A main bearing fault characterization method based on feature information parameter weighting reconstruction

Abstract

The application provides a main bearing fault characterization method based on feature information parameter weighting reconstruction, and relates to the technical field of bearing fault diagnosis. The method firstly optimizes parameters in a VMD algorithm by using a particle swarm algorithm, then performs weighted reconstruction on all obtained IMF components according to a weighted feature parameter information reconstruction formula, the formula balances the weight of effective information and invalid information of each modal component, maximally retains the effective component, and reduces the interference of noise components on the overall signal. Finally, bearing weak fault feature information is extracted by an envelope spectrum. Through experiment verification, the method can be used as one of effective methods for extracting feature information of an aero-engine main shaft bearing and fault diagnosis.

Description

Technical Field

[0001] This invention relates to the field of bearing fault diagnosis technology, and in particular to a method for characterizing main bearing faults based on weighted reconstruction of feature information parameters. Background Technology

[0002] In recent years, aerospace, as a high-precision field in national defense science and technology, has developed rapidly. Aero-engines, as the power source for aircraft soaring through the sky, are considered the "flower of industry," possessing precise and highly complex operating characteristics. The main bearing of an aero-engine is one of the core components of the engine's support and transmission system. Its operating conditions are extremely harsh, with high temperatures, heavy loads, and high speeds. It is susceptible to failure during operation due to factors such as wear, fatigue, and poor lubrication. The working condition of the aero-engine main bearing directly affects the stability of the aero-engine. However, since the main bearing is installed inside the engine, it is difficult to frequently disassemble the engine to diagnose faults in the main bearing. Therefore, developing effective and accurate methods for the condition control and fault diagnosis of aero-engine main bearings is of paramount importance for aviation development, ensuring stable engine operation.

[0003] Given the uncertainties surrounding the failure of major bearings in aero-engines, the significant background noise, and the complex transmission methods, the time-domain and frequency characteristics of their information also change. Therefore, further analysis and processing of the time-domain and frequency characteristics data within a specific timeframe is necessary. Liu Qianjin et al. used the Variational Mode Decomposition (VMD) algorithm to analyze bearing fault signals under various speed conditions, effectively extracting weak fault characteristic signals for dynamic monitoring of rolling bearing faults. Ma Zengqiang et al. performed variational mode analysis on fault signals, using the Teager energy operator to demodulate components with high kurtosis, thereby reducing the influence of interference clutter and significantly improving the effectiveness of the analysis method, enabling rapid and accurate diagnosis of rolling bearing faults. Compared to the iterative screening process in Empirical Mode Decomposition (EMD), the VMD algorithm is more robust to noise interference and can reduce the impact of noise on the decomposition results.

[0004] Most existing methods screen and reconstruct the decomposed bearing signals based on one or a few sensitive parameters, but they ignore the fact that each component signal contains effective information about bearing fault characteristics. Artificially removing a few components will affect the diagnostic results. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a main bearing fault characterization method based on feature information parameter weighted reconstruction, which retains the effective components in the bearing fault vibration signal to the greatest extent, suppresses the interference of noise components, and extracts bearing fault feature information more accurately.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A main bearing fault characterization method based on feature information parameter weighted reconstruction includes the following steps:

[0008] Step 1: Collect vibration signals from the rolling bearing using a vibration sensor;

[0009] Step 2: Optimize the parameters in the variational mode decomposition algorithm (VMD) using the particle swarm optimization (PSO) algorithm, and use it as a pre-parameter to process the acquired original vibration signal of the rolling bearing to obtain the IMF signal component;

[0010] Step 3: Reconstruct all IMF components of the formula based on the weighted feature parameter information to obtain the reconstructed signal;

[0011] Step 4: Perform envelope demodulation on the weighted reconstructed signal, extract bearing fault feature information, and diagnose the fault.

