Bearing fault diagnosis method based on adaptive optimization of demodulation frequency band selection

Abstract

The present invention discloses a bearing fault diagnosis method based on adaptive optimization demodulation frequency band selection, which uses forward difference method to calculate instantaneous angular velocity IAS. i ; A bivariate spectrogram consisting of cyclic order and spectral order is obtained by using a cyclic spectrum correlation algorithm, cyclic spectrum coherence CSCoh is obtained by normalization, and improved envelope spectrum IES of each sub-band is obtained by integration; the improved envelope spectrum IES of each sub-band is segmented, and the reweighted kurtosis value RK of the improved envelope spectrum IES of each sub-band is calculated and used as the RK value of the corresponding sub-band, the sub-bands are merged and reconstructed, and the merged sub-band corresponding to the maximum RK value after the merge and reconstruction is selected as the optimized demodulation band and envelope analysis is performed to complete the fault feature extraction; the method of the present invention realizes the optimal selection of cyclic spectrum correlation demodulation band, and the fault feature extraction effect is better than the traditional algorithm, and compared with the existing IESFOgram algorithm and CIESFOgram algorithm, no prior parameter input is required.

Description

Technical Field

[0001] The invention relates to a bearing fault diagnosis method based on adaptive optimization demodulation frequency band selection, belonging to the technical field of fault diagnosis technology and signal processing and analysis technology. Background Art

[0002] Rolling bearings are an indispensable component of rotating machinery, and their health directly impacts the safety and reliability of the equipment. Vibration analysis is a commonly used technique for rolling bearing fault diagnosis; however, it cannot meet application requirements in some scenarios. Therefore, research on rolling bearing fault feature extraction methods based on signals from other types of sensors is of great significance. Furthermore, in recent years, instantaneous angular velocity (IAS) has gradually become a promising tool for rotating machinery fault diagnosis. Research has shown that, compared to vibration signals, IAS signals offer advantages such as a high signal-to-noise ratio, strong fault sensitivity, and a direct correlation with rotor dynamics. Therefore, rolling bearing fault feature extraction based on IAS signals is a hot topic in the field of fault diagnosis.

[0003] Rolling bearing fault information is often obscured by background noise and strongly interfering component features (such as gears). Furthermore, rolling elements exhibit random sliding, resulting in non-stationary signals from faulty bearings, complicating the extraction of rolling bearing fault features. Envelope analysis is an effective method for bearing fault feature extraction. Its core objective is to accurately identify demodulation frequency bands rich in fault information. However, rolling bearings do not transmit torque, so IAS signals, which carry localized fault information, are typically weak and susceptible to background noise and interference. Integrating the entire frequency band introduces interference components, making it difficult to identify characteristic spectral lines associated with rolling bearing fault defects. To enhance fault feature recognition, integrating along the spectral frequency band with the richest modulation information can effectively extract fault features. However, these methods lack criteria for optimizing the demodulation frequency band selection. A literature review reveals that existing methods, such as the IESFOgram and CIESFOgram algorithms, require prior knowledge or fail to determine a single optimal demodulation frequency band. However, the IESFOgram algorithm adopts a 1 / 3 binary tree frequency band division structure, which has a fixed bandwidth and cannot be adaptively divided according to signal characteristics. Moreover, as the frequency band is further subdivided, fault information may be lost or interference components may be introduced. Summary of the Invention

[0004] To solve the problems analyzed above, the present invention provides a bearing fault diagnosis method based on adaptive optimization of demodulation frequency band selection to solve the problem that cyclic spectrum correlation requires expert experience to determine the demodulation frequency band rich in fault information.

