Method for bearing fault diagnosis based on spectral modulation fourier decomposition

Abstract

This invention relates to a bearing fault diagnosis method based on spectral modulation Fourier decomposition, comprising: acquiring vibration signals of a target wind turbine bearing; performing a Fourier transform on the vibration signals and updating the spectral amplitude to obtain a modulation spectrum; discretizing the modulation spectrum and performing a discrete Fourier transform to obtain a modulation key function; performing an inverse Fourier transform on the target part of the modulation key function to obtain a trend spectrum of the modulation spectrum; dividing the modulation spectrum into several sub-frequency bands; reconstructing each sub-frequency band into a sub-mode using a zero-phase filter bank; and calculating the harmonic correlation index of each sub-mode, wherein the zero-phase filter bank is constructed based on the spectral boundaries, with the minimum points in the trend spectrum as the spectral boundaries between modes; and selecting the sub-mode corresponding to the maximum harmonic correlation index for envelope demodulation analysis to achieve targeted diagnosis of bearing faults. This invention can effectively enhance and separate fault features in the frequency domain.

Description

Technical Field

[0001] This invention relates to the field of bearing fault diagnosis technology, and in particular to a bearing fault diagnosis method based on spectral modulation Fourier decomposition. Background Technology

[0002] In recent years, wind power equipment has achieved leapfrog development, with installed capacity growing exponentially year by year. The fault characteristics of wind turbine bearings are easily interfered with by modulation and noise in the transmission system, making it difficult for traditional methods to easily isolate fault features. The lack of diagnostic parameters for new equipment and the approaching failure lifespan of older equipment have driven the updating of fault diagnosis methods and placed higher demands on the complexity of algorithms.

[0003] Fourier Decomposition (FDM) achieves mode decomposition of time series by constructing zero-phase filters. Theoretically, FDM essentially represents the ideal Fourier transform and its inverse transform, implying a lack of rigor in its physical meaning. Researchers, sacrificing the inverse transform aspect, have developed a faster segmentation concept, constructing Fourier intrinsic frequency band functions—corresponding to intrinsic mode functions in empirical mode decomposition. A common problem in many real-world signals is the random superposition of multiple non-stationary signals, constructing complex Fourier spectra. The theoretical separability of modes depends on the intensity of interference and modulation. FDM was initially applied in the medical field to address power line interference and baseline drift in electrocardiogram (ECG) signals. M. Rebiai introduced the Teager energy operator into mode recognition, enhancing the algorithm's adaptability. To further enhance FDM's adaptability, Zhou introduced scale-space representation from the empirical wavelet transform algorithm into the frequency band segmentation part. This approach uses Meyer wavelets to construct the filter bank. Although the construction method does not adopt a universal form, researchers have provided proof of orthogonality. This spectral segmentation method is based on previous research using high signal-to-noise ratio. However, sufficient research has demonstrated that weak noise has a significant impact on the accuracy of mode separation. By considering the correlation between the power spectrum and the frequency spectrum, Zhao designed a peak-based spectral envelope to distinguish different modes. This is a fast spectral envelope calculation method that not only increases the algorithm's running speed but also reduces the influence of extreme points on the envelope. Pang optimized the scale-space representation method and designed a fine-to-coarse segmentation method to suppress the problem of over-segmentation of the spectrum. The algorithm's accuracy improved while the computation speed decreased. At the same time, an adjacent mode merging framework based on the envelope spectral kurtosis (ESK) and envelope spectral overlap coefficient (ESOC) indices was designed to suppress excessive mode decomposition. Zheng focused on frequency domain mode decomposition and innovatively designed an adaptive parameterless frequency band separation method. However, the threshold coefficient requires further research to adapt to more engineering scenarios. Subsequently, the "Locmax" and "Locmaxmin" algorithms were used to optimize spectral segmentation, but the problem of multi-component signal processing at intersecting instantaneous frequencies was not solved.

[0004] In summary, research on Fourier decomposition methods has focused on the problem of spectrum segmentation. This is crucial and deserves further investigation. However, no scholars have yet considered the low signal-to-noise ratio (SNR) issue in the signal. When modulation and interference information in the signal suppresses the amplitude of fault information, current spectrum segmentation methods are affected by high spectral amplitudes, resulting in erroneous mode separation results. Summary of the Invention

[0005] The purpose of this invention is to provide a bearing fault diagnosis method based on spectral modulation Fourier decomposition, which solves the problems of enhancing and separating multiple modulation features.

