Traveling wave front calibration method based on ICEEMDAN-NTEO

Abstract

The application relates to a traveling wave head calibration method based on ICEEMDAN-NTEO, and belongs to the technical field of fault detection and positioning of power systems. The method comprises the following steps: collecting a three-phase voltage traveling wave signal and obtaining a line mode component through Karenbauer transformation decoupling; an improved wavelet threshold function is used for adaptive denoising of the signal, and a particle swarm algorithm is used for optimizing and adjusting a factor to balance noise suppression and feature reservation; an ICEEMDAN algorithm is applied to decompose the denoised signal to obtain multiple IMF components; effective IMF components are selected through an entropy ridge ratio minimum principle; and finally, a non-linear energy operator NTEO is used for enhancing a mutation feature and accurately extracting a traveling wave head arrival time. The application effectively solves the problem of difficult extraction of the traveling wave head in a strong noise environment, and significantly improves the accuracy and reliability of fault positioning.

Description

Technical Field

[0001] This invention belongs to the field of power system fault detection and location technology, and relates to a method for accurate extraction of traveling wavefronts by integrating wavelet denoising, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), and nonlinear energy operator (NTEO). Background Technology

[0002] With the continuous expansion and increasing complexity of power systems, rapid and accurate detection of distribution network faults is crucial for ensuring power supply reliability. Among distribution network fault detection and location technologies, the traveling wave method is widely used due to its fast response speed and high location accuracy.

[0003] The core of traveling wave fault location lies in analyzing the voltage traveling wave signal generated by the fault, with accurate extraction of the traveling wave front being a crucial step in achieving precise location. However, in actual power distribution network operation environments, the acquired voltage traveling wave signals often face complex operating conditions and are highly susceptible to multiple factors such as electromagnetic noise interference, mode aliasing, and nonlinear distortion. These interferences obscure the weak traveling wave front characteristics, making it difficult for traditional methods to accurately identify the arrival time of the wave front, thus severely affecting the accuracy of fault location. Traditional methods also have limitations in noise suppression and feature enhancement.

[0004] Currently, commonly used methods for traveling wave signal processing include wavelet transform, empirical mode decomposition (EMD), and their improved algorithms. While wavelet transform has some denoising capabilities, the choice of threshold function significantly impacts the denoising effect; traditional hard and soft thresholding functions struggle to balance preserving signal details with noise suppression. EMD-like methods can adaptively decompose signals, but suffer from mode aliasing and endpoint effects. The improved adaptive noise-complete ensemble empirical mode decomposition (ICEEMDAN), as an improved algorithm, suppresses noise interference and mode aliasing to some extent, but further integration with noise suppression and feature enhancement strategies is needed to improve the accuracy of wavefront extraction.

[0005] In addition, existing energy operators (such as the Teager energy operator) perform well in enhancing abrupt components, but are sensitive to low-frequency noise and their performance degrades in complex noise environments.

[0006] In summary, existing single signal processing techniques are insufficient to simultaneously address complex issues such as strong noise interference, mode aliasing, and weak features. Therefore, there is an urgent need to develop a traveling wave front extraction method that can effectively integrate noise suppression, signal decomposition, and feature enhancement to overcome the shortcomings of existing technologies. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a traveling wave front calibration method that integrates wavelet denoising and ICEEMDAN-NTEO. By acquiring three-phase voltage traveling wave signals and decoupling them, denoising is performed using an improved wavelet threshold function. Then, effective IMF components are selected through ICEEMDAN decomposition and frequency domain comparison. Finally, NTEO is used to highlight abrupt change characteristics and accurately extract the wave front arrival time. This method effectively improves the noise resistance and positioning accuracy of traveling wave front detection, thereby improving the accuracy and reliability of fault location in distribution networks.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A traveling wave head calibration method based on ICEEMDAN-NTEO specifically includes the following steps: S1: Collect the three-phase voltage traveling wave signals measured at each detection point, and use Karenbauer to decouple and transform the collected three-phase voltage traveling wave signals to obtain the line-mode voltage signals at the two measurement points. S2: Denoising the line-mode voltage signal using an improved wavelet threshold function; S3: The denoised line-mode voltage signal is decomposed using ICEEMDAN (an improved adaptive noise complete set empirical mode decomposition) to obtain multiple IMF components; S4: Select effective IMF components based on the principle of minimizing entropy kurtosis ratio; S5: The selected effective IMF components are used to highlight the abrupt change characteristics of the wavefront using NTEO (nonlinear energy operator), thereby achieving accurate extraction of the wavefront arrival time.

