Wind turbine generator transmission chain fault vibration signal denoising method

Abstract

A method for denoising vibration signals from wind turbine drivetrain faults mainly includes the steps of transmission, waveform acquisition, calculation, waveform reconstruction, and localization. It optimizes a novel joint denoising algorithm for fault vibration signals by combining empirical wavelet transform, kurtosis, correlation coefficient, and singular value decomposition. First, it uses empirical wavelet transform combined with frequency band boundary exploration to optimize the spectrum allocation and obtain intrinsic mode components. Second, it uses the kurtosis-correlation coefficient criterion to screen the principal components among the intrinsic mode components. Then, it uses the Hankel matrix to construct the effective component signals, thereby achieving white noise and random interference removal through singular value decomposition denoising. Finally, it reconstructs the fault vibration signal based on the denoised components.

Description

Technical Field

[0001] This invention belongs to the field of wind turbine signal processing and noise reduction technology, and relates to a method for noise reduction of vibration signals from wind turbine transmission chain faults. Background Technology

[0002] As a clean and pollution-free renewable energy source, wind energy has become increasingly problematic due to the large-scale construction of wind farms. This has led to higher failure rates and higher operation and maintenance costs for wind turbine equipment. In particular, the high failure rate and long downtime of the transmission chain in wind turbines seriously affect power generation quality, increase the operation, maintenance and repair costs of wind farms, and cause huge losses to wind farms.

[0003] Key components of a wind turbine's drivetrain include gearboxes, bearings, generators, and blades. Among these, the failure rate of critical energy transmission components (gearboxes and bearings) accounts for approximately 60% of the entire wind turbine's failure rate and 20% of its total lifespan downtime. Vibration analysis is the primary means of monitoring the condition of a wind turbine's drivetrain to reflect fault signals. Because fault vibration signals are often non-stationary and non-linear modulated signals, and due to the harsh installation environment, complex structure, variable loads, and frequent impacts in actual operation, wind turbine drivetrains experience severe noise interference and complex transmission paths, resulting in low signal-to-noise ratios, masked fault information, and various noise disturbances that are difficult to remove.

[0004] Currently, traditional methods for decomposing and denoising vibration signals from wind turbine drivetrain faults typically employ two methods: wavelet transform and empirical mode decomposition (EMD). Wavelet transform offers the advantage of multi-resolution capabilities, but when processing vibration signals, the mother wavelet coefficients, once determined, cannot be changed, and different wavelet bases result in different calculations. Empirical mode decomposition is applied to non-stationary and nonlinear signals; when applied to vibration signals, it decomposes into several eigenfunctions and a single residual. However, during the calculation of the instantaneous frequency of the eigenfunctions, EMD encounters negative frequencies that cannot be explained scientifically, lacks theoretical verification, and suffers from unreasonable convergence conditions, over-envelope and under-envelope issues, leading to mode aliasing and endpoint effects.

[0005] In recent years, empirical wavelet transform has been increasingly widely used in fault diagnosis systems in fields such as power and machinery due to its reliable theoretical support and ability to effectively extract intrinsic modal components. However, its drawbacks include the fact that the intrinsic modal components obtained by empirical wavelet transform alone are often not effectively filtered, each component still contains significant noise and has complex frequency components, and the number of frequency bands needs to be manually determined. Excessive or inappropriate selection of the number of frequency bands can lead to mode aliasing, thereby compromising the integrity of the periodic impact characteristics of the vibration signal.

[0006] Therefore, it is evident that traditional methods for decomposing and reducing vibration signals from wind turbine drivetrain faults have inherent drawbacks.

[0007] 1) The number of intrinsic modal components in the decomposition is large, making it impossible to effectively filter them, resulting in invalid time-frequency components interfering with the results.

[0008] 2) The decomposed intrinsic mode components contain a large amount of noise and spurious frequencies, which affects the identification of fault frequencies.

[0009] 3) There are problems with mode aliasing and endpoint effects. Summary of the Invention

[0010] The technical problem to be solved by this invention is to provide a noise reduction method for vibration signals of wind turbine drivetrain faults. This method is based on empirical wavelet transform combined with kurtosis, correlation coefficient and singular value decomposition to jointly reduce the noise of vibration signals of wind turbine drivetrain faults. It solves the industrial application bottlenecks of traditional decomposition noise reduction methods, such as mode mixing, spurious frequencies, endpoint effects, multiple components and large noise, and large computational load, and achieves effective noise reduction processing of vibration signals of wind turbine drivetrain faults.

