Barkhausen signal processing method based on wavelet packet algorithm

Abstract

The invention discloses a Barkhausen signal processing method based on a wavelet packet algorithm. The method comprises the following steps: magnetizing a test piece to obtain a Barkhausen signal; the signals are decomposed according to high frequency and low frequency, the signal frequency resolution is improved through signal decomposition, and more information is covered; signal reconstruction is inverse change of decomposition, and redundant information on a frequency band can be removed through signal reconstruction; the method comprises the following steps of: setting a threshold value through a heuristic threshold value principle and a penalization threshold value principle of Birge-Massart; performing signal noise reduction on the action threshold; and the signal processing effect is evaluated through two parameters of the energy ratio and the root-mean-square error. The Barkhausen signal processing method based on the wavelet packet algorithm disclosed by the invention can solve the problems of large external interference and low signal-to-noise ratio during conventional MBN signal processing, provides a new signal processing method for the problems, and achieves the effects of reducing the external interference, improving the signal-to-noise ratio and keeping a real target signal.

Description

Technical Field

[0001] The invention relates to the field of electromagnetic signal processing, and in particular to a Barkhausen signal processing method based on a wavelet packet algorithm. Background Art

[0002] P92 steel is an important material for thermal power plants. Due to its non-replaceability, its working life directly determines the life of the thermal power plant. It is listed as the key equipment with the highest priority in all national classifications. Creep fatigue is the main source of various performance changes of P92 steel. Therefore, it is very important to evaluate the hardness or strain damage degree of P92 steel. The Barkhausen signal is very sensitive to the hardness or stress changes of ferromagnetic materials. We can use the Barkhausen principle to detect and evaluate the performance of P92 steel. The MBN signal is a small jumping signal, so the processing of the MBN signal becomes an important issue in the detection process. In view of the above problems, the present invention proposes a Barkhausen signal processing method based on a wavelet packet algorithm. Summary of the invention

[0003] In view of the above defects or deficiencies in the prior art, it is desirable to provide a Barkhausen signal processing method based on a wavelet packet algorithm.

[0004] The present application provides a Barkhausen signal processing method based on a wavelet packet algorithm, comprising the following steps:

[0005] S1: Magnetize the specimen by exciting the U-shaped magnetic yoke and collect the noisy Barkhausen signal using the detection coil;

[0006] S2: A more refined decomposition based on wavelet transform through wavelet packet algorithm;

[0007] S3: Through signal reconstruction, the information on the required frequency band is retained and the redundant information on other frequency bands is removed;

[0008] S4: Determine the threshold selection method and set the optimal threshold;

[0009] S5: Signal noise reduction by applying threshold;

[0010] S6: The signal processing effect is evaluated by two parameters: energy ratio and root mean square error.

[0011] Furthermore, step S3 is specifically as follows:

[0012] The wavelet packet reconstruction formula is as follows:

[0013]

[0014] In the formula and The original signal jThe kth decomposition sequence obtained after layer wavelet packet decomposition;

[0015] Based on Pasay's theorem: The energy of each signal segment distributed on different scales is: E i =∑d i 2 (n,j,k).

[0016] Furthermore, step S4 is specifically as follows:

[0017] Assume that the high-frequency coefficients of the i-th layer wavelet decomposition {s i (k)} is of length l, let:

[0018]

[0019] When eta<crit, a fixed threshold is used, otherwise the minimum of the two thresholds is selected;

[0020] Among them, the unbiased likelihood estimation principle is to transform the signal s i The values ​​in (k) are arranged in ascending order after taking their absolute values, and u(k) is Ascending sequence of , σ is used as the standard deviation estimate of the noise level of each layer of wavelet packet decomposition coefficients:

[0021]

[0022] The expression of the threshold is as follows:

[0023]

[0024] Where thr1 represents the stratified threshold of the unbiased likelihood estimate, and min is the value corresponding to the subscript of the minimum value of r(k) in the u1(k) sequence;

[0025] The threshold thr2 calculated by the fixed threshold principle is the global threshold, and the calculation formula is as follows:

[0026]

[0027] Where n is the total length of wavelet coefficients, σ ​​is {s(k)} is any wavelet sequence.