[0006] To achieve the above objectives, the present invention provides the following solution: Bearing fault diagnosis methods based on spectral modulation Fourier decomposition include: Collect vibration signals from the bearings of the target wind turbine equipment; The vibration signal is subjected to Fourier transform, and the spectral amplitude is updated to obtain the modulation spectrum; The modulation spectrum is discretized and subjected to discrete Fourier transform to obtain the modulation key function. The target part of the modulation key function is then subjected to inverse Fourier transform to obtain the trend spectrum of the modulation spectrum. The modulation spectrum is divided into several sub-bands, and each sub-band is reconstructed into a sub-mode using a zero-phase filter bank. The harmonic correlation index of each sub-mode is calculated. The zero-phase filter bank is constructed based on the spectral boundaries, where the minimum points in the trend spectrum are the spectral boundaries between modes. Envelope demodulation analysis is performed on the sub-mode corresponding to the maximum harmonic correlation index to achieve targeted diagnosis of bearing faults.

[0007] Optionally, updating the spectral amplitude includes: exponentially editing the spectral amplitude using a weighted modulation factor to obtain the modulation spectrum; The modulation spectrum for: ; in, The weighted modulation factor for the spectral amplitude. Indicates amplitude. This represents the phase, and j is the imaginary unit.

[0008] Optionally, performing an inverse Fourier transform on the target portion of the modulation key function includes: truncating the low-frequency portion of the modulation key function as the target portion, and obtaining the fluctuation curve of the modulation spectrum as the trend spectrum.

[0009] Optionally, the fluctuation curve of the modulation spectrum for: ; in, Let i be the key function, i be the imaginary unit, u be the variable in the transform domain, and f be the frequency.

[0010] Optionally, the zero-phase filter bank includes a scaling function and an empirical function; The scaling function for: ; The empirical function for: ; in, .

[0011] Optionally, reconstructing each sub-band into a sub-mode includes: The modulation spectrum is corrected, and approximation coefficients are calculated based on the corrected modulation spectrum and scaling function; Calculate the detail coefficients based on the modified modulation spectrum and empirical function; Based on the approximation coefficients and the detail coefficients, each sub-band is reconstructed into a sub-mode.

[0012] Optionally, the calculation of the harmonic correlation index for each submode includes: A digital twin fault model of the bearing of the target wind turbine is constructed, and the Hilbert transform envelope spectrum of the digital twin fault model and the Hilbert transform envelope spectrum of each sub-mode are calculated. The linear correlation between the digital twin fault model and the Hilbert transform envelope spectrum of each submode is evaluated using the Pearson product-moment correlation coefficient to obtain the harmonic correlation index.

[0013] Optionally, calculating the Hilbert transform envelope spectrum of the digital twin fault model includes: Calculate the Hilbert transform of the digital twin fault model, and calculate the Fourier transform of the envelope signal based on the Hilbert transform of the digital twin fault model; The Hilbert envelope spectrum of the digital twin fault model is obtained based on the Fourier transform of the envelope signal.

