Application of self-adaptive fault sensitive frequency band identification method in hydroelectric generating set fault diagnosis

Abstract

The invention relates to the technical field of power equipment state monitoring, in particular to an application of a self-adaptive fault sensitive frequency band identification method in hydroelectric generating set fault diagnosis, which comprises the following steps of: performing trend elimination on a hydroelectric generating set rolling bearing vibration signal; estimating the power spectrum density by adopting a Welch method and performing self-adaptive smoothing; adaptively segmenting a frequency band based on a smooth spectrum local valley point; extracting kurtosis and envelope spectrum entropy of each candidate frequency band, and constructing a weighted comprehensive scoring index through normalization; determining a self-adaptive threshold screening sensitive frequency band through inter-class variance maximization; a sensitive frequency band envelope is demodulated, a diagnosis result is output, frequency band segmentation is carried out according to a signal frequency spectrum structure, and comprehensive score fusion impact sensitivity and energy distribution orderliness measurement are carried out. According to the method, the fault sensitive frequency band can still be accurately recognized under strong noise and variable working conditions, the clear fault characteristic frequency is extracted, the operation efficiency is excellent, and an efficient and reliable solution is provided for automatic and accurate early fault diagnosis of the hydroelectric generating set rolling bearing.

Description

Technical Field

[0001] This invention relates to the field of power equipment condition monitoring technology, specifically to the application of an adaptive fault-sensitive frequency band identification method in fault diagnosis of hydropower units. Background Technology

[0002] Rolling bearings are core supporting components in the generator, main shaft system, and auxiliary equipment of hydropower units. Their operating status directly determines the stability and reliability of the unit, which is crucial for the continuous and safe operation of power production. In the actual operation of hydropower units, they often face complex and variable operating conditions. Rolling bearings are prone to local defects due to wear, fatigue, and other factors. The vibration characteristics of such early faults are often masked by strong background noise, complex dynamic behavior, and multi-component signal coupling effects. If they are not detected and identified in time, they may lead to equipment downtime, soaring maintenance costs, or even serious safety accidents. Therefore, accurate diagnosis of early faults in rolling bearings is of great engineering significance.

[0003] Fault-sensitive frequency band identification is a core step in rolling bearing vibration signal fault diagnosis. Its goal is to filter out the frequency bands containing the richest fault information from complex vibration signals, laying the foundation for subsequent envelope demodulation and feature extraction. Current rolling bearing fault diagnosis technologies can be mainly categorized into three types: adaptive signal decomposition, blind deconvolution, and optimal demodulation frequency band selection methods. However, all these technologies have significant limitations and are insufficient to meet the diagnostic needs of complex hydropower units under various operating conditions.

[0004] In the field of adaptive signal decomposition technology, various decomposition methods have been proposed to handle nonlinear and non-stationary bearing vibration signals. Empirical Mode Decomposition (EMD) is prone to mode aliasing, affecting the accuracy of fault feature extraction. Ensemble Empirical Mode Decomposition (EMD) suppresses mode aliasing by introducing white noise, but still suffers from insufficient decomposition efficiency and stability. Adaptive Variational Mode Decomposition (VMD) relies on optimization methods such as differential evolution algorithms to find the optimal parameter combination, and the parameter optimization process is complex and time-consuming. Although Fourier decomposition provides a generalized adaptive decomposition approach based on Fourier theory, its ability to capture weak impact features in the signal is limited. Differential Mode Decomposition (DMD) achieves signal decomposition based on convex optimization and Fourier transform, showing certain advantages in bearing and gear fault diagnosis, but its robustness in strong noise environments still needs improvement.

[0005] Blind deconvolution techniques enhance fault characteristics by designing inverse filters to recover the original impact source, but their application is also limited by various factors. Minimum entropy deconvolution (MED) faces the challenge of solving for filter coefficients when enhancing pulse characteristics; maximum correlation kurtosis deconvolution (MCKD) depends on the setting of prior fault period and shift, limiting its applicability under unknown operating conditions; improved MCKD (IMCKD) estimates the iteration period through the autocorrelation of the envelope signal, reducing dependence on prior information, but the iteration process is complex; adaptive multi-point optimal minimum entropy deconvolution (MOMEDA) uses a periodic modulation intensity strategy to estimate the pulse period and overcome boundary effects, but the efficiency of filtering signal processing needs improvement; blind deconvolution methods based on maximizing cyclostationarity perform well under variable speed conditions, but the algorithm complexity is high, making it difficult to meet real-time diagnostic requirements.

[0006] Optimal demodulation band selection methods focus on screening sensitive bands through effective indicators and visualization tools. Among them, the fast spectral kurtosis (Kurtogram) is a classic method that can locate the band that maximizes the kurtosis of the impact signal, but it is prone to failure in high-intensity non-Gaussian noise or high fault pulse repetition rate scenarios. The Protrugram method based on the amplitude kurtosis of the demodulated signal envelope spectrum has insufficient band identification accuracy under complex noise interference. The SKRgram method for planetary bearing fault diagnosis suppresses gear noise through the ratio of spectral kurtosis matrix, but its adaptability to different types of bearing faults is limited. The Infogram method captures repetitive transient features based on the square envelope and the negative entropy of the square envelope spectrum, but its ability to distinguish between multiple faults is weak. The method combining wavelet scattering transform and improved soft thresholding denoising provides a new perspective for composite fault diagnosis, but the preprocessing process is cumbersome and the real-time performance is poor.

