A variable speed condition train wheel bearing fault diagnosis method and system
By employing an adaptive segmentation and filter bank construction method, combined with a time-frequency harmonic signal-to-noise ratio matrix, the problem of difficulty in extracting wheel bearing fault characteristics under variable speed conditions was solved, achieving highly accurate fault diagnosis.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHIJIAZHUANG TIEDAO UNIV
- Filing Date
- 2026-03-09
- Publication Date
- 2026-06-05
AI Technical Summary
Under variable speed conditions, the non-stationary characteristics and noise interference of wheelset bearing vibration signals make it difficult to extract fault features. The evaluation indicators of existing methods have poor robustness, and traditional periodic indicators are not applicable.
The vibration signal is adaptively segmented using a spectral trend function. An adaptive filter bank is constructed by combining empirical wavelet transform and short-time Fourier transform. The cumulative time-frequency harmonic signal-to-noise ratio matrix is calculated, and the characteristic frequency trend line of potential instantaneous faults is extracted. The bearing fault type is determined by the time-frequency harmonic signal-to-noise ratio matrix of the optimal demodulated signal.
It improves the accuracy of wheelset bearing fault diagnosis under variable speed conditions, overcomes the problem of difficulty in extracting instantaneous fault characteristic frequency ridges in traditional methods, and realizes effective extraction and accurate judgment of fault features.
Smart Images
Figure CN122153591A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of rail transit fault diagnosis technology, and in particular to a method and system for diagnosing train wheelset bearing faults under variable speed operating conditions. Background Technology
[0002] Wheelset bearings are one of the core components of a train's running gear. During actual train service, frequent starts, stops, accelerations, and decelerations cause wheelset bearings to operate at variable speeds for extended periods. Compared to constant-speed conditions, the vibration signals of wheelset bearings under variable-speed conditions exhibit significant non-stationary characteristics and are easily affected by wheel-rail noise, making it difficult to extract wheelset bearing fault characteristics.
[0003] Resonance demodulation technology is widely used for feature extraction of bearing faults under strong background noise. This method selects a resonant frequency band containing rich fault feature information for bandpass filtering and envelope demodulation analysis, which can reduce the interference of strong background noise and effectively extract fault features. However, in variable speed scenarios: on the one hand, blind indicators such as kurtosis, Gini index, and entropy have weak noise resistance and are easily affected by random impacts, resulting in poor robustness of evaluation indicators for selecting the optimal demodulation frequency band and easy selection of incorrect frequency bands; on the other hand, since the bearing fault impact signal under variable speed conditions no longer has periodic characteristics, periodic indicators based on the fault period or fault feature frequency cannot be applied to variable speed conditions. Summary of the Invention
[0004] The purpose of this invention is to provide a method for diagnosing train wheelset bearing faults under variable speed conditions, which improves the accuracy of fault diagnosis for train wheelset bearings under variable speed conditions.
[0005] To achieve the above objectives, the present invention provides the following technical solution:
[0006] A method for diagnosing train wheelset bearing faults under variable speed operating conditions includes:
[0007] The vibration signal of the bearing is loaded and converted into a spectrum signal. The spectrum signal is adaptively segmented based on the spectrum trend function to obtain the segmentation boundary of the spectrum signal.
[0008] Empirical wavelet transform is introduced, and an adaptive filter bank is constructed based on the spectrum signal segmentation boundary to decompose and reconstruct the vibration signal, thereby obtaining the demodulated signal of the vibration signal;
[0009] Short-time Fourier transform is introduced to calculate the envelope time-frequency distribution of the demodulated signal and the time-frequency harmonic signal-to-noise ratio matrix of the envelope time-frequency distribution. Based on the time-frequency harmonic signal-to-noise ratio matrix, the cumulative time-frequency harmonic signal-to-noise ratio value of each demodulated signal is calculated. The demodulated signal with the largest cumulative time-frequency harmonic signal-to-noise ratio value is selected as the optimal demodulated signal. Based on the maximum value of the time-frequency harmonic signal-to-noise ratio matrix of the optimal demodulated signal under different time slices, the potential instantaneous fault characteristic frequency trend line is extracted.
[0010] The optimal demodulated signal is resampled at an angle and subjected to spectral analysis based on the instantaneous fault characteristic frequency trend line to obtain the order ratio spectrum. The bearing fault type is determined based on the fault characteristic coefficients and the order ratio spectrum.
[0011] More specifically, the vibration signal is converted into a spectral signal, and the spectral signal is adaptively segmented based on a spectral trend function to obtain the segmentation boundary of the spectral signal, specifically including:
[0012] Perform a Fourier transform on the vibration signal of the bearing to obtain the spectral signal of the vibration signal;
[0013] The amplitude spectrum of the spectral signal is discretized into a non-negative sequence, and a discrete Fourier transform is performed on the non-negative sequence to obtain the key function;
[0014] By reconstructing a portion of the data points of the key function, a spectral trend function is obtained;
[0015] The minimum value of the spectral trend function is selected as the spectral segmentation boundary.
