Data Processing

Figure 7 shows the time and frequency domain diagrams of the original signal of 12CrMo at 625 °C. Through acquiring and analyzing data, it was determined that pulsating noise was mainly focused in the low-frequency domain. The resonance phenomenon for EMAT was inevitable, which led to a noise signal and the generation of random fluctuations. This resulted in a deviation of the extreme value point in the envelope extracting process. It was necessary to filter out the noise. Based on the original signal in the time and the frequency domain diagram, the echo signal and some high-frequency electrical noise could be found, as shown in Figure 7(a, b). As the emission signal frequency was presented, the effective echo signal center frequency was distributed around the emission frequency. The high-frequency part was invalid white noise, which did not have any useful information. This caused the SNR of the echo signal to deteriorate, which resulted in the need for filtering.

Figure 7
figure 7

Original ultrasonic signal in (a) time domain and (b) frequency domain

In the frequency domain, the distribution of the two kinds of noise did not overlap with the effective signal, which provided a signal processing direction. In this research, VMD was used to select the medium and high-frequency IMF where the useful signal resided. This method could effectively filter out the low-frequency noise and the high-frequency noise.

Figures 8 and 3 show the time domain and frequency domain diagrams of the original signals after VMD, respectively. It can be found from Figure 8 that the time domain EMAT signals were successfully decomposed into four IMFs.

Figure 8
figure 8

Signal after VMD decomposition in the time domain

Since the pre-set excitation frequency was 3.25 MHz, the useful echo signal was located in IMF 2, which was selected to reconstruct the signal for the VMD, as shown in Figure 9(a). Then WT denoising was carried out, as presented in Figure 9(b). The noise reduction method in this research applied to any condition, rather than a fixed excitation frequency. Different excitation frequencies resulted in different center frequencies of ultrasonic echo signals. As an effective time-frequency analysis method, the denoised signal had less interference in narrow-band IMF 2.

Figure 9
figure 9

(a) Reconstruction signal of VMD decomposition, (b) WT denoising signal

To eliminate the noise with a similar frequency to the effective signal, the wavelet denoising method was used. The wavelet can be analyzed in both time and frequency domain and can deal with the abrupt change in the thickness measurement signal. Therefore, before using the signal, it was necessary to conduct further noise reduction processing and improve the SNR.

The signal noise was effectively suppressed after VMD-WT processing. However, the noise in the signal could not be completely filtered out and the filtering process also suppressed the effective signal. Hence the noise suppression in this link tended to be conservative. Then the EEMD was used for further signal processing. The IMF with the largest kurtosis factor was selected as the final extracted echo signal. Following this, the Hilbert transform was used to extract the envelope of the final signal, as shown in Figure 10. The EEMD method showed an ability to decrease the cumulative errors of the WT and improve the resolution after the time-frequency analysis to eliminate white noise. Furthermore, the Hilbert transform could present the instantaneous amplitude and frequency.

Figure 10
figure 10

Signal processed with VWEE

Comparison of Noise Reduction Ability Among Different Methods

To verify the effectiveness and feasibility of the proposed VWEE method, the same received signal for 12CrMo at 625 °C was selected, with a 250 V excitation voltage, a 50 MHz sampling frequency, and the sampling number of 4096. The following methods were used for noise reduction.

  1. 1)

    VMD: The original signal was decomposed with VMD. The decomposition layer (K) was set as 4, and the penalty factor (alpha) was set as 1500. This method could effectively deal with nonlinear and non-stationary signals. However, it was sensitive to noise. When there was noise, modal aliasing might occur in the decomposition, and the noise suppression ability was weak.

  2. 2)

    WT denoising: The “sym8” wavelet was selected and the decomposition level was set to 5. The hard threshold function was adopted, and the “sqtwolog” rule was used.

  3. 3)

    EMD: The EMD has the disadvantages of mode aliasing and the endpoint effect. The filtering effect could easily produce waveform distortion and it could not retain the original characteristics of the signal to the maximum extent.