[0007] In summary, existing rolling bearing fault diagnosis technologies generally suffer from problems such as strong reliance on prior knowledge, high requirements for manual parameter setting, poor adaptability to complex operating conditions, and difficulty in balancing robustness and computational efficiency. These limitations fail to fully meet the automated and precise diagnostic needs for early-stage rolling bearing faults in the complex operating environment of hydropower units. Therefore, developing a fault-sensitive frequency band identification method that requires no manual intervention, possesses strong adaptability, excellent robustness, and is highly efficient and reliable has become an urgent technical challenge to be solved in the field of hydropower unit fault diagnosis. Summary of the Invention

[0008] The purpose of this invention is to provide an adaptive fault-sensitive frequency band identification method for the application of fault diagnosis in hydropower units, so as to solve the problems mentioned in the background art, that traditional methods rely on prior knowledge and manual parameters and have poor adaptability to complex operating conditions.

[0009] To achieve the above objectives, the present invention provides the following technical solution: An adaptive fault-sensitive frequency band identification method is applied to fault diagnosis of hydropower units, comprising the following steps: (1) Perform trend elimination processing on the vibration signal of the rolling bearing of the hydropower unit to remove baseline drift; (2) The power spectral density of the vibration signal is estimated by Welch method and then smoothed by adaptive moving mean to obtain a smoothed spectrum; (3) Based on the local valley points of the smooth spectrum, adaptive segmentation of the frequency band is performed to obtain candidate frequency bands; (4) Perform bandpass filtering on each candidate frequency band, extract the kurtosis and envelope spectral entropy of each frequency band, and construct a weighted comprehensive scoring index after normalization to obtain the score vector of all candidate frequency bands; (5) Determine the adaptive threshold based on the strategy of maximizing inter-class variance, and select the sensitive frequency band according to the score vector and the adaptive threshold; (6) Perform envelope demodulation analysis on the sensitive frequency band and output the fault diagnosis results of the rolling bearing of the hydropower unit.

[0010] Preferably, the process of estimating the power spectral density using the Welch method in step (2) is as follows: A discrete-time signal x[n] of length N is divided into i segments, each of length M. Then the signal in segment i is... i [m] is represented as: ; Where D is the overlap length between the segmented signals. A Hanning window of length M is used. The segmented signals are processed separately to obtain the windowed signals. : ; For windowed signals Perform a discrete Fourier transform and calculate its periodogram. The periodogram of the k-th segment can be expressed as: ; The i-th periodic plot is averaged to obtain the final power spectral density estimate: ; The power spectrum estimation window length of the Welch method is 1024, and the overlap length is 512.

[0011] Preferably, the adaptive frequency band segmentation process in step (3) is as follows: right Apply adaptive moving mean smoothing: ; in Frequency points, smoothing window length It adaptively adjusts with signal length to ensure that it is not overly smoothed at high resolution. In the smoothed spectrum... Find local valleys as frequency band boundaries: ; Take the one with the highest significance points ( ), forming a selected index set The final set of frequency band boundaries is: ; in Indicates index The corresponding frequency values ​​are arranged in ascending order of their boundaries.

[0012] Preferably, the bandpass filtering in step (4) uses a fourth-order Butterworth zero-phase bandpass filter to obtain the sub-signal. .

[0013] Preferably, the kurtosis mentioned in step (4) is a statistical measure of the signal's deviation from a Gaussian distribution and is sensitive to weak periodic shocks; the envelope spectral entropy is obtained by enveloping the envelope signal. One-sided FFT spectrum The calculated entropy, used to assess the orderliness of the energy distribution in the envelope spectrum, is... A smaller value indicates a higher degree of ordered aggregation of information; the normalization of the envelope spectrum entropy is performed by inverse normalization with 3 as the baseline, and the normalized value is... The larger the value, the more concentrated the information.

[0014] Preferably, the kurtosis weight of the weighted comprehensive scoring index in step (4) is 0.4, and the envelope spectral entropy weight is 0.6. The weights are determined by analyzing 10 sets of measured data using a particle swarm optimization algorithm. The comprehensive score S i The weighted sum of the normalized kurtosis and the envelope spectral entropy: .

[0015] Preferably, the inter-class variance mentioned in step (5) is: ; in, It is a background class The proportion; Is it a foreground category? The proportion; and These are the mean scores for the background and foreground categories, respectively.

[0016] Preferably, the process for determining the adaptive threshold in step (5) is as follows: The first step is to initialize the optimal separation to 0 and the initial threshold to 0.5; The second step involves traversing the [0.3, 0.7] interval with a step size of 0.05. For each candidate threshold, the frequency band is divided into two groups: and If the current separation is greater than the historical best value, then update the optimal threshold and the optimal separation. The third step is to restore the found optimal normalization threshold to the true rating scale: S_max is the maximum value in the score vector.

[0017] As a preferred option, when screening sensitive frequency bands in step (5), the frequency band with the highest comprehensive score is selected as the optimal frequency band, and envelope demodulation analysis is performed on the optimal frequency band.