[0012] Furthermore, in step 2, the parameters in the variational mode decomposition algorithm VMD are [a0, K0], where a0 is the penalty factor and K0 is the number of modes. These parameters are used as pre-parameters to process the original vibration signal collected by the vibration sensor, resulting in K0 IMF signal components. The fitness function is the value of the minimum envelope entropy among the K0 components.

[0013] Furthermore, the specific method for obtaining the IMF signal components in step 2 is as follows:

[0014] Step 2.1: Assuming the original vibration signal consists of K IMF components, perform a Hilbert transform on each amplitude-modulated and frequency-modulated signal to obtain the one-sided spectrum of the IMF component. The one-sided spectrum of the IMF component is calculated according to equation (7):

[0015]

[0016] In the formula, δ(t) is the impulse function, t is time, j is the imaginary unit, * denotes convolution, and u k (t) is the k-th IMF component;

[0017] Step 2.2: Add an exponential term to the unilateral spectrum Frequency mixing is performed, and the spectrum of each mode is modulated to the corresponding fundamental frequency band. The spectrum of each mode modulated to the corresponding fundamental frequency band is calculated according to equation (8):

[0018]

[0019] In the formula, {ω k (t)}={ω1,...,ω K} represents the center frequency of each component;

[0020] Step 2.3: Calculate the gradient of the demodulated signal after spectral adjustment, use its L2 norm squared to estimate the bandwidth of each mode signal, and sum all components to equal the original signal as a constraint condition to obtain the constrained variational model description, as shown in Equation (9):

[0021]

[0022] In the formula, This indicates that the partial derivative of the function with respect to t, {u k}={u1,...,u K} represents the decomposed IMF component, and x(t) represents the original vibration signal;

[0023] Step 2.4: To solve the constrained variational model, the Lagrange multiplier λ(t) and the quadratic penalty factor α are introduced, and the optimization result of the Lagrange function is iteratively searched using the alternating direction multiplier method. Finally, the original signal is decomposed into K0 IMF components; the extended Lagrange function is calculated according to equation (10):

[0024]

[0025] Further, step 3 includes:

[0026] The definition of skewness is:

[0027]

[0028] The definition of kurtosis is:

[0029]

[0030] The mathematical expression for the correlation coefficient is:

[0031]

[0032] Where X and Y represent two sample variables; u is the average amplitude of the signal component; σ is the standard deviation of the signal component amplitude; Cov(X,Y) represents the covariance of variables X and Y. This represents the variance of the sample variable X. This represents the variance of Y;

[0033] Skewness, kurtosis, and correlation coefficient are normalized, and all components are fused according to the weighted feature parameter reconstruction formula:

[0034]

[0035]

[0036]

[0037]

[0038] In the formula, s i k i r i Let s be the skewness, kurtosis, and correlation coefficient of the i-th modal component. max k max r max S represents the maximum skewness, kurtosis, and correlation coefficient among the modal components; i K i R i Here are the normalized skewness, kurtosis, and correlation coefficient of the i-th modal component; IMF i Let i be the i-th modal component, and Newsignal be the reconstructed signal after weighting each modal component.