[0009] Furthermore, in step S2, the improved wavelet threshold function expression is as follows:

[0010] In the formula, These are the wavelet coefficients after thresholding. Wavelet coefficients before thresholding; As a regulating factor, and always ensuring ; The threshold value is used.

[0011] Furthermore, in step S2, the regulating factor The principle for selecting the value is: the optimal value should be selected for different signals. At that time, using the signal-to-noise ratio (SNR) function as the fitness function, the particle swarm optimization algorithm is used to find the optimal value, and the value obtained when the SNR is maximized is obtained. The optimal value is found; the signal-to-noise ratio function is expressed as:

[0012] In the formula, Where is the signal-to-noise ratio, and N is the signal duration. It is a noisy signal. The signal after denoising. For discrete time series indexes.

[0013] Furthermore, in step S2, the threshold The expression is:

[0014] In the formula, Wavelet coefficients after thresholding The standard deviation value, N This represents the signal duration.

[0015] Furthermore, in step S3, the denoised line-mode voltage signal is decomposed using ICEEMDAN. The specific steps are as follows: The denoised signal is used as input, and Gaussian white noise is added; The first IMF component was obtained by decomposing the original time series using the ICEEMDAN algorithm. Continue calculating to find the first... k Each IMF component is expressed as follows:

[0016] In the formula, For the first Expected signal-to-noise ratio at the next decomposition express Order residual; Indicates the first One IMF value, represent First-order intrinsic modal components, Operators for generating local means, This represents the number of samples used to calculate the local mean.

[0017] Furthermore, in step S4, the formula for calculating the entropy kurtosis ratio is:

[0018] In the formula, GK is the entropy kurtosis ratio, and GCMPE is the entropy of the generalized composite multi-scale arrangement. K This represents the kurtosis value.

[0019] Furthermore, in step S4, the calculation steps for the generalized composite multiscale permutation entropy (GCMPE) are as follows: (1) Time series After generalized coarsening, the generalized coarsening process is as follows:

[0020] In the formula, Representing scale Down shift The corresponding number One coarsening value; , representing the local mean; This represents the length of the window at scale s. N The duration of the signal; (2) The coarse-grained sequence obtained after step (1) is shown in the following formula:

[0021] (3) For Sequences Calculate the permutation entropy of each sequence. ; (4) The mean of the permutation entropy values ​​is used as the original time series. The GCMPE value is calculated as follows:

[0022] in, m The embedding dimension represents the permutation entropy, which is the number of sample points contained in each pattern vector.

[0023] Furthermore, in step S4, the kurtosis value K The calculation formula is as follows:

[0024] In the formula, This represents the mean value of the data within the set time window of the signal. This represents the standard deviation of the data within the set time window of the signal. Expressing expectations, A random variable representing the amplitude of a signal; When the signal is discrete, at time point At this point, the time window length is [value missing]. Calculate the kurtosis value of the data within the time window. K As shown below:

[0025] In the formula, , indicating time window The local mean of the internal signal is used to calculate the kurtosis value. ; Indicates the kurtosis value. Represents a time series.

[0026] Furthermore, in step S5, the expression for NTEO is:

[0027] In the formula, For energy operators; It is a discrete signal; For a certain discrete time point; For resolution parameters, , Sampling frequency, This is the fundamental frequency.

[0028] The beneficial effects of this invention are as follows: (1) This scheme, through the improved wavelet threshold function, combined with the adaptive adjustment factor and particle swarm optimization algorithm, can effectively remove noise in a strong noise environment, while retaining the weak but key fault traveling wave characteristics, thus overcoming the contradiction between noise removal and detail preservation in the traditional hard / soft threshold function.