[0018] Preferably, the vibration signal includes periodic pulses caused by local defects in the rolling bearing, system harmonic interference, random pulses generated by external impacts, and environmental noise, and the fault diagnosis result includes fault characteristic frequencies and their multi-order components.

[0019] Compared with the prior art, the beneficial effects of the present invention are: (1) This invention estimates the smooth power spectrum of the signal and uses an improved local extremum detection algorithm. This method can adaptively divide candidate frequency bands with clear physical meaning based on the spectral structure of the signal itself. This process avoids the subjectivity of traditional fixed filter banks and lays a solid foundation for subsequent analysis.

[0020] (2) This invention introduces a threshold decision mechanism based on maximizing inter-class variance, which can automatically determine the optimal segmentation threshold according to the score distribution, and finally achieve sensitive frequency band screening without any manual intervention. This solves the key problem that parameter setting in traditional methods depends on expert experience, and significantly improves the automation level and engineering applicability of the method.

[0021] (3) The present invention was verified by simulation signals and public bearing datasets and compared with existing advanced methods. The results show that it can still accurately and stably locate the fault-sensitive frequency band under strong noise background and successfully extract clear fault feature frequencies, which proves its excellent robustness and adaptability. Attached Figure Description

[0022] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are explained in detail together with the embodiments of the invention, but do not constitute a limitation thereof.

[0023] Figure 1 The present invention provides the time-domain waveforms of the simulated signal and its components. Figure 1 (a) Pulse component; Figure 1 (b) Harmonic components; Figure 1 (c) Random pulse; Figure 1 (d) Noise components; Figure 1 (e) Simulated signal; Figure 2 This represents the result of processing the simulation signal using the traditional Kurtogram method. Figure 2 (a) kurtogram; Figure 2 (b) Input vibration time-domain signal; Figure 2 (c) The processed signal result; Figure 2 (d) A magnified view of the envelope spectrum of the processed signal; Figure 3 This represents the processing result of the simulation signal using the traditional EMD method. Figure 3 (a) Input vibration time-domain signal; Figure 3 (b) The processed signal result; Figure 3 (c) A magnified view of the envelope spectrum of the processed signal; Figure 3 (d) The degree of correlation between all IMFs and the original signal; Figure 4 This represents the processing result of the simulation signal using the traditional VMD method. Figure 4 (a) Input vibration time-domain signal; Figure 4 (b) The processed signal result; Figure 4 (c) A magnified view of the envelope spectrum of the processed signal; Figure 4 (d) The degree of correlation between all IMFs and the original signal; Figure 5 This represents the processing result of the simulation signal using the traditional MCKD method. Figure 5 (a) Input vibration time-domain signal; Figure 5 (b) The processed signal result; Figure 5 (c) A magnified view of the envelope spectrum of the processed signal; Figure 5 (d) The degree of correlation during the iteration process; Figure 6 The result of processing the simulation signal by the method proposed in this invention; Figure 6 (a) Input vibration time-domain signal; Figure 6 (b) The PSD distribution obtained after processing the original signal; Figure 6 (c) The processed signal result; Figure 6 (d) A magnified view of the envelope spectrum of the processed signal; Figure 7 This invention relates to the CWRU experimental platform; Figure 8 This is the result of processing the CWRU inner circle signal using the traditional Kurtogram method. Figure 8 (a) kurtogram; Figure 8 (b) Input vibration time-domain signal; Figure 8 (c) The processed signal result; Figure 8 (d) A magnified view of the envelope spectrum of the processed signal; Figure 9 The results of processing the CWRU inner ring signal using the traditional EMD method are shown below: (a) Input vibration time-domain signal; (b) Processed signal result; (c) Enlarged view of the envelope spectrum of the processed signal result; (d) Correlation between all IMFs and the original signal. Figure 10 The results of processing the CWRU inner circle signal using the traditional VMD method are shown below: (a) Input vibration time-domain signal; (b) Processed signal result; (c) Enlarged view of the envelope spectrum of the processed signal result; (d) Correlation between all IMFs and the original signal. Figure 11 The results of processing the CWRU inner circle signal using the traditional MCKD method are shown below: (a) Input vibration time-domain signal; (b) Processed signal result; (c) Enlarged view of the envelope spectrum of the processed signal result; (d) Correlation degree during the iteration process. Figure 12 The following are the processing results of the CWRU inner ring signal by the method proposed in this invention: (a) Input vibration time-domain signal; (b) PSD distribution obtained after processing the original signal; (c) Signal result after processing; (d) Local magnified view of the envelope spectrum of the signal result after processing. Figure 13 This is the result of processing the CWRU rolling element signal using the traditional Kurtogram method; Figure 13 (a) kurtogram; Figure 13 (b) Input vibration time-domain signal; Figure 13 (c) The processed signal result; Figure 13 (d) A magnified view of the envelope spectrum of the processed signal; Figure 14 The results of processing CWRU rolling body ring signals using the traditional EMD method are shown below: (a) Input vibration time-domain signal; (b) Processed signal result; (c) Enlarged view of the envelope spectrum of the processed signal result; (d) Correlation between all IMFs and the original signal. Figure 15 The results of processing CWRU rolling body ring signals using the traditional VMD method are as follows: (a) Input vibration time-domain signal; (b) Processed signal result; (c) Enlarged view of the envelope spectrum of the processed signal result; (d) Correlation degree between all IMFs and the original signal. Figure 16The results of processing CWRU rolling body signals using the traditional MCKD method are as follows: (a) Input vibration time-domain signal; (b) Processed signal result; (c) Local magnified view of the envelope spectrum of the processed signal result; (d) Correlation degree during the iteration process. Figure 17 The following are the processing results of the CWRU rolling element signal by the method proposed in this invention: (a) Input vibration time-domain signal; (b) PSD distribution obtained after processing the original signal; (c) Signal result after processing; (d) Local magnified view of the envelope spectrum of the signal result after processing. Figure 18 This is a flowchart illustrating the process of the present invention. Detailed Implementation