[0016] More specifically, an adaptive filter bank is constructed based on the spectral signal segmentation boundary to decompose and reconstruct the vibration signal, obtaining the demodulated signal of the vibration signal, specifically including:
[0017] The empirical scaling function and empirical wavelet function are calculated based on the spectral signal segmentation boundary and empirical wavelet transform.
[0018] The detail coefficients and approximation coefficients of the empirical wavelet are obtained based on the empirical scaling function and the empirical wavelet function.
[0019] The demodulated signal of the vibration signal is obtained based on the empirical scaling function, empirical wavelet function, detail coefficients, and approximation coefficients.
[0020] More specifically, the empirical scaling function and empirical wavelet function, calculated based on the spectral signal segmentation boundary and empirical wavelet transform, are derived from the following formula: ; ;
[0021] In the formula, Represents the empirical scaling function; Represents the empirical wavelet function; ω n Let β(x) be the segmentation boundary of the spectral signal, β(x) be the transition function, and γ be the coefficient, with a value range of [value missing]. .
[0022] More specifically, the step of introducing a short-time Fourier transform to calculate the envelope time-frequency distribution of the demodulated signal and the time-frequency harmonic signal-to-noise ratio matrix of the envelope time-frequency distribution specifically includes:
[0023] A sliding window algorithm is introduced into the demodulated signal, and the short-time Fourier transform is used to calculate the demodulated signal within the window to obtain the envelope time-frequency distribution of the demodulated signal;
[0024] Based on the cumulative signal-to-noise ratio of the fundamental frequency and harmonics in each time slice of the envelope time-frequency distribution, a time-frequency harmonic signal-to-noise ratio matrix is constructed.
[0025] More specifically, the short-time Fourier transform is introduced to calculate the time-frequency distribution of the envelope of the demodulated signal, which is obtained by the following formula: ;
[0026] In the formula, G k (τ,ω) represents the envelope time-frequency distribution of the narrowband signal; This represents the magnitude of the analytic signal obtained after the Hilbert transform of the k-th demodulated signal; Indicates that the center is located at The window function at time step.
[0027] More specifically, based on the cumulative signal-to-noise ratio (SNR) of the fundamental frequency and harmonics in each time slice of the envelope time-frequency distribution, a time-frequency harmonic SNR matrix is constructed and calculated using the following formula: ;
[0028] In the formula, TFHSNRM k (t,f) represents the time-frequency harmonic signal-to-noise ratio matrix; H represents the harmonic accumulation order; The expression indicates taking the absolute value; `max` indicates taking the maximum value. This indicates the harmonic tolerance band.
[0029] More specifically, the extracted potential instantaneous fault feature frequency trend line is calculated by the following formula: ;
[0030] In the formula, This represents the instantaneous fault characteristic frequency of the k-th demodulated signal at time t. This represents the time-frequency harmonic signal-to-noise ratio matrix value of the k-th demodulated signal; This represents the frequency value f that maximizes the time-frequency harmonic signal-to-noise ratio matrix at a given time t.
[0031] Compared with the prior art, the train wheelset bearing fault diagnosis method under variable speed conditions provided by the present invention has the following beneficial effects:
[0032] This invention proposes a novel evaluation metric—cumulative time-frequency harmonic signal-to-noise ratio (CNR). This metric fully utilizes the fault characteristic harmonics of each time slice in the time-frequency distribution of the envelope signal, effectively quantifying the fault characteristic intensity in variable-speed signals. Essentially a periodic metric, it is suitable for situations with strong background noise and a lack of prior knowledge such as speed information. Furthermore, based on the maximum values of the CNR matrix of the optimal demodulated signal in different time slices, a potential instantaneous fault characteristic frequency trend line is extracted. This overcomes the difficulty in extracting instantaneous fault characteristic frequency ridges in traditional time-frequency analysis methods, effectively improving the fault characteristic extraction effect and fault category determination accuracy of wheel-pair bearings under variable-speed conditions.
[0033] This invention also provides a train wheelset bearing fault diagnosis system for variable speed operating conditions, employing the aforementioned train wheelset bearing fault diagnosis method for variable speed operating conditions. The system includes:
[0034] The signal loading unit is used to load the vibration signal of the bearing, convert the vibration signal into a spectrum signal, and adaptively segment the spectrum signal based on the spectrum trend function to obtain the segmentation boundary of the spectrum signal;
[0035] The signal demodulation unit is used to introduce empirical wavelet transform and construct an adaptive filter bank based on the signal spectrum segmentation boundary to decompose and reconstruct the vibration signal to obtain the demodulated signal of the vibration signal.
