A method for extracting fault features of rolling bearings based on chaos theory

Abstract

The application discloses a rolling bearing fault feature extraction method based on chaos theory. Firstly, the vibration signal of the rolling bearing during operation is collected, then the vibration signal is subjected to CEEMDAN noise reduction processing, and then phase space reconstruction is carried out, the step state of the chaotic oscillator is observed, the maximum distance is calculated to quantize the period state change of the chaotic oscillator, and finally whether the rolling bearing is faulty is judged through the chaotic oscillator and the maximum distance. The chaotic oscillator is introduced, the maximum distance is used as the rolling bearing fault feature, early fault detection of the rolling bearing is realized, CEEMDAN is used for data noise reduction, in the decomposition process, white noise obtained by EMD decomposition is added to each order IMF component, finally, the noise residual in the reconstructed signal is smaller, and the screening times are reduced. Compared with other noise reduction methods, the method has better noise reduction effect, and the corresponding fault frequency multiplication and rotation frequency of the fault bearing can be more intuitively found.

Description

Technical Field

[0001] The invention belongs to the technical field of bearing monitoring, and in particular relates to a rolling bearing fault feature extraction method based on chaos theory, and belongs to a method for monitoring early-stage rolling bearing faults. Background Art

[0002] Currently, commonly used rolling bearing signal analysis methods include time domain statistical analysis, frequency domain analysis, and time-frequency analysis. Time domain statistical analysis directly analyzes the time domain signals of rolling bearings; frequency domain analysis extracts features that can characterize fault information based on changes in the frequency structure of the vibration signal when a rolling bearing fails.

[0003] Due to the complex and variable operating conditions of rolling bearings, their vibration signals exhibit strong non-stationary and nonlinear characteristics. Traditional time-domain or frequency-domain analysis methods often fail to effectively extract signal features. In recent years, many time-frequency analysis methods suitable for processing non-stationary signals have been proposed and widely used. However, these methods are computationally complex and difficult to implement for denoising.

[0004] Chaotic oscillators are highly sensitive to small periodic signals. Chaotic oscillator detection methods detect rolling bearing faults by observing the transition of the oscillator from a chaotic state to a large-scale periodic state. The maximum distance is used to quantify the change in the chaotic oscillator's periodic state. A method for early bearing fault detection based on chaos theory is proposed, using the maximum distance as a rolling bearing fault signature to achieve early detection of rolling bearing faults. Summary of the Invention

[0005] In view of the above problems, the present invention provides a rolling bearing fault feature extraction method based on chaos theory to detect early bearing faults, thereby solving the problem of difficulty in detecting early rolling bearing faults in the prior art.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for detecting early faults in rolling bearings based on chaos theory is proposed. First, the vibration signal of the rolling bearing is collected during operation. Then, the vibration signal is subjected to CEEMDAN noise reduction processing and phase space reconstruction. The step state of the chaotic oscillator is observed. At the same time, the maximum distance is calculated to quantify the periodic state change of the chaotic oscillator. Finally, the rolling bearing fault is determined based on the relationship between the chaotic oscillator and the maximum distance.

[0008] Please follow the steps below to implement it:

[0009] 1. Collect the vibration acceleration signal x(t) of the rolling bearing;

[0010] 2. Let E i(*) is the i-th eigenmode component obtained after EMD decomposition, is the i-th eigenmode component obtained after CEEMDAN decomposition, v j For a Gaussian white noise signal that satisfies the standard normal distribution, j = 1, 2, ..., NN is the number of times white noise is added, ε is the standard table of white noise, and x(t) is the vibration acceleration signal to be decomposed. The CEEMDAN decomposition steps are as follows:

[0011] 1) Add Gaussian white noise to the signal to be decomposed x(t) to obtain the new signal x(t)+

[0012] (-1) q εv j (t), where q = 1, 2, ..., perform EMD decomposition on the new signal to obtain the first-order eigenmode component C1.