[0039] The beneficial effects of adopting the above technical solution are as follows: The main bearing fault characterization method based on feature information parameter weighted reconstruction provided by this invention selects PSO optimized VMD decomposition to determine the precondition parameters [a0, K0]. The parallelization of the PSO algorithm is relatively easy, and the calculation of each particle is independent and can be performed simultaneously. This feature makes the PSO algorithm suitable for application in multi-processor or distributed computing environments, improving the efficiency and speed of the algorithm, and it is applicable to nonlinear, non-convex, and high-dimensional optimization problems. The selected VMD decomposition can maintain the invariance of the total energy during the signal decomposition process, that is, the sum of the energies of each mode after decomposition is equal to the energy of the original signal. This makes VMD more effective in... The method offers greater reliability in signal processing applications, avoiding energy loss and bias issues. VMD also avoids mode overlap, ensuring that each decomposed mode has a different frequency range and is independent of the others. This facilitates the analysis and extraction of local signal features, aiding in subsequent mode reconstruction and signal recovery. The proposed weighted feature parameter information reconstruction formula not only reconstructs all modal component signals with weights, avoiding the loss of effective information caused by manual signal selection, but also increases the proportion of IMF components with more effective information in the final reconstructed signal through weighting, highlighting fault characteristic information and making it easier to extract bearing fault characteristic frequencies and their harmonics. The method provided by this invention was applied to the analysis of test vibration data of a faulty bearing component of a certain type of turbofan aero-engine. It can effectively identify bearing fault characteristic information and can serve as one of the methods for diagnosing aero-engine main shaft bearing faults. Compared with PSO-VMD-Kurt and the WPD-KVI-Hilbert algorithm, the method of this invention can extract bearing fault characteristic frequencies and their harmonics more clearly. Attached Figure Description

[0040] Figure 1 A flowchart of a main bearing fault characterization method based on feature information parameter weighted reconstruction provided in an embodiment of the present invention;

[0041] Figure 2 The original spectrum diagram of the bearing rolling element provided in the embodiment of the present invention;

[0042] Figure 3 This is a partial 0-400Hz image of the bearing rolling element provided in an embodiment of the present invention;

[0043] Figure 4 The bearing rolling element reconstruction signal envelope spectrum provided in the embodiments of the present invention includes (4a) the reconstruction signal envelope spectrum obtained by the method of the present invention, (4b) the reconstruction signal envelope spectrum obtained by PSO-VMD-Kurt, and (4c) the reconstruction signal envelope spectrum obtained by WPD-KVI-Hilbert.

[0044] Figure 5 The bearing inner ring reconstruction signal envelope spectrum provided in the embodiment of the present invention, wherein (5a) is the reconstruction signal envelope spectrum obtained by the method of the present invention, and (5b) is the reconstruction signal envelope spectrum obtained by WPD-KVI-Hilbert;

[0045] Figure 6 The bearing outer ring reconstruction signal envelope spectrum provided in the embodiment of the present invention, wherein (6a) is the reconstruction signal envelope spectrum obtained by the method of the present invention, and (6b) is the reconstruction signal envelope spectrum obtained by WPD-KVI-Hilbert. Detailed Implementation

[0046] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0047] This embodiment proposes a main bearing fault characterization method based on feature information parameter weighted reconstruction. The method first optimizes the parameters in the VMD algorithm using a particle swarm optimization algorithm. Then, it reconstructs all obtained IMF components using a weighted feature parameter information reconstruction formula. This formula balances the weights of effective and ineffective information in each modal component, maximizing the preservation of effective components and reducing the interference of noise components on the overall signal. Finally, weak bearing fault feature information is extracted from the envelope spectrum.

[0048] This embodiment uses real experimental data for analysis, selecting a five-point main shaft bearing of a certain type of aero-engine as the research object. The sampling frequency for the vibration data of the bearing rolling elements, inner ring, and outer ring is all set to 25.6kHz. Figure 1 As shown, the method of this embodiment is described below.

[0049] Step 1: Collect vibration signals from the rolling bearing using a vibration sensor;

[0050] Step 2: Optimize the penalty factor and mode number [a0,K0] in the variational mode decomposition algorithm (VMD) using the particle swarm optimization (PSO) algorithm. Use these as pre-parameters to process the acquired original vibration signal of the rolling bearing, and obtain K0 IMF signal components. The fitness function is the value of the minimum envelope entropy among the K0 components.