[0036] The calculation unit introduces short-time Fourier transform to calculate the envelope time-frequency distribution of the demodulated signal and the time-frequency harmonic signal-to-noise ratio matrix of the envelope time-frequency distribution. Based on the time-frequency harmonic signal-to-noise ratio matrix, it calculates the cumulative time-frequency harmonic signal-to-noise ratio value of each demodulated signal, selects the demodulated signal with the largest cumulative time-frequency harmonic signal-to-noise ratio value as the optimal demodulated signal, and extracts the potential instantaneous fault characteristic frequency trend line based on the maximum value of the time-frequency harmonic signal-to-noise ratio matrix of the optimal demodulated signal under different time slices.
[0037] The fault determination unit is used to perform angle resampling and spectral analysis on the optimal demodulated signal in the demodulated signal according to the instantaneous fault characteristic frequency trend line to obtain the order ratio spectrum, and to determine the bearing fault type according to the fault characteristic coefficient and the order ratio spectrum.
[0038] Compared with the prior art, the beneficial effects of the train wheelset bearing fault diagnosis system under variable speed conditions provided by the present invention are the same as the beneficial effects of the train wheelset bearing fault diagnosis system method under variable speed conditions described in the above technical solution, and will not be repeated here. Attached Figure Description
[0039] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 A flowchart of a method provided by the present invention; Figure 2 The time-domain waveform, spectrum, and envelope spectrum of the wheelset bearing inner ring fault signal in this embodiment of the invention are shown. Figure 2 (a) is the time-domain waveform of the inner ring fault signal of the wheelset bearing in an example of the present invention; Figure 2 (b) shows the waveform of the fault signal spectrum of the inner ring of the wheelset bearing in the example of the present invention, analyzed across the entire frequency range; Figure 2 (c) shows the waveform of the envelope spectrum of the wheelset bearing inner ring fault signal in the low-frequency range in an example of the present invention; Figure 3 This is the result of frequency band division and optimal demodulation signal selection based on the spectral trend function in an example of the present invention; Figure 4 This is the short-time Fourier transform of the optimal demodulated signal envelope in the example of this invention; Figure 5 This is a potential instantaneous fault characteristic frequency trend line in the examples of this invention; Figure 6 This is the order ratio spectrum in an example of the present invention. Detailed Implementation
[0040] It should be noted that in this invention, the terms "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in this invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.
[0041] The embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.
[0042] like Figure 1 As shown in the figure, this embodiment of the invention provides a method for diagnosing train wheelset bearing faults under variable speed conditions, and its main process is described as follows.
[0043] Step S1: Load the vibration signal of the bearing and convert the vibration signal into a spectrum signal. Adaptively segment the spectrum signal based on the spectrum trend function to obtain the segmentation boundary of the spectrum signal.
[0044] During bearing operation, defects in the raceways or rolling elements of the inner and outer rings will lead to repeated collisions and transient impacts. These fault impacts will cause resonance in the bearing system and modulate the fault characteristics to mid / high frequencies. The frequency components within the resonance band exhibit a distinct "haystack" phenomenon, i.e., high-amplitude frequency clustering. Therefore, the fluctuation trend of the Fourier spectrum can effectively characterize the distribution characteristics of different feature components in the frequency domain. By identifying significant fluctuation regions in the spectral signal, fault modes can be effectively distinguished from interference components. Compared to traditional uniform partitioning strategies (such as the 1 / 3 binary tree method), this adaptive partitioning method is more reasonable and has a clear physical meaning, specifically including the following calculation steps:
[0045] Step S11: Perform a Fourier transform on the vibration signal of the bearing to obtain the spectrum signal of the vibration signal.
[0046] Assuming the bearing fault impact signal containing noise at any time t is x(t), the formula for calculating the absolute value after performing a Fourier transform is as follows: ;
[0047] In the formula, A(f) is the amplitude spectrum of the vibration signal; X ( f The result is the Fourier transform of the vibration signal. t represents the absolute value; x(t) represents the bearing fault impact signal; j is the imaginary part.
[0048] Step S12: Discretize the amplitude spectrum of the spectral signal into a non-negative sequence, and perform a discrete Fourier transform on the non-negative sequence to obtain the key function.
[0049] Here, the non-negative sequence is A(n) (where n = 0, 1, 2, 3, ..., L-1). This non-negative sequence A(n) is considered as a new signal, and L is the length of the new signal. The formula for calculating the Discrete Fourier Transform of this non-negative sequence is as follows: ;
[0050] In the formula, K(u) represents the key function (where u = 0, 1, 2, 3, ..., L-1); j represents the imaginary part.
[0051] Step S13: Reconstruct some data points of the key function to obtain the spectral trend function.
[0052] The spectral trend function can be derived from the following formula: ;
[0053] In the formula, T i (f) represents the spectral trend function; j represents the imaginary part; This indicates taking the absolute value; i represents the number of reconstructed points.
[0054] Step S14: Select the minimum value of the spectral trend function as the segmentation boundary of the spectral signal.