[0005] The bearing fault diagnosis method based on adaptive optimization demodulation frequency band selection of the present invention is as follows:

[0006] 1. Use the PicoScope signal acquisition system to obtain the instantaneous angular displacement and corresponding time of the optical encoder containing the bearing fault information, and use the forward difference method to calculate the instantaneous angular velocity IAS i The signal is calculated as follows:

[0007]

[0008] Where IAS i represents the instantaneous angular velocity at the i-th moment, i = 1, 2, 3, ..., Δφ = 2π / N, Δt i =t i+1 -t i ; N represents the number of raster grids of the encoder;

[0009] 2. Using cyclic spectrum correlation algorithm to analyze the instantaneous angular velocity IAS i An analysis is performed to obtain a bivariate spectrum of spectral order and cyclic order. To effectively suppress the identification of fault features by background noise and other interference components, the cyclic spectrum correlation is normalized to obtain the cyclic spectrum coherence CSCoh. The cyclic spectrum coherence CSCoh spectrum is divided according to the initial sub-band bandwidth to obtain sub-bands. The improved envelope spectrum IES of each sub-band is obtained by integration along the spectral order axis of the cyclic spectrum coherence CSCoh spectrum. To select a demodulation band with rich fault information, the improved envelope spectrum IES of each sub-band is divided into equal parts. The reweighted kurtosis value RK of the improved envelope spectrum IES of each sub-band is calculated. The obtained reweighted kurtosis value RK of the improved envelope spectrum IES of the sub-band is used as the RK value of the sub-band corresponding to the improved envelope spectrum IES. The sub-band merging and reconstruction algorithm is used to merge and reconstruct the sub-bands along the spectral order axis. The merged sub-band corresponding to the maximum RK value after merging and reconstruction is selected as the optimized demodulation band.

[0010] 2-1. Cyclic spectrum correlation is expressed as a distribution function of two frequency variables: the cyclic frequency related to the modulation, and the spectral frequency related to the carrier signal. That is, cyclic spectrum correlation can describe the correlation distribution of the characteristic carrier and modulation frequencies in the signal. Since there is a 1%-2% random slip between the rolling element and the roller during the operation of the rolling bearing, its fault impact does not have a strict periodicity, that is, it is a second-order cyclostationary signal; the shaft and gear have a strict periodic characteristic when they are engaged, and its signal is a first-order cyclostationary signal; the background noise is not periodic, and the signal is a high-order cyclostationary signal; based on the different cyclic characteristics between different components, the cyclic spectrum correlation algorithm is used to analyze the instantaneous angular velocity IAS. i Signal analysis extracts components related to bearing faults and obtains a bivariate spectrum of spectral order and cyclic order. The cyclic spectrum-related CSC calculation formula is:

[0011]

[0012] Where f is the spectral order, α is the cyclic order, T is the cyclic period, τ is the time delay, FFT[·] is the fast Fourier transform, [·]* is the conjugate, and E{·} is the mathematical expectation. To suppress the influence of noise on the cyclic spectral correlation CSC, the spectral correlation is normalized to obtain the cyclic spectral coherence CSCoh, which is:

[0013]

[0014] 2-2. To further highlight the fault characteristics, the cyclic spectrum coherence CSCoh spectrum is divided according to the initial sub-band bandwidth to obtain sub-bands. The improved envelope spectrum IES of each sub-band is obtained by integrating along the spectral order axis of the cyclic spectrum coherence CSCoh spectrum. The calculation formula is:

[0015]

[0016] Where |·| represents the absolute value, f1 represents the lower limit of integration, and f2 represents the upper limit of integration.

[0017] 2-3. In order to avoid the influence of strong non-Gaussian noise, the improved envelope spectrum IES of each sub-band is divided into equal parts. The kurtosis value Kurt of each part after equal division is expressed as:

[0018]

[0019] Where O represents the data length of IES, p represents the IES after segmentation, μ p is the average value of IES;

[0020] After equally dividing the IES, the kurtosis values ​​of each part are arranged in ascending order, expressed as:

[0021] Kurt asc =asc[(Kurt1,Kurt2…,Kurt M )]

[0022] Where M represents the number of equal parts, Kurt asc represents the kurtosis value in ascending order, asc[·] represents ascending order, Kurt1, Kurt2, ... represent the IES kurtosis value Kurt of the first, second, ... parts after the IES is divided equally, and the kurtosis proportion of each part after the IES is divided equally is expressed as:

[0023]

[0024] Where W desc represents the proportion of kurtosis values ​​in descending order, desc[·] represents descending order, and the reweighted kurtosis RK of the sub-band is expressed as:

[0025]

[0026] Where h represents transpose.