[0024] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. 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 of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0025] This invention provides an application of an adaptive fault-sensitive frequency band identification method in the fault diagnosis of hydropower units. The following embodiments illustrate the proposed adaptive fault-sensitive frequency band identification method in detail: 1. Rolling bearings are core components of rotating machinery, and the key to their fault diagnosis lies in accurately capturing the vibration characteristics related to the fault. However, vibration signals under actual operating conditions are characterized by strong noise, non-stationarity, and multi-component coupling. Traditional frequency band selection methods based on experience or fixed thresholds (such as directly selecting high-frequency bands or preset frequency ranges) have significant limitations: first, they cannot adapt to the frequency band drift of fault characteristics caused by changes in rotational speed and load; second, they are easily affected by noise interference, misjudging false frequency bands as sensitive frequency bands; and third, they ignore the structural differences between frequency bands, making it difficult to quantify the contribution of different frequency bands to the fault. Therefore, a fully adaptive frequency band detection method is urgently needed to dynamically identify sensitive frequency bands containing fault information based on the structural characteristics of the signal itself.

[0026] First, the Welch method is used to extract the smooth spectral trend. Given a discrete-time signal of length N... Divide it into i segments, each segment having a length of M, then the signal of the i-th segment... It can be represented as: (1) Where D is the overlap length between the segmented signals. A Hanning window of length M is used. The segmented signals are processed separately to obtain the windowed signals. : (2) For windowed signals Perform a discrete Fourier transform and calculate its periodogram. The periodogram of the k-th segment can be expressed as: (3) The i-th periodic plot is averaged to obtain the final power spectral density estimate: (4) To further suppress random noise fluctuations and preserve the true spectral structure, Apply adaptive moving mean smoothing: (5) in Frequency points, smoothing window length It adaptively adjusts with signal length to ensure that it is not overly smoothed at high resolution. In the smoothed spectrum... Find local valleys as frequency band boundaries: (6) Take the one with the highest significance points ( ), forming a selected index set The final set of frequency band boundaries is: (7) in Indicates index The corresponding frequency values ​​are arranged in ascending order of their boundaries.

[0027] To address the complexity of rolling bearing fault states and the limitations of single characterization indicators, this section constructs an information fusion evaluation index, using objectively quantified frequency band segmentation as the reliability of sensitive resonant frequency bands. The core of this scheme lies in fusing two complementary features: kurtosis and envelope spectral entropy. The former is highly sensitive to transient shocks and is the most direct statistical measure of a signal deviating from a Gaussian distribution; the latter is used to assess the orderliness of energy distribution in the envelope spectrum. The formulas for both are as follows: (8) (9) in, envelope signal The one-sided FFT spectrum. The significant reduction reflects the orderly aggregation of information.

[0028] To achieve additive fusion of the two features, dimensionless normalization is required. Therefore, a kurtosis of 10 is used as the saturation threshold, which is mapped to [0,1].

[0029] (10) For a typical sampling length, the upper limit of the spectral entropy of a random signal is approximately Actual measurements show that the strong fault envelope spectrum... Therefore, inversion normalization is performed using 3 as the baseline. The larger the value, the more concentrated the information.

[0030] (11) Ultimately, this constitutes the weighted composite scoring index: (12) To objectively determine the feature weights, this invention uses a particle swarm optimization algorithm to analyze 10 sets of measured data. The optimal weight combination for kurtosis and spectral entropy is found to be 0.4 and 0.6, respectively. A higher weight is assigned to the envelope spectral entropy because it is based on the overall energy distribution of the signal, exhibiting stronger resistance to transient interference and better statistical robustness. Meanwhile, the kurtosis index has irreplaceable sensitivity for the initial detection of weak periodic shocks, playing a crucial role in early fault identification.

[0031] To obtain the composite score of all candidate frequency bands ( After that, an adaptive threshold needs to be determined. Frequency bands with scores significantly higher than the background are identified as sensitive resonance bands. An adaptive threshold decision method is proposed to achieve statistical optimization and parameter-free threshold determination.