[0055] Due to the trend spectrum T i (f) The peak value of the spectral signal component of the bearing is well-fitted. Selecting the minimum value of the spectral trend function as the segmentation boundary of the spectral signal allows for adaptive segmentation of the spectral signal. The number of reconstructed points, i, determines the smoothness of the spectral trend. i When the value is small (e.g., less than 5), the reconstructed spectrum trend is relatively smooth, and it contains fewer minimum points, making it difficult to achieve effective narrowband division of the spectrum. i As the value gradually increases, the spectral trend becomes more complex, and the number of local minima, i.e., spectral segmentation boundaries, also increases. However, excessively large values... i Excessive subdivision of the spectrum can lead to redundant modal components, which not only increases computational overhead but may also cause the effective characteristic information of bearing failures to be scattered or destroyed.
[0056] In order to fully preserve the effective fault components in the signal, in this embodiment, the maximum number of frequency bands to be divided is set to: ; In the formula: Fs Sampling frequency, This indicates the characteristic frequency of the maximum inner ring failure in the bearing. Indicates rounding down. Number of reconstructed points. i The initial value is 5, which is gradually increased in increments of 1, until... i The optimal value is determined based on the maximum value achieved while satisfying the narrowband decomposition limit. Under the same speed conditions, the inner ring has the highest fault characteristic frequency among the three parts of the bearing: outer ring, inner ring, and rollers. That is, at a speed of 350 km / h, the theoretical maximum fault characteristic frequency of the bearing inner ring will be reached, which is also the theoretical maximum value of the fault characteristic frequency that the three parts of the bearing will reach. The purpose of dividing in the above formula is to ensure that the average value of the divided frequency band bandwidth is three times the theoretical maximum fault characteristic frequency, which can fully preserve the effective fault components in the signal.
[0057] Step S2: Introduce empirical wavelet transform and construct an adaptive filter bank based on the segmentation boundary to decompose and reconstruct the spectral signal to obtain the demodulated signal of the vibration signal.
[0058] After obtaining the spectral segmentation boundary, adaptive narrowband signal extraction is achieved using empirical wavelet transform. Empirical wavelet transform treats the amplitude spectrum A(f) of the vibration signal as a set of continuous frequency bands, each corresponding to a mode with a specific center frequency. Specifically, obtaining the demodulated signal of the vibration signal includes the following steps:
[0059] Step S21: Calculate the empirical scaling function and empirical wavelet function based on the spectral signal segmentation boundary and empirical wavelet transform.
[0060] Based on the Littlewood-Paley and Meyer wavelets, we construct empirical wavelets and define the empirical scaling function. and empirical wavelet function for: ; ;
[0061] In the formula, Represents the empirical scaling function; Represents the empirical wavelet function; ω n The spectral boundary is defined by β(x); β(x) is the transition function, typically taking the value... γ is a coefficient, and its range is... .
[0062] Step S22: Obtain the detail coefficients and approximation coefficients of the empirical wavelet based on the empirical scaling function and the empirical wavelet function.
[0063] The detail coefficients and approximation coefficients of the empirical wavelet are represented by the following formula: ; ;
[0064] In the formula, Represents the detail coefficients of the empirical wavelet. The symbols above the characters represent the approximation coefficients of the empirical wavelet; the symbol "^" above the characters indicates the Fourier transform; the symbol "-" above the characters indicates the complex conjugate; the symbol " " indicates the inverse Fourier transform.
[0065] Step S23: Obtain the demodulated signal of the vibration signal based on the empirical scaling function, empirical wavelet function, detail coefficients, and approximation coefficients.
[0066] Combining the above formulas, the reconstruction formula for the vibration signal can be expressed as the demodulated signal of the vibration signal, as shown in the following equation: ;
[0067] In the formula: The demodulated signal represents the vibration signal; ^ represents Fourier transform; * represents convolution. This represents the inverse Fourier transform.
[0068] After obtaining the segmentation boundary, the above process can be used to construct an adaptive filter bank to complete the decomposition and reconstruction of the vibration signal. At the same time, the original vibration signal can be adaptively decomposed into modes with consistent frequency resolution, avoiding the limitations of fixed parameters in traditional wavelet transform.
[0069] Step S3: Introduce short-time Fourier transform to calculate the envelope time-frequency distribution of the demodulated signal and the time-frequency harmonic signal-to-noise ratio matrix of the envelope time-frequency distribution. Calculate the cumulative time-frequency harmonic signal-to-noise ratio value of each demodulated signal based on the time-frequency harmonic signal-to-noise ratio matrix. Select the demodulated signal with the largest cumulative time-frequency harmonic signal-to-noise ratio value as the optimal demodulated signal. Based on the maximum value of the time-frequency harmonic signal-to-noise ratio matrix of the optimal demodulated signal under different time slices, extract the potential instantaneous fault characteristic frequency trend line.
