Modal component selection method based on unbiased autocorrelation Gini coefficient index

Abstract

The invention relates to a modal component selection method based on an unbiased autocorrelation Gini coefficient index, and aims to solve the problem that the optimal modal component of a plurality of modal decomposition methods is difficult to select. The method is characterized by comprising the following steps: S1, decomposing an original signal by adopting a modal decomposition method (such as variational modal decomposition (VMD)) to obtain a series of modal component signals; s2, calculating an unbiased autocorrelation Gini coefficient value corresponding to each modal component, and selecting the modal component corresponding to the maximum value as an optimal component; and S3, carrying out envelope spectrum demodulation on the optimal modal component, obtaining and analyzing the real fault characteristic frequency of the bearing, and further determining the fault type of the bearing. Compared with the existing index, the index can comprehensively evaluate the impact and periodicity of the fault features of the bearing, so that the modal component containing the most fault features can be selected.

Description

Technical Field

[0001] The invention relates to an application of a modal component selection method in the field of bearing faults, and in particular to a modal component selection method based on an unbiased autocorrelation Gini coefficient index. Background Art

[0002] Bearings are important connecting parts of mechanical equipment and are widely used in rail transportation, aerospace, machine tool processing and other fields. The transmission system failure caused by bearings can reach 48%. Rolling bearing failure will not only affect the operation of the equipment, causing huge economic losses, but also cause casualties. Therefore, accurate diagnosis of rolling bearing failure is particularly important.

[0003] The modal decomposition method has good adaptive decomposition characteristics for non-stationary and nonlinear bearing vibration signals, so it is widely used in the field of bearing fault diagnosis.

[0004] The modal decomposition method obtains a series of modal component signals after decomposing the signal. Different component signals contain different information. Accurately selecting the modal component containing the most fault characteristics is the key to accurately judge the bearing fault characteristics. Summary of the invention

[0005] In view of the problem that it is difficult to select the optimal modal component of the modal decomposition method, the purpose of the present invention is to provide a modal component selection method based on the unbiased autocorrelation Gini coefficient indicator, which can effectively select the component containing the most fault characteristics from a series of modal components.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] The present invention provides a modal component selection method based on an unbiased autocorrelation Gini coefficient index, comprising the following steps:

[0008] S1: Decompose the original signal using a modal decomposition method (such as variational mode decomposition (VMD)) to obtain a series of modal component signals.

[0009] S2: Calculate the unbiased autocorrelation Gini coefficient value corresponding to each modal component, and select the modal component corresponding to the maximum value as the optimal component.

[0010] S3: Perform envelope spectrum demodulation on the best modal component to obtain and analyze the true fault characteristic frequency of the bearing, and then determine the bearing fault type.

[0011] Preferably, the S1 is specifically:

[0012] Taking the vibration acceleration signal of faulty bearing as the research object, the modal decomposition method is used to decompose the original signal and obtain a series of modal components.

[0013] Preferably, the calculation process of S2 is as follows:

[0014] S2.1: Solve for each component signal x i The unbiased autocorrelation of is used to remove the noise, random pulses and other components in the signal that are irrelevant to the fault information, thereby enhancing the periodic characteristics. The solution expression is:

[0015]

[0016] Where N represents the total number of time series signals, n = 1, 2...N; τ represents the hysteresis coefficient, τ = -(N-1), -(N-2),..., 0,...(N-2), (N-1).

[0017] S2.2: Solve for each unbiased autocorrelation signal AC i The square envelope spectrum of (τ) is expressed as follows:

[0018] ACSES i =abs(FFT|AC i (τ)| 2 )

[0019] [Where FFT stands for Fast Fourier Transform.

[0020] S2.3: Arrange the unbiased autocorrelation signals after each square envelope in ascending order: ACSES i =[ACSES(1),ACSES(2),...ACSES(k),...ACSES(K)], ACSES(1)≤ACSES(2)...≤ACSES(k)...≤ACSES(K), K represents the total number of sequences of component signals after unbiased autocorrelation solution, K=2N-1.

[0021] S2.4: Arrange the ACSES in ascending order i Substituting into the Gini coefficient index, the unbiased autocorrelation Gini coefficient index AC-GISES is constructed. i , and its solution expression is:

[0022]

[0023] Where k represents the kth item in K, and ∥·∥1 is the L1 norm operation.