[0011] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for noise reduction of vibration signals in wind turbine drivetrain faults, comprising the following steps:

[0012] Step 1, transmission: After the wind turbine is started, the first contactor is in working condition, and the second contactor transmits the vibration data of the wind turbine drive chain to the terminal.

[0013] Step 2: Obtain waveform diagrams. The collected vibration data of the wind turbine drive chain is Fourier transformed to obtain the time-frequency waveform diagram of the vibration signal. The empirical wavelet transform is optimized and the spectrum bandwidth is allocated according to the boundary exploration method to obtain the time-frequency waveform diagram of the inherent modal components of the vibration signal.

[0014] Step 3: Calculation. By calculating kurtosis and correlation coefficient, select the components with large kurtosis values ​​and high correlation coefficients among the intrinsic mode components as principal components.

[0015] Step 4: Reconstruct the waveform. Construct the Hankel matrix for the principal components and denoise the principal components through singular value decomposition. Then, reconstruct the time-frequency waveform of the wind turbine drive chain vibration signal after denoising.

[0016] Step 5: Locating the fault vibration signal time-frequency waveform after the wind turbine drive chain reconstruction is envelope-adjusted to observe and accurately locate the fault characteristic frequency.

[0017] In step 2, a Fourier transform is performed on the original signal to normalize its Fourier spectrum to the range [0, π], obtaining the frequency domain signal x(n), and the k-th frequency domain window p. kThe frequency domain signal is:

[0018]

[0019] In the formula, Let be the left boundary frequency of the window and the right boundary frequency after the i-th expansion.

[0020] In step 3, for The signal undergoes an inverse Fourier transform to calculate the kurtosis index, and then the right boundary of the frequency domain window is... A single right translation yields:

[0021]

[0022] In the formula, f b For extended frequency bands.

[0023] In step 3, based on the kurtosis index and Perform a frequency band expansion loop step and calculate the kurtosis index of adjacent i-1, i, i+1. If i≥max(i-1, i+1), it indicates that there is the strongest frequency periodic impact component in the frequency range corresponding to the i kurtosis index, which is the location of the optimal width of the resonant frequency band.

[0024] In step 3, After performing i-th expansion on the k-th frequency band, the corresponding boundary frequencies are divided according to... The corresponding boundary frequency can be obtained:

[0025]

[0026] The left boundary update frequency can be obtained as follows:

[0027]

[0028] Repeat the above steps until the frequency band satisfies the following formula to achieve frequency band range search.

[0029]

[0030] This segmentation method divides the interval [0,π] into n frequency bands with unequal bandwidths, and the bandwidth of each frequency band can be represented as Λ. n =[ω n-1 ,ω n The transition band between different frequency bands is defined as T. n =2τ n .

[0031] In step 3, the detail coefficients w of the empirical wavelet transform x (n,t) and approximation coefficient w x (0,t) represent the inner products of x with the wavelet function and the scaling function, respectively.

[0032]

[0033]

[0034] The reconstruction formula for signal x(t) is:

[0035]

[0036] In the formula, and φ n (t) and The Fourier transform function; F -1 The expression represents the inverse Fourier transform; <> represents the inner product operation.

[0037] In step 3, the formulas for calculating the correlation coefficients for samples X and Y are as follows:

[0038]

[0039] In the formula, R is the correlation coefficient; Cov(X,Y) is the covariance of sample X and sample Y; It is the variance of sample X. The variance of sample Y.

[0040] The formula for calculating kurtosis is:

[0041]

[0042] In the formula, K is the kurtosis value; x Ave Let σ be the mean of signal x; σ be the standard deviation of signal x.

[0043] In step 4, singular value decomposition is performed on matrix A, yielding the following equation:

[0044]

[0045] In the formula, u i ∈Q m×1 v i ∈Q 1×n , i = 1, 2, 3, ..., q.

[0046] The beneficial effects of this invention are as follows:

[0047] The optimized empirical wavelet transform not only solves the problem of unsatisfactory frequency band division in traditional empirical wavelet transform, but also solves the problems of mode aliasing, endpoint effect, and parameter setting in traditional time-frequency processing methods, and suppresses frequency band aliasing to a large extent.