[0070] For the k-th demodulated signal First, the analytic signal of the demodulated signal is constructed using the Hilbert transform. The specific calculation process is shown in the following formula: ; ;
[0071] In the formula, The Hilbert transform signal representing the demodulated signal; Represents the Hilbert transform; Let represent the analytic signal of the k-th demodulated signal; j is the imaginary part. Here, is the analytic signal used to construct the demodulated signal. Used to prepare for calculating the short-time Fourier transform.
[0072] The short-time Fourier transform algorithm is widely used due to its computational simplicity and ability to intuitively reflect the time-varying distribution of energy. By introducing a sliding time window, non-stationary signals are treated as stationary over a short period of time, and a Fourier transform is performed on the data within the window to construct a time-varying spectrum. Based on this short-time stationarity assumption, the "short-time spectrum" obtained in each window can be approximated as the "envelope spectrum of the stationary signal" at that moment.
[0073] In this embodiment, the calculation of the envelope time-frequency distribution of the demodulated signal and the time-frequency harmonic signal-to-noise ratio matrix of the envelope time-frequency distribution specifically includes the following steps:
[0074] Step S31: Introduce a sliding window algorithm into the demodulated signal, and use the short-time Fourier transform to calculate the demodulated signal within the window to obtain the envelope time-frequency distribution of the demodulated signal. The calculation process is as follows: ;
[0075] In the formula, G k (τ,ω) represents the time-frequency distribution of the envelope of the demodulated signal; This represents the magnitude of the analytic signal obtained after the Hilbert transform of the k-th demodulated signal; Indicates that the center is located at The window function at time step.
[0076] In applications of short-time Fourier transform, the time-frequency resolution and the effectiveness of fault feature extraction are highly dependent on the selection of window length and overlap rate. To balance the localization characteristics in both the time and frequency domains, this embodiment selects a window length of 5% of the total signal length and sets an 85% overlap rate between adjacent windows. This aims to significantly enhance the continuity of the envelope time-frequency distribution without introducing excessive computational burden.
[0077] Step S32: Construct a time-frequency harmonic signal-to-noise ratio matrix based on the cumulative signal-to-noise ratio of the fundamental frequency and harmonics in each time slice of the envelope time-frequency distribution.
[0078] Specifically, for any time slice in the envelope time-frequency distribution, if a certain frequency f is assumed to be the potential fundamental frequency, then its Time-Frequency Harmonic Signal-to-Noise Ratio Matrix (TFHSNRM) is defined as the cumulative set of ratios between the peak energy of each harmonic and the average energy of the local background noise of the harmonics. The calculation formula is as follows: ;
[0079] In the formula, TFHSNRM k (t,f) represents the time-frequency harmonic signal-to-noise ratio matrix; H represents the harmonic accumulation order, which is set to 3 in this embodiment. The expression indicates taking the absolute value; `max` indicates taking the maximum value. mean This indicates taking the average value; hf Indicates input frequency f The h order; Δf h This indicates the harmonic tolerance band, which is set to a tolerance band of 0.02f to accommodate the frequency shift of each harmonic.
[0080] To achieve robust extraction of wheel bearing fault characteristics under variable speed conditions, quantitative evaluation of fault information contained in different demodulated signals, and selection of the most diagnostically valuable components, a Cumulative Time-Frequency Harmonic Signal-to-Noise Ratio (CTFHSNR) index is defined based on TFHSNRM. The CTFHSNR is a novel index applicable to variable speed conditions proposed in this invention based on the harmonic characteristics of each time slice of the envelope time-frequency distribution. This index can adaptively quantify fault information in each narrowband signal, which helps to accurately locate the resonant frequency band.
[0081] The formula for calculating the cumulative time-frequency harmonic signal-to-noise ratio (CTFHSNR) is as follows: ;
[0082] Where M is the total number of discrete time series in the time-frequency distribution, i.e., the number of time slices; max represents taking the maximum value.
[0083] A higher CTFHSNR value means that the fault characteristics contained in the narrowband signal are more obvious. Therefore, the maximum value of CTFHSNR is selected as the optimal demodulation frequency band.
[0084] Based on the short-time stationarity assumption of the short-time Fourier transform, the signal within any time slice can be considered a constant-velocity signal. Therefore, based on TFHSNRM, the most dominant modulation component in different time slices can be effectively located, thereby estimating the potential instantaneous fault characteristic frequency trend line in the time-frequency distribution of the demodulated signal envelope: ;
[0085] In the formula, This represents the instantaneous fault characteristic frequency of the k-th demodulated signal at time t. This represents the time-frequency harmonic signal-to-noise ratio matrix value of the k-th demodulated signal; This represents the frequency value f that maximizes the time-frequency harmonic signal-to-noise ratio matrix at a given time t.
