric (A0) mode being the predominant mode. Even under 100 µs two distinct energetic zones can be observed but the first energetic zone is the resulting zone for fundamental anti-symmetric Lamb mode. It is seen that the first arrival of any mode does not result in maximum energy concentration in the signal, so for better location results one needs to consider the section length (time duration) of signal to be analysed. Keeping this in mind, all the other WTs are calculated and source location method is applied.

However, the WT localisation method is applied on both 200 µs and 100 µs of section length of AE signals obtained on small plate, to check the difference of location results. Figure 7 shows the WT diagrams for 200 µs of AE signals (S1P3 stands for sensor at S1 and PLB at P3). Multiple energetic zones are clearly visible in the figures.

Fig. 7.
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WT diagrams of obtained AE signals on small aluminium plate for 200 µs – (a) S1P1, (b) S1P2, (c) S1P3, (d) S2P1, (e) S2P2, and (f) S2P3.

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The location results are tabulated in Table 3. From the table, it can be seen that the error is higher with maximum error of 287.2% and minimum error of 27.3%. Obviously, this location results are erroneous due to multiple energetic zones caused by influence of edge reflection.

Table 3. Source localisation results for small aluminium plate – considering 200 µs
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Fig. 8.
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Obtained AE signals on small aluminium plate and their WT diagrams, for 100 µs – (a) S1P1, (b) S1P2, (c) S1P3, (d) S2P1, (e) S2P2, and (f) S2P3.

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Table 4. Source localisation results for small aluminium plate - considering 100 µs
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The WT diagrams for 100 µs are shown in Fig. 8 and source location results are shown in Table 4. For S1P3 and S2P2, the maximum errors occurred at 31.70% and 27.36% respectively. For these two, the PLB positions are very near to sensor positions – at 47 mm distance apart, and both the PLBs and sensors are in very close proximity of the edges of the plate. However, for other positions the maximum error is 10.9% for 142 mm distance. Comparing with location results tabulated in Table 3 for 200 µs, it is observed that the source location method is efficient enough if the considered signal time length is restricted to few tenth of microseconds while encountering small plate like structures.

4 Conclusion

A wavelet transform (WT) based AE source localisation method is applied on small plates for checking its applicability under influences of edge reflection of AE waves. AE waveforms or signals are obtained experimentally in large aluminium plate and small aluminium plate. In all cases, PLB is used as simulated AE source.

The WT localisation method is checked on large plate and satisfactory results are observed. For small aluminium plate, it is seen that multiple energetic zone are occurring due to interference of edge reflection. However, shortening the signal section length (i.e. duration of signal) for WT analysis gives satisfactory results in small plates as the most energetic Lamb mode, anti-symmetric mode in this case, arrives very early in case of AE event in small plates. So, we may shorten the considered signal section length for WT analysis to get more accurate results in case of small plate-like structures. But in case of very close proximity of sensor and AE source, the error in location increases. So, it can be said in case of small plates, depending on plate size, varying the signal section length can give better results with WT localisation method. A parametric study can be done based on distance from sensor to boundary of plate to establish a relation of signal section length and plate size to obtain more accurate location results.