[0029] (2) This scheme uses the ICEEMDAN (improved adaptive noise complete set empirical mode decomposition) method to decompose the signal, effectively suppressing mode mixing and endpoint effects, and adaptively selects the IMF component containing the main fault information through the frequency domain ratio criterion, providing a high-quality, high signal-to-noise ratio signal basis for subsequent wavefront detection.

[0030] (3) This scheme introduces NTEO (nonlinear energy operator) to enhance the selected IMF component by abrupt change, accurately captures the small amplitude changes and abrupt change points of the traveling wave front, significantly improves the timing accuracy of the wave front and the anti-interference capability, and is suitable for fault location in complex power grid environments.

[0031] In summary, this solution can effectively and accurately extract the traveling wave front during distribution network faults, thereby improving the accuracy and reliability of distribution network fault location.

[0032] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0033] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a flowchart of the traveling wave head calibration method proposed in this invention; Figure 2 A schematic diagram for improving wavelet denoising; Figure 3A schematic diagram for selecting effective IMF components for entropy cuboidal ratio. Detailed Implementation

[0034] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0035] Please see Figures 1-3 This invention provides a traveling wave head calibration method based on ICEEMDAN-NTEO, specifically including the following steps: 1. Three-phase voltage decoupling transformation during faults Since there is a coupling relationship between the three-phase voltage traveling waves, the Karenbauer transform is needed to decouple the fault components of the voltage traveling waves to obtain the fault voltage traveling wave mode components for fault location analysis. The voltage traveling wave fault components can be obtained from equation (1), and the Karenbauer transform is shown in equation (2).

[0036] (1) (2) In the formula, For voltage traveling wave fault components, The voltage traveling wave during the fault. This is the voltage traveling wave during normal operation. , , The voltages are for phases A, B, and C. , , For the fault voltage traveling wave 0, , Mode components. Since the zero-mode component propagates through a loop between the phase line and the ground, it is significantly attenuated and its wave velocity is unstable during propagation due to external factors such as grounding resistance and soil conductivity. Modulus and The modulus component propagates in the phase-to-phase loop, and its propagation speed is relatively stable. Compare the 0-mode component and... Modulus component, The modulus component has a higher amplitude and stronger noise immunity, which is especially advantageous in situations where the distribution network lines are short and the branches are complex. Therefore, it is adopted... The modulus component is more suitable for fault traveling wave analysis.

[0037] 2. Regarding the collected data Modulus component denoising using improved wavelet thresholding To effectively suppress noise interference mixed in the modulus component and better preserve the characteristics of the fault transient signal, the calculated... The modulus component is denoised using an improved wavelet thresholding function. This improved function aims to overcome the shortcomings of traditional hard thresholding functions (which produce unsmooth results) and soft thresholding functions (which have constant biases). Its formula is as follows: (3) In the formula, These are the wavelet coefficients after thresholding. Wavelet coefficients before thresholding; As a regulating factor, and always ensuring ; The threshold value is used.

[0038] Regulatory factors The principle for determining the value of is: when the signal-to-noise ratio of the noisy signal is small, A larger value helps to remove more noise wavelet coefficients; when the signal-to-noise ratio of the noisy signal is high, Smaller values ​​are beneficial for preserving wavelet coefficients of weaker signals. Generally, a value of [value missing] is used. This can achieve a relatively good noise reduction effect. However, the optimal method needs to be chosen for different signals. At that time, using the signal-to-noise ratio (SNR) function as the fitness function, the particle swarm optimization algorithm is used to find the optimal value, and the value obtained when the SNR is maximized is obtained. This is the optimal value. The signal-to-noise ratio function can be expressed as: (4) In the formula, Where N is the signal-to-noise ratio; and N is the signal duration. It is a noisy signal; This is the denoised signal; For discrete time series indexes.

[0039] threshold A fixed threshold value, which is fast to calculate and widely applicable, is selected. The expression for the fixed threshold value is: (5) In the formula, Wavelet coefficients after thresholding The standard deviation value, N This represents the signal duration.