[0086] Step S4: Based on the instantaneous fault characteristic frequency trend line, perform angle resampling and spectral analysis on the optimal demodulated signal in the demodulated signal to obtain the order ratio spectrum. Determine the bearing fault type based on the fault characteristic coefficients and the order ratio spectrum.
[0087] The bearing failure factor is calculated based on the structural parameters of the rolling bearing and is a constant value, namely: ; ; ; ;
[0088] In the formula: f r Instantaneous Rotational Frequency (IFr); n F is the bearing rotational speed. i F o F b These are the Fault Characteristic Coefficients (FCCs) for the inner ring, outer ring, and rollers of the bearing, respectively; f i f o f b These are the instantaneous fault characteristic frequencies (IFCF) of the inner ring, outer ring, and roller, respectively; f r IFr is the instantaneous rotational frequency; d is the rolling element diameter; D is the bearing pitch diameter; a is the contact angle; and Z is the number of rolling elements.
[0089] Therefore, when the rotational speed of a rolling bearing changes dynamically over time, its fault characteristic frequency changes synchronously with the rotational frequency, and the proportional relationship between the two remains constant. This characteristic makes the bearing's fault characteristic frequency an equivalent parameter that can replace the rotational frequency.
[0090] Based on the instantaneous fault characteristic frequency trend line, angle resampling and spectral analysis can be performed on the optimal demodulated signal to obtain the order spectrum. Since the order spectrum is essentially a compressed version of the classical angular domain order spectrum, the horizontal coordinates corresponding to the peak values of the fault characteristic frequencies are uniformly compressed to the unit "1". If the bearing under analysis has a fault, the peak values representing the fault characteristic frequencies and their harmonics in the order spectrum will be concentrated at the unit order ("1") and its harmonics ("2, 3, ..."). It should be noted that peak values at integer order positions in the order spectrum can only be used to determine if the rolling bearing under analysis has a fault, and cannot further distinguish the fault type. The rotational frequency order (RFO, denoted as: This method plays a crucial role in identifying the fault type of rolling bearings. The order value representing the rotational frequency is compressed to below the unit "1", and its horizontal axis value is the reciprocal of the corresponding fault characteristic coefficient (1 / FCC). The horizontal axis values corresponding to the octave peaks are 2 / FCC, 3 / FCC, and so on. Finally, by finding the fault characteristic coefficient corresponding to the reciprocal of the rotational frequency order in the order spectrum, the fault category of the rolling bearing can be determined.
[0091] The following examples demonstrate the effectiveness of the method of this invention:
[0092] Analyzing the measured signals of a high-speed railway wheelset bearing with an inner race fault, the main parameters of which are shown in Table 1 are presented. The analysis is performed using the formula... The inner ring fault characteristic coefficient F can be obtained by calculation. i =9.7, corresponding to the reciprocal of the fault characteristic coefficient, i.e., the first-order frequency response factor (RFO), which is 0.103. (This is derived from the formula...) The bearing's rotational frequency at 350 km / h is 33.8 Hz, calculated using the formula... The characteristic frequency of inner ring faults can be obtained. f i It is 328Hz (i.e., the characteristic frequency of the maximum inner ring failure of the bearing).
[0093]
[0094] The sampling frequency was set to 25600Hz, and the sampling duration was 10s. Calculations showed that the maximum number of frequency band divisions, m, was 13. The time-domain waveform, spectrum, and envelope spectrum of the test signal are as follows: Figure 2 As shown in (a)-(c), frequency blurring can be clearly observed in the envelope spectrum.
[0095] The experimental signals were processed using the method proposed in this invention. The results of narrowband division based on the spectral trend function and the calculation of CTFHSNR values for each demodulated signal are as follows: Figure 3 As shown in the figure, the CTFHSNR value corresponding to the third demodulated signal exhibits a significant peak, indicating that this demodulated signal contains the richest fault feature information, which is the optimal demodulated signal. Figure 3 The instantaneous fault characteristic frequency ridges are clear and continuous, and the harmonic ridges are clearly identifiable. Figure 4 The time-frequency distribution results of the optimal demodulated signal envelope are presented.
[0096] Based on the time-frequency harmonic signal-to-noise ratio matrix of the optimal demodulated signal (the 3rd narrowband signal), according to the formula... Extract its potential instantaneous fault characteristic frequency (IFCF) ridge, the results are as follows Figure 5 As shown.
[0097] The demodulated signal is resampled in the angular domain based on the potential instantaneous frequency trend line, and then Fourier transform is used to finally obtain the order spectrum that can be used for bearing fault diagnosis. The results are as follows: Figure 6 As shown. In Figure 6In the model, peak values with coordinates of 1.0, 1.998, 2.997, 3.996, 4.995, and 5.994 can be found at the unit fault characteristic order and its 2nd to 6th harmonics. In the region below the unit "1", peak values characterizing the bearing's rotational frequency order and its 2nd to 4th harmonics can be detected, and these values are approximately consistent with the theoretical rotational frequency order values of the bearing with the inner ring fault. Therefore, it can be determined that there is a fault in the inner ring of the bearing.
