Partial discharge signal denoising method combining singular value decomposition and wavelet transform

Abstract

The present application relates to a kind of partial discharge signal denoising method combined with singular value decomposition and wavelet transform, belong to signal processing field.The method includes: selecting suitable Hankel matrix is used to construct adaptive singular value decomposition model, responsible for the singular value decomposition of original noisy partial discharge signal;Calculate singular entropy increment, find the position of the maximum bending degree of singular entropy curve according to its asymptotic property;Use the position of maximum curvature as threshold, singular value greater than threshold is used to reconstruct original signal;Select suitable wavelet base function is used to construct one-dimensional two-stage double-tree complex wavelet transform, responsible for the decomposition and reconstruction of signal;Using q-shift scheme joint construction filter bank in DT-CWT interior.The present application can not only inhibit the narrow-band noise and white noise on PD signal well, but also can retain waveform mutation details, while having very low root mean square error and very high waveform similarity in index.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and relates to a method for denoising partial discharge signals that combines singular value decomposition and wavelet transform. Background Technology

[0002] In recent years, with technological development and advancements, gas-insulated switchgear (GIS) has been widely used in the power industry. Substation GIS equipment operates under high-voltage environments for extended periods, making it prone to partial discharge (PD), a phenomenon where only a portion of the insulation between conductors is broken down. PD is a significant symptom of power system insulation degradation and a major cause of further insulation deterioration and even breakdown. Therefore, timely and accurate monitoring of GIS equipment partial discharge signals is crucial for ensuring the stable and safe operation of the power system and preventing large-scale power outages. Due to its strong anti-interference capability and high sensitivity, ultra-high frequency (UHF) detection is currently the mainstream method for partial discharge detection.

[0003] However, noise is still inevitably introduced in practical applications, mainly including narrowband interference signals caused by power line carrier communication and radio transmission, as well as white noise interference generated by system amplifiers and other hardware circuits. The introduction of noise makes it difficult to accurately extract PD signals, resulting in a sharp decrease in detection sensitivity. Many research results have been achieved in suppressing narrowband noise and white noise, including Empirical Mode Decomposition (EMD), Mathematical Morphology Filters (MMF), Wavelet Transform (WT), and Singular Value Decomposition (SVD). EMD has significant advantages in processing non-stationary and nonlinear data, but it has drawbacks such as non-negligible endpoint effects and mode aliasing. WT, with its excellent time-frequency analysis capabilities, is also widely used in signal denoising, but its denoising effect on narrowband noise is far less effective than its effect on suppressing white noise. SVD achieves denoising by distinguishing and reconstructing the singular values ​​of noise and signal, but this method suffers from the problem of difficulty in selecting singular values ​​when processing white noise. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method for denoising partial discharge signals that combines singular value decomposition (SVD) and wavelet transform (WT). This method combines the ideas of SVD and WT to denoise the signal, using an improved SVD to remove narrowband noise and an improved WT to remove white noise. While preserving waveform abrupt changes, it can also effectively suppress noise on the PD signal.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for denoising partial discharge signals combining singular value decomposition and wavelet transform, comprising the following steps:

[0007] S1: Use hardware devices to acquire partial discharge signals containing narrowband noise and white noise in a real or simulated environment, and use them as the original input signal;

[0008] S2: Construct a suitable Hankel matrix, perform eigenvalue decomposition to obtain two eigenma matrices based on the properties of symmetric matrices, and then take the square root to obtain all the singular values;

[0009] S3: Calculate the singular entropy increment of the obtained singular values, and calculate the position with the maximum curvature on the singular entropy curve;

[0010] S4: Sort the singular values ​​in descending order, select the singular values ​​before the position of maximum curvature to reconstruct the narrowband signal, and subtract the noisy partial discharge signal from the noisy one to obtain the denoised signal.

[0011] S5: Select appropriate real and imaginary wavelet functions according to the definition of DT-CWT, which have translation invariance and anti-aliasing effect;

[0012] S6: Construct the filter bank of DT-CWT using the q-shift scheme and calculate the filter parameters of length 10;

[0013] S7: The signal reconstruction process uses a globally unified threshold and hard threshold processing scheme to eliminate the interference of the white noise mentioned above while preserving the abrupt changes in the signal.