[0032] Bandwidth rating This can be viewed as a one-dimensional grayscale distribution containing two types of frequency bands: one is a small number of highly scored sensitive frequency bands (containing fault cycle impacts), and the other is a large number of low-scoring background frequency bands (mainly noise or irrelevant resonances). The goal is to find a threshold. This maximizes the separation between the two frequency bands in the scoring space, enabling automatic and objective sensitive frequency band identification. First, the inter-class variance is defined as: (13) in, It is a background class The proportion; Is it a foreground category? The proportion; and These are the mean scores of the background and foreground classes, respectively. The optimal threshold is defined as: (14) When inter-class variance When the threshold is at its maximum, it indicates that the two frequency bands have the least overlap and the clearest separation in the scoring space; this threshold is the statistically optimal solution. The calculation process of the adaptive threshold involves the following steps: The first step is to initialize the optimal separation to 0 and the initial threshold to 0.5; The second step involves traversing the [0.3, 0.7] interval with a step size of 0.05. For each candidate threshold, the frequency band is divided into two groups: and If the current separation is greater than the historical best value, then update the optimal threshold and optimal separation. The third step is to restore the found optimal normalization threshold to the true rating scale: (15) The overall flow of the method proposed in this invention is as follows: Step 1: Perform trend elimination processing on the signal to remove baseline drift; Step 2: Estimate the power spectral density using the Welch method. And perform adaptive moving mean smoothing to obtain .

[0033] Step 3: Apply a fourth-order Butterworth zero-phase bandpass filter to obtain the sub-signal. ; Step 4: Extract kurtosis and envelope spectrum entropy Two core features were identified and normalized. Step 5: Calculate the... The composite scoring index for each frequency band is used to obtain the score vector for all frequency bands. Step 6: Adaptive Threshold Decision and Sensitive Frequency Band Identification Step 7: Obtain the optimal frequency band and perform envelope demodulation analysis.

[0034] 2. Simulation Verification This invention evaluates the fault diagnosis performance of the proposed method using simulated signals and compares it with existing methods. The simulated signal is generated based on a numerical model of an outer ring bearing fault and consists of four components: periodic pulses caused by outer ring defects, system harmonic interference, random pulses generated by external impacts, and environmental noise in the operating environment. The sampling frequency is set to 12,500 Hz, and the signal duration is 1 second. The composite signal expression is: (16) This represents the cyclic impulse response triggered by a local peripheral defect, and its mathematical expression is: (17) Among them, the The amplitude of each periodic pulse is set to 5%. The fault characteristic frequency is... ,in =5.26 (fault characteristic coefficient) and =20Hz (shaft rotation frequency). Resonant frequency. and attenuation parameters They are configured to 2,680Hz and 800Hz respectively. The sliding effect of the rolling element is achieved through... The model indicates that it follows a uniform distribution: sliding factor =1%.

[0035] (18) in It is the first The amplitude of a random pulse, =5 is the total number of random pulses. Indicates the first The occurrence time of each pulse. Resonant frequency. and attenuation parameters Set them to 5,200Hz and 700Hz respectively; (19) amplitude =0.25, =0.3, frequency =7Hz, =14Hz, phase = , = .at last, It is Gaussian white noise that simulates environmental interference during bearing operation.

[0036] like Figure 1 The figure shows the time-domain waveforms of the simulated signal and its components, where Figure 1 (a) Pulse component; Figure 1 (b) Harmonic components; Figure 1 (c) Random pulse; Figure 1 (d) Noise components; Figure 1 (e) Simulated signal.

[0037] In summary, the waveforms of each component of the simulated signal are as follows: Figure 1 As shown. The effectiveness of the proposed method is verified using simulation signals, and it is compared with other methods. The parameter settings of other methods are as follows: (1) The fast kurtosis plot method determines the optimal bandpass filter parameters by quickly selecting the frequency band with the maximum kurtosis value. This invention uses a 4-layer binary tree structure to subdivide the signal frequency band by 1 / 3 binary. The center frequency and bandwidth corresponding to the global maximum value in the kurtosis plot are selected, and a 4th-order Butterworth bandpass filter is designed to filter the original signal.

[0038] (2) The EMD decomposition layer is set to 8 layers to ensure that the signal is fully decomposed without over-decomposition. The stopping criterion for the screening process is set to the change in three consecutive screenings being less than a threshold, in order to balance computational efficiency and decomposition accuracy. After obtaining a series of intrinsic mode functions (IMFs) through decomposition, the cross-correlation coefficient between each IMF and the original signal is calculated, and the component with the largest correlation coefficient is selected as the most correlated IMF.

[0039] (3) VMD sets the number of decomposition modes K to 5 to balance feature completeness with computational complexity. The bandwidth penalty factor α is set to 2000 to control the bandwidth of each IMF component, ensuring it has a specific center frequency. After decomposition, the cross-correlation coefficient between each IMF and the original signal is calculated, and the most relevant component is selected.

[0040] (4) Key parameters for maximum correlation kurtosis deconvolution include: filter length set to 180 to ensure sufficient degrees of freedom to shape the impact response; fault period set to 100 sampling points, corresponding to the expected bearing fault characteristic frequency; and shift count set to 4 to account for the time extension of the impact waveform. The optimization process uses gradient ascent, with a maximum of 30 iterations, a learning rate set to 0.01, and a convergence criterion (relative improvement less than 10). -6 ).

[0041] (5) The proposed method uses a Welch power spectrum estimation window of 1024 and an overlap length of 512, and employs an adaptive smoothing technique to suppress spectral fluctuations. After bandpass filtering for each frequency band, its comprehensive sensitivity score is calculated. The sensitive frequency band is determined by an adaptive threshold that maximizes the inter-class variance, and the frequency band with the highest score is selected as the optimal frequency band for envelope spectrum analysis.