[0098] This invention employs a demodulation method based on the cumulative time-frequency harmonic signal-to-noise ratio (HFNR) index, which utilizes the resonant frequency band of the adaptive positioning wheelset bearing fault signal. Simultaneously, based on the maximum HFNR value under different time slices, it extracts the potential instantaneous fault characteristic frequency trend line from the optimal demodulated signal, overcoming the difficulty in extracting the instantaneous fault characteristic frequency ridge line in traditional time-frequency analysis methods. This effectively improves the accuracy of analyzing fault characteristics and fault categories in train wheelsets under variable speed conditions.
[0099] This invention also discloses a train wheelset bearing fault diagnosis system under variable speed operating conditions, employing the aforementioned train wheelset bearing fault diagnosis method under variable speed operating conditions. The system includes:
[0100] The signal loading unit is used to load the vibration signal of the bearing, convert the vibration signal into a spectrum signal, and adaptively segment the spectrum signal based on the spectrum trend function to obtain the segmentation boundary of the spectrum signal;
[0101] The signal demodulation unit is used to introduce empirical wavelet transform and construct an adaptive filter bank based on the signal spectrum segmentation boundary to decompose and reconstruct the vibration signal to obtain the demodulated signal of the vibration signal.
[0102] The calculation unit introduces short-time Fourier transform to calculate the envelope time-frequency distribution of the demodulated signal and the time-frequency harmonic signal-to-noise ratio matrix of the envelope time-frequency distribution. Based on the time-frequency harmonic signal-to-noise ratio matrix, it calculates the cumulative time-frequency harmonic signal-to-noise ratio value of each demodulated signal, selects the demodulated signal with the largest cumulative time-frequency harmonic signal-to-noise ratio value as the optimal demodulated signal, and extracts the potential instantaneous fault characteristic frequency trend line based on the maximum value of the time-frequency harmonic signal-to-noise ratio matrix of the optimal demodulated signal under different time slices.
[0103] The fault determination unit is used to perform angle resampling and spectral analysis on the optimal demodulated signal in the demodulated signal according to the instantaneous fault characteristic frequency trend line to obtain the order ratio spectrum, and to determine the bearing fault type according to the fault characteristic coefficient and the order ratio spectrum.
[0104] The train wheelset bearing fault diagnosis system under variable speed operating conditions provided by this invention has the same beneficial effects as the above-mentioned technical solutions and methods, and will not be elaborated here.
[0105] In the embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the system embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system.
[0106] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.
[0107] Although the invention has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made therein without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely exemplary descriptions of the invention as defined by the appended claims, and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if such modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include such modifications and modifications.
Claims
1. A method for diagnosing train wheelset bearing faults under variable speed operating conditions, characterized in that, include: The vibration signal of the bearing is loaded and converted into a spectrum signal. The spectrum signal is adaptively segmented based on the spectrum trend function to obtain the segmentation boundary of the spectrum signal. Empirical wavelet transform is introduced, and an adaptive filter bank is constructed based on the segmentation boundary to decompose and reconstruct the vibration signal, thereby obtaining the demodulated signal of the vibration signal. Short-time Fourier transform is introduced to calculate the envelope time-frequency distribution of the demodulated signal and the time-frequency harmonic signal-to-noise ratio matrix of the envelope time-frequency distribution. Based on the time-frequency harmonic signal-to-noise ratio matrix, the cumulative time-frequency harmonic signal-to-noise ratio value of each demodulated signal is calculated. The demodulated signal with the largest cumulative time-frequency harmonic signal-to-noise ratio value is selected as the optimal demodulated signal. Based on the maximum value of the time-frequency harmonic signal-to-noise ratio matrix of the optimal demodulated signal under different time slices, the potential instantaneous fault characteristic frequency trend line is extracted. The optimal demodulated signal is resampled at an angle and subjected to spectral analysis based on the instantaneous fault characteristic frequency trend line to obtain the order ratio spectrum. The bearing fault type is determined based on the fault characteristic coefficients and the order ratio spectrum.
2. The method for diagnosing train wheelset bearing faults under variable speed conditions according to claim 1, characterized in that, The vibration signal is converted into a spectral signal, and the spectral signal is adaptively segmented based on a spectral trend function to obtain the segmentation boundary of the spectral signal, specifically including: Perform a Fourier transform on the vibration signal of the bearing to obtain the spectral signal of the vibration signal; The amplitude spectrum of the spectral signal is discretized into a non-negative sequence, and a discrete Fourier transform is performed on the non-negative sequence to obtain the key function; By reconstructing a portion of the data points of the key function, a spectral trend function is obtained; The minimum value of the spectral trend function is selected as the segmentation boundary of the spectral signal.
