Rolling bearing fault feature extraction method based on NRBO-FMD decomposition and reconstruction

Abstract

The invention discloses a rolling bearing fault feature extraction method based on NRBO-FMD decomposition and reconstruction. Firstly, vibration signals of a rolling bearing are collected through a vibration sensor and subjected to standardization processing; secondly, an NRBO algorithm is adopted to optimize decomposition parameters of the FMD, self-adaptive decomposition of the vibration signals is achieved, and the vibration signals are decomposed into a plurality of intrinsic mode components IMFs; screening and reconstructing the IMFs obtained by decomposition by adopting a kurtosis-frequency domain correlation coefficient screening criterion to obtain a reconstructed signal; envelope demodulation is carried out on the reconstructed signal, an envelope spectrum is calculated, and a bearing fault characteristic frequency is extracted; and finally, comparing with the theoretical fault characteristic frequency of the bearing to determine the fault type of the bearing. Through a signal decomposition and reconstruction method, effective extraction of fault impact signals under noise and interference conditions is realized, and the accuracy of fault diagnosis is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of rolling bearing fault diagnosis, and particularly relates to a method for extracting rolling bearing fault features based on NRBO-FMD decomposition and reconstruction. Background Technique

[0002] As an indispensable key component in rotating machinery, rolling bearings are widely used in many industrial fields such as aerospace, automobile manufacturing, electric power, and metallurgy. It plays important roles in mechanical equipment, such as supporting the rotating shaft, reducing friction, and ensuring transmission accuracy. The quality of its operation directly affects the performance and reliability of the entire mechanical equipment. Once a rolling bearing fails, it may cause equipment shutdown, production interruption, and even trigger serious safety accidents, resulting in huge economic losses.

[0003] When a rolling bearing has a local fault, during the operation of the equipment, periodic and pulsed vibration signals will be generated at the corresponding position. By collecting and analyzing the vibration signals during the operation of the equipment through vibration sensors, it is possible to determine whether the bearing has failed. However, due to the complex structure of mechanical equipment and its operation in a complex noise environment, the weak periodic pulsed signals generated are often submerged by complex noises and other interference components. Therefore, it is of great significance to study the extraction of fault feature signals from vibration signals containing complex noises and interferences.

[0004] At present, various methods have been proposed for extracting rolling bearing fault features. These methods can achieve the extraction of fault features to a certain extent, but they also have their own limitations. Due to the non-stationary and non-linear characteristics of vibration signals, traditional time-frequency analysis methods are difficult to effectively handle such signals. Signal decomposition methods have good performance in dealing with non-stationary and non-linear signals. However, traditional empirical mode decomposition (EMD) and its improved methods will have different degrees of mode mixing during signal decomposition, and there is also the problem of unstable decomposition results. The feature mode decomposition method (FMD) solves the problems of mode mixing and decomposition stability compared with traditional EMD and its improved methods. Compared with the current relatively advanced variational mode decomposition (VMD) method, it takes into account both the impact and periodicity of fault signals and is robust to other noises and interferences. Therefore, it has natural advantages in the field of fault diagnosis. However, the FMD decomposition requires manual parameter setting, which makes the decomposition of signals lack self-adaptability.

[0005] To address the above problems, the present invention uses a Newton-Raphson-based optimizer (NRBO) to optimize the parameters of FMD, proposes a new NRBO-FMD vibration signal decomposition method based on parameter optimization, and reconstructs the decomposed signal, thereby realizing the extraction of bearing fault features, which is also a technical problem that needs to be urgently solved by researchers in this field. Summary of the Invention

[0006] In view of the problem that the fault features of rolling bearings are weak and difficult to extract under noise and interference conditions, and the need to artificially set parameters in the feature mode decomposition (FMD), the present invention proposes an adaptive feature mode decomposition method based on NRBO-FMD to decompose and reconstruct the collected vibration signals, which can effectively extract the fault features of vibration signals under noise interference conditions and realize the fault diagnosis of rolling bearings.

[0007] To solve the above technical problems, the technical solution adopted by the present invention is: a method for extracting rolling bearing fault features based on NRBO-FMD decomposition and reconstruction, including the following steps:

[0008] Step 1: Collect the vibration signals of the rolling bearing.

[0009] Step 2: Preprocess the collected signals to standardize them.