[0042] The processing results of each method are as follows Figures 2 to 6 As shown. From Figure 2 It can be seen that the fast kurtosis method mainly extracts the frequency band components with larger kurtosis. Therefore, the processed signal retains a strong impact component, resulting in insufficient clarity of the fault characteristic frequencies in the envelope spectrum. Figure 3 and Figure 4 The results are for EMD and VMD methods, respectively. Due to the influence of noise interference, the fault characteristic frequencies are not obvious in the sensitive components extracted by these two methods. Figure 5 and Figure 6The results of the MCKD method and the method proposed in this invention are presented, showing that both can accurately identify the multi-order components of fault characteristic frequencies. However, the MCKD method requires multiple iterations, resulting in high computational costs; in contrast, the method of this invention has higher computational efficiency while maintaining diagnostic performance.

[0043] Figure 2 This represents the result of processing the simulation signal using the Kurtogram method. Among them, Figure 2 (a) kurtogram; Figure 2 (b) Input vibration time-domain signal; Figure 2 (c) The processed signal result; Figure 2 (d) A magnified view of the envelope spectrum of the processed signal.

[0044] Figure 3 The EMD method processes the simulated signal. Among other things, Figure 3 (a) Input vibration time-domain signal; Figure 3 (b) The processed signal result; Figure 3 (c) A magnified view of the envelope spectrum of the processed signal; Figure 3 (d) The degree of correlation between all IMFs and the original signal.

[0045] Figure 4 The VMD method processes the simulated signal. Among other things, Figure 4 (a) Input vibration time-domain signal; Figure 4 (b) The processed signal result; Figure 4 (c) A magnified view of the envelope spectrum of the processed signal; Figure 4 (d) The degree of correlation between all IMFs and the original signal.

[0046] Figure 5 The MCKD method processes the simulated signal. Among other things, Figure 5 (a) Input vibration time-domain signal; Figure 5 (b) The processed signal result; Figure 5 (c) A magnified view of the envelope spectrum of the processed signal; Figure 5 (d) Correlation kurtosis during the iteration process.

[0047] Figure 6 The proposed method processes the simulation signal. Among other things, Figure 6 (a) Input vibration time-domain signal; Figure 6 (b) The PSD distribution obtained after processing the original signal; Figure 6 (c) The processed signal result; Figure 6 (d) A magnified view of the envelope spectrum of the processed signal; 3. Experimental verification To verify the effectiveness of the proposed method, this invention uses experimentally measured vibration data from an experimental platform provided by the Bearing Data Center at Case Western Reserve University (CWRU) for experimental analysis. A schematic diagram of the experimental setup is shown below. Figure 7 As shown, it mainly consists of a three-phase induction motor, a torque sensor, and a dynamometer. The study selects the acceleration data of a faulty rolling element bearing at the motor fan end as the analysis object; the fault size is 1.778 mm. The bearing used is a 6203-2RS deep ball bearing, with structural parameters including: rolling element diameter 6.75 mm, pitch diameter 28.5 mm, and 8 rolling elements. Based on these parameters, the theoretical fault frequencies of the inner ring and rolling elements can be calculated to be 162.19 Hz and 141.17 Hz, respectively.

[0048] To effectively extract fault features from bearing vibration signals under strong noise backgrounds, this invention compares the proposed method with four advanced signal processing techniques: empirical mode decomposition, variational mode decomposition, fast kurtosis plotting, and maximum correlation kurtosis deconvolution. Their performance is evaluated under a uniform -2dB additive white Gaussian noise background. The parameter settings for each method are the same as in Section 3.

[0049] The processing results of each method are as follows: Figures 8 to 12 As shown. Figure 8 The fast kurtosis plot method can effectively identify the first-order characteristic frequency of inner ring faults, but the fault harmonic components are not shown in its envelope spectrum. Figure 9 The empirical mode decomposition method identifies the first IMF as a sensitive component, and its envelope spectrum clearly extracts the first three fault characteristics. However, due to its excessively wide filtering bandwidth, the analysis band contains a lot of irrelevant frequency components. Figure 10 The variational mode decomposition results are severely affected by noise, resulting in unsatisfactory feature extraction. Figure 11 The maximum correlation kurtosis deconvolution method also successfully extracted the first three fault features, but its effective bandwidth is still relatively wide, similar to EMD, and it suffers from the problem of extracting too many component elements. In contrast, the method proposed in this invention benefits from its bandwidth adaptive segmentation strategy, resulting in an extremely clear envelope spectrum that contains almost only significant first three fault feature frequency components, effectively suppressing irrelevant interference. This characteristic makes it more suitable for real-time condition monitoring and accurate feature extraction in practical engineering applications, helping to significantly reduce the risk of false alarms and missed alarms.

[0050] Figure 8 The results of processing the CWRU inner ring signal using the Kurtogram method. Among them, Figure 8 (a) kurtogram; Figure 8 (b) Input vibration time-domain signal; Figure 8 (c) The processed signal result; Figure 8 (d) A magnified view of the envelope spectrum of the processed signal.

