A non-convex variable overlapping group sparse variational method for denoising of steel ingot ultrasonic signal

Abstract

The present invention discloses a non-convex variable overlapping group sparse variational method for denoising the ultrasonic signal of steel ingots, which belongs to the field of non-destructive testing. The existing sparse noise reduction method can effectively ensure the effect of noise reduction by adjusting the regularization parameter, but it will cause the signal to have waveform distortion and amplitude attenuation problems. This method takes into account that the ultrasonic detection signal of the steel ingot is affected by the grain structure to produce scattering noise, which interferes with the defect signal. According to the clustering properties and variational characteristics of different amplitude points of the signal, the non-convex variable function has good sparsity. The non-convex variable overlapping group sparse variational method is proposed to achieve the noise reduction of the ultrasonic detection signal of the steel ingot, suppress waveform distortion, maintain the signal amplitude level, and improve the signal-to-noise ratio of defect imaging. In order to achieve a good noise reduction effect in the noise reduction process, the non-convex variable function type, regularization parameter and multiplication factor in the noise reduction method are optimized.

Description

Technical Field

[0001] The invention relates to a non-convex variable overlapping group sparse variational method for reducing the noise of an ingot ultrasonic signal. The method is suitable for eliminating scattering noise in an ingot ultrasonic signal and improving the signal-to-noise ratio of defect imaging, and belongs to the field of non-destructive testing. Background Art

[0002] With the rapid development of my country's manufacturing industry, large forgings are widely used in many fields such as oil, natural gas, aerospace, and nuclear industry. Modern large forgings are all rolled or forged from steel ingots. Therefore, the quality of the steel ingots and the condition of the ingot shape have a very important impact on large forging products. Ultrasonic testing is currently the most widely used non-destructive testing method because of its high sensitivity to various types of defects in components. The grains inside the steel ingots are of different sizes and unevenly distributed in shape. When ultrasonic waves are used to detect the steel ingots, the ultrasonic waves will generate scattering noise and attenuation. Scattering noise will interfere with the defect signal, resulting in a decrease in the quality of the echo signal, and even the defect signal will be completely annihilated in the scattering noise, resulting in deviations in defect positioning and reducing the signal-to-noise ratio of the imaging.

[0003] In order to solve the interference of scattered noise in ultrasonic echo signals and improve the signal-to-noise ratio of ultrasonic signals, domestic and foreign scholars have conducted a lot of research on noise reduction methods. Grevillot et al. [1] The split spectrum method with mobile broadband minimization is used to reduce the noise of ultrasonic signals, and the noise-reduced signal is obtained through a set of narrowband filters with superimposed frequency bands. However, the noise reduction performance of the split spectrum method is too dependent on the selection of parameters such as the number of filters and frequency intervals, and has a low degree of adaptability. Praveen et al. [2] The TOFD signal of austenitic stainless steel weld is denoised by high-order wavelet. The experimental results show that the use of high-order wavelet denoising can make the signal have a higher signal-to-noise ratio. However, the denoising method based on wavelet analysis is overly dependent on the selection of wavelet basis functions, and wavelet analysis may distort the signal, resulting in distortion of the denoised signal.

[0004] The signal sparse denoising method is relatively simple to calculate and has fast algorithm iteration efficiency. It can express important information of the target signal through sparse approximation. In recent years, scholars at home and abroad have proposed a variety of sparse denoising methods. For example, Deng et al. [3] The regularization parameters in the overlapping group sparse variation method were optimized by Bayesian method, and the overlapping group sparse variation method was applied to the denoising of heart sound signals. Liu et al. [4]Considering the sparsity of the signal and the total variation information of each adjacent amplitude point, the sparse characteristics of the overlapping group are used to eliminate the step effect of the variational model, and good results are achieved. When using the above method to perform sparse denoising on the signal, the denoising effect can only be guaranteed by adjusting the regularization parameter, which will cause the signal amplitude to attenuate. Due to its good sparsity, non-convex variable functions have become an effective means to solve the problem of signal amplitude attenuation. For example, Zhao et al. [5] The non-convex variable function is combined with the enhanced group sparse periodic lasso algorithm and applied to the bearing vibration signal processing, which effectively maintains the amplitude level of the signal on the basis of noise reduction. Chen et al. [6] The non-convex variable function was added to the cost function of the overlapping group sparse method, and the non-convex variable overlapping group sparse method was used for speech signal denoising and image processing, achieving good results. Parekh et al. [7] A variety of non-convex variable functions are used as penalty terms to process heart sound signals, which effectively improves their signal-to-noise ratio.

