PSI - Issue 37

Reza Soleimanpour et al. / Procedia Structural Integrity 37 (2022) 956–963 4 Reza Soleimanpour, Sayed Mohamad Soleimani and Naser Khaled Mohammad / Structural Integrity Procedia 00 (2019) 000 – 000 incident wave and second harmonic guided waves which can be simply extracted using signal processing even though the signal are mixed and hard to interpret. 2.4 Signal Processing As discussed in previous section, in this study damage localisation is carried out based on determining the time of arrival for incident wave and the time of arrival for SHG. Therefore the signal processing task will be focused on calculation of these two parameters. In this study, a combination of several signal processing approaches is used to interpret the signals. The data is acquired in time domain, Hilbert transform is used to extract the signal envelopes and the time of arrival for incident wave frequency ( ) is estimated using signal envelopes in time domain. Fast Fourier transform is implemented to transform the guided wave signals from the time domain to the frequency domain and then a high pass filter is implemented to extract nonlinear wave data (e.g SHG) by eliminating unwanted frequency components. The filter must be able to cut off the unwanted frequency components in frequency domain and reconstruct the signal with least data loss e.g change in wave parameters. Chebyshev and Butterworth are two common high pass filters used in guided waves. It should be noted that the wavelet can also be used for filtering the signal. However because of its computational cost, Butterworth filter is preferred. CWT will be still used for enhanced demonstration of arrival time of wave packets with different frequencies. In this study Buttherworth followed by continuous wavelet transform (CWT) using Gabor mother wavelet is used. Once unwanted frequency components are removed from data, invert Fast Fourier transform is implemented to transform extracted nonlinear guided waves data from frequency domain to time domain. This will provide time domain data associated with higher harmonics of guided waves. Hilbert transform is then used to determine the time of arrival for SHG ( 2 ) . Once the time of arrival for linear and nonlinear guided waves is calculated, the distance between the defect and the transducer ( − ) can be calculated using Eq.1 which indicates the location of the defect. 3 3D Finite element simulation 3.1 Numerical case studies The specimen consist of two A36 steel plates with dimension of 200 mm × 25 mm × 2.5 mm. The mechanical properties for A36 steel is shown in Table 1. The total length of the specimen varies depending on bolt size as the length of bolt join overlap is different for each case. There are two bolts with B1 being loosened and B2 fully clamped. The bolt diameter is swiped from 5mm to 20mm in 2.5mm steps to investigate the applicability of proposed damage detection and damage localization method for different defect sizes. Fig. 2 shows the schematic diagram of 3D FE simulation model including the transducers network and location of each transducer. As can be seen, a network of two transducers was used for excitation and data acquisition. The receiver is located at 10cm away from the actuator and is used to capture the out of plane time domain data for damage detection and damage localisation. 959

Table 1. Material properties of the A36 steel plate Young’s modulus 200 GPa Poison ratio 0.26 Density 7800 kg/m 3

Fig. 2 Schematic diagram of 3D FE simulation model