[0051] The Particle Swarm Optimization (PSO) algorithm searches for the optimal solution by simulating each individual in a swarm, referred to as a particle, and observing their movement in the search space. The position of the o-th particle is denoted as s. o =(s o1 ,s o2 ,,s oD ) T Velocity is represented as: v o =(v o1 ,v o2 ,,v oD ) T Each particle updates its velocity and position based on its individual optimal solution and the global optimal solution in order to move in the direction of the optimal solution; the velocity update of each particle based on its individual optimal solution and the global optimal solution is calculated according to equation (1), and the position update of each particle based on its individual optimal solution and the global optimal solution is calculated according to equation (2):

[0052]

[0053]

[0054] In the formula, o represents the index of the particle, ranging from 1 to 0; h represents the h-th iteration; Let the velocity of particle o be the velocity in the d-dimensional search space during the h-th iteration; c1 and c2 are inertial weights, ranging from [0,1]; c1 and c2 are learning factors, and η is a random number in the interval [0,1]. Let h be the individual extreme point of the particle in the h-th iteration. Let $o$ be the current position of particle $o$ in the $h$-th iteration. This is the global extreme point of the entire population in the h-th iteration.

[0055] Variational Mode Decomposition (VMD) decomposes the vibration signal into multiple amplitude-modulated and frequency-modulated signals with fixed bandwidths, i.e., the product of the instantaneous amplitude and phase of the fixed frequency band. The product of the instantaneous amplitude and phase of the fixed frequency band is calculated according to equation (3):

[0056]

[0057] In the formula, Ak (t) is the instantaneous amplitude of the Kth amplitude-frequency modulated signal. Let uk(t) represent the signal phase, and uk(t) be the Kth IMF component.

[0058] After the above steps, K0 components are selected from the fitness function of the variational mode decomposition algorithm (VMD), and the minimum envelope entropy value is selected from the K0 components for particle swarm optimization (PSO).

[0059] The envelope entropy Ep, used as an indicator to evaluate the sparsity of a signal, is determined by the Variational Mode Decomposition (VMD) algorithm. If the obtained components contain a lot of noise, it will mask the perturbation features in the signal, resulting in weak sparsity of the component signals, i.e., a large envelope entropy. Conversely, if each component contains regular perturbation features, then the sparsity of the component signals is strong, and the envelope entropy is small.

[0060] The minimum envelope entropy value is selected from the K0 components for Particle Swarm Optimization (PSO) to evaluate the quality of the solution. The envelope entropy value Ep is calculated according to Equation (6).

[0061] The sequence of signal x(j) (j=1,2,...,m) after Hilbert demodulation is calculated according to equation (4):

[0062]

[0063] Normalize the demodulated sequence a(j) and calculate it according to equation (5):

[0064]

[0065]

[0066] In the formula, a(j) represents the sequence of signal x(j) demodulated by the Hilbert envelope, j = 1, 2, ..., m; H represents the Hilbert transform; p j It is the normalized form of a(j).

[0067] The specific steps for obtaining the IMF components through decomposition are as follows:

[0068] Step 2.1: Assuming the original vibration signal consists of K IMF components, perform a Hilbert transform on each amplitude-modulated and frequency-modulated signal to obtain the one-sided spectrum of the IMF component. The one-sided spectrum of the IMF component is calculated according to equation (7):

[0069]

[0070] In the formula, δ(t) is the impulse function, t is time, j is the imaginary unit, * denotes convolution, and u k(t) is the k-th IMF component;

[0071] Step 2.2: Add an exponential term to the unilateral spectrum Frequency mixing is performed, and the spectrum of each mode is modulated to the corresponding fundamental frequency band. The spectrum of each mode modulated to the corresponding fundamental frequency band is calculated according to equation (8):

[0072]

[0073] In the formula, {ω k (t)}={ω1,...,ω K} represents the center frequency of each component;

[0074] Step 2.3: Calculate the gradient of the demodulated signal after spectral adjustment, use its L2 norm squared to estimate the bandwidth of each mode signal, and sum all components to equal the original signal as a constraint condition to obtain the constrained variational model description, as shown in Equation (9):

[0075]

[0076] In the formula, This indicates that the partial derivative of the function with respect to t, {u k}={u1,...,u K} represents the decomposed IMF component; x(t) represents the original vibration signal;

[0077] Step 2.4: To solve the constrained variational model, the Lagrange multiplier λ(t) and the quadratic penalty factor α are introduced, and the optimization result of the Lagrange function is iteratively searched using the alternating direction multiplier method. Finally, the original signal is decomposed into K0 IMF components; the extended Lagrange function is calculated according to equation (10):

[0078]

[0079] Step 3: Reconstruct all IMF components of the formula based on the weighted feature parameter information to obtain the reconstructed signal.