[0013]

[0014] 2) The first intrinsic mode component of CEEMDAN decomposition is obtained by averaging the N generated modal components:

[0015]

[0016] 3) Calculate the residual after removing the first modal component:

[0017]

[0018] 4) Add positive and negative paired Gaussian white noise to r1(t) to obtain a new signal. Use the new signal as the carrier to perform EMD decomposition to obtain the first-order modal component D1, from which the second eigenmode component of CEEMDAN decomposition can be obtained:

[0019]

[0020] 5) Calculate the residual after removing the second modal component:

[0021]

[0022] 6) Repeat the above steps until the residual signal is a monotonic function and cannot be decomposed further, and the algorithm ends. At this time, the number of intrinsic mode components obtained is K, and the original signal x(t) is decomposed into:

[0023]

[0024] 7) Signal reconstruction is performed based on the correlation coefficients between the IMF components decomposed by CEEMDAN and the signal to be decomposed x(t).

[0025] 3. Perform phase space reconstruction on the reconstructed vibration signal y(t). Before performing phase space reconstruction, the delay time and embedding dimension must be calculated first.

[0026] 1) The mutual information method is used to calculate the delay time τ.

[0027] Mutual information method is used for two independent time series X={x1,x2,…,x m} and Y={y1,y2,…,y m}, let event x i The probability of occurrence is P(x i ), then the information entropy of the two sequences are:

[0028]

[0029]

[0030] The joint entropy of sequences X and Y is:

[0031]

[0032] Where P x,y (x i ,y j ) is x i ,y j The joint probability of .

[0033] Depends on the conditional entropy H(X|Y): When the variable Y is a known quantity, the mutual information function I(X,Y) is:

[0034] I(X,Y)=H(X)-H(X|Y)=H(X)+H(Y)-H(X,Y)

[0035] When the mutual information function I(X,Y) reaches a minimum value for the first time, the corresponding time is the delay time τ.

[0036] 2) Use the CAO method to calculate the embedding dimension.

[0037] E1(m)=E(m+1) / E(m) (1)

[0038] E2(m)=E * (m+1) / E * (m) (2)

[0039] Where: E1(m) and E2(m) are functions related to the embedding dimension m and the delay time τ.

[0040] From formula (1), we can see that as the embedding dimension m continues to increase, when m>m0, E1(m) no longer changes with m, and at this time there is an embedding dimension m.

[0041] 4. After determining the delay time and embedding dimension, perform phase space reconstruction and calculate the maximum distance. The maximum distance can quantitatively characterize the degree of fluctuation of the bearing vibration signal phase trajectory during the phase space evolution process, thereby revealing the dynamic characteristics and evolution law of the vibration signal. The maximum distance calculation formula is as follows:

[0042] Based on the reconstruction matrix Y, the Euclidean distance between any two vectors in the reconstruction matrix Y is obtained, that is,

[0043] d i,j =|Y i -Y j |i,j=1,2,…N

[0044] Thus we get the distance matrix d:

[0045]

[0046] Then, find the maximum value in the distance matrix d:

[0047] d max =max(d)=max{d i,j ,i,j=1,2,…,N}

[0048] d max This is the maximum distance.

[0049] At the maximum distance d max Fault diagnosis of rolling bearings as fault characteristics.

[0050] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0051] 1) Introducing chaotic oscillators and using the maximum distance as the rolling bearing fault characteristic

[0052] Given the high sensitivity of chaotic oscillators to small periodic signals, chaotic oscillator detection methods detect rolling bearing faults by observing the transition of the oscillator from a chaotic state to a large-scale periodic state. The maximum distance is used to quantify the change in the chaotic oscillator's periodic state. A method for early bearing fault detection based on chaos theory is proposed, using the maximum distance as a rolling bearing fault signature to achieve early detection of rolling bearing faults.

[0053] 2) Data denoising using CEEMDAN

[0054] During the decomposition process, the various IMF components derived from the EMD decomposition of white noise are added. This results in a smaller residual noise in the reconstructed signal (compared to the EEMD result), reducing the number of screening attempts. Compared to other noise reduction methods, this method offers superior noise reduction effectiveness, allowing for more intuitive identification of a large number of high-amplitude fluctuations near the fault frequency multiplication and rotational frequency corresponding to the faulty bearing. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a flow chart of a rolling bearing fault diagnosis method according to the present invention;

[0056] Figure 2 is the maximum distance in phase space corresponding to each time slice of the rolling bearing reconstructed signal of the present invention;