[0040] 3. ICEEMDAN (Improved Adaptive Noise-Complete Empirical Mode Decomposition) The ICEEMDAN algorithm is an improvement upon the CEEMDAN algorithm. The improved ICEEMDAN algorithm can effectively handle nonlinear and non-stationary signals, solve noise interference and mode aliasing problems, and decompose current traveling wave signals into stationary IMF components and residual components. The ICEEMDAN algorithm decomposes the input sample by iteratively adding Gaussian white noise and taking the mean of the signal components. The specific steps are as follows: 1) The denoised signal As the input signal Z, Gaussian white noise is added. ,get (6) In the formula, This represents the expected signal-to-noise ratio during the first decomposition. This represents the first-order intrinsic mode component, generated by EMD decomposition.

[0041] 2) The first IMF component was obtained by decomposing the original time series using the ICEEMDAN algorithm: (7) In the formula, Representing the first-order residual: This represents the first IMF value. Operators for generating local means, This represents the number of samples used to calculate the local mean.

[0042] 3) Continue calculating the second IMF component: (8) In the formula, The expected signal-to-noise ratio during the second decomposition. Represents the second-order residual; This indicates the second IMF value; This represents the second-order intrinsic mode component.

[0043] By analogy, the number of... One IMF component: (9) In the formula, For the first Expected signal-to-noise ratio at the next decomposition express Order residual; Indicates the first One IMF value; represent The first-order intrinsic mode components.

[0044] 4. Select effective IMF mode components based on entropy kurtosis ratio. 4.1) Permutation Entropy Permutation entropy (PE), proposed by Bandt et al., is used to measure the complexity of a signal. The higher the distortion and randomness of the signal, the greater the calculated permutation entropy. Furthermore, permutation entropy is highly sensitive to signal abrupt changes, amplifying even subtle shifts. This paper introduces the Generalized Composite Multi-scale Permutation Entropy (GCMPE) to measure the complexity of each IMF modal component. By calculating the mean PE of multiple coarse-grained sequences, it suppresses the random error of a single partition, enhances the ability to represent complex signals, and overcomes the limitations of single permutation entropy and multi-scale permutation entropy in modal component selection. The calculation steps are as follows: 1) Time series After generalized coarsening, the generalized coarsening process is as follows: (10) In the formula, Representing scale Down shift The corresponding number One coarsening value, , representing the local mean; This represents the length of the window at scale s. N This represents the signal duration.

[0045] 2) After step 1), the coarse-grained sequence is obtained as shown in the following formula: (11) 3) For Sequences Calculate the permutation entropy of each sequence; 4) The mean of the permutation entropy values ​​is used as the original time series. The GCMPE value is calculated as follows: (12) 4.2) Kurtosis Kurtosis is a statistical measure describing the steepness of a signal distribution; it is a dimensionless parameter highly sensitive to abrupt changes in signal intensity. The formula for calculating the kurtosis value K is shown below: (13) In the formula, This represents the mean value of the data within the set time window of the signal; This represents the standard deviation of the data within the set time window of the signal. Expressing expectations; A random variable representing the amplitude of a signal.

[0046] When the signal is a discrete signal, at time point At this point, the time window length is [value missing]. Calculate the kurtosis value of the data within the time window. As shown below: (14) In the formula: , indicating time window The local mean of the internal signal is used to calculate the kurtosis value. , Indicates the kurtosis value. Represents a time series.

[0047] In summary, combining the entropy and kurtosis of the generalized composite multi-scale arrangement, the kurtosis ratio GK of the traveling wave signal eigenvalue is constructed as follows: (15) The smaller the entropy kurtosis ratio of an IMF mode component, the more pronounced its wavefront characteristics, and the easier it is to calibrate its wavefront. Therefore, based on the definition of entropy kurtosis ratio, the IMF mode component with the smallest GK value can be selected as the effective mode component for wavefront calibration.

[0048] 5. NTEO wave head calibration NTEO is an improvement on TEO, enhancing the detection capability of signal singularities by introducing a resolution parameter. It uses NTEO to highlight the abrupt changes in the wavefront of the selected effective IMF components, achieving accurate extraction of the wavefront arrival time. The expression for NTEO for discrete signals is: (16) In the formula, For energy operators; It is a discrete signal; For a certain discrete time point; For resolution parameters, , Sampling frequency, This is the fundamental frequency.