[0080] Rolling bearings exhibit non-stationary and non-linear characteristics during operation, resulting in vibration signals containing redundant information. To balance the inclusion of effective and ineffective IMF components during the screening process and to retain the most effective information, this embodiment proposes a novel weighted feature parameter information reconstruction formula. This formula uses three feature parameters—skewness, kurtosis, and correlation coefficient—to perform weighted reconstruction calculations with their corresponding IMF components to obtain the reconstructed signal. This formula not only avoids the problem of missing effective information caused by manual signal screening but also, through weighting, ensures that IMF components with more effective information have a larger proportion in the final reconstructed signal, highlighting fault characteristic information, while IMF components with less effective information have a smaller proportion, reducing the interference of noise components on the overall signal. This makes it easier to extract the bearing fault characteristic frequencies and their harmonics.

[0081] When a bearing is operating normally, its skewness value is approximately ±1.6, and its kurtosis value is around 3. When a bearing malfunctions, the skewness and kurtosis values ​​will change. Generally, the skewness and kurtosis values ​​tend to increase, and the abnormal signals during operation tend to increase. Both skewness and kurtosis are dimensionless parameters, reflecting the degree of deviation of the signal probability distribution from the normal distribution.

[0082] The skewness is calculated according to formula (11):

[0083]

[0084] Kurtosis is calculated according to formula (12):

[0085]

[0086] Where u is the average value of the signal component amplitude; σ is the standard deviation of the signal component amplitude.

[0087] The correlation coefficient is a statistic describing the degree of linear correlation between variables. It uses the Pearson correlation coefficient calculation method and ranges from -1 to 1. When the correlation coefficient is close to 1, it indicates a strong positive correlation between the variables; that is, when one variable increases, the other variable tends to increase as well. When the correlation coefficient is close to -1, it indicates a strong negative correlation between the variables; that is, when one variable increases, the other variable tends to decrease. When the correlation coefficient is close to 0, it indicates that there is no linear correlation between the variables.

[0088] The mathematical expression for the correlation coefficient is calculated according to equation (13):

[0089]

[0090] Where X and Y represent two sample variables; Cov(X,Y) represents the covariance of variables X and Y. This represents the variance of the sample variable X. This represents the variance of Y.

[0091] The new weighted feature parameter information reconstruction formula first calculates the skewness value s of the i-th IMF component according to equations (14), (15), and (16). i kurtosis value k i and correlation coefficient r i The skewness value s of the component with the largest skewness in the mode max kurtosis value k max and correlation coefficient r max Normalized value S i K i and R i That is, dimensionless value; finally, all components are fused according to the weighted characteristic parameter reconstruction formula, and calculated according to formula (17):

[0092]

[0093]

[0094]

[0095]

[0096] In the formula, IMF i IMF i Let i be the i-th IMF component, and Newsignal be the reconstructed signal after weighting each IMF component.

[0097] This embodiment provides 7 IMF component parameters as shown in Table 1. These 7 IMF component parameters can be calculated according to the weighted feature parameter information reconstruction formula (17) to balance the modal components containing effective and invalid information during the screening process, and retain the effective information to the greatest extent, thereby obtaining the reconstructed signal after weighting each IMF component.