To evaluate the advantages and disadvantages of the various methods, the peak SNR was adopted as the evaluation index of the denoising effect. In general, the larger an SNR is, the better the signal denoising effect is.

Equation (9) was used to calculate the SNR, where (SNR_{dB}) is the SNR of the signal, (A_{signal}) is the maximum amplitude within a wave packet intercepted, and (A_{noise}) denotes the average noise amplitude within a selected region next to the echo:

$$SNR_{dB} = 20{text{lg}}frac{{A_{signal} }}{{A_{noise} }}.$$


To validate the denoising ability of the method proposed in this paper, several popular denoising methods were compared. Figure 11 gives comparison of the original electromagnetic ultrasonic signal with the signal processed by VMD, WT denoising, and EMD method, respectively. The denoising effect of the other three denoising methods was not ideal, and there were still many noise components in the signal after denoising. As shown in Figure 10, the proposed VWEE denoising method could better preserve the useful part of the signal, and it could effectively remove most of the target signal noise. As adaptive multiresolution techniques, the EMD and VMD could adjust to unknown signal characteristics varying over time. Compared with the VMD, the EMD was more sensitive to noise. The WT-based thresholding technique was better in combination with the VMD method than in use alone.

Figure 11
figure 11

Ultrasonic signal of 12CrMo at 625 °C; (a) original signal, (b) VMD decomposition and reconstruction signal, (c) WT denoising signal, and (d) EMD denoising signal

From Figure 11, the denoising ability of various methods can be seen directly. The SNR values were further compared with the indicator for denoising ability, as shown in Table 1. The higher the SNR of the output signal was, the better the denoised effect was. From Table 1, it can be seen that the denoised effect of VWEE was significantly better than those of the VMD, WT, and EMD methods. The denoising effects of VMD and EMD were similar, and these effects slightly better than those of the WT. Compared with the other methods, the SNR of the high-temperature EMAT signal was improved 2–3 times using the VWEE method.

Table 1 Comparison of noise reduction performances of various methods

Applicability of VWEE Denoising Method for Different Materials at Different Temperatures

To verify the applicability of the denoising method proposed in this study, experiments were conducted on Cr25Mo3Ti and Fe materials. Each specimen of the materials was in the shape of a cake and had a diameter of 100 mm and a thickness of 60 mm. Additionally, all the specimen surfaces were polished. The ultrasonic signal was detected with an excitation voltage of 250 V. All of the samples were heated from 25 to 700 °C. The electromagnetic ultrasonic signals measured at intervals of 50°C were selected for VWEE denoising, and good SNRs were obtained, as shown in Figure 12(a, b). The results demonstrated that the proposed algorithm could be applied to conditions other than a fixed temperature.

Figure 12
figure 12

SNR at different temperatures of (a) Cr25Mo3Ti and (b) Fe

As can be seen from Figure 12(a), the SNR of the original electromagnetic ultrasonic signal, detected on the Cr25Mo3Ti specimen from 25 to 700 °C, was the lowest, which was maintained at about 20 dB. Compared with the original signal, the SNR of the signals processed with the WT denoising method and the EMD method was improved to some scale. But the SNR was still low compared with the VWEE method, which was between 50 dB and 60 dB, up to 60.579 dB. The experimental results showed that the VWEE method had a good noise reduction ability for the Cr25Mo3Ti electromagnetic ultrasonic signal, and the echo signal was more obvious, which was more conducive to the extraction of the echo signal information.

As shown in Figure 12(b), the SNR of the original electromagnetic ultrasonic signal that detected on a Fe specimen from 25 to 700 °C was the lowest, and the signal was maintained between 10 dB and 20 dB. Compared with the original signal, the SNR of the WT denoising method and the EMD method were improved to some extent, but the SNR was still lower than that of the proposed method. The SNR of the electromagnetic ultrasonic signals obtained with the VWEE denoising method was about 50 dB, up to 59.330 dB. The experimental results showed that the VWEE denoising method also had a good denoising effect on Fe, so the proposed method had certain advantages in high-temperature signal processing compared with the EMD method and the WT denoising method.