[0014] S8: Reduces or eliminates narrowband noise and white noise on the original signal, outputting a clean signal for subsequent feature extraction or analysis.

[0015] Optionally, the denoising method specifically includes:

[0016] Signal modeling and simulation were performed. Based on extensive field observations of PD signals, single-exponential damped oscillation pulses and double-exponential damped oscillation pulses were used as mathematical models for PD signal simulation. Their mathematical expressions are as follows:

[0017]

[0018]

[0019] Where A is the amplitude, τ is the attenuation coefficient, and f c The oscillation frequency is used; these two basic signals are used to simulate four typical partial discharge signals;

[0020] The PD signal in the field environment includes white noise and narrowband noise; the periodic narrowband noise interference caused by wireless communication is simulated by superimposing sinusoidal signals of different frequencies, that is, the periodic narrowband noise is expressed as follows:

[0021]

[0022] Where A i f represents amplitude. i Indicates frequency, Indicate the initial phase; this narrowband noise is superimposed onto the original signal for simulation;

[0023] By utilizing the significant difference in singular values ​​between narrowband interference, white noise, and PD signals, narrowband noise can be reconstructed and eliminated. Singular value decomposition is an important matrix decomposition in linear algebra, and it is a generalization of eigenvalue decomposition onto matrices.

[0024] For a matrix A of rank R and size m×n, its singular value decomposition expression is as follows:

[0025]

[0026] Where [U] and [V] are m-dimensional and n-dimensional identity orthogonal matrices, respectively, and [Σ] is a diagonal matrix; for the partial discharge signal sequence Y = [Y(1), Y(2), ..., Y(N)], its Hankel matrix is ​​as follows:

[0027]

[0028] In the above formula, n satisfies 1≤n≤N, m satisfies m=N-n+1, ​​where N represents the number of sampling points of the partial discharge sequence, H represents a Hankel matrix, m is the number of rows of the Hankel matrix, and n is the number of columns of the Hankel matrix;

[0029] When m = N / 4, it is difficult to find the singular values ​​of the Hankel matrix using the direct method. The characteristic matrices [U] and [V] are obtained by eigenvalue decomposition using the following formula:

[0030] HH T =UΣV T VΣ T U T =UΣΣT U T

[0031] H T H=VΣU T UΣ T V T =VΣ T ΣV T

[0032] HH T and H T H is a symmetric matrix; for Σ T Σ or ΣΣ T The singular value matrix obtained by taking the square root is as follows:

[0033] Σ=[diag(σ1,σ2,σ3,…,σ R ),Ο]

[0034] Where O is a zero matrix, σ1,σ2,σ3,…,σ R These are the singular values ​​of matrix H;

[0035] Singular value decomposition (SVD) decomposes a noisy PD signal into a noise subspace and a signal subspace. Larger singular values ​​contain more information, while smaller singular values ​​contain less information. Based on the asymptotic property of the singular entropy increment, a threshold is used to distinguish between useful signals and noise. The singular entropy increment is defined as follows:

[0036]

[0037] Where σ i Represents singular values; singular entropy increment ΔE i The normalized singular values ​​have curvature spectra that reflect the degree of change at different singular values. The larger the curvature value, the greater the increase in singular entropy, and the greater the change in singular values. The curvature calculation formula for a continuous signal is as follows:

[0038]

[0039] Where y' and y″ represent the first and second derivatives of the curve function, respectively; discretizing the above equation yields the following formula for calculating the curvature of the singular entropy:

[0040] l i '=ΔE i+1 -ΔE i

[0041] l i "=ΔE i+1 -2ΔE i +ΔE i-1

[0042] In the above formula, i∈[2,3,…,R-1], where li 'and l i "" represents the first and second derivatives after discretization, respectively;

[0043] In the noisy PD signal, the singular values ​​of narrowband noise are higher than those of white noise and PD signal. The maximum value of the curvature of the mixed noise PD signal is the corresponding threshold. The current optimal threshold is 9. The singular values ​​are sorted in descending order, and the first 9 singular values ​​are selected as the singular values ​​of the reconstructed narrowband signal. The partial discharge signal after removing the narrowband signal is obtained by subtracting the noisy partial discharge signal from the reconstructed narrowband signal.