[0005] In order to solve the problems of waveform distortion and amplitude attenuation in traditional denoising methods, this application proposes a non-convex variable overlapping group sparse variational method that can be used for denoising of steel ingot ultrasonic signals. Summary of the invention

[0006] The purpose of the present invention is to propose a steel ingot ultrasonic signal denoising method based on non-convex variable overlapping group sparse variation. The method performs non-convex variable overlapping group sparse variation processing on the steel ingot ultrasonic signal, and by adjusting the regularization parameter and the multiplication factor, the scattering noise in the steel ingot ultrasonic signal is eliminated while keeping the signal undistorted, thereby improving the detection capability of defects in the steel ingot.

[0007] The steel ingot ultrasonic signal denoising method based on non-convex variable overlapping group sparse variation proposed in the present invention has the following basic principles:

[0008] When ultrasonic testing is performed on steel ingot materials, due to the scattering effect of grain boundaries, the ultrasonic testing signal can be expressed as:

[0009] y=x+w (1)

[0010] Among them, y is the ultrasonic detection signal, x is the useful signal, and w is the scattered noise.

[0011] In order to reduce the influence of the regularization parameter on the amplitude level of the original signal, this application uses a non-convex variable function for the overlapping group sparse variation penalty term to enhance the sparsity of the overlapping group sparse variation method. Therefore, when the noisy detection signal y is subjected to non-convex variable overlapping group sparse variation denoising, the cost function that needs to be optimized can be expressed as:

[0012]

[0013] Among them, the first half of the cost function The L2 norm is used for constraint, which is to ensure the approximation of the denoised signal and the original signal; the latter part φ(||[D2x] n,K ||2; a) is a penalty term used to ensure the sparsity of the signal, where a is the multiplication factor, D2 is the second-order variation matrix; λ is a regularization parameter used to adjust the balance between signal noise reduction level and fidelity.

[0014] In formula (2), the meaning of overlapping group sparse variation is to perform overlapping group sparse variation on K amplitude points of the original signal (K is the size of overlapping group sparse group), and its expansion is:

[0015]

[0016] Where [D2x] n,K =[D2x(n),...,D2x(n+K-1)], where n=1,2,...N, and N is the length of the signal.

[0017] The cost function shown in formula (2) is a typical convex optimization problem, which is difficult to solve directly. By using the optimization-minimization method to iteratively solve it, the sparse variational denoising of the signal's non-convex variable overlapping group can be achieved. After obtaining the cost function, the optimization-minimization method is used to select the optimal convex function. The relationship between the signal to be solved and the optimal convex function is:

[0018]

[0019] Among them, the optimal convex function satisfies:

[0020]

[0021] In the formula C is a constant term and can be ignored in the calculation process of the desired signal. Substituting equation (5) into equation (4), the result is:

[0022]

[0023] In the formula, x i＝0 =y, i is the number of iterations. By solving the above formula within the set number of iterations, the signal's non-convex variable overlapping group sparse variational denoising can be achieved.

[0024] From the above analysis, it can be seen that when the non-convex variable overlapping group sparse variation method is used to denoise the ingot ultrasonic signal, it is necessary to determine the parameters such as the non-convex function type, regularization parameter and multiplication factor. Commonly used non-convex variable functions are shown in Table 1:

[0025] Table 1 Non-convex variable function table

[0026]

[0027] Among them, as a function of the v value, when the trend of the non-convex variable function value changes slowly, when the v value is infinitely close to 0, the concavity of the non-convex variable function becomes stronger, which can induce better sparsity. Compared with the other two functions, atan has the strongest concavity, and better sparsity can be obtained in the noise reduction process. Therefore, this application adopts atan function as a non-convex variable function for sparse variational processing of non-convex variable overlap groups of ultrasonic signals.

[0028] At the same time, the present application adaptively determines the above two parameters based on the relationship between the noise standard deviation and the regularization parameter, and the relationship between the noise amplitude and the multiplication factor. According to the relationship between the regularization parameter and the noise standard deviation, the regularization parameter is selected according to the following formula:

[0029] λ=βσ (7)

[0030] In formula (7), σ is the noise standard deviation, and β is the unknown coefficient. This parameter can be determined according to the following formula:

[0031]

[0032] Where γ is 0.95 and N is the length of the signal. In actual signals, the standard deviation σ of the scattering noise can be estimated by the following formula:

[0033] σ=median(|y(n)-median(y)|) / 0.645 (9)

[0034] Where median(y) represents the median absolute deviation of signal y.