Low Voltage Detection Signal Noise Reduction

Figure 13 shows the original signal of the Cr25Mo3Ti excited at 250 V and 25 ℃. It can be seen from the diagram that the echo signal with 250 V excitation was obvious. As shown in Figure 14, when 35 V low voltage excitation was used, the echo signal was almost buried in the noise signal and the noise level of the system had almost the same amplitude as the effective echoes, so the detection capability could not be provided. The echo signal was obvious after VWEE denoising, which was very important for the actual defect detection of the high-temperature EMAT, both for the detection accuracy and the minimum detection capability. The original electromagnetic ultrasonic signal and the denoising signal for 35 V low voltage detection are shown in Figure 14.

Figure 13
figure 13

Detection of electromagnetic ultrasonic signals in Cr25Mo3Ti at 25 ℃ and 250 V

Figure 14
figure 14

35 V excited original electromagnetic ultrasonic signal and VVWE noise reduction signal at (a) 25 °C, (b) 150 °C, (c) 300 °C, (d) 450 °C, (e) 550 °C, and (f) 700 °C

Table 2 shows the SNR of the Cr25Mo3Ti specimen at different temperatures at low excitation voltage before and after VWEE denoising. The SNR of the original signal detected from 25 to 700 °C was about 13 dB, and the echo signal was buried in the noise signal. The SNR after VWEE processing was about 40 dB, with the highest value of 49.878 dB. It can be seen from the table that the proposed method had better noise reduction performance for the Cr25Mo3Ti raw signals at different temperatures. Figure 14 shows the original electromagnetic ultrasonic signal and the VWEE denoising signal of Cr25Mo3Ti for 35 V low-voltage detection from 25 to 700 °C. It can be seen that the original signal was buried in the noise signal and it was difficult to read the echo signal information, which brought some difficulties to detection. The VWEE noise reduction method solved the above problems well, made the echo signal obvious, and preserved the local characteristics of ultrasonic waves.

Table 2 Comparison of the noise reduction performance of Cr25Mo3Ti at different temperatures for low voltage detection

In this research, the accuracy of the thickness measurement was taken as a new indicator to verify the performance of VWEE. The ultrasonic pulse emitted by the EMAT probe passed through the measured object to the material interface and then reflected to the EMAT probe. The amplitude of the ultrasonic wave gradually decreased. The time difference between the first and second peak of the extracted echo signal could be used to calculate the material thickness, given in Eq. (10):

$$h = vleft( T right) times frac{{t_{2} – t_{1} }}{2},$$


where (vleft( T right)) is the shear wave sound velocity of the materials at different temperatures (T), (h) is the thickness of the material, and (t_{1}) and (t_{2}) are the adjacent echo time.

It can be seen from Eq. (10) that the thickness measurement error is mainly affected by the variation of the sound velocity of the material and the time difference between different echo packets. Table 3 shows that the sound velocity of materials changes with the shifting of temperature. In practice, errors caused by the sound velocity changing can be eliminated by calibrating the sound velocity or referring to the standard sound velocity library [30]. However, in electromagnetic ultrasonic detection under high-temperature environment, due to the influence of temperature, the low SNR of the detection signal often leads to the failure in accurately identifying the wave packet. Therefore, the effectiveness of the algorithm can be evaluated by the accuracy of the material thickness calculated by the denoised signal.

Table 3 Thickness measurement of Cr25Mo3Ti at different temperatures

The actual thickness of the Cr25Mo3Ti specimen at room temperature was 60 mm. The electromagnetic ultrasonic signals of the Cr25Mo3Ti specimen from 25 to 700 °C were processed with the VWEE noise reduction method in experiments, and the time difference between the first and second echo was calculated to obtain the thickness of the material. The comparison results are presented in Table 3, which shows the effective noise reduction and thickness feature extraction.

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