[0010] Step 3: Use the NRBO algorithm to optimize the parameters of the FMD algorithm to obtain the best parameter combination of FMD, and use the FMD with the best parameter combination to decompose the standardized signal described in Step 2 to obtain the best intrinsic mode functions (IMFs). Specifically, it includes the following steps:

[0011] Step 3(1): Initialize the iteration times and population size of the NRBO algorithm, and set the optimization range of the FMD algorithm parameters.

[0012] Step 3(2): Use the NRBO algorithm to iteratively decompose the standardized signal described in Step 2 within the FMD algorithm parameter range set in Step 3(1) to obtain the intrinsic mode functions (IMFs). Calculate the fitness value of each intrinsic mode function (IMF) through the objective function OF constructed by approximate entropy (ApEn) and kurtosis (Kurtosis), and take the smallest fitness value as the fitness value of this iteration. When the final fitness value reaches the minimum or the maximum iteration times, stop the iteration; otherwise, update the population position and repeat this step.

[0013] Step 3(3): Save the optimal FMD parameter combination and substitute it into the FMD algorithm to decompose the standardized signal described in Step 2 to obtain the intrinsic mode functions (IMFs).

[0014] Step 4. Apply the kurtosis-frequency domain correlation coefficient modal screening criterion to screen and reconstruct the intrinsic mode functions (IMFs) described in Step 3. Specifically, it includes the following steps:

[0015] Step 4 (1). Perform FFT transformation on the standardized signal x described in Step 2 * to calculate its spectrum X(f).

[0016] Step 4 (2). Perform FFT transformation on each intrinsic mode function IMF described in Step 3 i to calculate its spectrum IMF i (f).

[0017] Step 4 (3). Use the results in Step 4 (1) and Step 4 (2) to calculate the frequency domain correlation coefficient of each intrinsic mode function IMF described in Step 3 i and the standardized signal x described in Step 2 *

[0018] Step 4 (4). Calculate the kurtosis value of the standardized signal x described in Step 2 *

[0019] Step 4 (5). Calculate the kurtosis value of each intrinsic mode function IMF described in Step 3 i

[0020] Step 4 (6). Use the results in Step 4 (3), Step 4 (4), and Step 4 (5) to calculate the kurtosis-frequency domain correlation coefficient index I of each intrinsic mode function IMF described in Step 3 i i

[0021] Step 4 (7). Calculate the threshold I of the kurtosis-frequency domain correlation coefficient index th

[0022] Step 4 (8). Compare the calculation result in Step 4 (6) with the threshold result in Step 4 (7), and screen the intrinsic mode function IMF corresponding to I i ≥I th for signal reconstruction. i

[0023] Step 5. Perform envelope demodulation analysis on the reconstructed signal described in Step 4 and calculate the envelope spectrum to extract the bearing fault characteristic frequency. Specifically, it includes the following steps:

[0024] Step 5 (1). Perform Hilbert transform on the reconstructed signal described in Step 4 to obtain the signal after Hilbert transform

[0025] ​​​​​​​Step 5 (2), calculate the signal envelope using the result of Step 5 (1) and the signal reconstructed in Step 4.

[0026] Step 5 (3), perform FFT transformation on the envelope described in Step 5 (2) to obtain the signal envelope spectrum.

[0027] Step 5 (4), extract the characteristic frequency using the envelope spectrum obtained in Step 5 (3).

[0028] Step 6, calculate the theoretical fault characteristic frequency of the bearing according to the bearing parameters, compare the fault characteristic frequency extracted in Step 5 with the theoretical fault characteristic frequency, and judge the bearing fault type to achieve fault diagnosis.

[0029] The present invention has the following beneficial effects compared with the prior art:

[0030] 1. The present invention proposes an adaptive signal decomposition method based on NRBO-FMD. By using the NRBO algorithm to adaptively search for the optimal parameters of FMD and constructing a fitness function by combining approximate entropy ApEn and kurtosis index KI, compared with traditional methods, it not only considers the sparse characteristics of fault signals but also takes into account their impact characteristics, so the decomposition result can be optimized.