[0014] The beneficial effects of this invention are as follows: This invention can solve signal processing problems involving modulation and interference. The designed spectral modulation process can enhance fault characteristics and improve the signal-to-noise ratio, solving the problem of amplitude suppression of fault information by modulation and interference, and also addressing the issue that current spectral segmentation methods are susceptible to erroneous mode separation results due to high spectral amplitudes. Mode separation can be made easier through the Fourier trend spectrum of the modulation spectrum. The designed harmonic correlation index with targeted diagnostic characteristics can adaptively screen fault frequency bands. Simulation signals demonstrate the effectiveness and efficiency of the algorithm. Experimental results prove that this method can effectively extract fault characteristics of the inner and outer races of bearings. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart of a bearing fault diagnosis method based on spectral modulation Fourier decomposition according to an embodiment of the present invention. Figure 2 This is a schematic diagram illustrating the effect of the weighted modulation factor on the modulation spectrum in an embodiment of the present invention, wherein (a) is a three-dimensional modulation spectrum and (b) is the modulation spectrum updated by different weighted modulation factors; Figure 3 This is a schematic diagram of calculating the trend spectrum and boundary based on the modulation key function according to an embodiment of the present invention, wherein (a) is the original modulation spectrum, (b) is the modulation key function, and (c) is the trend component and boundary division; Figure 4 This is a schematic diagram of a Fourier filter bank according to an embodiment of the present invention; Figure 5 The following are examples of fault signals and their spectrum diagrams according to embodiments of the present invention, wherein (a) is a fault signal and (b) is a spectrum diagram of the fault signal; Figure 6 This is a schematic diagram of the envelope spectrum and correlation in an embodiment of the present invention, wherein (a) is the envelope spectrum and (b) is a schematic diagram of the correlation. Figure 7 The following are analog signals and spectrum diagrams according to an embodiment of the present invention, wherein (a) is the waveform and spectrum of the pulse information after adding interference and noise, and (b) is the envelope spectrum of the pulse information after adding interference and noise; Figure 8 This is a schematic diagram of the modal boundaries of EWT and EFD decomposition in an embodiment of the present invention; Figure 9 This is a schematic diagram of the modal boundaries of HFD decomposition according to an embodiment of the present invention, wherein (a) is the power spectral density and the obtained boundary, (b) is the harmonics, and (c) is the result obtained by HFD. Figure 10 This is a boundary diagram of SMFD decomposition according to an embodiment of the present invention, wherein (a) is the key function, (b) is the boundary division, and (c) is the HCI index; Figure 11 This is a schematic diagram of the MFD decomposition result according to an embodiment of the present invention, wherein (a) is the waveform after SMFD decomposition, and (b) is the envelope spectrum of the enhanced modulation band; Figure 12 This is a schematic diagram of the results of HFD and SMFD decomposition in an embodiment of the present invention, wherein (a) is the result of HFD decomposition and (b) is the result of SMFD decomposition; Figure 13 This is a schematic diagram showing the decomposition results of HFD and SMFD under different signal-to-noise ratios in an embodiment of the present invention; Figure 14 The present invention provides bearing outer ring fault data and its envelope spectrum, wherein (a) is bearing outer ring fault data and (b) is bearing outer ring fault data envelope spectrum. Figure 15This is a schematic diagram of the HFD decomposition result according to an embodiment of the present invention, wherein (a) is the waveform of each component after division, and (b) is the spectrum of each component; Figure 16 This is a schematic diagram of the HSK screening results of HFD according to an embodiment of the present invention, wherein (a) shows the boundary division and index trend, and (b) shows the waveform and spectrum of the maximum component of the HSK value; Figure 17 This is a schematic diagram of the spectrum modulation result of an embodiment of the present invention, wherein (a) is the modulation spectrum and (b) is the modulated signal and its envelope spectrum; Figure 18 The following are the HCI screening results and their spectrograms according to an embodiment of the present invention, wherein (a) shows the boundary division and HCI index, and (b) shows the comparison between the original spectrum and the SMFD enhanced spectrum; Figure 19 This is a diagram showing the result of SMFD processing according to an embodiment of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] like Figure 1 As shown, this embodiment proposes a bearing fault diagnosis method based on spectral modulation Fourier decomposition, including: Step 1: Collect and store the vibration signals of the bearings of the target wind turbine through monitoring equipment; Step 2: Perform Fourier transform on the vibration signal to separate the amplitude and phase, and perform exponential editing on the spectral amplitude to obtain the modulation spectrum for updating; Step 3: Discretize the modulation spectrum and perform discrete Fourier transform to obtain the modulation key function. Perform inverse Fourier transform on the target part of the modulation key function to obtain the trend spectrum of the modulation spectrum. Step 4: Using the minimum points in the trend spectrum as the spectral boundaries between modes, construct a zero-phase filter bank based on the spectral boundaries; Step 5: Divide the modulation spectrum into several sub-bands, reconstruct each sub-band into a sub-mode using a zero-phase filter bank, and calculate the harmonic correlation index (HCI) of each sub-mode; Step 6: Select the sub-mode corresponding to the maximum harmonic correlation index for envelope demodulation analysis to achieve targeted diagnosis of bearing faults.

[0020] Furthermore, the update of the spectral amplitude by exponential editing includes: exponentially editing the spectral amplitude using a weighted modulation factor to obtain the modulation spectrum.

[0021] Specifically, traditional methods mainly address the problems of Fourier spectrum segmentation and mode separation based on spectral envelope. Low signal-to-noise ratios leading to mode aliasing and strong interference pose significant challenges to modal analysis. This embodiment performs nonlinear editing of the spectrum before mode separation, which enhances frequency components related to modulation and damage and facilitates the diagnostic process. For the acquired bearing vibration signal... The frequency domain expression can be obtained through the basic formula of Fourier transform. : (1); Where j is the imaginary unit, For amplitude, For phase.

