shows the acoustic signals for sensor 1 and artificial
source position of A(200, 100) in time, frequency and time–
frequency domains. In Fig. 4a the waveform of acoustic signal is
shown. It is clear that the lead breaking source generates burst
waves which propagate in frequency range of 0–400 kHz
(Fig. 4b). From time–frequency distribution (Fig. 4c) it is found that
the maximum energy of signals is carried out per frequencies of
about 115 and 130 kHz. To determine wave arrival time, wavelet
packet transform was used to decompose the raw signal into frequency
bands. Analysis the amplitudes of signal in each wavelet
packet can help to identify the frequency range related to the significant
components of the raw signal. To obtain more details
about significant amplitudes, a three-level wavelet packet transform
was used to decompose raw signal to eight levels of
125 kHz bandwidth. Fig. 5 shows the wavelet packets of threelevel
decomposition for sensor 1 and source position of A(200,
100). Theoretically by increasing the level of wavelet packet
decomposition, the constant bandwidth of frequency ranges will
decrease and consequently high accuracy of signal analysis will
be achieved. After three-level wavelet packet decomposition, the
packet with frequency range of 0.125–0.25 MHz was selected for
calculating time delay between two sensors. The cross correlation
of these packets (from sensor 1 and 2) are obtained in time, frequency
and frequency-time domains as shown in Fig. 6. In Fig. 6a
the cross-correlation of these packets is shown in time domain
and the peak time represents the time delay between collected signals.
Fast Fourier transform was taken from cross correlation of
packets and time–frequency and cross spectrums are obtained as
shown in Fig. 6b and c. The frequency range of the cross spectrum
is 0–200 kHz and the peak frequency is about 130 kHz. From the
cross-time frequency spectrum, the peak frequency and corresponding
peak time can be obtained. The real-time determined
wave velocity can be obtained from the group speed of the acoustic
wave (S0 mode) showed in Fig. 3 under the peak frequency. In this
study a MATLAB code based on wavelet packet transform and cross
shows the acoustic signals for sensor 1 and artificial
source position of A(200, 100) in time, frequency and time–
frequency domains. In Fig. 4a the waveform of acoustic signal is
shown. It is clear that the lead breaking source generates burst
waves which propagate in frequency range of 0–400 kHz
(Fig. 4b). From time–frequency distribution (Fig. 4c) it is found that
the maximum energy of signals is carried out per frequencies of
about 115 and 130 kHz. To determine wave arrival time, wavelet
packet transform was used to decompose the raw signal into frequency
bands. Analysis the amplitudes of signal in each wavelet
packet can help to identify the frequency range related to the significant
components of the raw signal. To obtain more details
about significant amplitudes, a three-level wavelet packet transform
was used to decompose raw signal to eight levels of
125 kHz bandwidth. Fig. 5 shows the wavelet packets of threelevel
decomposition for sensor 1 and source position of A(200,
100). Theoretically by increasing the level of wavelet packet
decomposition, the constant bandwidth of frequency ranges will
decrease and consequently high accuracy of signal analysis will
be achieved. After three-level wavelet packet decomposition, the
packet with frequency range of 0.125–0.25 MHz was selected for
calculating time delay between two sensors. The cross correlation
of these packets (from sensor 1 and 2) are obtained in time, frequency
and frequency-time domains as shown in Fig. 6. In Fig. 6a
the cross-correlation of these packets is shown in time domain
and the peak time represents the time delay between collected signals.
Fast Fourier transform was taken from cross correlation of
packets and time–frequency and cross spectrums are obtained as
shown in Fig. 6b and c. The frequency range of the cross spectrum
is 0–200 kHz and the peak frequency is about 130 kHz. From the
cross-time frequency spectrum, the peak frequency and corresponding
peak time can be obtained. The real-time determined
wave velocity can be obtained from the group speed of the acoustic
wave (S0 mode) showed in Fig. 3 under the peak frequency. In this
study a MATLAB code based on wavelet packet transform and cross
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