[0031] 2. In the signal reconstruction stage of the present invention, kurtosis-frequency domain correlation sparse screening is used to screen and reconstruct the modal components obtained by decomposition. While retaining the correlation with the original signal, the modal components containing the most fault information are used to reconstruct the signal. It has a better effect than the screening criterion of a single feature and stronger anti-noise ability than using time-domain correlation sparsity. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is the flow chart of the present invention;

[0033] Figure 2 is the flow chart of optimizing the FMD parameters by the NRBO algorithm;

[0034] Figure 3 is the time-domain waveform diagram of the collected vibration signal;

[0035] Figure 4 is the envelope spectrum of the collected vibration signal;

[0036] Figure 5 is the iterative curve diagram of the fitness value of the NRBO-FMD algorithm;

[0037] Figure 6 is the decomposition result diagram of the NRBO-FMD of the vibration signal;

[0038] Figure 7 is the time-domain waveform diagram of the reconstructed signal;

[0039] Figure 8 For reconstructing the signal envelope spectrum; Specific implementation

[0040] The present invention will be further described below with reference to the accompanying drawings:

[0041] As Figure 1 shown, the present invention provides a rolling bearing fault feature extraction method based on NRBO-FMD decomposition and reconstruction, which specifically includes the following steps:

[0042] Step 1: Collect the vibration signal of the rolling bearing.

[0043] Specifically, the vibration signal is collected by a vibration sensor in cooperation with a data acquisition card. The vibration sensor is fixed on the motor bearing seat and connected to the data acquisition card for data acquisition.

[0044] Step 2: Preprocess the collected signal to standardize it. As shown in the following formula:

[0045]

[0046] In the formula, x represents the collected vibration signal sequence, N represents the sequence length, μ represents the sequence mean, σ represents the sequence standard deviation, and x * represents the standardized signal sequence.

[0047] Step 3: Use the NRBO algorithm to optimize the FMD algorithm parameters to obtain the optimal FMD parameter combination, and use the FMD with the optimal parameter combination to decompose the standardized signal described in Step 2 to obtain the optimal intrinsic mode functions IMFs. Specifically, it includes the following steps:

[0048] Step 3(1): Initialize the iteration times and population size of the NRBO algorithm, and set the optimization range of the FMD algorithm parameters. Specifically:

[0049] The initial value of the population size of the NRBO algorithm is: 10, the initial value of the iteration times is: 20, and the FMD parameter setting range is: FilterSize ∈ [10, 50], modenum ∈ [3, 7].

[0050] Step 3(2): Use the NRBO algorithm to iteratively decompose the standardized signal described in Step 2 within the FMD algorithm parameter range set in Step 3(1) to obtain the intrinsic mode functions IMFs. Calculate the fitness value of each intrinsic mode function IMF through the objective function OF constructed by approximate entropy (ApEn) and kurtosis (Kurtosis), and take the smallest fitness value as the fitness value of this iteration. Stop the iteration when the final fitness value reaches the minimum or reaches the maximum iteration times, otherwise update the population position and repeat this step.

[0051] Specifically, the expression of the objective function OF constructed by approximate entropy (ApEn) and kurtosis is as follows:

[0052]

[0053] ApEn = φ m (r) - φ m+1 (r)(2b)

[0054]

[0055] In the formula, IMF i is the calculated ith intrinsic mode function component, N is the length of IMF i , K is the kurtosis of IMF i , ApEn is the approximate entropy value of IMF i , m is the embedding dimension, r is the similarity tolerance, and OF is the objective function.

[0056] Step 3: Save the optimal FMD parameter combination and substitute it into the FMD algorithm to decompose the standardized signal described in Step 2 to obtain the intrinsic mode function components IMFs.

[0057] Step 4: Adopt the kurtosis-frequency domain correlation coefficient mode screening criterion to screen and reconstruct the intrinsic mode function components IMFs described in Step 3. Specifically, it includes the following steps:

[0058] Step 4(1): Perform FFT transformation on the standardized signal x * described in Step 2 to calculate its spectrum X(f).

[0059] Step 4(2): Perform FFT transformation on each intrinsic mode function component IMF i described in Step 3 to calculate its spectrum IMF i (f).

[0060] Step 4(3): Use the results in Step 4(1) and Step 4(2) to calculate the frequency domain correlation coefficient i of each intrinsic mode function component IMF * described in Step 3 and the standardized signal x described in Step 2 as follows:

[0061]

[0062] In the formula, and respectively represent the means of IMF i (f) and X(f), and respectively represent IMF i (f) and the standard deviation of X(f).

[0063] Step Four (4), calculate the kurtosis value of the standardized signal x described in Step Two * as shown in the following formula:

[0064]

[0065] In the formula, x * is the standardized signal described in Step Two, N is the sequence length of x * and K o is the kurtosis value of x * .

[0066] Step Four (5), calculate the kurtosis value of each intrinsic mode function IMF described in Step Three i as shown in the following formula:

[0067]

[0068] In the formula, IMF i is the calculated ith intrinsic mode function, N is the sequence length of IMF i and K i is the kurtosis value of IMF i .