[0048] The combination of kurtosis-correlation coefficient criteria can effectively extract fault vibration characteristic signals of wind turbine drive trains and effectively screen the intrinsic mode components decomposed by empirical wavelet transform, thus demonstrating good practicality.

[0049] Denoising using Hankel matrix reconstruction and singular value decomposition can effectively remove noise and purify effective information. Attached Figure Description

[0050] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0051] Figure 1 This is a schematic diagram of the wind turbine transmission chain structure of the present invention.

[0052] Figure 2 This is a flowchart of the present invention.

[0053] Figure 3 This is a diagram showing the time-frequency waveform and frequency band optimization allocation of the transmission chain fault vibration signal in this invention.

[0054] Figure 4 This is a schematic diagram of the spectrum band and a flowchart of the optimization allocation process of the present invention.

[0055] Figure 5 The time-frequency waveform diagram of the empirical wavelet transform decomposition of the vibration signal of the transmission chain fault in this invention is shown.

[0056] Figure 6 The waveform diagram of the singular value decomposition and noise reduction of the vibration signal of the transmission chain fault in this invention is shown in the time-frequency waveform diagram.

[0057] Figure 7 This is a graph showing the correlation coefficient-kurtosis calculation of the present invention.

[0058] Figure 8 This is the principal component diagram of the empirical wavelet transform of the vibration signal of the transmission chain fault in this invention.

[0059] Figure 9 Principal component diagram of singular value decomposition and noise reduction of vibration signal in transmission chain fault of the present invention.

[0060] Figure 10 This is a time-frequency waveform diagram of the reconstructed fault vibration signal after combined noise reduction of the transmission chain according to the present invention.

[0061] Figure 11 This is the envelope spectrum of the fault vibration signal after combined noise reduction of the transmission chain in this invention. Detailed Implementation

[0062] like Figures 1 to 11 A method for noise reduction of vibration signals from wind turbine drivetrain faults includes the following steps:

[0063] First, considering the non-stationary and transient characteristics of vibration signals, time-frequency decomposition is performed on the vibration signals using optimized empirical wavelet functions. Second, principal components are obtained by kurtosis-correlation coefficient calculation and analysis. Then, Hankel matrices are constructed for each principal component. Finally, noise reduction is performed using singular value decomposition to reduce the influence of noise and eliminate random interference. The signal is then reconstructed, and envelope spectrum analysis is performed on the reconstructed signal to obtain the bearing fault characteristic frequencies.

[0064] Step 1, Transmission: After the wind turbine starts, the first contactor is in working condition, and the second contactor transmits the vibration data of the wind turbine drive train to the terminal; for example... Figure 1 As shown, the main structure of the wind turbine drive train includes a gearbox and bearings.

[0065] Step 2: Obtain waveform diagrams. The collected wind turbine drivetrain vibration data is subjected to Fourier transform to obtain the time-frequency waveform diagram of the vibration signal; the empirical wavelet transform is optimized using boundary exploration methods to allocate the frequency band and obtain the time-frequency waveform diagrams of the inherent modal components of the vibration signal; For example... Figure 3 As shown, from Figure 3 It can be seen from the above that the amplitude and fluctuation of the vibration signal of the faulty bearing are very large; at the same time, the frequency domain waveform reflects that the frequency components of the signal are rich, and due to the influence of noise, it is impossible to determine the interval between the high amplitude lines, so it is difficult to judge the bearing condition through the spectrum. According to Equation (5), when the frequency band boundary exploration condition is met, the empirical wavelet transform spectrum frequency band optimization is completed, such as Figure 3 The frequency domain waveform is shown; the root spectrum band segmentation diagram and spectrum band optimization process are as follows: Figure 4 As shown. According to equation (13), the vibration signal of the wind turbine drive chain bearing fault is decomposed according to the time series to obtain the inherent modal components at different frequencies, denoted as c1(t), c2(t), ..., c n (t)[ Figure 2 [Already annotated]. Based on the aforementioned intrinsic modal components, such as Figure 5 As shown, singular value decomposition is performed for denoising, resulting in the time-frequency waveforms of the denoised intrinsic mode components, as follows. Figure 6 As shown, this process is for verifying the effectiveness of the joint noise reduction method, and the results are excellent.