[0028] Furthermore, step S5 is specifically as follows:

[0029] After the threshold is selected, the method of applying the threshold is divided into hard threshold or soft threshold. The hard threshold method removes the signal value whose absolute value is less than the set threshold; the soft threshold method compares the wavelet coefficient with the set threshold. If it is greater than the set threshold, the difference between the signal value at that point and the set threshold is taken, otherwise the signal value at that point is set to zero.

[0030] The hard threshold and soft threshold methods based on the heuristic threshold principle were used to carry out MBN-based testing on P92 steel specimens with hardness of 165, 175, 185 and 205, and the test results were quantified.

[0031] Further, step S6 is specifically as follows:

[0032] Assume that the mathematical model of a one-dimensional signal containing noise components is:

[0033] s(t)=f(t)+σ ε e e (t)

[0034] Where s(t) is the detection signal with noise interference, f(t) is the actual signal, and e e (t) is the noise, σ ε is the noise intensity. The purpose of MBN signal noise reduction is to suppress e e (t) to recover f(t);

[0035] The signal-to-noise ratio (SNR) and root mean square error (RMSE) are used as the criteria for measuring the noise reduction effect:

[0036]

[0037] in,

[0038] The Barkhausen signal processing method based on wavelet packet algorithm provided in this application solves the problem of low signal-to-noise ratio caused by large external interference during conventional MBN signal processing, and proposes a new signal processing method to achieve the effect of reducing external interference, improving signal-to-noise ratio, and retaining the real target signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A simplified flow chart for a Barkhausen signal processing method based on wavelet packet algorithm;

[0040] Figure 2 Schematic diagram of three-layer decomposition of wavelet packet;

[0041] Figure 3 It is the energy distribution diagram of MBN signal decomposed by 4 layers of wavelet;

[0042] Figure 4 Wavelet packet decomposition signal for MBN signal;

[0043] Figure 5 Figure 2 shows the MBN original signal and various noise reduction signal diagrams. Specific implementation methods

[0045] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0046] See also Figure 1 , a Barkhausen signal processing method based on wavelet packet algorithm, comprising the following steps:

[0047] S1: The specimen is magnetized by exciting the U-shaped magnetic yoke and the noisy Barkhausen signal is collected by the detection coil.

[0048] S2: More refined decomposition based on wavelet transform through wavelet packet algorithm (optimal subalgebraic structure).

[0049] S3: Through signal reconstruction, the information on the required frequency band is retained and the redundant information on other frequency bands is removed.

[0050] S4: Determine the threshold selection method, set the optimal threshold, and prepare for signal noise reduction.

[0051] S5: Reduce signal noise and improve signal-to-noise ratio by applying threshold.

[0052] S6: The signal processing effect is evaluated by two parameters: energy ratio and root mean square error.

[0053] Further, the S1 includes:

[0054] The sensor consisting of a U-shaped magnetic yoke, an excitation coil and a detection coil is placed close to the test piece. By applying a magnetic field to the test piece, the magnetic domain of the test piece is flipped and the magnetic domain wall moves, emitting a series of chaotic voltage pulse signals, which we call Barkhausen signals, or MBN signals for short. The detection coil is used to collect these MBN signals, but the signal-to-noise ratio of the MBN signal is low due to interference from the hardware and the surrounding environment during the collection process.

[0055] In order to solve the problem of low signal-to-noise ratio of MBN signals, the present invention proposes a MBN signal processing method based on wavelet packet algorithm, which can realize signal decomposition by combining time domain and frequency domain.

[0056] Further, the S2 includes:

[0057] The wavelet packet algorithm, also known as the optimal subalgebraic structure, is a more sophisticated decomposition and reconstruction method based on the wavelet transform. The wavelet packet algorithm adds the decomposition of high-frequency components, making the frequency resolution higher and covering more information. The wavelet packet algorithm can reflect both the time domain characteristics and the frequency domain characteristics, and is suitable for denoising MBN signals. The wavelet packet algorithm is divided into two algorithms: decomposition and reconstruction.

