In this paper, we propose a new denoising algorithm for electromagnetic ultrasonic signals based on the improved EEMD method, which can adaptively adjust for added noise and average times in different noisy environments, so that the effect of the residual difference of white noise on the results can be eliminated as far as possible. First, the way to add white noise in the EEMD method is processed, and then the permutation entropy algorithm is used to identify the nature of the components obtained during the decomposition. Then the wavelet transform modulus maximum denoising method is used to deal with the IMF components of the high-frequency part obtained before. Finally, the processed IMF results and residual difference are summed up. The results show that after processing, the noise component in the signal is less and the original information is more reserved, which prevents the signal distortion to a great extent and provides more effective data for subsequent processing. In the experiment, the crack defect data collected by the electromagnetic ultrasonic experiment system were processed by the improved EEMD method. Compared with the traditional EEMD method, it can retain the information of crack location more accurately, which proves the effectiveness of the proposed method.

In recent years, the electromagnetic ultrasonic nondestructive testing technology for pipeline defect detection has been paid more and more attention. Compared with the traditional ultrasonic testing technology, it is simpler and more effective, having a variety of different detection modes. However, due to the influence of environment, human operation, and other factors, there are some singularities in the data collected by the receiving end of the electromagnetic ultrasonic transducer. What is more, it contains a certain degree of noise interference, so that it may cause great disturbance to the identification of signal position and feature in the later period.

Literature [

The core of the improved algorithm in this paper is to adaptively adjust the added noise and the average times under different noise environments, so that the effect of the residual difference of white noise on the results can be eliminated as far as possible.

In this paper, we first introduce the conception of modulus maxima denoising method based on wavelet transform and EEMD denoising method. Then, the differential threshold method is used to remove the singularities in the data. Next, we make innovative improvements to the EEMD algorithm so that it can adaptively get the ratio coefficient, and the useless residual difference of the added white noise can be reduced to the maximum extent at the same time. Aiming at the added white noise in the EEMD method, we use the permutation entropy algorithm to identify the nature of the components obtained during the decomposition.

For the remaining signal of the low-frequency stationary part, the EMD (Empirical Mode Decomposition) is directly used in the processing, while the other high-frequency IMF (Intrinsic Mode Function) components are continuously obtained by the EEMD decomposition, thereby reducing the influence of noise on the effective part.

Afterwards, the wavelet transform modulus maximum denoising method is used to deal with the IMF components of the high-frequency part obtained before. Finally, the processed IMF components and residual difference are summed up. The results show that after processing, the noise component in the signal is less and the original information is more reserved, which can prevent the signal distortion to a great extent and provide more effective data for subsequent processing.

There are many traditional discrete data denoising methods. At the following, the applicable characteristics of various methods will be combined to explain the relevant knowledge involved in this article algorithm. And then the method proposed in this paper is applied to the processing of electromagnetic ultrasonic nondestructive testing signal. By comparison, the advantages of this article algorithm are highlighted.

In order to compare the denoising effects of several methods, we used the ETG-100 ultrasonic thickness gauge to test three steel plates of the same material as X56 in the laboratory environment. Their length is 50 cm, the width is 30 cm, and the thickness is 12.37 mm, 13.35 mm, and 15.21 mm. Three sets of clean thickness echo signals are obtained. Noise is added to the first set of signals, as shown in Figure

Adding noise to the original signal.

EMD is suitable for the analysis of nonlinear, unsteady signals. The core of the method is to decompose the more complex signals and get the IMF components of the signals. The IMF components obtained by this method represent the characteristics of the data series at different time scales, respectively. In this way, the fluctuation trend of the signal under different scales of the original signal can be decomposed and refined and then analyzed.

For the IMF, Huang et al., had given the qualified conditions [

In the whole data set, the number of extrema and zero-crossings must either be equal or differ at most by one

The average value of the envelope of the maximum and the minimum value of a data sequence is zero

For the signal sequence

After using the original signal and the average line signal to deal with the difference component, we have

After getting the component, we first judge whether it is IMF. According to the two principles mentioned above, if the conditions are met, we define

The

For the EMD method, it is difficult to ensure that the local mean value limited by condition (2) is equal to zero during the screening process because of the complexity of the electrical signals collected by electromagnetic ultrasound. When the signal is abnormal, it will affect the signal envelope, and the IMF component, resulting in model aliasing, which may lead to the loss of the original physical meaning of the component.

The improvement proposed by Norden. E. Huang to the EMD method in solving the problem of model aliasing is called EEMD [

Add a white noise sequence in the original signal.

Get IMF components with EMD decomposition method.

Repeat the above two steps, and the added white noise is different each time. When a signal is applied to a uniformly distributed white noise background, the signal regions at different scales are automatically mapped to the appropriate scales associated with the background white noise. The decomposed IMF components are shown in Figure

Integrate and average the IMF components obtained each time. Since the noise is different in each individual test, the noise will be removed when the overall mean at a sufficient number of tests is used. After that, the overall mean will eventually be considered as the true result. With more and more repetitions of the above steps, additional noise can be eliminated, and the only permanent part is the signal itself. The general EEMD decomposition flowchart is shown in Figure

Decomposition results of EEMD method. (a) IMF 1–8. (b) IMF 9–16.