[0066] Step 3: Calculation. By calculating kurtosis and correlation coefficient, the components with large kurtosis values ​​and high correlation coefficients among the intrinsic mode components are selected as principal components. Based on the verification results, the kurtosis index is calculated according to equation (14), and the correlation coefficient is calculated according to equation (15), resulting in the kurtosis and correlation coefficient calculation curves, as shown below. Figure 7 As shown. According to Figure 7 The modal components with high correlation coefficients and kurtosis in the actual intrinsic modal components of the optimized empirical wavelet transform decomposition are selected as the principal components of the vibration signal of the wind turbine drivetrain fault. The principal components are as follows: Figure 8 As shown.

[0067] Step 4: Reconstruct the waveform. Construct the Hankel matrix for the principal components and simultaneously perform singular value decomposition (SVD) to reduce noise in the principal components. Reconstruct the time-frequency waveform of the wind turbine drive chain vibration signal after noise reduction. Since the bearing vibration signal of the wind turbine drive system is a one-dimensional signal, SVD cannot be directly applied. Therefore, a multi-dimensional matrix must be constructed. Construct the Hankel matrix for the principal components described in Step 3 according to Equation (19). Perform SVD according to Equation (20). The singular values ​​after decomposition will be arranged from largest to smallest. Since the main signal is mainly concentrated in the first few larger singular values, smaller singular values ​​can be set to 0 and the signal reconstructed to achieve the noise reduction target. Finally, perform SVD to reduce noise in the principal components, such as... Figure 9 As shown, the noise-reduced vibration signal time-frequency waveform is obtained by reconstructing the signal. Figure 10 As shown. This concludes the main process of the combined noise reduction method of this invention.

[0068] Step 5: Locating the fault vibration signal time-frequency waveform after the wind turbine drive chain reconstruction is envelope-adjusted to observe and accurately locate the fault characteristic frequency.

[0069] The empirical wavelet transform and spectral band optimization process in step 2 are based on the following principles:

[0070] A time-domain kurtosis index-based frequency band boundary exploration method is employed for frequency band optimization using empirical wavelet transform. A single frequency window is used as the basis function. Expanding the right boundary frequency of the window enables the detection of resonant frequency bands, while shifting the left boundary segmentes the entire frequency band. The window width can be adjusted based on actual data to ensure that the frequency window width covers at least one resonant spectral line during each shift, thus enabling the search of the resonant region and the entire frequency band. A Fourier transform is performed on the original signal, normalizing its Fourier spectrum to the range [0, π] to obtain the frequency domain signal x(n), and the k-th frequency domain window p. k The frequency domain signal is:

[0071]

[0072] In the formula, Let be the left boundary frequency of the window and the right boundary frequency after the i-th expansion.

[0073] against The signal undergoes an inverse Fourier transform to calculate the kurtosis index, and then the right boundary of the frequency domain window is... A single right translation yields:

[0074]

[0075] In the formula, fb For extended frequency bands.

[0076] According to the kurtosis index and Equation (2), the frequency band expansion cycle is performed to calculate the kurtosis index of adjacent i-1, i, i+1. If i≥max(i-1, i+1), it indicates that there is the strongest frequency periodic impact component in the frequency range corresponding to the i kurtosis index, that is, the location of the optimal width of the resonance frequency band.

[0077] After the k-th frequency band is expanded i times, the corresponding boundary frequencies can be obtained according to equation (2):

[0078]

[0079] The left boundary update frequency can be obtained as follows:

[0080]

[0081] Repeat the above steps until the frequency band satisfies equation (13), thus achieving frequency band range search.

[0082]

[0083] This segmentation method divides the interval [0,π] into n frequency bands with unequal bandwidths, and the bandwidth of each frequency band can be represented as Λ. n =[ω n-1 ,ω n The transition band between different frequency bands is defined as T. n =2τ n .

[0084] The empirical wavelet transform algorithm constructs wavelet functions in the frequency domain. and scaling function φ n (ω) is used for calculation:

[0085]

[0086]

[0087] In the formula, the β(x) function must satisfy:

[0088]

[0089] Let τ n =γω n If 0 < γ < 1, then:

[0090]

[0091] According to equations (6)(7)(8)(9), the detail coefficients w of the empirical wavelet transform x(n,t) and approximation coefficient w x The calculation process for (0,t) is as follows:

[0092]

[0093]

[0094] The reconstruction formula for signal x(t) is:

[0095]

[0096] In the formula, and φ n (t) and The Fourier transform function; F -1 The expression represents the inverse Fourier transform; <> represents the inner product operation.