[0044] The white noise removal is achieved by decomposing, filtering, and reconstructing the signal based on the DT-CWT framework; DT-CWT is defined as follows:

[0045] ψ(t)=ψ h (t)+iψ g (t)

[0046] Where ψ h (t) and ψ g (t) represent orthogonal real wavelets and imaginary wavelets, respectively, forming a Hilbert transform pair;

[0047] Let φ h , and ψ h , These are the scaling function and the dual wavelet, h0(n), respectively. and h1(n), These are the corresponding low-pass and high-pass filters, whose real and imaginary parts satisfy the following equation:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] DT-CWT is implemented using two Discrete Wavelet Transforms (DWTs): the first DWT provides the real part of the transform, while the second DWT provides the imaginary part; where h0(n) and h1(n) represent the low-pass and high-pass filters of the real part filter bank, respectively, generating the wavelet coefficients of the real part; g0(n) and g1(n) represent the low-pass and high-pass filters of the imaginary part filter bank, respectively, generating the wavelet coefficients of the imaginary part; the final DT-CWT output is obtained by averaging the two sets of signals.

[0057] The two-stage DT-CWT filter bank is constructed using a q-shift scheme; the designed filter satisfies the following equation:

[0058] g0(n)=h0(N-1-n)

[0059] Where h0(n) and g0(n) represent the real and imaginary parts of the low-pass filter, respectively, and N is the length of h0(n), which is an even number; note that g0(n) is the time-reversed version of h0(n). Taking the Fourier transform of the above equation, we get that g0(n) and h0(n) satisfy the following equation:

[0060] ∠G0(e jω )=-∠H0(e jω )-(N-1)ω

[0061] Finally, h0(n) that satisfies the half-frame shift condition satisfies the following equation:

[0062] ∠H0(e jω )≈-0.5(N-1)ω+0.25ω

[0063] Design a filter bank using the q-shift scheme that satisfies the above equation and the complete reconstruction condition, and design h0(n).

[0064] Compared to partial discharge signals, white noise causes most signals with lower amplitudes and smaller wavelet coefficients. Thresholding the wavelet coefficients before reconstruction effectively eliminates white noise interference. A globally unified thresholding method defined by the following formula is used:

[0065]

[0066] Where σ represents the standard deviation of the signal, and N is the length of the signal sequence; a globally unified threshold is used to suppress random Gaussian white noise, and the threshold is calculated using the above formula for the wavelet coefficients after each level of processing; the threshold processing method adopts hard threshold decision, and its function is defined by the following formula:

[0067]

[0068] In the above formula, λ represents the threshold point;

[0069] By cascading two processing models—Adaptive Singular Value Decomposition (ASVD) and Dual-Tree Complex Wavelet Transform (DT-CWT)—a method for denoising partial discharge signals combining singular value decomposition and wavelet transform is obtained.

[0070] The beneficial effects of this invention are as follows:

[0071] 1. A relatively general noise suppression scheme for partial discharge scenarios is presented, which mainly eliminates narrowband noise and white noise.

[0072] 2. A relatively simple method for selecting singular values ​​is given, which facilitates signal reconstruction.

[0073] 3. Combining SVD for noise reduction solves the problem that using WT alone is far less effective at suppressing narrowband noise than suppressing white noise.

[0074] 4. It performs better in terms of signal-to-noise ratio, root mean square error, and waveform similarity.

[0075] 5. The use of hard decision-making better preserves the waveform information of the original signal.

[0076] 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

[0077] 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:

[0078] Figure 1 This is a flowchart of the adaptive singular value decomposition noise removal module proposed in this invention;

[0079] Figure 2 The flowchart shows the dual-tree complex wavelet transform white noise removal module proposed in this invention.

[0080] Figure 3 This is the internal flowchart of two-level dual-tree complex wavelet transform signal decomposition and reconstruction. Detailed Implementation

[0081] 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.

[0082] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0083] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0084] This invention relates to a method for denoising partial discharge signals combining singular value decomposition and wavelet transform, comprising two noise suppression modules connected in series. Their execution flows are described below. Figure 1 and Figure 2 The first module is based on Adaptive Singular Value Decomposition (ASVD), which mainly suppresses narrowband noise. The second module is Double Tree Complex Wavelet Transform (DT-CWT), which mainly suppresses white noise. Specifically, the overall execution process of this method includes the following steps:

[0085] S1: Use hardware devices to acquire partial discharge signals containing narrowband noise and white noise in a real or simulated environment, and use them as the original input signal of this method.