[0058] If the orthogonal scaling function φ(t) and the orthogonal wavelet function are given The relationship between the two is as follows:

[0059]

[0060] Where h k and g k They are low-pass and high-pass filters respectively. Figure 2 The figure shows the schematic diagram of three-layer decomposition of wavelet packet. The signal is decomposed into 8 frequency bands. In the figure, (m, n) represents the nth decomposition node of the mth layer. Each layer of decomposition decomposes the signal into low-frequency and high-frequency signals, and then decomposes them separately. Each time the data on the decomposition frequency band is halved, the time domain resolution is also reduced. Wavelet packet transform has higher time-frequency resolution, and both low-frequency and high-frequency components are taken into account.

[0061] The application of wavelet packet algorithm requires the selection of appropriate wavelet basis functions and decomposition levels. The present invention uses the Dmey wavelet function as the wavelet basis function, which has good symmetry and smoothness, can perform fast discrete wavelet transform, and can effectively present useful information in the MBN signal. For the selection of the number of decomposition levels, it is necessary to first analyze the spectrum of the MBN signal. The frequency band range of the MBN signal obtained by testing the standard P92 steel (hardness value is 205) is 0-20kHz, the frequency domain is concentrated at 11-13kHz, and the main frequency band is around 12kHz. This characteristic interval is used as the characteristic subband. The number of wavelet packet decomposition levels should be selected so that a certain subband after decomposition can just contain the characteristic subband. For example Figure 3 The following is the energy distribution diagram of MBN signals of different scales obtained by 4-layer wavelet decomposition of MBN signals. 4-layer wavelet decomposition can concentrate the energy in a certain frequency band, so 4 layers are selected for decomposition. The waveform of MBN signals in each frequency band after 4-layer wavelet decomposition is as follows: Figure 4 shown.

[0062] Further, the S3 includes:

[0063] Signal reconstruction is the inverse transformation of decomposition, retaining the information on the required frequency band and removing the redundant information on other frequency bands. The wavelet packet reconstruction formula is as follows:

[0064]

[0065] In the formula and The original signal j The kth decomposition sequence obtained after layer wavelet packet decomposition.

[0066] The solution to the signal energy distributed at different scales is based on Passet's theorem, that is, the total energy in the time domain and the frequency domain is equal:

[0067]

[0068] Using this characteristic, the energy of each signal segment can be obtained as:

[0069] E i =∑d i 2 (n,j,k) (5)

[0070] For the wavelet packet algorithm, it is necessary to select the appropriate wavelet basis function and decomposition layer number. The appropriate wavelet basis function can characterize more key information in the MBN signal. The fewer the decomposition layers, the faster the decomposition, but the signal resolution is low; the more layers, the higher the signal resolution, but the slower the decomposition.

[0071] Further, the S4 includes:

[0072] Noise usually only accounts for a small part in the wavelet coefficients. Signal denoising using the wavelet packet algorithm is achieved by filtering out wavelet coefficients whose absolute values ​​are less than the set threshold. There are several methods for selecting thresholds: unbiased likelihood estimation principle, fixed threshold principle, extreme threshold principle, heuristic threshold principle, and the threshold method proposed by Birge-Massart. The extreme threshold method is more conservative and sets some coefficients to zero to achieve noise reduction; the fixed threshold method will cause the loss of useful high-frequency information; the heuristic threshold combines the unbiased likelihood estimation principle with the fixed threshold principle, and the noise reduction effect is more flexible and accurate; the threshold method proposed by Birge-Massart can meet the estimation principle of minimum variance in the worst case. The following is an introduction to the latter two methods:

[0073] (1) Heuristic Threshold Principle

[0074] The heuristic threshold principle can automatically select a threshold between the fixed threshold principle and the unbiased likelihood estimation principle according to the energy ratio. Assume that the high-frequency coefficients of the i-th layer wavelet decomposition {s i (k)} is of length l, let:

[0075]

[0076] When eta<crit, a fixed threshold is used; otherwise, the minimum of the two thresholds is selected.