[0051] Figure 9 The EMD method is used to process the inner ring signal of the CWRU. Figure 9 (a) Input vibration time-domain signal; Figure 9 (b) The processed signal result; Figure 9 (c) A magnified view of the envelope spectrum of the processed signal; Figure 9 (d) The degree of correlation between all IMFs and the original signal.

[0052] Figure 10 The VMD method is used to process the inner ring signal of the CWRU. Figure 10 (a) Input vibration time-domain signal; Figure 10 (b) The processed signal result; Figure 10 (c) A magnified view of the envelope spectrum of the processed signal; Figure 10 (d) The degree of correlation between all IMFs and the original signal.

[0053] Figure 11 The processing results of the CWRU inner ring signal using the MCKD method. Figure 11 (a) Input vibration time-domain signal; Figure 11 (b) The processed signal result; Figure 11 (c) A magnified view of the envelope spectrum of the processed signal; Figure 11 (d) Relevant kurtosis during the iterative process.

[0054] Figure 12 The proposed method is used to process the inner ring signal of the CWRU. Figure 12 (a) Input vibration time-domain signal; Figure 12 (b) The PSD distribution obtained after processing the original signal; Figure 12 (c) The processed signal result; Figure 12 (d) A magnified view of the envelope spectrum of the processed signal.

[0055] Subsequently, the effectiveness of the proposed method was verified using CWRU rolling element bearing fault data, and compared with several existing methods. The experiment used a signal length of 12,000 points, corresponding to a duration of 1 second. The processing results of each method are as follows: Figures 13 to 17 As shown. By Figure 13 It is evident that the envelope spectrum obtained based on the fast kurtosis method has low frequency amplitudes for fault features and the entire frequency band is subject to strong noise interference, making it difficult to effectively extract fault features. Figure 14 In the EMD method, the second IMF component is identified as a sensitive component, but its envelope spectrum still fails to clearly show the fault frequency component. Figure 15The results show that the VMD method identifies the last IMF component as a sensitive component and can extract the first two fault features from the signal, but the amplitudes of other frequency components are also quite significant, indicating some interference. Figure 16 and Figure 17 The envelope spectrum analysis results are shown for the MCKD method and the proposed method, respectively. Both methods can effectively identify the first two fault characteristics with minimal interference from other frequency components. However, the MCKD method requires multiple iterations, resulting in lower computational efficiency; in contrast, the proposed method maintains diagnostic performance while achieving superior computational efficiency.

[0056] Figure 13 The results of processing CWRU rolling element signals using the Kurtogram method. Figure 13 (a) kurtogram; Figure 13 (b) Input vibration time-domain signal; Figure 13 (c) The processed signal result; Figure 13 (d) A magnified view of the envelope spectrum of the processed signal.

[0057] Figure 14 The EMD method is used to process the CWRU rolling body ring signal. Figure 14 (a) Input vibration time-domain signal; Figure 14 (b) The processed signal result; Figure 14 (c) A magnified view of the envelope spectrum of the processed signal; Figure 14 (d) The degree of correlation between all IMFs and the original signal.

[0058] Figure 15 The VMD method is used to process the CWRU rolling body ring signal. Figure 15 (a) Input vibration time-domain signal; Figure 15 (b) The processed signal result; Figure 15 (c) A magnified view of the envelope spectrum of the processed signal; Figure 15 (d) The degree of correlation between all IMFs and the original signal.

[0059] Figure 16 The processing results of the CWRU rolling element signal using the MCKD method. Figure 16 (a) Input vibration time-domain signal; Figure 16 (b) The processed signal result; Figure 16 (c) A magnified view of the envelope spectrum of the processed signal; Figure 16 (d) Relevant kurtosis during the iterative process.

[0060] Figure 17 The proposed method is used to process the CWRU rolling element signal. Figure 17 (a) Input vibration time-domain signal; Figure 17 (b) The PSD distribution obtained after processing the original signal; Figure 17 (c) The processed signal result; Figure 17 (d) A magnified view of the envelope spectrum of the processed signal.

[0061] 4. Conclusion This invention addresses the challenges of fault diagnosis in rolling bearings of hydroelectric generators under complex operating conditions, and overcomes the reliance of traditional methods on prior knowledge and manual parameter settings. It proposes a fully adaptive fault-sensitive frequency band identification method. This method, through a systematic "segmentation-evaluation-decision" process, automatically and accurately extracts the resonant frequency band with the most fault information from vibration signals. The main conclusions and advantages of this invention are summarized as follows: (1) By estimating the smooth power spectrum of the signal and using an improved local extremum detection algorithm, this method can adaptively divide candidate frequency bands with clear physical meaning based on the signal's own spectral structure. This process avoids the subjectivity of traditional fixed filter banks and lays a solid foundation for subsequent analysis.

[0062] (2) A threshold decision mechanism based on maximizing inter-class variance is introduced, which can automatically determine the optimal segmentation threshold according to the score distribution, and finally achieve sensitive frequency band screening without any manual intervention. This solves the key problem that parameter setting in traditional methods depends on expert experience, and significantly improves the automation level and engineering applicability of the method.

[0063] (3) The results show that the method can still accurately and stably locate the fault-sensitive frequency band under strong noise background and successfully extract clear fault feature frequencies, which proves its excellent robustness and adaptability.