[0027] 3. The reweighted kurtosis RK of the improved envelope spectrum IES of each sub-band obtained in step 2 is used as the RK value of the sub-band corresponding to the improved envelope spectrum IES. With the goal of maximizing fault information, the sub-bands are merged and reconstructed along the spectral order axis using a sub-band merging and reconstruction algorithm. The sub-band merging and reconstruction algorithm includes initial sub-band setting and sub-band merging.

[0028] According to Δf=f s / N w , f s is the sampling frequency, N w The first sub-band is set as the window width. If the reweighted kurtosis value RK of the adjacent second sub-band is larger than the reweighted kurtosis value RK of the first sub-band, the reweighted kurtosis value RK of the first sub-band and the adjacent second sub-band is added. The sub-band merger is valid and the added value is retained. Otherwise, the reweighted kurtosis value RK of the first sub-band is retained as the merged RK value. Then, the reweighted kurtosis value RK of the second sub-band is compared with the reweighted kurtosis value RK of the third sub-band. And so on. Repeat the above process until the end. The sub-bands are merged and reconstructed by sliding right along the spectral order axis.

[0029] The rightward sliding of the sub-band along the spectral order axis is expressed as:

[0030] Q na w[m]=w[m-na]

[0031] Where w[·] is the bandwidth of the first sub-band, n is the number of slips, a is the slip distance, Q na w[·] represents a sliding operation, m = 1, 2, 3, ...;

[0032] Sub-band merging is effectively expressed as:

[0033]

[0034] Where x wl 、x wr 、x wTl They represent the merged sub-band, the first sub-band involved in the merge, and the adjacent sub-band respectively, and max means taking the maximum value;

[0035] 4. Select the merged sub-band corresponding to the maximum RK value after merging and reconstruction as the optimized demodulation band, perform envelope analysis on the optimized demodulation band, complete fault feature extraction, and the optimized demodulation band is expressed as:

[0036]

[0037] Where Nm is the number of merged sub-bands, f c is the center frequency, b w is the bandwidth, RK ri [x w ] represents the RK value corresponding to the merged sub-band, and k represents the search of the sub-band;

[0038] The beneficial effects of the present invention are:

[0039] (1) Compared with the existing demodulation frequency band selection algorithm, the method of the present invention can determine a unique optimized demodulation frequency band without the need for input of prior parameters;

[0040] (2) The present invention utilizes a sub-band merging and reconstruction algorithm, which can adaptively merge and reconstruct sub-bands according to signal characteristics to obtain an optimized demodulation band, thereby guiding the adaptive selection of cyclic spectrum correlation demodulation bands, and the fault feature extraction effect is better than that of traditional algorithms;

[0041] (3) The method of the present invention provides a new approach for fault diagnosis of rotating mechanical equipment in situations where the application of vibration sensors is limited. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The figure shows a bearing with an outer ring fault (right) and a test bench (left) in an embodiment of the present invention;

[0043] Figure 2 is the original encoder signal in the embodiment;

[0044] Figure 3 is the instantaneous angular velocity IAS obtained by forward difference method i Signal;

[0045] Figure 4 To directly access the original IAS i Envelope analysis results of the signal;

[0046] Figure 5 Bispectral variable spectrogram of spectral coherence CSCoh obtained by normalization;

[0047] Figure 6 is the result of direct full-band integration of the cyclic spectrum coherence CSCoh;

[0048] Figure 7 Schematic diagram of the sub-band merging and reconstruction process, where Figure a shows the sub-band before merging, and Figure b shows the result after merging and reconstruction;

[0049] Figure 8 Optimize the demodulation frequency band selection result of the method of the present invention;

[0050] Figure 9The result of envelope analysis for optimized demodulation frequency band;

[0051] Figure 10 is the energy integral graph obtained by the traditional IESFOgram algorithm;

[0052] Figure 11 Improved envelope spectrum IES obtained by traditional IESFOgram algorithm;

[0053] Figure 12 CIESFOgram graph obtained by CIESFOgram algorithm;

[0054] Figure 13 is the combined envelope order spectrum corresponding to CIESFOgram. DETAILED DESCRIPTION

[0055] The following is a clear and complete description of the technical solutions in the examples of the invention herein, in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the invention herein, and therefore the present invention is not limited to the specific embodiments disclosed below.