[0057] Figure 3 is a chaotic oscillator phase diagram of the rolling bearing reconstructed signal time slice 454 of the present invention;

[0058] Figure 4 is a chaotic oscillator phase diagram of the rolling bearing reconstructed signal time slice 455 of the present invention;

[0059] Figure 5 is a spectrum diagram of the original vibration signal before reconstruction of the present invention;

[0060] Figure 6 is a spectrum diagram of the vibration signal of time slice 454 after reconstruction according to the present invention;

[0061] Figure 7 It is a spectrum diagram of the vibration signal of time slice 455 after reconstruction according to the present invention. DETAILED DESCRIPTION

[0062] The following examples clearly and completely describe the technical solutions of the present invention. It is obvious that the described examples are only some of the embodiments of the present invention, rather than all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0063] like Figure 1 As shown in the figure, a rolling bearing fault feature extraction method based on chaos theory belongs to the rolling bearing early fault detection method, which includes the following steps: first, collecting the vibration signal during the operation of the rolling bearing, then performing CEEMDAN noise reduction processing on the vibration signal, and then reconstructing the phase space, observing the step state of the chaotic oscillator, and calculating the maximum distance to quantify the periodic state change of the chaotic oscillator. Finally, judging whether the rolling bearing is faulty by the chaotic oscillator and the maximum distance.

[0064] Please follow the steps below to implement it:

[0065] 1. Collect the vibration acceleration signal x(t) of the rolling bearing;

[0066] 2. Let E i (*) is the i-th eigenmode component obtained after EMD decomposition, is the i-th eigenmode component obtained after CEEMDAN decomposition, vj For a Gaussian white noise signal that satisfies the standard normal distribution, j = 1, 2, ..., NN is the number of times white noise is added, ε is the standard table of white noise, and x(t) is the vibration acceleration signal to be decomposed. The CEEMDAN decomposition steps are as follows:

[0067] 1) Add Gaussian white noise to the signal to be decomposed x(t) to obtain the new signal x(t)+

[0068] (-1) q εv j (t), where q = 1, 2, ..., perform EMD decomposition on the new signal to obtain the first-order eigenmode component C1.

[0069]

[0070] 2) The first intrinsic mode component of CEEMDAN decomposition is obtained by averaging the N generated modal components:

[0071]

[0072] 3) Calculate the residual after removing the first modal component:

[0073]

[0074] 4) Add positive and negative paired Gaussian white noise to r1(t) to obtain a new signal. Use the new signal as the carrier to perform EMD decomposition to obtain the first-order modal component D1, from which the second eigenmode component of CEEMDAN decomposition can be obtained:

[0075]

[0076] 5) Calculate the residual after removing the second modal component:

[0077]

[0078] 6) Repeat the above steps until the residual signal is a monotonic function and cannot be decomposed further, and the algorithm ends. At this time, the number of intrinsic mode components obtained is K, and the original signal x(t) is decomposed into:

[0079]

[0080] 7) Signal reconstruction is performed based on the correlation coefficients between the IMF components decomposed by CEEMDAN and the signal to be decomposed x(t).

[0081] 3. Perform phase space reconstruction on the reconstructed vibration signal y(t). Before performing phase space reconstruction, the delay time and embedding dimension must be calculated first.

[0082] 1) The mutual information method is used to calculate the delay time τ.

[0083] Mutual information method is used for two independent time series X={x1,x2,…,x m} and Y={y1,y2,…,y m}, let event x i The probability of occurrence is P(x i ), then the information entropy of the two sequences are:

[0084]

[0085]

[0086] The joint entropy of sequences X and Y is:

[0087]

[0088] Where P x,y (x i ,y j ) is x i ,y j The joint probability of .

[0089] Depends on the conditional entropy H(X|Y): When the variable Y is a known quantity, the mutual information function I(X,Y) is:

[0090] I(X,Y)=H(X)-H(X|Y)=H(X)+H(Y)-H(X,Y)

[0091] When the mutual information function I(X,Y) reaches a minimum value for the first time, the corresponding time is the delay time τ.

[0092] 2) Use the CAO method to calculate the embedding dimension.