[0086] S2: Construct a suitable Hankel matrix, perform eigenvalue decomposition based on the properties of symmetric matrices to obtain two eigenma matrices, and then take the square root to obtain all the singular values.

[0087] S3: Calculate the singular entropy increment of the obtained singular values, and calculate the position with the maximum curvature on the singular entropy curve.

[0088] S4: Sort the singular values ​​in descending order, select the singular values ​​before the position of maximum curvature to reconstruct the narrowband signal, and subtract the noisy partial discharge signal from them to obtain the denoised signal.

[0089] S5: Select appropriate real and virtual wavelet functions according to the definition of DT-CWT. They have translation invariance and anti-aliasing effect.

[0090] S6: Construct the filter bank of DT-CWT using the q-shift scheme and calculate the filter parameters of length 10.

[0091] S7: The signal reconstruction process uses a globally unified threshold and hard thresholding scheme to better preserve the abrupt changes in the signal while eliminating the interference of the white noise mentioned above.

[0092] S8: The above steps reduce or eliminate narrowband noise and white noise in the original signal, and the clean output signal can be used for subsequent feature extraction or further analysis.

[0093] The steps described above will be explained in detail below. Signal processing begins with signal modeling and simulation. Through extensive field observations of PD signals, single-exponential damped oscillation pulses and double-exponential damped oscillation pulses were used as mathematical models for PD signal simulation. Their mathematical expressions are as follows:

[0094]

[0095]

[0096] Where A is the amplitude, τ is the attenuation coefficient, and f c The oscillation frequency is used. These two fundamental signals are used to simulate four typical partial discharge signals, with the parameters set as shown in the table below:

[0097]

[0098] Signals numbered I and II are constructed from single-exponential damped oscillating pulses, while signals numbered II and IV are constructed from double-exponential damped oscillating pulses.

[0099] The PD signal in the field environment contains a lot of noise, mainly including white noise and narrowband noise. Periodic narrowband noise interference caused by wireless communication can be simulated by superimposing sinusoidal signals of different frequencies; that is, periodic narrowband noise can be expressed as follows:

[0100]

[0101] Where A i f represents amplitude. i Indicates frequency, This represents the initial phase. This narrowband noise is superimposed onto the original signal for simulation, with the parameters set as shown in the table below:

[0102]

[0103] By leveraging the significant difference in singular values ​​between narrowband interference, white noise, and PD signals, narrowband noise can be reconstructed and eliminated. SVD is an important matrix decomposition in linear algebra, and singular value decomposition is a generalization of eigenvalue decomposition to general matrices. Taking a matrix A of rank R and size m×n as an example, its singular value decomposition expression is as follows:

[0104]

[0105] Where [U] and [V] are m-dimensional and n-dimensional identity orthogonal matrices, respectively, and [Σ] is a diagonal matrix. For a general partial discharge signal sequence Y = [Y(1), Y(2), ..., Y(N)], its Hankel matrix is ​​as follows:

[0106]

[0107] In the above formula, n satisfies 1≤n≤N, m satisfies m=N-n+1, ​​where N represents the number of sampling points of the partial discharge sequence, H represents a Hankel matrix, m is the number of rows of the Hankel matrix, and n is the number of columns of the Hankel matrix.

[0108] The value of m ranges from (N / 20 to N / 2), and the method involved in this invention takes m = N / 4. Finding the singular values ​​of the Hankel matrix directly is difficult; however, the eigenvalues ​​[U] and [V] can be obtained through eigenvalue decomposition using the following formula:

[0109] HH T =UΣV T VΣ T U T =UΣΣ T U T

[0110] H T H=VΣU T UΣ T V T =VΣ T ΣV T

[0111] It is easy to know HH T and H T H is a symmetric matrix. For ΣT Σ or ΣΣ T The singular value matrix obtained by taking the square root is as follows:

[0112] Σ=[diag(σ1,σ2,σ3,…,σ R ),Ο]

[0113] Where O is a zero matrix, σ1,σ2,σ3,…,σ R Let H be the singular values ​​of matrix H.