[0069] Step Four (6), use the results in Step Four (3), Step Four (4), and Step Four (5) to calculate the kurtosis-frequency domain correlation coefficient index I i of each intrinsic mode function IMF described in Step Three i as shown in the following formula:

[0070]

[0071] In the formula, K i is the kurtosis value of IMF i , K o is the kurtosis value of x * and is the frequency domain correlation coefficient between x * and IMF i .

[0072] Step Four (7), calculate the kurtosis-frequency domain correlation coefficient index threshold I th as shown in the following formula:

[0073]

[0074] In the formula, is the frequency domain correlation coefficient between x * and IMF i , is the average value of the frequency-domain correlation coefficients of all modal components and x * , and n is the number of modal components.

[0075] Step Four (Eight): Compare the calculation result in Step Four (Six) with the threshold result in Step Four (Seven), and select the intrinsic mode function IMF corresponding to I i ≥I th for signal reconstruction. The signal reconstruction formula is shown as follows: i S

[0076] S reconstructed = ∑ i∈selected IMF i (8)

[0077] Step Five: Conduct envelope demodulation analysis on the reconstructed signal described in Step Four and calculate the envelope spectrum to extract the bearing fault characteristic frequencies. Specifically, it includes the following steps:

[0078] Step Five (One): Perform Hilbert transform on the reconstructed signal described in Step Four to obtain the signal after Hilbert transform

[0079] Step Five (Two): Calculate the signal envelope using the result of Step Five (One) and the reconstructed signal described in Step Four. As shown in the following formula:

[0080]

[0081] Step Five (Three): Perform FFT transform on the envelope described in Step Five (Two) to obtain the signal envelope spectrum.

[0082] Step Five (Four): Extract the characteristic frequencies using the envelope spectrum obtained in Step Five (Three).

[0083] Step Six: Calculate the theoretical fault characteristic frequencies of the bearing according to the bearing parameters, compare the fault characteristic frequencies extracted in Step Five with the theoretical fault characteristic frequencies, and judge the bearing fault type to achieve fault diagnosis.

[0084] Specifically, the calculation formula for the bearing theoretical fault characteristic frequencies is:

[0085]

[0086] In the formula, f o , f i , f b are the outer ring, inner ring, and rolling element fault characteristic frequencies respectively, F is the bearing rotation frequency, d is the ball diameter, D is the bearing pitch diameter, and α is the ball contact angle.

Claims

1. A rolling bearing fault feature extraction method based on NRBO-FMD decomposition and reconstruction, characterized in that It includes the following steps: Step 1: Collect the vibration signals of the rolling bearing. Step 2: Preprocess the collected signals to standardize them. Step 3: Use the Newton-Raphson-based optimizer (NRBO) algorithm to optimize the parameters of the Feature Mode Decomposition (FMD) algorithm to obtain the optimal parameter combination of FMD, and use FMD with the optimal parameter combination to decompose the standardized signal described in Step 2 to obtain the optimal Intrinsic Mode Functions (IMFs). Step 4: Use the kurtosis-frequency domain correlation coefficient mode screening criterion to screen and reconstruct the Intrinsic Mode Functions (IMFs) described in Step 3. Step 5: Conduct envelope demodulation analysis on the reconstructed signal described in Step 4 and calculate the envelope spectrum to extract the bearing fault characteristic frequencies. Step 6: Calculate the theoretical fault characteristic frequencies of the bearing according to the bearing parameters, compare the fault characteristic frequencies extracted in Step 5 with the theoretical fault characteristic frequencies, judge the bearing fault type, and realize fault diagnosis.

2. The method for extracting fault features of a rolling bearing based on NRBO-FMD decomposition and reconstruction according to claim 1, wherein The calculation formula for preprocessing the collected signals to standardize them in Step 2 is: Where \(x\) represents the collected vibration signal sequence, \(N\) represents the sequence length, \(\mu\) represents the sequence mean, \(\sigma\) represents the sequence standard deviation, and \(x\) * represents the signal sequence after standardization.