[0035] The selection of the multiplication factor is based on the following: when there is obvious scattering noise in the time domain waveform of the noise reduction signal, the average noise amplitude index is large, and vice versa. Therefore, in the corresponding scattering noise part, the average amplitude index of the scattering noise under different parameter combinations is calculated. If the average amplitude index of the scattering noise does not change under the current parameter combination, the selection ends, otherwise continue to select, and finally, extract the appropriate multiplication factor.

[0036] The present invention proposes a non-convex variable overlapping group sparse variational method for ingot ultrasonic signal noise reduction, which is implemented by the following steps, and its flow chart is as follows: Figure 1 As shown:

[0037] (1) Constructing a cost function model for the signal to be analyzed: Determine the penalty term for the ingot ultrasonic signal to be analyzed in the form of non-convex variable overlapping group sparse variation to construct the cost function of the ingot ultrasonic signal. Taking into account the different signal types, for different ultrasonic detection methods, when the ultrasonic signal is processed using the method of the present application, for the analysis of one-dimensional ultrasonic signals, the overlapping group sparse variation form is constructed according to formula (3) to obtain a non-convex variable overlapping group sparse variation penalty term, where the number of overlapping group sparse groups is one; for the full matrix signal analysis, the overlapping group sparse variation is transformed according to formula (10) to obtain a non-convex variable overlapping group sparse variation penalty term for the full matrix signal, where the number of overlapping group sparse groups is three. After the above changes in the full matrix data, by only giving a set of regularization parameters and multiplication factors, it is possible to achieve simultaneous noise reduction processing of signals excited by different array elements and received by different array elements.

[0038]

[0039] (2) Determine the relevant parameters in the non-convex variable overlapping group sparse variation method: First, under the condition of determined regularization parameters and multiplication factors, three non-convex variable functions are used to perform non-convex variable overlapping group sparse variation processing on the same signal to determine the non-convex variable function with better sparsity; secondly, the regularization parameter and multiplication factor are adaptively determined according to the noise standard deviation and the noise average amplitude.

[0040] (3) Solving convex optimization problems through optimization-minimization algorithm: Using the optimization-minimization algorithm, we can obtain a convex function related to the cost function that is easy to optimize, and solve the equation for optimizing the convex function.

[0041] (4) Iterative update to solve the noise reduction signal: Within the corresponding number of iterations, the signal equation to be solved is calculated. When the iteration stop condition is met, the useful ingot ultrasonic signal can be extracted from the scattered noise.

[0042] The present invention has the following advantages: (1) Compared with the existing sparse denoising methods, the non-convex variable overlapping group sparse variational method proposed in this application can effectively improve the problems of waveform distortion and signal amplitude attenuation; (2) Based on the non-convex variable overlapping group sparse variational method, by selecting appropriate parameters, the influence of scattering noise generated by coarse crystals in the steel ingot on the imaging effect can be eliminated. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of the sparse variational method for overlapping groups of non-convex variables.

[0044] Figure 2 It is the time domain waveform of the ingot ultrasonic signal.

[0045] Figure 3 It is the time domain waveform of the denoised signal of different non-convex variable functions.

[0046] Figure 4 It is the local waveform diagram near the defect of different non-convex variable functions.

[0047] Figure 5 It is a schematic diagram of the relationship between the average amplitude and the multiplication factor.

[0048] Figure 6 It is the time domain waveform of the noise reduction signal and the local waveform near the defect.

[0049] Figure 7 It is the time domain waveform of the noise reduction signal with different parameter combinations and the local waveform near the defect.

[0050] Figure 8 This is a comparison of the time domain waveforms before and after 4-element excitation and 8-element noise reduction.

[0051] Fig. 9 This is a comparison of full focus imaging and local details before and after noise reduction. DETAILED DESCRIPTION

[0052] Combine the following Figures 1 to 9 Taking typical steel ingot ultrasonic signals and ultrasonic imaging as examples, the implementation process of the non-convex variable overlapping group sparse variational method is explained in detail.

[0053] (I) Analysis of denoising of ultrasonic signal of steel ingot by sparse variational method using non-convex variable overlapping groups

[0054] The following are the specific implementation steps of the non-convex variable overlapping group sparse variational method for denoising of typical steel ingot ultrasonic signals.

[0055] 1. Use the DPR 500 ultrasonic pulse transmitter and receiver and the Shanchao 1Z30N probe to collect the ultrasonic signal of the 42CrMo die-cast steel ingot. Figure 2 The time domain waveform of the ingot ultrasonic signal is given.