Processing flow of EEMD.

The traditional EEMD algorithm is based on the principle of noise-assisted signal processing; the mode aliasing phenomenon is effectively solved by adding a small amplitude of white noise to equalize the signal. The real signal is retained by using the zero-mean characteristic of Gaussian white noise, which is a great improvement to the traditional EMD analysis method.

But the disadvantage of the traditional EEMD method is that the added white noise can not be completely offset from each other in practical application, so the signal is still affected by noise to a certain extent. In the decomposed component, the high-frequency part contains a lot of noise, which is usually removed directly, and then the signal with a large correlation is reconstructed to get the denoised signal.

Because the high-frequency IMF component which is removed directly contains effective information, it will affect the original signal to some extent. In addition, the added white noise and the number of processing have a greater impact on the decomposition results, so that mode aliasing cannot be completely eliminated and may produce more useless components. Therefore, EEMD cannot adjust these decomposition parameters according to the actual situation, especially when the noise is changeable.

Before the postprocessing of the data, some “damage data” of the data collected by electromagnetic ultrasound needs to be checked and removed. In this paper, the differential threshold method is used to distinguish the numerical changes between the sampling points of the collected data. When the absolute value of the difference between two adjacent points is greater than the set threshold, it is regarded as the wrong data and will be replaced. The principle of differential threshold method is as follows:

When the data difference between two adjacent points is less than the selected threshold, the original data will continue to be used. For the mutation data, the data of the two sample points before and after the mutation sample data can be used to supplement.

In view of the lack of traditional EEMD in electromagnetic ultrasonic testing data processing, for the first time, a new denoising algorithm based on the improved EEMD method, which can adaptively adjust for added noise and integrated average times in different noisy environments, is proposed in this paper.

Permutation entropy [

For a time series

The reconstructed data are sorted in the ascending order of magnitude. Then the position index of each element in the reconstruction component is labeled as

After that, we process the simulation signal for the combined sequence of noise and related sinusoidal signals. According to relevant research experience, we set the parameters

The sequence is processed to obtain the permutation entropy values, which are 0.9897, 0.9722, 0.9815, 0.2443, 0.1159, and 0.2105. We can see that the entropy of the noise is large and irregular, while the entropy of the sinusoidal composite signal is low. We can set a threshold value of 0.58 to provide the parameter support for the improved follow-up study of the EEMD algorithm mentioned below.

Wavelet transform is used to decompose the original signal into high-frequency part and low-frequency part. The low-frequency parameters are retained while the high-frequency part is decomposed again, followed by progress [

The modulo-maximum method is a typical method in the wavelet denoising method. Wavelet coefficients can reflect the transient characteristics of the original signal at different scales. Modular-maximum denoising based on wavelet transform is to process the modulus maxima of wavelet decomposition coefficients. Since the modulus maximum point of the signal will increase with the expansion of the scale, the noise maximum modulus point will be opposite, and the signal will be reconstructed from the modulus maxima at different scales by the processed wavelet coefficient, which is the basic idea of WTMM (wavelet transform modulus maxima

Because of the complexity of the signal processing, the extreme point of the wavelet decomposition coefficient usually corresponds to the abrupt point of the signal, and the singularity of the signal corresponds to the variation rule of the modulus of the wavelet coefficients. Therefore, the paper incorporates the WTMM method into the EEMD denoising algorithm, and a new improved EEMD denoising algorithm is proposed. The following describes the specific implementation process.

The improved method first determines the principle of adding noise and the average number of times. Different from the traditional empirical judgment, through a considerable number of experimental studies, the specification of adding white noise in the EEMD method has been derived:

So, Equation (

In normal conditions, we choose

Another important parameter is the average number of times. Empirical studies have shown that the formula is chosen as shown in

According to the above formula, the average number of integration

Obviously, the standard deviation of artificially added white noise and the average number of integration are all related to the ratio coefficient

The core of the improved algorithm is to adaptively adjust the added noise and the average times under different noise environments, so that the effect of the residual difference of white noise on the results can be eliminated as far as possible. Research shows that the white noise added to the high-frequency part of the EEMD method has negligible influence on the mode aliasing, while the white noise added to the low-frequency part has a greater influence factor, so the low-frequency part is directly decomposed by the EMD method to eliminate the influence of mode aliasing.

Firstly, we make improvements to the EEMD algorithm so that it can adaptively get the ratio coefficient. At the same time, it can minimize the useless residual difference caused by added white noise in the result. Secondly, aiming at the way to add white noise to the EEMD method, we use the permutation entropy algorithm to identify the nature of the components obtained during the decomposition. As for the remaining signal of the low-frequency stationary part, the EMD decomposition is directly used in the processing, while the others are continuously obtained by the EEMD decomposition, thereby reducing the influence of noise on the effective part. Afterwards, the wavelet transform modulus maximum denoising method is used to deal with the IMF components of the high-frequency part obtained before. Finally, the processed IMF results and residual difference are summed up. The results show that after processing, the noise content in the signal is less and the original information is more reserved, which prevents the signal distortion to a great extent and provides effective data for subsequent processing.