[0056] Example 1: This example describes the method of the present invention used to extract the fault characteristics of the outer ring of an actual rolling bearing.

[0057] Use Figure 1 The rolling bearing test platform shown in the figure was used for verification. The test platform includes a motor, support bearings, encoder, faulty bearing, magnetic powder brake, and radial loader. The encoder used in the experiment is a SZGLK9040G2 grating encoder with a line count of N = 5000 and a TTL output. The rolling bearing (NU206) was used as the research object. The bearing parameters were (pitch diameter D = 46 mm, rolling element diameter d = 9 mm, contact angle β = 0°, number of rolling elements n = 13). A small groove with a width of approximately 0.5 mm and a depth of approximately 1 mm was machined on the bearing outer ring using wire cutting technology to simulate a localized fault in the rolling bearing outer ring. The characteristic frequency of the rolling bearing outer ring fault is calculated as 5.22× using the following formula.

[0058]

[0059] Formula O out Indicates the characteristic order of outer race fault, O r Indicates the frequency conversion, where the frequency conversion is 1×.

[0060] 1. The SZGLK9040G2 optical encoder installed on the experimental table is used with a sampling rate of 10 6 The PicoScope high-speed acquisition device obtains Figure 2 The raw encoder signal shown is used to obtain the instantaneous angular velocity IAS using the forward difference method. i Signals such as Figure 3 As shown, first directly to the original IAS i Envelope analysis of the signal, such as Figure 4 As shown in Figure 2, it can be found that due to the influence of other interference spectra, it is difficult to effectively identify the bearing fault spectrum.

[0061] 2. According to the sampling frequency f s =5000, window width N w =64, using the cyclic spectrum correlation algorithm CSC to calculate the instantaneous angular velocity IAS i Perform analysis to obtain a bivariate spectrum consisting of cyclic order and spectral order. The calculation formula is:

[0062]

[0063] where f is the spectral order, α is the cycle order, T is the cycle period, τ is the time delay, FFT[·] is the fast Fourier transform, [·]* is the conjugate, and E{·} is the mathematical expectation.

[0064] In order to reduce the influence of uneven noise distribution on CSC, the spectral coherence function CSCoh is obtained by normalizing CSC. The obtained CSCoh spectrum is shown as Figure 5 As shown;

[0065]

[0066] 3. The envelope spectrum obtained by directly performing full-band integration on the cyclic spectrum coherence CSCoh is as follows Figure 6 As shown (comparison), it can be found that the background noise and interference components in the envelope spectrum are strong, and the characteristic order corresponding to the fault is not easy to identify accurately;

[0067] The method of the present invention is used according to the initial sub-band bandwidth (Δf=f s / N w , f s =5000, window width N w =64, i.e., Δf=39.1×) divides the cyclic spectrum coherence CSCoh spectrum into 64 sub-bands, and integrates along the spectral order axis of the cyclic spectrum coherence CSCoh spectrum to obtain the improved envelope spectrum IES of each sub-band. The calculation formula is:

[0068]

[0069] Where |·| represents the absolute value, f1 represents the lower limit of integration, and f2 represents the upper limit of integration.