[0114] Singular value decomposition (SVD) decomposes a noisy PD signal into a noise subspace and a signal subspace. Larger singular values ​​contain more information, while smaller singular values ​​contain less. Typically, Gaussian white noise has relatively small singular values, while narrowband interference has relatively large singular values. The threshold for distinguishing useful signals from noise can be determined based on the asymptotic nature of the singular entropy increment, defined as follows:

[0115]

[0116] Where σ i Represents singular values. The singular entropy increment ΔE i This can be understood as the normalized singular values, and their curvature spectrum reflects the degree of change at different singular values. The larger the curvature value, the greater the increment of singular entropy, and the greater the change in singular values. The formula for calculating the curvature of a continuous signal is as follows:

[0117]

[0118] Where y' and y″ represent the first and second derivatives of the curve function, respectively. Discretizing the above equation yields the following formula for calculating the curvature of the singular entropy:

[0119] l i '=ΔE i+1 -ΔE i

[0120] l i "=ΔE i+1 -2ΔE i +ΔE i-1

[0121] In the above formula, i∈[2,3,…,R-1], where l i 'and l i "" represents the first and second derivatives after discretization, respectively.

[0122] In the noisy PD signal, the singular values ​​of narrowband noise are significantly higher than those of white noise and the PD signal. Therefore, the singular values ​​of narrowband noise are larger and vary more. Consequently, the corresponding singular entropy curvature is larger. However, the singular values ​​of noise and PD signals are relatively close and vary less, with no inflection point in the singular entropy increment curve and curvature close to zero. Analysis shows that the maximum curvature of the mixed noise PD signal is the corresponding threshold. The current optimal threshold is 9. Therefore, the singular values ​​are sorted in descending order, and the first 9 singular values ​​are selected as the singular values ​​for reconstructing the narrowband signal. By subtracting the noisy partial discharge signal from the reconstructed narrowband signal, the partial discharge signal after removing the narrowband signal can be obtained. The overall process of narrowband denoising based on ASVD is as follows: Figure 1 .

[0123] Existing methods suffer from drawbacks such as shift invariance, spectral aliasing, and limited directional selectivity. This invention addresses these drawbacks by using the DT-CWT framework to decompose, filter, and reconstruct signals for white noise removal. DT-CWT, derived from wavelet transform, offers superior time-frequency localization capabilities and perfect reconstruction. Compared to other wavelet transform algorithms, it not only maintains the excellent time-frequency localization analysis capabilities of traditional wavelets but also possesses advantages such as shift invariance, good directional selectivity, limited data redundancy, fulfillment of complete reconstruction conditions, and anti-aliasing properties. DT-CWT is defined as follows:

[0124] ψ(t)=ψ h (t)+iψ g (t)

[0125] Where ψ h (t) and ψ g (t) represent orthogonal real wavelets and imaginary wavelets, respectively, forming a Hilbert transform pair.

[0126] Let φ h , and ψ h , These are the scaling function and the dual wavelet, h0(n), respectively. and h1(n), These are the corresponding low-pass and high-pass filters, whose real and imaginary parts satisfy the following equation:

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] DT-CWT can be implemented using two Discrete Wavelet Transform (DWT) methods: the first DWT gives the real part of the transform, and the second DWT gives the imaginary part. The two-level DT-CWT decomposition and reconstruction process is as follows: Figure 3 As shown in the diagram. Here, h0(n) and h1(n) represent the low-pass and high-pass filters of the real part filter bank, respectively, which generate wavelet coefficients in the real part; g0(n) and g1(n) represent the low-pass and high-pass filters of the imaginary part filter bank, respectively, which generate wavelet coefficients in the imaginary part. The final DT-CWT output is obtained by averaging the two sets of signals.