[0097] According to equation (12), the signal x(t) has the following modal components:

[0098]

[0099] The empirical wavelet transform and spectral band optimization process in step 3 are based on the following principles:

[0100] The kurtosis index is a dimensionless parameter used to describe the peak size of a signal waveform. The mathematical expression for the kurtosis of the original signal x(t) after empirical wavelet transform decomposition, yielding several intrinsic mode components, is as follows:

[0101]

[0102] In the formula, K is the kurtosis value; x Ave Let σ be the mean of signal x; σ be the standard deviation of signal x.

[0103] When the wind turbine drivetrain is under normal operating conditions, its vibration signal approximates a normal distribution with a kurtosis of 3, and periodic impacts are not significant. However, when a local fault occurs, the kurtosis increases significantly, and the impact component in the signal increases markedly. This is because the impact excitation generated by vibration causes natural vibrations in different frequency bands of the drivetrain bearings, resulting in the natural modal components containing natural vibration components of different frequency bands. Therefore, the greater the kurtosis of the natural modal components, the more pronounced the impact component in the vibration signal.

[0104] The correlation coefficient criterion is a key indicator reflecting the degree of correlation between a variable and the original signal. The commonly used Pearson product-moment correlation coefficient is employed to calculate the correlation coefficient between each intrinsic mode component and the original signal x(t). Let X and Y be samples, then their correlation coefficient is:

[0105]

[0106] In the formula, R is the correlation coefficient; Cov(X,Y) is the covariance of sample X and sample Y; and is a dimensionless parameter used to describe the kurtosis of the signal waveform. The mathematical expression for the kurtosis of several intrinsic mode components obtained after empirical wavelet transform decomposition of the original signal x(t) is: It is the variance of sample X. The variance of sample Y.

[0107] The correlation coefficient R ranges from -1 to 1. A larger absolute value of the correlation coefficient indicates a higher degree of linear correlation between the two samples. By calculating the correlation coefficients between several intrinsic modal components and the original signal, interference from uncorrelated quantities is reduced when acquiring vibration signals from the wind turbine drivetrain. Therefore, the kurtosis value, reflecting the strength of the fault vibration impact and the sensitivity of the correlation coefficient to interference signals, is defined as the KR value of the intrinsic modal component.

[0108] KR=αK+(1-α)R (16)

[0109] In the formula, K represents the kurtosis value of the intrinsic mode component, R is the correlation coefficient between the intrinsic mode component and the original signal, and α is the weight of the kurtosis value of the intrinsic mode component to KR.

[0110] In summary, the overall expression for the empirical wavelet transform kurtosis-correlation coefficient criterion is given by , denoted as Empirical Wavelet Transform. KR :

[0111]

[0112] The empirical wavelet transform and spectral band optimization process in step 4 are based on the following principles:

[0113] Singular value decomposition is a nonlinear filtering method. For any set of real matrices A∈Q m×n All can be decomposed into:

[0114] A = USV T (18)

[0115] In the formula: U and V represent orthogonal matrices U∈Q m×n V∈Q m×n S represents a diagonal matrix, S = [diag(σ1, σ2, ..., σ...)] q ), O] or expressed as the transpose, where O represents the zero matrix, σ i This represents the order of singular values ​​from largest to smallest; q = rank(S).

[0116] Since the vibration signal of the wind turbine drive train is a one-dimensional signal, singular value decomposition cannot be directly applied. Therefore, a multi-dimensional matrix must be constructed, and the Hankel matrix is ​​used:

[0117] Let the signal x = [x1, x2, x3, ..., xn] N And 1 <n<N。

[0118]

[0119] Performing singular value decomposition on matrix A yields the following equation:

[0120]

[0121] In the formula, u i ∈Q m×1 v i ∈Q 1×n , i = 1, 2, 3, ..., q.

[0122] The values ​​after singular value decomposition will be arranged from largest to smallest. Since the main signal is concentrated in the first few larger singular values, the signal can be reconstructed by setting the smaller singular values ​​to 0 to achieve the noise reduction target.

[0123] The envelope analysis in step 5 is based on the following principle:

[0124] The target signal is subjected to Hilbert transform to obtain the analytic signal, then the magnitude of the analytic signal is calculated to obtain the envelope signal, and finally the envelope signal is subjected to Fourier transform to obtain the Hilbert envelope spectrum.