[0056] 2. Under the same regularization parameter and multiplication factor level, three non-convex variable functions are used to perform non-convex variable overlapping group sparse variation processing on the ingot ultrasonic signal. Figure 3 Three types of non-convex variable function denoising signal time domain waveforms are given. Figure 4 The local waveforms of defect echoes after denoising by three non-convex variable functions. Analysis shows that compared with the other two (rat, log) non-convex variable functions, the denoising effect is better when the signal is processed by the atan function, which can effectively remove the scattered noise in the ingot ultrasonic signal. Therefore, this application uses the atan function as a non-convex variable function for non-convex variable overlapping group sparse variation processing of ultrasonic signals; then, according to the relationship between the regularization parameter and the noise standard deviation in formula (7), determine Figure 2The regularization parameter of the ingot ultrasonic signal is 0.1430. Finally, after determining the non-convex variable function type and the regularization parameter, the multiplication factor parameter of the ultrasonic signal is determined by the relationship between the noise average amplitude index and the noise amplitude when the noise average amplitude does not change. Figure 5 The locations of the echoes without obvious defects and the end echoes in the ultrasonic signal of the steel ingot, the schematic diagram of the average amplitude of the noise and the multiplication factor are given, and the multiplication factor is determined to be 0.02.

[0057] 3. After determining the relevant parameters in the sparse variational method of overlapping groups of non-convex variables, the optimal convex function is determined through the optimization-minimization method to solve the denoised signal.

[0058] 4. Within the set number of iterations, calculate the signal equation to be solved and obtain Figure 6 The time domain waveform of the noise reduction signal and the local waveform near the defect are shown. Figure 7 The time domain waveform of the denoised signal and the local waveform near the defect using different parameter combinations. Figure 6 shows that the sparse variational method using non-convex variable groups can effectively remove the scattering noise in the ultrasonic signal and effectively retain the defect echo information. Figure 7 Analysis shows that the noise reduction effect of the parameter combination determined by the parameter selection method in this application is better than the noise reduction effect of any parameter combination.

[0059] (II) Non-convex variable overlapping group sparse variational method to improve imaging signal-to-noise ratio analysis

[0060] The following are specific implementation steps of the non-convex variable overlapping group sparse variational method for improving the signal-to-noise ratio of ultrasound imaging.

[0061] 1. Use Multi2000 ultrasonic phased array detector to collect ultrasonic signals of 4140 continuous casting ingots using ultrasonic array probe. Figure 8 The time domain waveform comparison diagram before and after 4-element excitation and 8-element noise reduction is given.

[0062] 2. Using atan function as a non-convex variable function, according to the relationship between the regularization parameter and the noise standard deviation in formula (7), determine Figure 8 The regularization parameter of the ingot ultrasonic signal is shown to be 2.7; finally, after determining the non-convex variable function type and the regularization parameter, the multiplication factor parameter of the ultrasonic signal is determined through the relationship between the noise average amplitude index and the noise amplitude when the noise average amplitude does not change, and the multiplication factor is determined to be 0.9.

[0063] 3. After determining the relevant parameters in the sparse variational method of overlapping groups of non-convex variables, the optimal convex function is determined through the optimization-minimization method to solve the denoised signal.

[0064] 4. Within the set number of iterations, calculate the equation for the matrix data to be completed and obtain Fig. 9 The comparison diagram of full-focus imaging and local details before and after noise reduction is shown. As shown in Figure 9, within the same gain range, the signal-to-noise ratio of the full-focus imaging of the signal after noise reduction is significantly higher than that of the direct full-focus imaging result, and the scattered noise in the imaging result after noise reduction is significantly eliminated.

[0065] From the above two cases, it can be seen that the non-convex variable group sparse variational method can effectively eliminate the scattering noise in the ingot ultrasonic signal while ensuring that the ultrasonic signal is not distorted, thereby retaining useful information such as defect echoes in the ingot signal and improving the signal-to-noise ratio of ultrasonic array imaging.

[0066] The above are typical applications of the present invention, and the application of the present invention is not limited thereto.

[0067] References

[0068] [1]Grevillot M, Cudel C, Meyer JJ, et al.Two approaches to multiplespecular echo detection using split spectrum processing:moving bandwidthminimization and mathematical morphology[J].Ultrasonics,1999,37(6):417-422.