[0022] definition The updated modulation spectrum can be expressed as a weighted modulation factor for the spectral amplitude: (2); This shows that the modulation process of the weighted modulation factor on the spectral amplitude is exponential. Therefore, it is necessary to ensure the stability of the phase information to avoid errors in the reconstruction process. Figure 2 (a)-(b) illustrate the effect of the weighted modulation factor on the modulation spectrum. The simulated signal contains three interfering cosine signals, a bearing outer race fault simulation signal, and high-frequency interference. The bearing outer race fault signal is located at 900Hz, and the high-frequency interference is located at 1800Hz. When the weighted modulation factor... When the value of is less than 1, high-amplitude spectra are suppressed, and noise is amplified. When the weighted modulation factor... When the value is greater than 1, the degree to which noise is suppressed is related to... The value is directly proportional to the value of . When When the value of is greater than 3, the noise will be forcibly suppressed. Some information in the modulation spectrum will be suppressed, which may result in the loss of effective information.

[0023] modulated spectrum Discretize into n = 1, 2, 3, ..., N, where N represents The length of . Its discrete Fourier transform can be calculated as follows: (3); Furthermore, performing an inverse Fourier transform on the target portion of the modulation key function includes: truncating the low-frequency portion of the modulation key function as the target portion, and obtaining the fluctuation curve of the modulation spectrum as the trend spectrum.

[0024] Specifically, It is a new domain without a clear physical meaning. For example... Figure 3 As shown in (a)-(c), this embodiment defines the dataset containing key information of the modulation spectrum as the modulation key function (MKF). Based on the fundamental principle of the inverse Fourier transform, the portion of the MKF near zero approximates low-frequency components, meaning that reconstructing this portion can yield the fluctuation curve of the modulation spectrum. (4); in, Let i be the key function, i be the imaginary unit, u be the variable in the transform domain, and f be the frequency.

[0025] Furthermore, reconstructing each sub-band into sub-modes includes: The modulation spectrum is corrected, and approximation coefficients are calculated based on the corrected modulation spectrum and scaling function; Calculate the detail coefficients based on the modified modulation spectrum and empirical function; Based on the approximation coefficients and the detail coefficients, each sub-band is reconstructed into a sub-mode.

[0026] Specifically, the modulation spectrum can also be reconstructed to obtain the corrected waveform, which requires initial phase assistance.

[0027] (5); Therefore, different modal components can be obtained by spectral segmentation and reconstruction of the modulation spectrum. The essence of Fourier decomposition is Fourier transform and its inverse transform. In the process of transformation, after ignoring the physical reality, the zero-phase filter bank has the function of solving practical problems. In the method proposed in this embodiment, the trend spectrum is first reconstructed according to formula (4). To determine the adaptive boundary for spectrum segmentation. Specifically, through a search... By finding local minima, a set of segmented frequency points was obtained. These points reflect the natural boundaries between different modal components, i.e., the low-lying regions of spectral energy density. In the method proposed in this embodiment, the modulation spectrum... It will be divided into n sub-bands, and the corresponding boundaries are defined as follows: : , The corresponding sub-band is defined as , , , … Set , The modulation spectrum can be represented as: Based on the above boundaries, a zero-phase filter bank including scaling functions and empirical functions can be constructed, such as... Figure 4 As shown below, the scaling function is defined. and empirical functions : (6); (7); in, The passband range variable of the filter. For the nth cut spectrum, the constant boundary value is... It is the constant boundary value of the (n+1)th cut spectrum.

[0028] At the same time, define the approximation coefficients. for: (8); in It is a Fourier transform. It is the inverse function of the Fourier transform. It is a scaling function, equivalent to the first scaling function of the lowest frequency corresponding to the bandpass range [0, ... , It is an integral variable. It is a signal Fourier transform, It is a scaling function Fourier transform.

[0029] Detail factor yes: (9); in, It is a signal Fourier transform, It is a scaling function Fourier transform, It is the nth empirical function Fourier transform.

[0030] The modulated signal can be reconstructed using the following formula: (10); in, and yes and The Fourier transform of N is the total number of sub-bands in the spectrum division.

[0031] One of the final filters constructed and N , can be represented as: (11).

[0032] in, These are low-frequency approximate modal components. This is the nth high-frequency detail mode component.

[0033] Furthermore, the harmonic correlation index of each sub-mode is calculated, including: A digital twin fault model of the bearing of the target wind turbine is constructed, and the Hilbert transform envelope spectrum of the digital twin fault model and the Hilbert transform envelope spectrum of each sub-mode are calculated. The linear correlation between the digital twin fault model and the Hilbert transform envelope spectrum of each submode is evaluated using the Pearson product-moment correlation coefficient to obtain the harmonic correlation index.