3. A rolling bearing fault feature extraction method based on NRBO-FMD decomposition and reconstruction according to claim 1, characterized in that Step 3 includes the following steps: Step 3(1): Initialize the iteration times and population size of the NRBO algorithm, and set the optimization range of the FMD algorithm parameters. Specifically: The initial value of the NRBO algorithm population size is: 10, the initial value of the iteration times is: 20, and the FMD parameter setting range is: FilterSize ∈ [10, 50], modenum ∈ [3, 7].[[]END]] Step 3(2): Use the NRBO algorithm to iteratively decompose the standardized signal described in Step 2 within the FMD algorithm parameter range set in Step 3(1) to obtain the Intrinsic Mode Functions (IMFs), calculate the fitness value of each Intrinsic Mode Function (IMF) through the objective function OF constructed by approximate entropy (ApEn) and kurtosis (Kurtosis), take the smallest fitness value as the fitness value of this iteration, stop the iteration when the final fitness value reaches the minimum or reaches the maximum iteration times, otherwise update the population position and repeat this step. Step 3(3): Save the optimal FMD parameter combination and substitute it into the FMD algorithm to decompose the standardized signal described in Step 2 to obtain the Intrinsic Mode Functions (IMFs).

4. A method for extracting fault features of a rolling bearing based on NRBO-FMD decomposition and reconstruction according to claim 3, characterized in that The expression of the objective function OF constructed by approximate entropy (ApEn) and kurtosis (Kurtosis) in Step 3(2) is: ApEn = φ m (r) - φ m+1 (r)(2b) where IMF i is the calculated ith intrinsic mode function component, N is the length of IMF i , K is the kurtosis of IMF i , ApEn is the approximate entropy value of IMF i , m is the embedding dimension, r is the similarity tolerance, and OF is the objective function.

5. A method for extracting fault features of a rolling bearing based on NRBO-FMD decomposition and reconstruction according to claim 1, characterized in that Step 4 includes the following steps: Step 4 (1): Perform FFT transformation on the standardized signal x described in Step 2 * to calculate its spectrum X(f). Step 4 (2), for each intrinsic mode function IMF described in Step 3 i perform FFT transformation to calculate its spectrum IMF i (f). Step 4(3), calculate each intrinsic mode function IMF described in Step 3 by using the results in Step 4(1) and Step 4(2). i and the normalized signal x described in Step 2 * for the frequency domain correlation coefficient as shown in the following formula: where and represent the mean values of IMF i (f) and X(f) respectively, and represent the standard deviations of IMF i (f) and X(f) respectively. Step Four (4), calculate the kurtosis value of the standardized signal x * described in Step Two. As shown in the following formula: where x * is the signal after normalization described in Step 2, N is the sequence length of x * , K o is the kurtosis value of x * . Step 4 (5), calculate the kurtosis value of each intrinsic mode function IMF described in Step 3. As shown in the following formula: i ​ where IMF i is the calculated ith intrinsic mode function component, N is the sequence length of IMF i , K i is the kurtosis value of IMF i . Step 4(6), use the results in Step 4(3), Step 4(4), and Step 4(5) to calculate each intrinsic mode function IMF described in Step 3 i of the kurtosis-frequency domain correlation coefficient index I i . As shown in the following formula: where K i is the kurtosis value of the IMF i , and K o is the kurtosis value of x * , and the kurtosis value of x * is the frequency domain correlation coefficient with the IMF i . Step 4(7), calculate the kurtosis-frequency domain correlation coefficient index threshold I th . As shown in the following formula: where is x * and the frequency domain correlation coefficient with the IMF i , is the average value of the frequency domain correlation coefficients of all modal components with x * , and n is the number of modal components. Step 4 (VIII), compare the calculation result in Step 4 (VI) with the threshold result in Step 4 (VII), and filter out the i ≥I th corresponding intrinsic mode function IMF i for signal reconstruction. The signal reconstruction formula is shown as follows: S reconstructed = ∑ i∈selected IMF i (8).

6. A method for extracting fault features of rolling bearings based on NRBO-FMD decomposition and reconstruction, characterized in that Step 5 includes the following steps: Step Five (1): Perform Hilbert transform on the reconstructed signal described in Step Four to obtain the signal after Hilbert transform Step 5(2): Calculate the signal envelope using the result of Step 5(1) and the reconstructed signal described in Step 4. As shown in the following formula: Step 5(3): Perform FFT transformation on the envelope described in Step 5(2) to obtain the signal envelope spectrum. Step 5(4): Extract the characteristic frequencies using the envelope spectrum obtained in Step 5(3).

7. A method for extracting fault features of a rolling bearing based on NRBO-FMD decomposition and reconstruction, as claimed in claim 1, wherein The calculation formula for the bearing theoretical fault characteristic frequencies in Step 6 is: where f o , f i , f b are the outer race, inner race, and rolling element fault characteristic frequencies respectively, F is the bearing rotation frequency, d is the ball diameter, D is the bearing pitch diameter, and α is the ball contact angle.

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