[0024] The method for selecting a modal component based on an unbiased autocorrelation Gini coefficient index according to claim 1 is characterized in that S3 is specifically:

[0025] Envelope demodulation is performed on the modal component with the largest unbiased autocorrelation Gini coefficient, the bearing fault characteristics are analyzed in the envelope spectrum, the actual fault characteristic frequency of the bearing is obtained, the real characteristic frequency of the bearing is compared with the theoretical fault characteristic frequency corresponding to each bearing fault type, and when the real characteristic frequency of the bearing is consistent with the fault characteristic frequency corresponding to one or more bearing fault types, it is determined that the bearing has this type of fault.

[0026] The theoretical failure of the bearing can be calculated through the speed and size parameters of the bearing, and its expression is as follows:

[0027] Theoretical fault characteristic frequency of outer ring:

[0028]

[0029] Theoretical fault characteristic frequency of inner ring:

[0030]

[0031] Theoretical characteristic frequency of rolling element failure:

[0032]

[0033] Theoretical characteristic frequency of cage failure:

[0034]

[0035] Where r represents the bearing speed, n represents the number of balls, d represents the rolling element diameter, D represents the bearing pitch diameter, and α represents the rolling element contact angle.

[0036] The present invention has the following advantages:

[0037] In order to better select the modal components containing more fault features, the present invention uses the unbiased autocorrelation Gini coefficient index to measure the modal component signal, and selects the modal component with the largest unbiased autocorrelation Gini coefficient as the optimal mode. This method can effectively extract the fault features of rolling bearings and avoid the diagnostic errors caused by improper manual selection. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A flowchart of a modal component selection method based on the unbiased autocorrelation Gini coefficient indicator is provided for the implementation of this example.

[0039] Figure 2 is the envelope spectrum of the original signal in the embodiment.

[0040] Figure 3 is the envelope spectrum of the optimal modal component in the embodiment. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0042] Example

[0043] Taking the vibration acceleration signal of the faulty bearing as the research object, the theoretical fault frequency of the bearing can be calculated through the speed and dimensional parameters of the bearing. The speed and dimensional parameters of the tested bearing are: speed r = 2100r / min, number of rolling elements n = 8, bearing center diameter D = 34.55mm, ball diameter d = 7.92mm, contact angle α = 0°.

[0044] Theoretical fault characteristic frequency of outer ring:

[0045]

[0046] Theoretical fault characteristic frequency of inner ring:

[0047]

[0048] Theoretical characteristic frequency of rolling element failure:

[0049]

[0050] Theoretical characteristic frequency of cage failure:

[0051]

[0052] The envelope spectrum of the test bearing signal is as follows: Figure 2 As shown, it is impossible to determine the fault type.

[0053] refer to Figure 1 As shown, this embodiment provides a modal component selection method based on an unbiased autocorrelation Gini coefficient indicator, the method comprising the following steps:

[0054] S1: The variational mode decomposition (VMD) algorithm is used to decompose the original signal and obtain the modal component signals.

[0055] S2: Calculate the unbiased autocorrelation Gini coefficient value of each component signal, and select the modal component corresponding to the maximum value as the optimal component of VMD.

[0056] S2.1: Solve for each component signal x iThe unbiased autocorrelation of is used to remove the noise, random pulses and other components in the signal that are irrelevant to the fault information, thereby enhancing the periodic characteristics. The solution expression is:

[0057]

[0058] Where N represents the total number of time series signals N=5000, n=1,2...5000; τ represents the hysteresis coefficient, τ=-4999,-4998,...,0,...4998,4999.

[0059] S2.2: Solve for each unbiased autocorrelation signal AC i The square envelope spectrum of (τ) is expressed as follows:

[0060] ACSES i =abs(FFT|AC i (τ)| 2 )

[0061] Where FFT stands for Fast Fourier Transform.

[0062] S2.3: Arrange the unbiased autocorrelation signals after each square envelope in ascending order: ACSES i =[ACSES(1),ACSES(2),...ACSES(k),ACSES(K)], ACSES(1)≤ACSES(2)...≤ACSES(k)...≤ACSES(K), K represents the total number of sequences of component signals after unbiased autocorrelation solution, K=2N-1=9999.