[0034] Furthermore, calculating the Hilbert transform envelope spectrum of the digital twin fault model includes: Calculate the Hilbert transform of the digital twin fault model, and calculate the Fourier transform of the envelope signal based on the Hilbert transform of the digital twin fault model; The Hilbert envelope spectrum of the digital twin fault model is obtained based on the Fourier transform of the envelope signal.

[0035] Specifically, the idea behind the index proposed in this embodiment stems from the uncertainty of signals. When a wind turbine bearing fails, the vibration signal often exhibits diverse and non-stationary characteristics. Regardless of whether there is a fault in the equipment, the acquired signal is continuous. However, after the continuous signal is acquired and stored in the memory, the truncation process causes discontinuity, resulting in uncertainty in the initial point position. For a device with a faulty bearing, the starting point of the waveform captured at different times may have different entropies or signal-to-noise ratios. The stability of the system is difficult to predict. Figure 5 (a) shows seven sets of waveforms at different start times, implying that finding waveforms with high similarity to the fault in the time domain is difficult. The Fourier spectra of these seven sets of waveforms are calculated. Figure 5 (b) illustrates the distribution with different inherent frequencies. Due to the unknown nature of the device's inherent frequency, the location of fault information in the spectrum needs to be searched by the algorithm. Fault information approximating in the time domain may be located in different frequency bands and have different energy intensities in the spectrum.

[0036] The usual way to determine a fault is to calculate its Hilbert transform envelope demodulation spectrum after obtaining the final component. Figure 6 In (a), the envelope spectra of the aforementioned seven signals almost overlap, indicating a high correlation between the envelope spectra of the same fault type. Using Sig-1 as the baseline, the waveforms, spectra, and envelope spectra of the other six signals were calculated and their correlation with the baseline. The results are shown in [the table / image]. Figure 6 (b) In this study, although the signals are highly similar due to their different start times, their correlation is low. Without added noise, the correlation between the spectra of different signals is greater than that between the waveforms. Although the inherent spectra of different signals differ, fault characteristics are distributed across the entire frequency band, and these fault information signals exhibit significant correlation. Notably, the correlation between the envelope spectra of the six sets of signals and the reference signal is close to 1. This characteristic, unaffected by waveform truncation and inherent frequencies, lays the foundation for the development of new indicators.

[0037] Therefore, this embodiment introduces a new harmonic correlation index (HCI) to screen fault information. This index requires estimation of the characteristic frequencies of the faulty component to be diagnosed. A digital twin fault model is designed based on existing parameters; this is termed targeted diagnosis in this embodiment. First, a digital twin fault model of the faulty bearing is designed. : (12); It is the natural frequency; This refers to the damping coefficient. The harmonic correlation index designed in this embodiment depends on the harmonics in the envelope spectrum and the fault characteristic frequency. Previous experiments have verified that the natural frequency and damping coefficient have little impact on the accuracy of the twin model. Figure 5 and Figure 6 This also proves that the position of the initial pulse has no impact on subsequent calculations. Therefore, the correlation between the envelope spectrum of the signal to be analyzed and the envelope spectrum of the twin model is calculated. High correlation means that there is more fault information in the signal to be analyzed, and its Hilbert envelope spectrum contains high-amplitude fault characteristic frequencies and harmonics. Low correlation means that the proportion of fault characteristic frequencies in the signal to be analyzed is relatively low.

[0038] First, calculate the Hilbert transform of the twin model. : (13); Secondly, calculate the Fourier transform of the envelope signal. : (14); Hilbert's envelope spectrum can be represented as: (15); make Let the envelope spectrum of the twin model be represented by... This represents the envelope spectrum of the signal to be analyzed. The Pearson product-moment correlation coefficient is used to assess the linear correlation between the two sets of signals. It is predictable that the signal to be analyzed may contain a large amount of noise and interference, while the twin model only contains fault information. The higher the proportion of fault features in the signal to be analyzed, the stronger the correlation. The Pearson correlation coefficient is defined as the product of the covariances of the two variables divided by their standard deviations: (16); in The expected value of the signal, the sample Pearson correlation coefficient, can be expressed as: (17); in, It is the mathematical expectation. is the population standard deviation, and n is the sample size.