[0070] 4. In order to avoid the influence of strong non-Gaussian noise, the improved envelope spectrum of each sub-band is divided into 4 equal parts. The kurtosis value of each part after equal division can be expressed as:

[0071]

[0072] Where O represents the data length of IES, p represents the IES after segmentation, μ p is the average value of IES;

[0073] After equal division, the kurtosis values ​​of each part are arranged in ascending order. The ascending order can be expressed as:

[0074] Kurt asc =asc[(Kurt1,Kurt2…,Kurt M )]

[0075] Where M = 4, Kurt asc represents the kurtosis value in ascending order, asc[·] represents ascending order, Kurt1, Kurt2, ... represent the kurtosis value Kurt of the 1st, 2nd, 3rd, and 4th parts of the IES after equal division, and the kurtosis proportion of each part after division is calculated as:

[0076]

[0077] Where W desc represents the proportion of kurtosis value in descending order, desc[·] represents descending order, then the reweighted kurtosis RK of the improved envelope spectrum IES of each sub-band is expressed as:

[0078]

[0079] Where h represents transpose.

[0080] 5. Use the reweighted kurtosis RK of the improved envelope spectrum IES of each sub-band obtained in step 4 as the RK value of the sub-band corresponding to the improved envelope spectrum IES, maximize the fault information as the goal, merge and reconstruct the sub-bands, and calculate the value of the sub-band according to Δf=f s / N w , f s =5000, window width N w=64, set the first sub-band, if the reweighted kurtosis value RK of the adjacent second sub-band is greater than the reweighted kurtosis value RK of the first sub-band, then add the reweighted kurtosis value RK of the first sub-band and the adjacent second sub-band, the sub-band merger is valid and the added value is retained, otherwise the reweighted kurtosis value RK of the first sub-band is retained as the merged RK value, and then compare the reweighted kurtosis value RK of the second sub-band and the third sub-band, and so on, repeat the above process until the end, the sub-bands slide right along the spectral order axis and merge and reconstruct, the above merging process is as follows Figure 7 As shown, Figure 7 (a) is the sub-band before merging and the center frequency f after sub-band merging and reconstruction ci and bandwidth B fi like Figure 7 As shown in (b), the sub-band sliding to the right is expressed as:

[0081] Q na w[m]=w[m-na]

[0082] Sub-band merging is effectively expressed as:

[0083]

[0084] The result of sub-band merging and reconstruction using the method of the present invention in this embodiment is as follows: Figure 8 As shown in the figure, the combined sub-band corresponding to the maximum RK value after the combined reconstruction is selected as the optimized demodulation band, and the optimized demodulation band selection result (f c =312.5×,b w =156.3×) Figure 8 As shown by the dotted circle in the middle, the optimal demodulation frequency band selection is expressed as:

[0085]

[0086] Where N m is the number of merged sub-bands, f c is the center frequency, b w is the bandwidth, RK ri [x w ] represents the RK value corresponding to the merged sub-band, and k represents the search of the sub-band;

[0087] According to the selected optimized demodulation frequency band, envelope analysis is performed and the envelope order spectrum is as follows: Figure 9 ,Depend on Figure 9 It can be seen that through the above method of the embodiment, the background noise and other interference components in the envelope order spectrum are effectively suppressed, and the characteristic order 5.22× of the rolling bearing outer ring fault and its harmonics can be clearly identified.

[0088] Therefore, under the working condition of strong background noise, the method of the present invention can effectively determine a unique optimized demodulation frequency band without the need for parameter input, thereby achieving effective extraction of the fault characteristics of the outer ring of the rolling bearing.

[0089] In order to further verify the effectiveness of the method proposed in this paper, the traditional IESFOgram algorithm was used to analyze the original IAS i The analysis is performed, where the sampling frequency is f s =5000, window width N w =64, fault characteristic order O out =5.22×, the demodulation frequency band obtained (f c =1113.3×,b w =39.1×) Figure 10 As shown, the corresponding improved envelope spectrum IES is as follows Figure 11 As shown in Figure 2, it can be found that due to the influence of the interference component in the envelope spectrum, the characteristic order of the rolling bearing outer ring fault cannot be effectively identified.