[0049] When the initial wavefront of the traveling wave mode component of the fault voltage reaches the measurement point, the voltage amplitude and frequency will fluctuate significantly. Since the energy mutation points in the NTEO energy spectrum correspond one-to-one with the signal singular points, the initial wavefront of the fault signal can be calibrated by detecting the point with the maximum energy amplitude.

[0050] Example: This embodiment uses a single-phase ground fault in a 10kV distribution network line as an example to illustrate the specific implementation steps of the present invention. The sampling frequency is set to 1MHz.

[0051] 1) At two detection points, one at the substation outgoing line and the other at the end of the line, traveling wave acquisition devices are used to simultaneously acquire the traveling wave signals of the three-phase voltages (A, B, and C) within a 1ms time window after the fault. The acquired three-phase voltage signals are decoupled using Karenbauer transform, converting them into line-mode and zero-mode components. Since the line-mode component is less affected by the frequency characteristics of the line parameters and has a faster propagation speed, this embodiment selects the line-mode component as the initial traveling wave signal for subsequent processing, with a discrete sequence length of 1000 points.

[0052] 2) Denoising was performed using an improved threshold function. The adjustment factor was optimized using a particle swarm optimization (PSO) algorithm with a population size of 20 and 50 iterations. The signal-to-noise ratio (SNR) was used as the fitness function, and the optimal value a = 2.3 was finally found. The db4 wavelet was selected as the basis wavelet, and the signal was decomposed into five levels of wavelet coefficients. Wavelet reconstruction was then performed on the processed coefficients to obtain the denoised traveling wave signal.

[0053] 3) Input the denoised signal into the ICEEMDAN algorithm. Set the white noise standard deviation to 0.2, the maximum number of iterations to 500, and the number of ensembles to 100. The algorithm automatically decomposes the signal into 8 IMF components (IMF1~IMF8) and one residual component (Res). Calculate the frequency domain specific entropy kurtosis ratio for each IMF component. Select the effective IMFs for subsequent fusion processing.

[0054] 4) The selected IMF components are superimposed to obtain the enhanced signal, which is then fed into the nonlinear energy operator (NTEO) for calculation to determine the modulus maxima of the NTEO output energy sequence. The moment the modulus maxima occurs corresponds to the moment the traveling wavefront arrives at the measurement point. After processing, an extremely sharp and prominent pulse peak is generated at the moment the reflected wave arrives at the fault point, which is much higher than the noise level, thus achieving accurate wavefront identification.

[0055] 5) Results Analysis Compared with traditional methods, the method of this invention has a higher recognition accuracy. The improved wavelet threshold function used in this invention, through adjustment factor optimization, better preserves signal details while suppressing noise, resulting in a significantly higher signal-to-noise ratio than traditional methods and smaller reconstruction error. The ICEEMDAN decomposition and frequency domain ratio screening mechanism effectively extracts key IMF components containing fault characteristics, avoiding interference from invalid modes. The NTEO operator operates on the optimized IMF components, greatly enhancing the energy performance of abrupt change points, ultimately achieving high-precision and robust extraction of wavefront arrival time, overcoming the shortcomings of traditional methods that are prone to failure in complex noise environments.

[0056] This embodiment verifies the effectiveness of the proposed method for extracting traveling wavefronts by fusing wavelet denoising and ICEEMDAN-NTEO. This method can effectively and accurately extract traveling wavefronts during distribution network faults.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calibrating the wavefront of a traveling wave based on ICEEMDAN-NTEO, characterized in that, This method is specific Includes the following steps: S1: Collect the three-phase voltage traveling wave signals measured at each detection point, and use Karenbauer to decouple and transform the collected three-phase voltage traveling wave signals to obtain the line-mode voltage signals at the two measurement points. S2: The line-mode voltage signal is denoised using an improved wavelet threshold function optimized by an adaptive adjustment factor; the adjustment factor is adaptively searched by the particle swarm optimization algorithm according to the signal-to-noise ratio maximization criterion. S3: Use ICEEMDAN to decompose the denoised line-mode voltage signal to obtain multiple IMF components; Where ICEEMDAN represents the improved adaptive noisy complete set empirical mode decomposition; S4: Based on the entropy kurtosis ratio calculated from the entropy and kurtosis value of the generalized composite multiscale arrangement, the IMF with the smallest entropy kurtosis ratio is selected as the effective component. S5: The selected effective IMF components are used to highlight the abrupt change characteristics of the wavefront using NTEO, thereby achieving accurate extraction of the wavefront arrival time; where NTEO represents the nonlinear energy operator.