[0093] E1(m)=E(m+1) / E(m) (1)

[0094] E2(m)=E * (m+1) / E * (m) (2)

[0095] Where: E1(m) and E2(m) are both functions related to the embedding dimension m and the delay time τ. From formula (1), we can see that as the embedding dimension m continues to increase, when m>m0, E1(m) no longer changes with m, and at this time the embedding dimension m exists.

[0096] 4. After determining the delay time and embedding dimension, the phase space is reconstructed and the maximum distance is calculated. The maximum distance can quantitatively represent the fluctuation degree of the bearing vibration signal phase trajectory in the evolution process of the phase space, so as to reveal the dynamic characteristics and evolution law of the vibration signal. The calculation formula of the maximum distance is as follows:

[0097] Based on the reconstructed matrix Y, the Euclidean distance between any two vectors in the reconstructed matrix Y is obtained, that is,

[0098] d i,j = |Y i -Y j |, i, j = 1, 2, … N

[0099] Thus, the distance matrix d is obtained:

[0100]

[0101] Then, the maximum value in the distance matrix d is obtained:

[0102] d max = max(d) = max{d i,j , i, j = 1, 2, …, N}

[0103] d max is the maximum distance. Take the maximum distance d max as the fault feature to diagnose the rolling bearing.

[0104] The specific implementation is as follows:

[0105] In order to verify the effectiveness of the rolling bearing fault feature extraction method based on chaos theory, the data of this embodiment is from the bearing data center of Xi'an Jiaotong University, the rolling bearing model is LDK UER204, the sampling frequency is set to 25.6KHz, the sampling interval is 1min, and the sampling time is 1.28s each time.

[0106] Table 1 is a fault sample of a rolling bearing

[0107]

[0108] Taking bearing 2-1 as an example, first, the full cycle time slice of bearing 2-1 is decomposed by CEEMDAN, and the bearing vibration signal is reconstructed according to the correlation coefficient to obtain a new denoising signal y(t).

[0109] The phase space of the noise reduction signal y(t) is reconstructed. The mutual information method is used to calculate the delay time τ, and the CAO method is used to calculate the embedding dimension m (these two parameters are preparations for phase space reconstruction and need to be determined before phase space reconstruction). After determining the two parameters, the phase space is reconstructed to obtain the chaotic oscillator phase diagram and maximum distance d corresponding to each time slice. max .Compare Figure 2 The maximum distance d corresponding to the time slice point max The bearing fault can be diagnosed by observing the mutation of the chaotic oscillator phase diagram. Figure 2 It can be seen that the maximum distance corresponding to the 455 time slice has a sudden change compared to the previous one, and the fluctuation of the maximum distance has been increasing since the 455 time slice. And compare the chaotic oscillator phase diagrams of time slices 454 and 455 (such as Figure 3 and Figure 4 As shown in the figure, the chaotic oscillator phase diagram at time slice 454 and before is ellipsoidal, indicating that the bearing vibration is relatively stable. However, starting at time slice 455, the chaotic oscillator phase diagram changes to a bird's nest shape, indicating that the bearing vibration is intensified, which means that the bearing has failed at this stage.

[0110] In order to verify the effectiveness of the maximum distance, the spectrum analysis of the bearing vibration signal after reconstructing time slices 454 and 455 is performed to compare Figures 5-7 visible, Figure 6 In the middle, there is no obvious high amplitude peak, the vibration of the bearing is relatively stable and the operation is normal. Figure 7 A large number of high-amplitude fluctuations appear near the fault frequency multiplier and rotational frequency corresponding to the middle bearing. This proves that the bearing is faulty at time slice 455, demonstrating the validity of the maximum distance.

[0111] Compare at the same time Figure 5 and Figure 7 ,from Figure 7 It can be seen that the bearing vibration signal after noise reduction by the CEEMDAN method can clearly see the fault frequency and its multiples as well as the side frequencies near the fault frequency. The feature information is rich and prominent, which is conducive to fault feature identification and fault diagnosis. Figure 5 The original signal without CEEMDAN processing shows redundant fault feature information, and the fault identification effect is poor.