[0039] To test the effectiveness and advantages of the method in this embodiment, a complex signal with bearing outer ring fault and interference was constructed. The specific formula is as follows: (18); The core of the signal is the bearing outer ring fault simulation signal. Damping coefficient. Its natural frequency is f Hz. The repetition period of the periodic pulse is , ). Figure 7 (a) shows the pulse information and the waveform and spectrum after adding interference and noise. It can be observed from the frequency domain that the other three components are sinusoidal signals. Due to the high energy of the interference in the frequency domain, the fault information is suppressed. Although there is no obvious correlation between the sinusoidal signals, modulation can be found between them in the envelope spectrum, which severely affects the results of the envelope analysis. Figure 7 (b) Visually demonstrates the envelope spectrum of the unprocessed synthetic signal. The amplitude at the true fault characteristic frequency (100 Hz) is extremely weak and almost completely obscured.

[0040] Traditional empirical wavelet transform and empirical Fourier decomposition methods employ a mode separation strategy based on scale-space representation, which means they have similar results in mode separation. Figure 8The results of EWT and EFD in the frequency domain mode separation are shown. The blue line represents the boundary distribution, and the red line represents the harmonic kurtosis of each component. The fault information is located around 2500Hz, but this frequency domain mode separation method is susceptible to small noises, resulting in significant errors. The fault information identified by the two current methods is located around 4000Hz, which does not match the simulated signal.

[0041] Harmonic Fourier Decomposition (HFD) is a newly developed frequency domain mode separation algorithm. This algorithm employs a spectral separation benchmark based on power spectral density. The approach of HFD is similar to that proposed in this embodiment, but there is a fundamental difference: the spectral modulation process. Different levels of accuracy in reconstructing the power spectral density can be achieved by controlling the window width of the power spectral density function. The spectral trend obtained by this method is sensitive to frequency components with lower amplitudes. Figure 9 (a) shows the power spectral density and the obtained boundary. Fault information at 2500 Hz was not separated into different frequency bands, which means that more fault information was retained in the same frequency band. Figure 9 (b) Visually displays the calculated results of the harmonic spectral kurtosis (HSK) index for each sub-band. The gray dashed lines in the figure correspond to... Figure 9 The spectral boundaries defined in (a) divide the spectrum into multiple sub-bands; it can be clearly observed that the HSK index reaches its global peak within the band containing 2500Hz. This further confirms that the index successfully locates the sensitive frequency band containing the richest periodic fault impacts, and that HSK has a higher sensitivity to periodic pulses compared to other frequency bands. Figure 9 (c) The results obtained by HFD are shown. The waveform and envelope spectrum are displayed. Numerous pulses appear in the waveform, indicating signal energy attenuation. The envelope spectrum shows fault characteristic frequencies and second harmonics, suggesting the presence of fault information with a characteristic frequency of 100Hz in the signal.

[0042] The signal is processed using the SMFD method proposed in this embodiment. Figure 10 The key modulation function and boundary distribution in the modulation spectrum are shown during the calculation process. For example... Figure 10 As shown in (a), the dataset is transformed to obtain the modulation key function (MKF) of the fluctuations, with the low-frequency core components serving as reconstruction points. Because this algorithm incorporates an amplitude enhancement step, the inverse transformation process from the key function has a high fault tolerance. Even with slightly different selection ranges of reconstruction points, effective trend information can still be stably extracted, and the final number of boundaries can be reduced to mitigate errors. The inverse transformation is performed based on the selected reconstruction points. Figure 10(b) shows the modulation spectrum fluctuation trend curve overlaid on the original spectrum. The algorithm automatically locates the minimum point of this trend curve and generates adaptive spectral boundaries thereon. Three boundaries were obtained, dividing the entire spectrum into four independent modes: the portion below 1000Hz represents three preset sinusoidal interferences; the portion including 2500Hz represents simulated bearing outer race fault information; the portion [3000Hz-4000Hz] represents designed interference; and the portion above 4000Hz represents noise. Harmonic correlation indices are extremely sensitive to the fault frequency band; after normalizing the HCI, they are plotted... Figure 10 In (c), it can be clearly seen that the HCI value of the frequency band corresponding to 2500Hz is much greater than that of other frequency bands, and the optimal fault frequency band has been successfully locked.