[0125] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The embodiments and features described in these embodiments can be arbitrarily combined without conflict. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for noise reduction of vibration signals from wind turbine drivetrain faults, characterized in that, Includes the following steps: Step 1, transmission: After the wind turbine is started, the first contactor is in working condition, and the second contactor transmits the vibration data of the wind turbine drive chain to the terminal. Step 2: Obtain waveform diagrams. The collected vibration data of the wind turbine drive chain is Fourier transformed to obtain the time-frequency waveform diagram of the vibration signal. The empirical wavelet transform is optimized and the spectrum bandwidth is allocated according to the boundary exploration method to obtain the time-frequency waveform diagram of the inherent modal components of the vibration signal. Step 3: Calculation. By calculating kurtosis and correlation coefficient, select the components with large kurtosis values ​​and high correlation coefficients among the intrinsic mode components as principal components. Step 4: Reconstruct the waveform. Construct the Hankel matrix for the principal components and denoise the principal components through singular value decomposition. Then, reconstruct the time-frequency waveform of the wind turbine drive chain vibration signal after denoising. Step 5, Locating: Perform envelope adjustment on the time-frequency waveform of the fault vibration signal after the wind turbine drive chain reconstruction, observe and accurately locate the fault characteristic frequency. In step 2, the empirical wavelet transform and spectral band optimization process employs a time-domain kurtosis index-based band boundary exploration method for spectral band optimization. A single frequency window is used as the basis function. The resonance band is detected by expanding the right boundary frequency of the window, and the entire band is segmented by shifting the left boundary of the window. The window width is adjusted based on actual data to ensure that the frequency window width covers at least one resonance spectral line during each shift, thus enabling the search of the resonance region and the entire frequency band. In step 2, a Fourier transform is performed on the original signal to normalize its Fourier spectrum to the range [0, π], thus obtaining the frequency domain signal. x ( n ), No. k Frequency domain window p k The frequency domain signal is: ； In the formula, , For the left boundary frequency of the window and the extended first i The next right boundary frequency; In step 3, for The signal undergoes an inverse Fourier transform to calculate the kurtosis index, and then the right boundary of the frequency domain window is... A single right translation yields: ； In the formula, f b For extended frequency bands.

2. The method for noise reduction of vibration signals from wind turbine drivetrain faults according to claim 1, characterized in that: In step 3, based on the kurtosis index and Perform a bandwidth extension cyclic step to calculate adjacent... i -1, i , i +1 kurtosis index, if i max( i -1, i +1) indicates that in i The strongest frequency periodic impact component exists within the frequency range corresponding to the kurtosis index, which is the location of the optimal width of the resonant frequency band.

3. The method for noise reduction of vibration signals from wind turbine drivetrain faults according to claim 2, characterized in that: In step 3, For the first k Sub-band i The boundary frequencies corresponding to the sub-expansion are divided according to... The corresponding boundary frequency can be obtained: ； The left boundary update frequency can be obtained as follows: ； Repeat the above steps until the frequency band satisfies the following formula to achieve frequency band range search; ； This segmentation method will divide [0, π Divide into intervals n There are several frequency bands with varying bandwidths, each of which can be represented as Λ. n =[ ω n-1 , ω n The transition band between different frequency bands is defined as... T n =2 τ n .

4. The method for noise reduction of vibration signals from wind turbine drivetrain faults according to claim 3, characterized in that: In step 3, the detail coefficients of the empirical wavelet transform w x ( n , t and approximation coefficients w x (0, t ) are respectively x The inner product of the wavelet function and the scaling function: ； ； The reconstruction formula for signal x(t) is: ； In the formula, and They are respectively and The Fourier transform function; F -1 Indicates the inverse Fourier transform; This is for inner product operations.

5. The method for noise reduction of vibration signals from wind turbine drivetrain faults according to claim 4, characterized in that: In step 3, the formulas for calculating the correlation coefficients for samples X and Y are as follows: ； In the formula, R The correlation coefficient; Cov ( X , Y ) as a sample X and samples Y covariance; It is a sample X variance sample Y variance The formula for calculating kurtosis is: ； In the formula, K This represents the kurtosis value. x Ave For signal x The mean; σ For signal x The standard deviation.

6. The method for noise reduction of vibration signals from wind turbine drivetrain faults according to claim 5, characterized in that: In step 4, the matrix A Performing singular value decomposition, we obtain the following equation: ； In the formula, u i Q m×1 , v i Q 1×n , i =1,2,3,... q。

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