[0136] Similar to the Fourier transform, the filter between the transform and inverse transform processes is the core component for noise reduction. This method chooses to use a q-shift scheme to jointly construct a two-stage DT-CWT filter bank. The designed filter satisfies the following equation:

[0137] g0(n)=h0(N-1-n)

[0138] Where h0(n) and g0(n) represent the real and imaginary parts of the low-pass filter, respectively, and N is the length of h0(n), which is an even number. Note that g0(n) is the time-reversed version of h0(n). Taking the Fourier transform of the above equation, we get that g0(n) and h0(n) satisfy the following equation:

[0139] ∠G0(e jω )=-∠H0(e jω )-(N-1)ω

[0140] Finally, h0(n) that satisfies the half-frame shift condition satisfies the following equation:

[0141] ∠H0(e jω )≈-0.5(N-1)ω+0.25ω

[0142] The filter bank designed using the q-shift scheme only needs to have an h0(n) that satisfies the above equation and the complete reconstruction condition. The parameters of h0(n) and g0(n) of length 10 designed using the q-shift scheme are shown in the table below:

[0143]

[0144] Compared to partial discharge signals, white noise causes most signals with lower amplitudes and smaller wavelet coefficients. Therefore, thresholding the wavelet coefficients before reconstruction can effectively eliminate white noise interference. Donoho and Johnstone proposed a globally unified threshold in 1994, which effectively suppresses random Gaussian white noise. This scheme uses a globally unified thresholding method defined by the following formula:

[0145]

[0146] Where σ represents the standard deviation of the signal, and N is the length of the signal sequence. Using this globally uniform threshold effectively suppresses random Gaussian white noise. Based on this, the threshold is calculated using the above formula for the wavelet coefficients after each processing stage. Thresholding methods typically include soft thresholding and hard thresholding. This invention uses hard thresholding, whose function is defined by the following formula:

[0147]

[0148] In the above formula, λ represents the threshold point. Soft thresholding can obtain a relatively smooth denoised signal, but it reduces the peak value of the processed pulse, which may prevent the extraction of partial discharge signals with abrupt changes. Hard thresholding can better maintain the pulse peak value, thus correctly extracting the partial discharge signal. Therefore, hard thresholding is adopted. The overall process of white noise denoising based on DT-CWT is shown below. Figure 2 By cascading the two processing models, ASVD and DT-CWT, we obtain the partial discharge signal denoising method of this invention, which combines singular value decomposition and wavelet transform. This method not only effectively suppresses narrowband interference and white noise interference, but also effectively preserves the waveform information of the original partial discharge signal.