The flowchart of improvement is shown in Figure

First of all, the original signal is decomposed by the EMD method to obtain the eigenfunction group, and the first set of high-frequency IMF components in the decomposition result is recorded as the high-frequency component of the original signal. Then, the ratio of the standard deviation of the original signal and the high-frequency IMF components, combined with the previous formula, is used to find the value of

Firstly, the original signal is decomposed into IMF components by EEMD algorithm, and then, all IMF components are sequentially calculated by using the permutation entropy algorithm. If the entropy value is greater than the set threshold, the next component will continue to be calculated.

The WTMM method is used to denoise the components whose entropy values are greater than the threshold. Then, the IMF components and the residuals of the high-frequency part can be obtained.

These high-frequency components whose entropy values are greater than the threshold are removed from the original signal, the remaining part of the signal is decomposed by the EMD method to get the low-frequency partial IMF components.

By summing the IMF components and the residuals obtained in the above two steps, the processed result is as shown in the following equation:

Improved method to handle flowchart.

IMFs obtained by the improved method. (a) IMF 1–8. (b) IMF 9–16.

In order to prove that the improved method is superior to the traditional EEMD method in the processing of electromagnetic ultrasonic detection signals and to verify that it has sufficient stability, the corresponding experiments have been carried out through simulation.

We used the ETG-100 ultrasonic thickness gauge to test three steel plates of the same material as X56 in the laboratory environment. Their length is 50 cm, the width is 30 cm, and the thickness is 12.37 mm, 13.35 mm, and 15.21 mm. Three sets of clean thickness echo signals are obtained.

In the first set of simulation experiments, the original signal is the clear thickness measurement data used in the previous section. The original signal is artificially added with noise and then denoised by the traditional EEMD method and the improved EEMD method, respectively. The comparison chart of denoising effect is shown in Figure

Denoising effect comparison chart.

The SNR (signal-noise ratio) of the original signal, the traditional EEMD method, and the improved EEMD method is calculated, which are shown in Table

Denoising effect comparison.

Method | The original signal-to-noise ratio | The traditional EEMD method | The improved EEMD method |
---|---|---|---|

SNR | 11.53 | 10.12 | 11.15 |

In the second and third sets of simulation experiments, the original signal uses different clean thickness echo data which are also artificially added with noise later, and the original signal is processed by the traditional EEMD method and the improved EEMD method, respectively. The SNR of the original signal, the traditional, and the improved EEMD method is presented below.

As can be seen from Tables

The other two sets of denoising effects comparison.

Method | The original signal-to-noise ratio | The traditional EEMD method | The improved EEMD method |
---|---|---|---|

SNR of the second set of experiments | 11.78 | 11.23 | 11.59 |

SNR of the third set of experiments | 10.45 | 9.68 | 10.23 |

In order to verify the validity of the improved method, we used the EMAT2000 electromagnetic ultrasonic crack detector on Central Offshore Oil Pipeline Test Platform to test the crack defects at Tanggu, Tianjin. The actual metal spline crack depth of the pipe wall was 0.5 mm. The echo signals obtained from electromagnetic ultrasonic testing are processed by the traditional method and improved method, respectively. Then, the denoising effects of the two methods are compared.

The collected signal data are shown in Figure

The original electrical signal of crack defects detected.

For the data collected from the crack defect, after eliminating the singular value of the data, the IMF components obtained by the traditional EEMD method are shown in Figure

The IMF components obtained by the traditional EEMD method. (a) IMF 1–8. (b) IMF 9–16.

The IMF obtained by the improved EEMD method. (a) IMF 1–8. (b) IMF 9–16.

Finally, the IMF components and the residual difference are reassembled, and the comparison results of the traditional EEMD method and the improved EEMD method are shown in Figure

The comparison results of the two methods.

As can be seen from Figure

Effective signal denoising location.

In this paper, a new denoising algorithm of electromagnetic ultrasonic testing signal based on the improved EEMD method is used to process the collected data. First of all, singular values in the data are removed. Then, aiming at the way that white noise is added to the EEMD method, the permutation entropy algorithm is used to identify the nature of the components obtained during the decomposition. Furthermore, the components of low-frequency signal are decomposed by EMD directly, while the components of other high-frequency IMF components are decomposed by EEMD. Afterwards, the wavelet transform modulus maximum denoising method is used to deal with the IMF components of the high-frequency part obtained before. Finally, the processed IMF results and residual difference are summed up. In the experiment, crack defect data collected by electromagnetic ultrasonic experiment system were processed by the improved EEMD denoising method. The results show the effectiveness and superiority of the proposed method.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (61374124, 6147306, and 61627809) and Major Undergraduate Research Project of Northeastern University in 2017 (ZD2017).