3. The method for diagnosing train wheelset bearing faults under variable speed conditions according to claim 1, characterized in that, An adaptive filter bank is constructed based on the spectral signal segmentation boundary to decompose and reconstruct the vibration signal, resulting in a demodulated signal of the vibration signal. Specifically, this includes: The empirical scaling function and empirical wavelet function are calculated based on the spectral signal segmentation boundary and empirical wavelet transform. The detail coefficients and approximation coefficients of the empirical wavelet are obtained based on the empirical scaling function and the empirical wavelet function. The demodulated signal of the vibration signal is obtained based on the empirical scaling function, empirical wavelet function, detail coefficients, and approximation coefficients.
4. The method for diagnosing train wheelset bearing faults under variable speed conditions according to claim 3, characterized in that, The empirical scaling function and empirical wavelet function, calculated based on the spectral signal segmentation boundary and empirical wavelet transform, are specifically derived from the following formula: ； ； In the formula, Represents the empirical scaling function; Represents the empirical wavelet function; ω n The spectral signal is defined by the segmentation boundary; β(x) is the transition function; γ is a coefficient with a range of values. .
5. The method for diagnosing train wheelset bearing faults under variable speed conditions according to claim 1, characterized in that, The introduction of short-time Fourier transform to calculate the envelope time-frequency distribution of the demodulated signal and the time-frequency harmonic signal-to-noise ratio matrix of the envelope time-frequency distribution specifically includes: A sliding window algorithm is introduced into the demodulated signal, and the short-time Fourier transform is used to calculate the demodulated signal within the window to obtain the envelope time-frequency distribution of the demodulated signal; Based on the cumulative signal-to-noise ratio of the fundamental frequency and harmonics in each time slice of the envelope time-frequency distribution, a time-frequency harmonic signal-to-noise ratio matrix is constructed.
6. The method for diagnosing train wheelset bearing faults under variable speed conditions according to claim 5, characterized in that, The short-time Fourier transform is introduced to calculate the time-frequency distribution of the envelope of the demodulated signal, which is obtained by the following formula: ； In the formula, G k (τ,ω) represents the time-frequency distribution of the envelope of the demodulated signal; This represents the magnitude of the analytic signal obtained after the Hilbert transform of the k-th demodulated signal; Indicates that the center is located at The window function at time step.
7. The method for diagnosing train wheelset bearing faults under variable speed conditions according to claim 5, characterized in that, Based on the cumulative signal-to-noise ratio (SNR) of the fundamental frequency and harmonics in each time slice of the envelope time-frequency distribution, a time-frequency harmonic SNR matrix is constructed and calculated using the following formula: ； In the formula, TFHSNRM k (t,f) represents the time-frequency harmonic signal-to-noise ratio matrix; H represents the harmonic accumulation order; The expression indicates taking the absolute value; `max` indicates taking the maximum value. This indicates the harmonic tolerance band.
8. The method for diagnosing train wheelset bearing faults under variable speed conditions according to claim 1, characterized in that, The extracted potential instantaneous fault characteristic frequency trend line is calculated using the following formula: ； In the formula, This represents the instantaneous fault characteristic frequency of the k-th demodulated signal at time t. This represents the time-frequency harmonic signal-to-noise ratio matrix value of the k-th demodulated signal; This represents the frequency value f that maximizes the time-frequency harmonic signal-to-noise ratio matrix at a given time t.
9. A fault diagnosis system for train wheelset bearings under variable speed operating conditions, comprising the method described in any one of claims 1 to 8, including: The signal loading unit is used to load the vibration signal of the bearing, convert the vibration signal into a spectrum signal, and adaptively segment the spectrum signal based on the spectrum trend function to obtain the segmentation boundary of the spectrum signal; The signal demodulation unit is used to introduce empirical wavelet transform and construct an adaptive filter bank based on the signal spectrum segmentation boundary to decompose and reconstruct the vibration signal to obtain the demodulated signal of the vibration signal. The calculation unit introduces short-time Fourier transform to calculate the envelope time-frequency distribution of the demodulated signal and the time-frequency harmonic signal-to-noise ratio matrix of the envelope time-frequency distribution. Based on the time-frequency harmonic signal-to-noise ratio matrix, it calculates the cumulative time-frequency harmonic signal-to-noise ratio value of each demodulated signal, selects the demodulated signal with the largest cumulative time-frequency harmonic signal-to-noise ratio value as the optimal demodulated signal, and extracts the potential instantaneous fault characteristic frequency trend line based on the maximum value of the time-frequency harmonic signal-to-noise ratio matrix of the optimal demodulated signal under different time slices. The fault determination unit is used to perform angle resampling and spectral analysis on the optimal demodulated signal in the demodulated signal according to the instantaneous fault characteristic frequency trend line to obtain the order ratio spectrum, and to determine the bearing fault type according to the fault characteristic coefficient and the order ratio spectrum.