[0069] [2]Praveen A,Vijayarekha K,Abraham ST,et al.Signal qualityenhancement using higher order wavelets for ultrasonic TOFD signals fromaustenitic stainless steel welds[J].Ultrasonics,2013,53(7):1288-1292

[0070] [3]Deng SW,Han J Q.Adaptive overlapping group sparse denoising forheart sound signals[J].Biomedical Signal Processing and Control, 2018,40(8):49-57.

[0071] [4]Liu G,Huang T Z,Liu J,et al.Total variation with overlapping groupsparsity for image dublurring under impulse noise[J].PLOS One,2015,10(4):62-75.

[0072] [5]Zhao Z B,Wu S M,Qiao B J,et al.Enhanced sparse period-group lassofor bearing fault diagnosis[J].IEEE Transactions on Industrial Electronics,2019,66(3):2143-2153.

[0073] [6]Chen P Y,Selesnick I W.Group-sparse signal denoising:non-convexregularization,convex optimization[J].IEEE Transactions on Signal Processing,2014,62(13):3464-3478.

[0074] [7]Parekh A,Selesnick I W.Convex fused lasso denoising with non-convex regularization and its use for pulse detection[C] / / IEEE SignalProcessing in Medicine and Biology Symposium.Philadelphia:IEEE,2015.

Claims

1. A non-convex variable overlapping group sparse variational method for denoising of ingot ultrasonic signals, characterized in that: The method is implemented by the following steps: (1) Constructing a cost function model for the signal to be analyzed: determining the penalty term for the steel ingot ultrasonic signal to be analyzed in the form of non-convex variable overlapping group sparse variation to construct the cost function of the steel ingot ultrasonic signal; considering the different signal types, for different ultrasonic detection methods, when processing the ultrasonic signal, for the analysis of one-dimensional ultrasonic signal, the overlapping group sparse variation form is constructed to obtain a non-convex variable overlapping group sparse variation penalty term, where the number of overlapping group sparse groups is one; for the analysis of the full matrix signal, the overlapping group sparse variation is transformed to obtain a non-convex variable overlapping group sparse variation penalty term for the full matrix signal, where the number of overlapping group sparse groups is three; after the above transformation in the full matrix signal, by only giving a set of regularization parameters and multiplication factors, it is possible to simultaneously perform noise reduction processing on the signals excited by different array elements and received by different array elements; (2) Determine the relevant parameters in the non-convex variable overlapping group sparse variation method: Under the condition of the determined regularization parameter and multiplication factor, use three non-convex variable functions atan, log, and rat to perform non-convex variable overlapping group sparse variation processing on the same signal to determine the sparse non-convex variable function; secondly, determine the regularization parameter and multiplication factor adaptively according to the noise standard deviation and the noise average amplitude; (3) Solving convex optimization problems through optimization-minimization algorithms: Using optimization-minimization algorithms, we can obtain a convex function related to the cost function that is easy to optimize, and solve the equation for optimizing the convex function. (4) Iteratively updating and solving the noise reduction signal: within the corresponding number of iterations, the equation for the full matrix signal is calculated, and when the iteration stop condition is met, the useful ingot ultrasonic signal is extracted from the scattered noise; The atan function is used as the non-convex variable function, and the regularization parameter of the ingot ultrasonic signal is determined according to the relationship between the regularization parameter and the noise standard deviation. After determining the type of non-convex variable function and the regularization parameter, the multiplication factor parameter of the ingot ultrasonic signal is determined through the relationship between the noise average amplitude index and the noise amplitude when the noise average amplitude does not change.

2. The non-convex variable overlapping group sparse variational method for denoising of ingot ultrasonic signals according to claim 1, characterized in that: The ultrasonic phased array detector is used to collect ultrasonic signals of the continuous casting ingot of the test piece using an ultrasonic array probe.

3. The non-convex variable overlapping group sparse variational method for denoising of ingot ultrasonic signals according to claim 1, characterized in that: After determining the relevant parameters in the sparse variational method for overlapping groups of non-convex variables, the optimal convex function is determined through the optimization-minimization method to solve the denoised signal.

4. The non-convex variable overlapping group sparse variational method for denoising of ingot ultrasonic signals according to claim 1, characterized in that: Within the set number of iterations, the equation for the full matrix signal is calculated to obtain the full-focus imaging and local detail comparison before and after denoising. Within the same gain range, the signal-to-noise ratio of the full-focus imaging of the signal after denoising is significantly higher than that of the direct full-focus imaging result, and the scattering noise in the imaging result after denoising is significantly eliminated.

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