[0064] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. An application of an adaptive fault-sensitive frequency band identification method in fault diagnosis of hydropower units, characterized in that, Includes the following steps: (1) Perform trend elimination processing on the vibration signal of the rolling bearing of the hydropower unit to remove baseline drift; (2) The power spectral density of the vibration signal is estimated by Welch method and then smoothed by adaptive moving mean to obtain a smoothed spectrum; (3) Based on the local valley points of the smooth spectrum, adaptive segmentation of the frequency band is performed to obtain candidate frequency bands; (4) Perform bandpass filtering on each candidate frequency band, extract the kurtosis and envelope spectral entropy of each frequency band, and construct a weighted comprehensive scoring index after normalization to obtain the score vector of all candidate frequency bands; (5) Determine the adaptive threshold based on the strategy of maximizing inter-class variance, and select the sensitive frequency band according to the score vector and the adaptive threshold; (6) Perform envelope demodulation analysis on the sensitive frequency band and output the fault diagnosis results of the rolling bearing of the hydropower unit.

2. The application of the adaptive fault-sensitive frequency band identification method according to claim 1 in the fault diagnosis of hydropower units, characterized in that, The process of estimating the power spectral density using the Welch method in step (2) is as follows: A discrete-time signal x[n] of length N is divided into i segments, each of length M. Then the signal in segment i is... i [m] is represented as: ； Where D is the overlap length between the segmented signals. A Hanning window of length M is used. The segmented signals are processed separately to obtain the windowed signals. : ； For windowed signals Perform a discrete Fourier transform and calculate its periodogram. The periodogram of the k-th segment can be expressed as: ； The i-th periodic plot is averaged to obtain the final power spectral density estimate: ； The power spectrum estimation window length of the Welch method is 1024, and the overlap length is 512.

3. The application of the adaptive fault-sensitive frequency band identification method according to claim 1 in the fault diagnosis of hydropower units, characterized in that, The adaptive frequency band segmentation process described in step (3) is as follows: right Apply adaptive moving mean smoothing: ； in Frequency points, smoothing window length Adaptive adjustment with signal length ensures that over-smoothing is not achieved at high resolution, and smooths the spectrum. Find local valleys as frequency band boundaries: ； Take the one with the highest significance points ( ), forming a selected index set The final set of frequency band boundaries is: ； in Indicates index The corresponding frequency values ​​are arranged in ascending order of their boundaries.

4. The application of the adaptive fault-sensitive frequency band identification method according to claim 1 in the fault diagnosis of hydropower units, characterized in that, The bandpass filtering in step (4) uses a fourth-order Butterworth zero-phase bandpass filter to obtain the sub-signal. .

5. The application of the adaptive fault-sensitive frequency band identification method according to claim 1 in the fault diagnosis of hydropower units, characterized in that, The kurtosis mentioned in step (4) is a statistical measure of the signal's deviation from a Gaussian distribution and is sensitive to weak periodic shocks; the envelope spectral entropy is obtained through the envelope signal. One-sided FFT spectrum The calculated entropy, used to assess the orderliness of the energy distribution in the envelope spectrum, is... A smaller value indicates a higher degree of ordered aggregation of information; the normalization of the envelope spectrum entropy is performed by inverse normalization with 3 as the baseline, and the normalized value is... The larger the value, the more concentrated the information.

6. The application of the adaptive fault-sensitive frequency band identification method according to claim 1 in the fault diagnosis of hydropower units, characterized in that, In step (4), the kurtosis weight of the weighted comprehensive scoring index is 0.4, and the envelope spectral entropy weight is 0.

6. These weights are determined by analyzing 10 sets of measured data using a particle swarm optimization algorithm. The comprehensive score S... i The weighted sum of the normalized kurtosis and the envelope spectral entropy: .

7. The application of the adaptive fault-sensitive frequency band identification method according to claim 1 in the fault diagnosis of hydropower units, characterized in that, The inter-class variance mentioned in step (5): ； in, It is a background class The proportion; Is it a foreground category? The proportion; and These are the mean scores for the background and foreground categories, respectively.

8. The application of the adaptive fault-sensitive frequency band identification method according to claim 1 in the fault diagnosis of hydropower units, characterized in that, The process of determining the adaptive threshold in step (5) is as follows: The first step is to initialize the optimal separation to 0 and the initial threshold to 0.5; The second step involves traversing the [0.3, 0.7] interval with a step size of 0.

05. For each candidate threshold, the frequency band is divided into two groups: and If the current separation is greater than the historical best value, then update the optimal threshold and the optimal separation. The third step is to restore the found optimal normalization threshold to the true rating scale: S_max is the maximum value in the score vector.

9. The application of the adaptive fault-sensitive frequency band identification method according to claim 1 in the fault diagnosis of hydropower units, characterized in that, When screening sensitive frequency bands in step (5), the frequency band with the highest comprehensive score is selected as the optimal frequency band, and envelope demodulation analysis is performed on the optimal frequency band.

10. The application of the adaptive fault-sensitive frequency band identification method according to claim 1 in the fault diagnosis of hydropower units, characterized in that, The vibration signal includes periodic pulses caused by local defects in the rolling bearing, system harmonic interference, random pulses generated by external impacts, and environmental noise. The fault diagnosis results include fault characteristic frequencies and their multi-order components.

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