[0077] Among them, the unbiased likelihood estimation principle is to transform the signal s i The values ​​in (k) are arranged in ascending order after taking their absolute values, and u(k) is Ascending sequence of , σ is used as the standard deviation estimate of the noise level of each layer of wavelet packet decomposition coefficients:

[0078]

[0079] u1(k)=u(k) 2 (9)

[0080]

[0081] The expression of the threshold is as follows:

[0082]

[0083] Where thr1 represents the stratified threshold of the unbiased likelihood estimate, and min is the value corresponding to the subscript of the minimum value of r(k) in the u1(k) sequence.

[0084] The threshold thr2 calculated by the fixed threshold principle is the global threshold, and the calculation formula is as follows:

[0085]

[0086] Where n is the total length of wavelet coefficients, σ ​​is {s(k)} is any wavelet sequence.

[0087] (2) Birge-Massart’s Penalization Threshold Principle

[0088] The threshold is calculated as follows:

[0089]

[0090] In the formula, t * In order to obtain the minimum value of t, c k The kth wavelet coefficient is arranged in descending order of the wavelet coefficient sequence, β is an empirical coefficient, and its value is a real number greater than 1, and the value of β is usually between 1.5 and 3. The present invention selects the value of β to be 3 through experiments. The larger β is, the smoother the reconstructed signal is.

[0091] For the setting of wavelet denoising threshold, the present invention selects the heuristic threshold principle and the Birge-Massart penalty threshold principle for setting respectively. The heuristic threshold combines the unbiased likelihood estimation principle with the fixed threshold principle, and the denoising effect is more flexible and accurate; the threshold method proposed by Birge-Massart can meet the estimation principle of minimum variance in the worst case. After setting the threshold, the hard threshold and soft threshold methods are used to perform denoising on the MBN signal. Figure 5 Shown are the MBN original signal and noise reduction signal diagram of standard P92 steel.

[0092] By observation Figure 5It can be seen that the original MBN signal of standard P92 steel has undergone corresponding changes after denoising using the heuristic threshold principle and the penalty threshold principle. Among them, the MBN signal after denoising based on the penalty threshold principle loses information excessively, and the method using this principle is not suitable for denoising MBN signals. By comparing the similarity and smoothness of the MBN signal after denoising using the heuristic threshold principle and the original MBN signal, it can be concluded that the heuristic principle has a better denoising effect on the MBN signal of P92 steel.

[0093] Further, the S5 includes:

[0094] After the threshold is selected, the thresholding methods are divided into hard thresholding and soft thresholding. The hard thresholding method removes signal values ​​whose absolute values ​​are less than the set threshold. Although it will cause oscillation of the reconstructed signal, it can retain good local feature information. The soft thresholding method compares the wavelet coefficient with the set threshold. If it is greater than the set threshold, the difference between the signal value at that point and the set threshold is taken, otherwise the signal value at that point is set to zero. The soft thresholding method compensates for the signal oscillation caused by signal discontinuity and makes the signal smoother, but it will also cause deviations between the original wavelet coefficients and the estimated wavelet coefficients.

[0095] The hard threshold and soft threshold methods based on the heuristic threshold principle were used to carry out MBN-based testing on P92 steel specimens with hardness of 165, 175, 185 and 205, and the test results were quantified.

[0096] Further, the S6 includes:

[0097] The purpose of processing MBN signals is to reduce the influence of low-frequency interference and environmental noise in MBN signals and retain the characteristic information of MBN signals. Suppose the mathematical model of a one-dimensional signal containing noise components is:

[0098] s(t)=f(t)+σ ε e e (t) (14)

[0099] Where s(t) is the detection signal with noise interference, f(t) is the actual signal, and e e (t) is the noise, σ ε is the noise intensity. The purpose of MBN signal noise reduction is to suppress e e (t) to recover f(t).

[0100] The evaluation of noise reduction effect should meet the following two criteria:

[0101] (1) Similarity: The variance estimate between the denoised signal and the original signal should be the minimum value in the worst case.

[0102] (2) Smoothness: The signals before and after noise reduction should have the same smoothness.

[0103] The signal-to-noise ratio (SNR) and root mean square error (RMSE) are usually used as criteria for measuring the effect of noise reduction:

[0104]

[0105] The energy ratio indicates the similarity between the original signal and the denoised signal. The larger the energy ratio, the better the denoising effect.