[0043] After extracting the frequency band corresponding to the maximum HCI, the fault information is modulated and enhanced. The amplitude of the fault information in the original signal's spectrum is less than 0.5. This is why the envelope demodulation process in HFD struggles to depict fault characteristics. By adding a spectral amplitude modulation process, SMFD can accurately demodulate the enhanced characteristic signal after accurately identifying the fault frequency band. The enhanced amplitude is approximately 20. This is 40 times the original amplitude. Figure 11 (a) A visual comparison chart showing the original spectrum and the modulation spectrum enhanced by the SMFD algorithm is presented. Figure 11 (b) shows the envelope spectrum of the enhanced modulation band. The fault characteristic frequencies and multiple harmonics are evident.

[0044] Because the simulated signal has less noise, the current SNR is -1dB. Figure 9 (c) shows that the HFD only obtains the second harmonic under the influence of weak noise, which means that the method is difficult to pick up more fault information from strong noise under the influence of interference. In order to prove this idea and verify the noise immunity of the SMFD proposed in this embodiment, three different noises were added to the formula (18): SNR=[-3dB, -5dB, -7dB]. Figure 12 (a)-(b) show the results of processing these three sets of data using two different methods. As expected, while HFD boasts excellent computational efficiency and fault identification accuracy, noise forcibly suppresses fault information within the frequency band. In this case, excellent filtering methods become ineffective. The spectral enhancement process designed in this embodiment can resolve fault characteristic frequencies and multiple harmonics under strong noise conditions, meaning that the algorithm can effectively identify and extract fault information in a strong noise background.

[0045] Finally, this embodiment tested the computational efficiency of the four classical methods described above: SNR = -1dB. Four sets of computation times were tested for each method. Figure 13The test results are presented. EWT and EFD employ the same spectral segmentation method, which relies on scale-space representation and histograms and is highly susceptible to sampling frequency. While the number of boundaries obtained by this method affects the algorithm's speed, the scale-flipping method is even more time-consuming. Compared to this method, HFD is faster. It reduces the number of boundaries while calculating the power spectral density, improving the identification efficiency of effective components. Although the algorithm proposed in this embodiment adds an amplitude modulation step, its computational efficiency is very high. Reducing the power spectral density requiring a wider window does not decrease modality recognition accuracy.

[0046] The algorithm was validated using a classic test bench from Xi'an Jiaotong University. According to the recorded data, the motor speed was approximately 2000 r / min, and the rotational frequency was 33.6 Hz.

[0047] Figure 14 (a)-(b) show 30k data points. Sampling frequency The signal waveform contains various noises, masking the periodic pulse characteristics and increasing the difficulty of the diagnostic process. In the frequency spectrum, the low-frequency portion below 1000Hz contains a large amount of high-amplitude unknown information. The portion above 1000Hz contains information, but with lower amplitude. The characteristic frequency of the outer ring bearing fault is... . Since the previously mentioned Empirical Wavelet Transform (EWT) and Empirical Fourier Decomposition (EFD) are computationally slow and have too many segmentation boundaries, their value in practical applications is low. Therefore, only the latest similar algorithm, HFD, is compared. Figure 15 (a)-(b) show the results of HFD processing. HFD decomposes the bearing outer race fault signal into 6 components. The previously mentioned low-frequency portion below 1000Hz is separated into the first component. The amplitudes of the second to sixth components in the frequency domain are very low, making it difficult to determine fault information from them.

[0048] Figure 16 As shown in (a)-(b), fault information in the components is filtered using harmonic spectral kurtosis (HSK) employed in HFD. The low-frequency component, which originally had the highest amplitude, has the highest HSK. Although fault information exists in the high-frequency part, the direct decomposition method cannot identify enough fault information. The lack of a feature enhancement step causes the HFD algorithm to lose its effectiveness.

[0049] The signal is processed using the SMFD method proposed in this embodiment. The modulated signal and its spectrum and envelope spectrum obtained in the first step are as follows: Figure 17As shown in (a)-(b), the spectral modulation enhancement step, while enhancing fault characteristics, also enhances other non-fault characteristics. The portion below 1000Hz is simultaneously enhanced. Amplifying the 1500Hz-5500Hz range reveals that high-frequency noise is suppressed. Periodic pulses appear in the enhanced signal, requiring envelope spectrum analysis to determine if they indicate a fault. Figure 17 In (b), the envelope spectrum is affected by low-frequency components, and the fault characteristic frequency is not obvious. The above results demonstrate the importance of subsequent steps in SMFD. Filtering the signal after feature enhancement can compensate for the influence of other interferences and also compensate for the defects of spectral modulation.