[0149] 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 partial discharge signal denoising method combining singular value decomposition and wavelet transform, characterized in that: The method comprises the following steps: S1: obtaining partial discharge signals containing narrow-band noise and white noise using a hardware device in a real or simulated environment, as original input signals; S2: constructing a Hankel matrix, performing eigenvalue decomposition according to the properties of a symmetric matrix to obtain two characteristic matrices, and then squaring to obtain all singular values; S3: calculating the singular entropy increment of the obtained singular values, and calculating the position of the maximum curvature on the singular entropy curve; S4: arranging the singular values in descending order, and selecting the singular values before the position of the maximum curvature to reconstruct the narrow-band signal, and subtracting the denoised partial discharge signal from the denoised partial discharge signal to obtain the denoised signal; S5: selecting real wavelet and imaginary wavelet functions according to the definition of DT-CWT, which has shift invariance and anti-aliasing effect; S6: constructing a filter bank of DT-CWT through a q-shift scheme, and calculating the filter parameters with a length of 10; S7: using a global unified threshold and a hard threshold processing scheme to access the reconstruction process of the signal, eliminating the interference of the white noise on the basis of retaining the mutation part of the signal; S8: weakening or eliminating the narrow-band noise and white noise on the original signal, and outputting a clean signal for subsequent feature extraction or analysis; The denoising method is specifically as follows: Modeling and simulation of signals, through observation of a large number of field measured PD signals, single exponential damping oscillation pulse and double exponential damping oscillation pulse are respectively taken as mathematical models of PD signals for simulation, and their mathematical expressions are as follows: wherein is the amplitude, is the damping coefficient, is the oscillation frequency; using these two basic signals, four typical partial discharge signals are simulated; Wherein, the PD signal in the field environment includes white noise and narrow-band noise; the periodic narrow-band noise interference caused by wireless communication is simulated by superimposing sine signals of different frequencies, that is, the periodic narrow-band noise is expressed as follows: wherein denotes the amplitude, denotes the frequency, denotes the initial phase; this narrow-band noise is superimposed on the original signal for simulation; The great difference between the singular values of the narrow-band interference and the white noise and the PD signal is utilized to realize the reconstruction and elimination of the narrow-band noise; SVD is an important matrix decomposition in linear algebra, and singular value decomposition is a generalization of eigenvalue decomposition on matrices; For a matrix of size with rank , its singular value decomposition expression is as follows: wherein and are respectively peacekeeping a unitary matrix, is a diagonal matrix; for the partial discharge signal sequence its Hankel matrix is as follows: In the above formula satisfies , satisfies wherein represents the number of partial discharge sequence sampling points, represents a Hankel matrix, is the number of rows of the Hankel matrix, is the number of columns of the Hankel matrix; It is difficult to find the singular values of Hankel matrix by direct method. The eigenvalue decomposition is used to find the eigenmatrix and : where and are symmetric matrices; and or the singular value matrix is obtained by squaring. wherein is a zero matrix, is a matrix singular values of the matrix The singular value decomposition decomposes the denoised PD signal into a noise subspace and a signal subspace; the greater the singular value, the more information it contains, and the smaller the singular value, the less information it contains; the threshold for distinguishing useful signals and noise is determined according to the asymptotic property of the singular entropy increment, and the singular entropy increment is defined as follows: wherein represents the singular value; the singular entropy increment is the normalized singular value, and its curvature spectrum reflects the change degree of different singular values. The greater the curvature value is, the greater the singular entropy increment is, and the greater the change of the singular value is. The curvature calculation formula of the continuous signal is as follows: where and denote the first and second derivative of the curve function, respectively. The curvature of the singularity entropy is calculated by discretizing the above equation as follows: In the above formulae wherein and respectively represent the first and second derivatives after discretization; In the denoised PD signal, the singular value of the narrow-band noise is higher than that of the white noise and the PD signal; for the mixed noise PD signal, the maximum value of the curvature is the corresponding threshold, and the current optimal threshold is 9; the singular values are arranged in descending order, and the first 9 singular values are selected as the singular values of the reconstructed narrow-band signal; the partial discharge signal after removing the narrow-band signal is obtained by subtracting the reconstructed narrow-band signal from the denoised partial discharge signal; The signal is decomposed, filtered and reconstructed based on the DT-CWT framework to remove white noise; the DT-CWT is defined as follows: wherein and denote orthogonal real and imaginary wavelets, respectively, and form a Hilbert transform pair; Let , and , be the scaling function and the dual wavelet, respectively, , and , be the corresponding low-pass filter and high-pass filter, respectively, with real and imaginary parts satisfying the following equations: The DT-CWT is implemented by two discrete wavelet transforms (DWTs): the first DWT gives the real part of the transform, while the second DWT gives the imaginary part; where and represent the low-pass and high-pass filters of a filter bank for the real part, yielding the real wavelet coefficients; and represent the low-pass and high-pass filters of a filter bank for the imaginary part, yielding the imaginary wavelet coefficients; and the two resulting signals are averaged to give the final DT-CWT output. The q-shift scheme is used to jointly construct a two-stage DT-CWT filter bank; the designed filter satisfies the following formula: in and These represent the real and imaginary parts of the low-pass filter, respectively. for The length of is an even number; note that... yes The time sequence is reversed, and the Fourier transform of the above equation is obtained. and Satisfy the following formula: Finally, the half-frame shift condition is met satisfies the following equation: A filter bank designed using a q-shift scheme is used to design a filter bank satisfying the above equation and the perfect reconstruction condition ; Compared with partial discharge signals, the amplitude of most signals caused by white noise is low, and the wavelet coefficients generated by white noise are also small, so the white noise interference can be effectively eliminated by corresponding threshold processing of the wavelet coefficients and then reconstruction; a global unified threshold processing method defined by the following formula is used: wherein denotes the standard deviation of the signal, is the length of the signal sequence; the global uniform threshold is used to suppress random Gaussian white noise, and the threshold of the wavelet coefficient after processing each level is calculated by the above formula; the threshold processing method is selected as the hard threshold decision, and its function is defined by the following formula: In the above formulae denotes the threshold point; The adaptive singular value decomposition (ASVD) and dual tree complex wavelet transform (DT-CWT) processing models are combined in series to obtain a partial discharge signal denoising method combining singular value decomposition and wavelet transform.

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