PSI - Issue 37

962 Reza Soleimanpour et al. / Procedia Structural Integrity 37 (2022) 956–963 Reza Soleimanpour, Sayed Mohamad Soleimani and Naser Khaled Mohammad/ Structural Integrity Procedia 00 (2019) 000 – 000 7

Fig. 4 Captured data at receiver 2 in a)time domain b)time-frequency domain for linear wave c)time-frequency domain for nonlinear wave

Table 2 Summary of the results for numerical cases based on data captured at receiver

Estimated location

True distance to center of the bolt

Estimated arrival time

(μsec) (μsec) d(d-r) (mm) 113.9 53.0 88

Bolt size

db (mm)

5

93 89 85 81 78 74 70

7.5

110.8 119.5 117.2 102.8 111.5

54.8 53.8 53.5 53.7 54.1 54.4

81 95 92 71 83 65

10

12.5

15

17.5

20

99.4

Next, the time of arrival for incident linear and reflected nonlinear guided waves was calculated using Hilbert transform. The estimated ∆t are also indicated in the figure. The linear wave arrives at sensor at 53.8 µs while the nonlinear wave packet (the second contour in Fig. c) arrives at sensor at 119.5 µs. The first refers to ( ) whereas the later refers to ( 2 ). Using Eq.1, the time difference ( ∆ ) and the distance to the sensor ( − ) are calculated as 65.7 µs and 95mm respectively which is close to the true location of the bolt from receiver 2 (85mm). It is worthy to mention that the true location of bolt is the distance of the sensor to the center of the bolt. However the loosened area covered by bolt which is the source of CAN is in range of few centimeters from the center of the bolt. As can be seen