## 4 Discussion  
From Figure 3, the signal start time at the distance of 1.6 cm is about 2.8 \(\upmu\)s and the signal start time at the distance of 2.7 cm is about 3.6 \(\upmu\)s. With the increase in distance, both A\({}_{1}\) and S\({}_{1}\) modes will continue to disperse. The amplitude of the signals will decrease, and the duration will extend. The A\({}_{1}\) mode signal at the distance of 1.6 cm is retrieved, as shown in Figure 4. The multimodal Lamb wave signal at the distance of 2.7 cm after compensation using the A\({}_{1}\) mode dispersion characteristic is shown in Figure 4a. The signal start time after compensation has been compensated back to around 2.8 \(\upmu\)s. The separated A\({}_{1}\) mode signal using the proposed method at the distance of 1.6 cm is shown in Figure 4b. The separated A\({}_{1}\) mode signal using the time-frequency blind signal separation method at the distance of 1.6 cm is shown in Figure 4c. Their amplitude spectra are shown in Figure 4d,e, respectively. Their time-frequency distributions are shown in Figure 4f,g, respectively. It can be seen from the time signals that the extracted signal using the time-frequency blind signal separation method has large errors due to the influence of Lamb wave dispersion and the source signal cross-term interference or local correlation under the calculation of global time-frequency distribution. It can be seen from the amplitude spectra and the time-frequency distributions that the separated A\({}_{1}\) mode signal using the time-frequency blind signal separation method still contains some part of the S\({}_{1}\) mode signal. There is still some part of the S\({}_{1}\) mode amplitude on the right side of the amplitude  
Figure 6: **(a)** The reconstructed multimodal signal using the time-frequency blind signal separation method and the original signal at the distance of 1.6 cm; **(b)** the reconstructed multimodal signal using the proposed method and the original signal at the distance of 1.6 cm; **(c)** the time-frequency distribution of the original signal at the distance of 1.6 cm; **(d)** the time-frequency distribution of the reconstructed signal at the distance of 1.6 cm. spectrum, and the tail energy remains in the time-frequency distribution. Therefore, the separation precision is low. However, the accuracy of separation is improved by using the proposed method. The separation result has better smoothness, which is consistent with the dispersion of the A\({}_{1}\) mode Lamb wave. From Figure 4f, the time-frequency of the extracted A\({}_{1}\) mode signal is non-stationary. From Figure 4d, the central frequency of the extracted A\({}_{1}\) mode signal is 2.98 MHz, and the frequency range is from 2.5 to 3.35 MHz. The S\({}_{1}\) mode signal at the distance of 1.6 cm is retrieved, as shown in Figure 5. The multimodal Lamb wave signal at the distance of 2.7 cm after compensation using the S\({}_{1}\) mode dispersion characteristic is shown in Figure 5a. The separated S\({}_{1}\) mode signal using the proposed method at the distance of 1.6 cm is shown in Figure 5b. The separated S\({}_{1}\) mode signal using the time-frequency blind signal separation method at the distance of 1.6 cm is shown in Figure 5c. Their amplitude spectra are shown in Figure 5d,e, respectively. Their time-frequency distributions are shown in Figure 5f,g, respectively. It can be seen from the time signals that the extracted signal using the time-frequency blind signal separation method has large errors due to the influence of Lamb wave dispersion and the source signal cross-term interference or local correlation under the calculation of global time-frequency distribution. There are even some irregular signals in the time signal. It can be seen from the amplitude spectra and the time-frequency distributions that the separated S\({}_{1}\) mode signal using the time-frequency blind signal separation method still contains some part of the A\({}_{1}\) mode signal and lacks some part of its mode signal. Therefore, the separation precision is low.