[0050] like Figure 18 As shown in (a), the modulation spectrum is divided into four parts using the SMFD algorithm, with the low-frequency component still identified as an important element. The difference between HCI and HFD is that HCI identifies the high-frequency component. The original spectrum and the modulation spectrum identified by SMFD are then compared... Figure 18 In (b), it can be seen that the part with an original amplitude of less than 0.04 is enhanced to 2.3. Figure 17 (a) demonstrates that the spectral modulation process suppresses noise. Therefore, the finally identified frequency band contains less noise and more fault information.

[0051] Figure 19 The processing results of SMFD are shown. It can be seen that the obtained components contain periodic pulses with pulse intervals similar to the fault period of the bearing outer ring. Fault characteristic frequencies and harmonics appear in the envelope spectrum, which means that the SMFD results enhance the fault characteristics and identify the frequency band with the richest features.

[0052] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A bearing fault diagnosis method based on spectral modulation Fourier decomposition, characterized in that, include: Collect vibration signals from the bearings of the target wind turbine equipment; The vibration signal is subjected to Fourier transform, and the spectral amplitude is updated to obtain the modulation spectrum; The modulation spectrum is discretized and subjected to discrete Fourier transform to obtain the modulation key function. The target part of the modulation key function is then subjected to inverse Fourier transform to obtain the trend spectrum of the modulation spectrum. The modulation spectrum is divided into several sub-bands, and each sub-band is reconstructed into a sub-mode using a zero-phase filter bank. The harmonic correlation index of each sub-mode is calculated. The zero-phase filter bank is constructed based on the spectral boundaries, where the minimum points in the trend spectrum are the spectral boundaries between modes. Envelope demodulation analysis is performed on the sub-mode corresponding to the maximum harmonic correlation index to achieve targeted diagnosis of bearing faults.

2. The bearing fault diagnosis method based on spectral modulation Fourier decomposition according to claim 1, characterized in that, Updating the spectral amplitude includes: exponentially editing the spectral amplitude using a weighted modulation factor to obtain the modulation spectrum; The modulation spectrum for: ； in, The weighted modulation factor for the spectral amplitude. Indicates amplitude. This represents the phase, and j is the imaginary unit.

3. The bearing fault diagnosis method based on spectral modulation Fourier decomposition according to claim 1, characterized in that, Performing an inverse Fourier transform on the target portion of the modulation key function includes: truncating the low-frequency portion of the modulation key function as the target portion, and obtaining the fluctuation curve of the modulation spectrum as the trend spectrum.

4. The bearing fault diagnosis method based on spectral modulation Fourier decomposition according to claim 3, characterized in that, The fluctuation curve of the modulation spectrum for: ； in, Let i be the key function, i be the imaginary unit, u be the variable in the transform domain, and f be the frequency.

5. The bearing fault diagnosis method based on spectral modulation Fourier decomposition according to claim 1, characterized in that, The zero-phase filter bank includes scaling functions and empirical functions; The scaling function for: ; The empirical function for: ; in, The passband range variable of the filter. For the nth cut spectrum, the constant boundary value is... It is the constant boundary value of the (n+1)th cut spectrum.

6. The bearing fault diagnosis method based on spectral modulation Fourier decomposition according to claim 5, characterized in that, Reconstructing each sub-band into sub-modes includes: The modulation spectrum is corrected, and approximation coefficients are calculated based on the corrected modulation spectrum and scaling function; Calculate the detail coefficients based on the modified modulation spectrum and empirical function; Based on the approximation coefficients and the detail coefficients, each sub-band is reconstructed into a sub-mode.

7. The bearing fault diagnosis method based on spectral modulation Fourier decomposition according to claim 1, characterized in that, The harmonic correlation index of each submode is calculated, including: A digital twin fault model of the bearing of the target wind turbine is constructed, and the Hilbert transform envelope spectrum of the digital twin fault model and the Hilbert transform envelope spectrum of each sub-mode are calculated. The linear correlation between the digital twin fault model and the Hilbert transform envelope spectrum of each submode is evaluated using the Pearson product-moment correlation coefficient to obtain the harmonic correlation index.

8. The bearing fault diagnosis method based on spectral modulation Fourier decomposition according to claim 7, characterized in that, Calculating the Hilbert transform envelope spectrum of the digital twin fault model includes: Calculate the Hilbert transform of the digital twin fault model, and calculate the Fourier transform of the envelope signal based on the Hilbert transform of the digital twin fault model; The Hilbert envelope spectrum of the digital twin fault model is obtained based on the Fourier transform of the envelope signal.

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