[0098] Table 1 Parameters of each component

[0099] 1 1 0.641 1 2 0.374 0.811 0.84 3 0.365 0.75 0.289 4 0.234 0.832 0.376 5 0.087 0.813 0.475 6 0.298 0.726 0.422 7 0.033 1 0.456

[0100] Step 4: Perform envelope demodulation on the weighted reconstructed signal, extract bearing fault feature information, and diagnose the fault.

[0101] Envelope spectrum analysis mainly includes two processes: resonance signal pickup and envelope detection. That is, the signal near the resonance peak (the natural frequency of the sensor or mechanical system) or at the resonant frequency of the high-frequency resonator is picked up to obtain a high-frequency vibration signal with a high signal-to-noise ratio. Then, the envelope waveform is obtained by envelope detection. The envelope waveform contains characteristic information related to rolling bearing fault diagnosis.

[0102] Hilbert transform is commonly used to extract fault information from signals by unwrapping the signal. The definition of Hilbert transform is:

[0103]

[0104] The principle of using Hilbert transform to envelop a signal is to induce a 90° phase shift in the test signal, thereby forming an analytic signal with the original signal to envelop the signal. Spectral analysis can then yield clear fault information.

[0105] In this embodiment, the calculated bearing fault characteristic frequency is 27Hz, and the frequency domain diagram of the original bearing vibration signal is as follows. Figure 2 As shown, the local 0-400Hz frequency range is as follows: Figure 3 As shown, although the original vibration signal contains a peak component in the low-frequency band (10th harmonic 271Hz), it also contains a lot of interference, making it difficult to extract other bearing fault characteristic frequency information, thus failing to identify the bearing fault. The reconstructed bearing rolling element fault signal is shown below. Figure 4 As shown in Figure (4a), the bearing characteristic frequency and its harmonics can be clearly extracted based on the method of this invention. If the four components with the largest kurtosis values ​​(PSO-VMD-Kurt) are selected for reconstruction and envelope demodulation, as shown in Figure (4a), the bearing characteristic frequency and its harmonics can be clearly extracted. Figure 4 In Figure (4b), although the corresponding harmonic frequencies from 1st to 11th can be found, there are many interference components, and only the 1st and 8th harmonic frequencies can be clearly identified. Therefore, the parameter harmonic formula and the threshold parameter decision screening criterion can balance the relationship between kurtosis and correlation coefficient, filtering out components with high kurtosis values ​​but little effective information, i.e., low signal-to-noise ratio signals. After WPD-KVI-Hilbert processing, the bearing rolling element fault reconstruction signal is as follows: Figure 4 As shown in Figure (4c), although some fault characteristic information can be found in the figure, its peak value is not obvious and there is too much interference information, making it difficult to accurately identify bearing faults.

[0106] Figure 5 Figure (5a) shows the envelope spectrum obtained by processing bearing inner ring fault data using the method of the present invention. The characteristic frequencies of bearing inner ring faults, from 1st to 5th harmonics (89Hz, 178Hz, 267Hz, 356Hz, 449Hz), can be clearly identified. Figure 5 Figure (5b) shows the envelope spectrum obtained by processing the same bearing inner ring fault data using the WPD-KVI-Hillbert method. Only the first fault characteristic frequency of the bearing inner ring can be clearly identified in the figure; other fault information is blurred, and the fault characteristic overtones are not obvious.

[0107] Figure 6 Figure (6a) shows the envelope spectrum obtained by processing bearing outer ring fault data using the method of the present invention, which can clearly identify the characteristic frequencies of outer ring faults from 1 to 5 harmonics. Figure 6 Figure (6b) shows the envelope spectrum obtained by processing the same bearing outer ring fault data using the WPD-KVI-Hillbert method. It is difficult to clearly identify the fault characteristic frequencies and their harmonics.