[0106]

[0107] The root mean square error represents the square root of the variance between the original signal and the noise reduction signal. The smaller the root mean square error, the smaller the error between the original signal and the noise reduction signal, and the closer it is to the ideal noise reduction effect.

[0108] Table 1 Energy ratio and RMS error of MBN signal of P92 steel with different hardness after wavelet packet denoising

[0109]

[0110]

[0111] The hard threshold and soft threshold methods based on the heuristic threshold principle were used to test P92 steel specimens with hardness of 165, 175, 185, and 205 respectively based on MBN, and the test results were quantified. The energy ratio and root mean square error are shown in Table 1. It can be seen from the table that the heuristic hard threshold method has a large energy ratio and a small root mean square error when denoising the MBN signal, and a better filtering effect can be obtained.

Claims

1. A Barkhausen signal processing method based on wavelet packet algorithm, characterized in that: The following steps are involved: S1: Magnetize the specimen by exciting the U-shaped magnetic yoke and collect the noisy Barkhausen signal using the detection coil; S2: A more refined decomposition based on wavelet transform through wavelet packet algorithm; S3: Through signal reconstruction, the information on the required frequency band is retained and the redundant information on other frequency bands is removed; S4: Determine the threshold selection method and set the optimal threshold; S5: Signal noise reduction by applying threshold; S6: The signal processing effect is evaluated by two parameters: energy ratio and root mean square error.

2. The Barkhausen signal processing method based on wavelet packet algorithm according to claim 1, characterized in that: The step S3 is specifically as follows: The wavelet packet reconstruction formula is as follows: In the formula and The original signal j The kth decomposition sequence obtained after layer wavelet packet decomposition; Based on Pasay's theorem: The energy of each signal segment distributed on different scales is: E i =vd i 2 (n,j,k).

3. The Barkhausen signal processing method based on wavelet packet algorithm according to claim 2, characterized in that: The step S4 is specifically as follows: Assume that the high-frequency coefficients of the i-th layer wavelet decomposition {s i (k)} is of length l, let: When eta<crit, a fixed threshold is used, otherwise the minimum of the two thresholds is selected; Among them, the unbiased likelihood estimation principle is to transform the signal s i The values ​​in (k) are arranged in ascending order after taking their absolute values, and u(k) is Ascending sequence of , σ is used as the standard deviation estimate of the noise level of each layer of wavelet packet decomposition coefficients: The expression of the threshold is as follows: Where thr1 represents the stratified threshold of the unbiased likelihood estimate, and min is the value corresponding to the subscript of the minimum value of r(k) in the u1(k) sequence; The threshold thr2 calculated by the fixed threshold principle is the global threshold, and the calculation formula is as follows: Where n is the total length of wavelet coefficients, σ ​​is {s(k)} is any wavelet sequence.

4. The Barkhausen signal processing method based on wavelet packet algorithm according to claim 3, characterized in that: The step S5 is specifically as follows: After the threshold is selected, the method of applying the threshold is divided into hard threshold or soft threshold. The hard threshold method removes the signal value whose absolute value is less than the set threshold; the soft threshold method compares the wavelet coefficient with the set threshold. If it is greater than the set threshold, the difference between the signal value at that point and the set threshold is taken, otherwise the signal value at that point is set to zero. The hard threshold and soft threshold methods based on the heuristic threshold principle were used to carry out MBN-based testing on P92 steel specimens with hardness of 165, 175, 185 and 205, and the test results were quantified.

5. The Barkhausen signal processing method based on wavelet packet algorithm according to claim 4, characterized in that: The step S6 is specifically as follows: Assume that the mathematical model of a one-dimensional signal containing noise components is: s(t)=f(t)+σ ε e e (t) Where s(t) is the detection signal with noise interference, f(t) is the actual signal, and e e (t) is the noise, σ ε is the noise intensity. The purpose of MBN signal noise reduction is to suppress e e (t) to recover f(t); The signal-to-noise ratio (SNR) and root mean square error (RMSE) are used as the criteria for measuring the noise reduction effect: in,

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