Claims

1. A rolling bearing fault feature extraction method based on chaos theory, characterized in that: The process includes the following steps: first, collecting the vibration signal of the rolling bearing during operation, then performing CEEMDAN noise reduction on the vibration signal, and then performing phase space reconstruction to observe the step state of the chaotic oscillator. At the same time, the maximum distance is calculated to quantify the periodic state change of the chaotic oscillator. Finally, the rolling bearing fault is determined based on the chaotic oscillator and the maximum distance. The process steps are specifically as follows: S1: Collect the vibration acceleration signal x(t) of the rolling bearing; S2: Perform CEEMDAN noise reduction processing on the vibration acceleration signal x(t); S3: Reconstruct the signal y(t) based on the correlation coefficient between each IMF component decomposed by CEEMDAN and the signal to be decomposed x(t); S4: Calculate the delay time and embedding dimension of the reconstructed signal y(t); S5: After determining the delay time and embedding dimension, reconstruct the phase space of the reconstructed vibration signal y(t) and calculate the maximum distance d max , with the maximum distance d max Use it as a fault feature to diagnose rolling bearing faults; The maximum distance calculation formula is as follows: Based on the reconstruction matrix Y, the Euclidean distance between any two vectors in the reconstruction matrix Y is obtained, that is: d i,j =|Y i -Y j |i,j=1,2,…N Thus we get the distance matrix d: Then, find the maximum value in the distance matrix d: d max =max(d)=max{d i,j ,i,j=1,2,…,N} d max That is the maximum distance, with the maximum distance d max Fault diagnosis of rolling bearings as fault characteristics.

2. The method for extracting rolling bearing fault features based on chaos theory according to claim 1, characterized in that: Let E i (*) is the i-th eigenmode component obtained after EMD decomposition, is the i-th eigenmode component obtained after CEEMDAN decomposition, v j For a Gaussian white noise signal that satisfies a standard normal distribution, j = 1, 2, ..., NN is the number of times white noise is added, ε is the standard table of white noise, and x(t) is the vibration acceleration signal to be decomposed. The decomposition steps of the CEEMDAN denoising process in step S2 are as follows: 1) Add Gaussian white noise to the signal to be decomposed x(t) to obtain a new signal x(t)+(-1) q εv j (t), where q = 1, 2…, perform EMD decomposition on the new signal to obtain the first-order eigenmode component C1, 2) The first intrinsic mode component of CEEMDAN decomposition is obtained by averaging the N generated modal components: 3) Calculate the residual after removing the first modal component: 4) Add positive and negative paired Gaussian white noise to r1(t) to obtain a new signal. Use the new signal as the carrier to perform EMD decomposition to obtain the first-order modal component D1, from which the second eigenmode component of CEEMDAN decomposition can be obtained: 5) Calculate the residual after removing the second modal component: 6) Repeat the above steps until the residual signal is a monotonic function and cannot be decomposed further, and the algorithm ends. At this time, the number of intrinsic mode components obtained is K, and the original signal x(t) is decomposed into:

3. The method for extracting rolling bearing fault features based on chaos theory according to claim 2, characterized in that: The mutual information method is used to calculate the delay time τ, specifically: Mutual information method is used for two independent time series X={x1,x2,…,x m } and Y={y1,y2,…,y m }, let event x i The probability of occurrence is P(x i ), then the information entropy of the two sequences are: The joint entropy of sequences X and Y is: Where P x,y (x i ,y j ) is x i ,y j The joint probability of Depends on the conditional entropy H(X|Y): When the variable Y is a known quantity, the mutual information function I(X,Y) is: I(X,Y)=H(X)-H(X|Y)=H(X)+H(Y)-H(X,Y) When the mutual information function I(X,Y) reaches a minimum value for the first time, the corresponding time is the delay time τ.

4. The method for extracting rolling bearing fault features based on chaos theory according to claim 2, characterized in that: The CAO method is used to find the embedding dimension, specifically: E1(m)=E(m+1) / E(m) (1) E2(m)=E * (m+1) / E * (m) (2) Where: E1(m) and E2(m) are functions related to the embedding dimension m and the delay time τ; From formula (1), we can see that as the embedding dimension m continues to increase, when m>m0, E1(m) no longer changes with m, and at this time there is an embedding dimension m.

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