2. The traveling wave head calibration method according to claim 1, characterized in that, In step S2, the expression for the improved wavelet threshold function is: In the formula, These are the wavelet coefficients after thresholding. Wavelet coefficients before thresholding; As a regulating factor, and always ensuring ; The threshold value is used.

3. The traveling wave head calibration method according to claim 2, characterized in that, In step S2, the adjustment factor The principle for selecting the value is: the optimal value should be selected for different signals. At that time, using the signal-to-noise ratio (SNR) function as the fitness function, the particle swarm optimization algorithm is used to find the optimal value, and the value obtained when the SNR is maximized is obtained. The optimal value is found; the signal-to-noise ratio function is expressed as: In the formula, For signal-to-noise ratio, N The duration of the signal. It is a noisy signal. The signal after denoising. For discrete time series indexes.

4. The traveling wave head calibration method according to claim 2, characterized in that, In step S2, the threshold The expression is: In the formula, Wavelet coefficients after thresholding The standard deviation value, N This represents the signal duration.

5. The traveling wave head calibration method according to claim 1, characterized in that, In step S3, the denoised line-mode voltage signal is decomposed using ICEEMDAN. The specific steps are as follows: The denoised signal is used as input, and Gaussian white noise is added; The first IMF component was obtained by decomposing the original time series using the ICEEMDAN algorithm. Continue calculating to find the first... k Each IMF component is expressed as follows: In the formula, For the first Expected signal-to-noise ratio at the next decomposition express Order residual; Indicates the first One IMF value, represent First-order intrinsic modal components, Operators for generating local means, This represents the number of samples used to calculate the local mean.

6. The traveling wave head calibration method according to claim 1, characterized in that, In step S4, the formula for calculating the entropy kurtosis ratio is: In the formula, GK is the entropy kurtosis ratio, and GCMPE is the entropy of the generalized composite multi-scale arrangement. K This represents the kurtosis value.

7. The traveling wave head calibration method according to claim 6, characterized in that, In step S4, the calculation steps for the generalized composite multiscale permutation entropy (GCMPE) are as follows: (1) Time series After generalized coarsening, the generalized coarsening process is as follows: In the formula, Representing scale Down shift The corresponding number One coarsening value; , representing the local mean; This represents the length of the window at scale s. N The duration of the signal; (2) The coarse-grained sequence obtained after step (1) is shown in the following formula: (3) For Sequences Calculate the permutation entropy of each sequence. ; (4) The mean of the permutation entropy values ​​is used as the original time series. The GCMPE value is calculated as follows: in, m The embedding dimension represents the permutation entropy, which is the number of sample points contained in each pattern vector.

8. The traveling wave head calibration method according to claim 6, characterized in that, In step S4, the kurtosis value K The calculation formula is as follows: In the formula, This represents the mean value of the data within the set time window of the signal. This represents the standard deviation of the data within the set time window of the signal. Expressing expectations, A random variable representing the amplitude of a signal; When the signal is a discrete signal, at time point At this point, the time window length is [value missing]. Calculate the kurtosis value of the data within the time window. K As shown below: In the formula, , indicating time window The local mean of the internal signal is used to calculate the kurtosis value. ; Indicates the kurtosis value. Represents a time series.

9. The traveling wave head calibration method according to claim 1, characterized in that, In step S5, the expression for NTEO is: In the formula, For energy operators; It is a discrete signal; For a certain discrete time point; For resolution parameters, , Sampling frequency, This is the fundamental frequency.

Images