[0063] S2.4: Arrange the ACSES in ascending order i Substituting into the Gini coefficient index, the unbiased autocorrelation Gini coefficient index AC-GISES is constructed. i , and its solution expression is:

[0064]

[0065] Where k represents the kth item in K, and ∥·∥1 is the L1 norm operation.

[0066] S3: Select the best component for envelope spectrum analysis and fault type judgment.

[0067] S3.1: The best component is analyzed by envelope spectrum. The envelope spectrum is as follows Figure 3 As shown, the inner ring theoretical fault frequency f g =107.9Hz and f=107.5Hz, there is an obvious peak, so it can be judged that the test bearing has an inner ring fault.

[0068] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A modal component selection method based on the unbiased autocorrelation Gini coefficient index, characterized in that: The following steps are involved: S1: Decompose the original signal using a modal decomposition method (such as variational mode decomposition (VMD)) to obtain a series of modal component signals. S2: Calculate the unbiased autocorrelation Gini coefficient value corresponding to each modal component, and select the modal component corresponding to the maximum value as the optimal component. S3: Perform envelope spectrum demodulation on the best modal component to obtain and analyze the true fault characteristic frequency of the bearing, and then determine the bearing fault type.

2. The method for selecting modal components based on the unbiased autocorrelation Gini coefficient index according to claim 1, characterized in that: Specifically, S1 takes the vibration acceleration signal of the faulty bearing as the research object, and uses the modal decomposition method to decompose the original signal to obtain a series of modal components.

3. The method for selecting modal components based on the unbiased autocorrelation Gini coefficient index according to claim 1, characterized in that: The unbiased autocorrelation Gini coefficient in S2 refers to an evaluation index that comprehensively evaluates the impact characteristics and periodic characteristics of bearing faults. The calculation process is as follows: S2.1: Solve the unbiased autocorrelation of each component signal to remove noise, random pulses and other components in the signal that are irrelevant to the fault information, thereby enhancing the periodic characteristics. The solution expression is: Where N represents the total number of time series signals, n = 1, 2...N; represents the hysteresis coefficient, = -(N-1), -(N-2),..., 0,...(N-2), (N-1). S2.2: Solve the square envelope spectrum of each unbiased autocorrelation signal ACi(), and the solution expression is: ACCESS i =abs(FFT|AC i (τ)| 2 ) Where FFT stands for Fast Fourier Transform. S2.3: Arrange the unbiased autocorrelation signals after each square envelope in ascending order: ACSESi = [ACSES(1), ACSES(2), ...ACSES(k), ...ACSES(K)], ACSES(1)≤ACSES(2)...≤ACSES(k)...≤ACSES(K), K represents the total number of sequences of component signals after unbiased autocorrelation solution, K = 2N-1. S2.4: Substitute the ACSESi in ascending order into the Gini coefficient index, thereby constructing the unbiased autocorrelation Gini coefficient index AC-GISESi, and its solution expression is: Where k represents the kth item in K, and ∥·∥1 is the L1 norm operation.

4. The method for selecting modal components based on the unbiased autocorrelation Gini coefficient index according to claim 1, characterized in that: The S3 is specifically: Envelope demodulation is performed on the modal component with the largest unbiased autocorrelation Gini coefficient, the bearing fault characteristics are analyzed in the envelope spectrum, the actual fault characteristic frequency of the bearing is obtained, the real characteristic frequency of the bearing is compared with the theoretical fault characteristic frequency corresponding to each bearing fault type, and when the real characteristic frequency of the bearing is consistent with the fault characteristic frequency corresponding to one or more bearing fault types, it is determined that the bearing has this type of fault. The theoretical failure of the bearing can be calculated through the speed and size parameters of the bearing, and its expression is as follows: Theoretical fault characteristic frequency of outer ring: Theoretical fault characteristic frequency of inner ring: Theoretical characteristic frequency of rolling element failure: Theoretical characteristic frequency of cage failure: Where r represents the bearing speed, n represents the number of balls, d represents the rolling element diameter, D represents the bearing pitch diameter, and α represents the rolling element contact angle.

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