[0108] Verification has shown that the weighted feature parameter information reconstruction formula not only reconstructs all modal component signals by weight, avoiding the loss of effective information caused by manual signal selection, but also increases the proportion of IMF components with more effective information in the final reconstructed signal through weighting, highlighting fault characteristic information and making it easier to extract bearing fault characteristic frequencies and their harmonics. This invention, based on a feature information parameter weighted reconstruction method for main bearing fault characterization, can comprehensively filter noise components and highlight fault information in complex transmission paths and strong interference environments, thus diagnosing bearing faults. Therefore, it can serve as one of the effective diagnostic methods for aero-engine main bearings.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A method for characterizing main bearing faults based on feature information parameter weighted reconstruction, characterized in that: The method includes the following steps: Step 1: Collect vibration signals from the rolling bearing using a vibration sensor; Step 2: Optimize the parameters in the variational mode decomposition algorithm (VMD) using the particle swarm optimization (PSO) algorithm, and use it as a pre-parameter to process the acquired original vibration signal of the rolling bearing to obtain the IMF signal component; Step 3: Reconstruct all IMF components of the formula based on the weighted feature parameter information to obtain the reconstructed signal; Step 3 includes: The definition of skewness is: (11) The definition of kurtosis is: (12) The mathematical expression for the correlation coefficient is: (13) in, X , Y Represents two sample variables; This represents the average amplitude of the signal components; Let X be the standard deviation of the signal component amplitude; Cov(X,Y) represents the covariance of variables X and Y. This represents the variance of the sample variable X. This represents the variance of Y; Skewness, kurtosis, and correlation coefficient are normalized, and all components are fused according to the weighted feature parameter reconstruction formula: (14) (15) (16) (17) In the formula, s i , k i , r i Let be the skewness, kurtosis, and correlation coefficient of the i-th modal component. , , These represent the maximum skewness, kurtosis, and correlation coefficient among the modal components; S i , K i , R i represents the normalized skewness, kurtosis, and correlation coefficient of the i-th modal component; IMF i For the first i One modal component, This is the reconstructed signal after weighting each modal component; Step 4: Perform envelope demodulation on the weighted reconstructed signal, extract bearing fault feature information, and diagnose the fault.

2. The main bearing fault characterization method based on feature information parameter weighted reconstruction according to claim 1, characterized in that: In step 2, the parameters in the Variational Mode Decomposition (VMD) algorithm are: , As a penalty factor, The modal number is used as a pre-parameter to process the raw vibration signal collected by the vibration sensor, resulting in K0 IMF signal components. The fitness function is the value of the minimum envelope entropy among the K0 components.

3. The main bearing fault characterization method based on feature information parameter weighted reconstruction according to claim 2, characterized in that: The specific method for obtaining the IMF signal components in step 2 is as follows: Step 2.1: Assume the original vibration signal is from K The signal is composed of several IMF components. A Hilbert transform is performed on each amplitude-frequency modulated signal to obtain the one-sided spectrum of the IMF component. The one-sided spectrum of the IMF component is calculated according to equation (7): (7) In the formula, It is an impulse function. t For time, j The imaginary unit, Represents convolution. It is the first k One IMF component; Step 2.2: Add an exponential term to the unilateral spectrum Frequency mixing is performed, and the spectrum of each mode is modulated to the corresponding fundamental frequency band. The spectrum of each mode modulated to the corresponding fundamental frequency band is calculated according to equation (8): (8) In the formula, , representing the center frequency of each component; Step 2.3: Calculate the gradient of the demodulated signal after spectral adjustment, use its L2 norm squared to estimate the bandwidth of each mode signal, and sum all components to equal the original signal as a constraint condition to obtain the constrained variational model description, as shown in equation (9): (9) In the formula, Representing function pairs t Find the partial derivative. This represents the decomposed IMF component components. x ( t () represents the original vibration signal; Step 2.4: To solve the constrained variational model, Lagrange multipliers are introduced. and secondary penalty factor α The optimization result of the Lagrangian function is searched iteratively using the alternating direction multiplier method, and the original signal is finally decomposed into K0 IMF components; the extended Lagrangian function is calculated according to equation (10): (10)。

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