[0090] In order to further verify the effectiveness of the method proposed in this paper, the CIESFOgram algorithm is used to analyze the original IAS i The analysis is performed, where the sampling frequency f s =5000, window width N w =64, fault characteristic order O out =5.22×, the obtained CIESFOgram is as follows Figure 12 As shown, the corresponding combined improved envelope spectrum is as follows Figure 13 It can be found that the fault characteristic spectral lines in the combined envelope spectrum are obscured by background noise and other interference components, making it difficult to identify the spectral lines related to the fault characteristics of the rolling bearing outer race.

Claims

1. A bearing fault diagnosis method based on adaptive optimization demodulation frequency band selection, characterized in that: Here are the steps: (1) Collect the instantaneous angular displacement and corresponding time of the optical encoder and calculate the instantaneous angular velocity IAS using the forward difference method i ; Using cyclic spectrum correlation algorithm to analyze the instantaneous angular velocity IAS i Perform analysis to obtain a bivariate spectrogram consisting of cyclic order and spectral order, normalize the bivariate spectrogram to obtain cyclic spectral coherence CSCoh, divide the cyclic spectral coherence CSCoh spectrogram according to the initial sub-band bandwidth to obtain sub-bands, and integrate along the spectral order axis of the cyclic spectral coherence CSCoh spectrogram to obtain the improved envelope spectrum IES of each sub-band; (2) The improved envelope spectrum IES of each sub-band is divided into equal parts, and the reweighted kurtosis value RK of the improved envelope spectrum IES of each sub-band is calculated. The obtained reweighted kurtosis value RK of the improved envelope spectrum IES of the sub-band is used as the RK value of the sub-band corresponding to the improved envelope spectrum IES. The sub-bands are merged and reconstructed along the spectral order axis using the sub-band merging and reconstruction algorithm, and the merged sub-band corresponding to the maximum RK value after the merging and reconstruction is selected as the optimized demodulation band; (3) Perform envelope analysis on the optimized demodulation frequency band to complete fault feature extraction.

2. The bearing fault diagnosis method based on adaptive optimization demodulation frequency band selection according to claim 1 is characterized in that: The kurtosis value Kurt of each part after the IES is divided into equal parts in step (2) is expressed as: Where O represents the data length of IES, p represents the IES after segmentation, μ p is the average value of IES; After equally dividing the IES, the kurtosis values ​​of each part are arranged in ascending order, expressed as: Kurt asc =asc[(Kurt1,Kurt2…,Kurt M , Where M represents the number of equal parts, Kurt asc represents the kurtosis value in ascending order, asc[·] represents ascending order, Kurt1, Kurt2, ... represent the kurtosis values ​​Kurt of the 1st, 2nd, ... parts after the IES is divided equally, and the kurtosis proportion of each part after the IES is divided equally is expressed as: Where W desc represents the proportion of kurtosis value in descending order, desc[·] represents descending order, then the reweighted kurtosis RK of the improved envelope spectrum IES of each sub-band is expressed as: Where h represents transpose.

3. The bearing fault diagnosis method based on adaptive optimization demodulation frequency band selection according to claim 1 is characterized in that: Sub-band merging and reconstruction is based on Δf=f s / N w , f s is the sampling frequency, N w The first sub-band is set as the window width. If the reweighted kurtosis value RK of the adjacent second sub-band is larger than the reweighted kurtosis value RK of the first sub-band, the reweighted kurtosis value RK of the first sub-band and the adjacent second sub-band is added. The sub-band merger is valid and the added value is retained. Otherwise, the reweighted kurtosis value RK of the first sub-band is retained as the merged RK value. Then, the reweighted kurtosis value RK of the second sub-band is compared with the reweighted kurtosis value RK of the third sub-band. And so on. Repeat the above process until the end. The sub-bands are merged and reconstructed by sliding right along the spectral order axis. The rightward sliding of the sub-band along the spectral order axis is expressed as: Q na w[m]=w[m-na] Where w[·] is the bandwidth of the first sub-band, n is the number of slips, a is the slip distance, Q na w[·] represents a sliding operation, m = 1, 2, 3, ...; Sub-band merging is effectively expressed as: Where x wl 、x wr 、x wTl They represent the merged sub-band, the first sub-band involved in the merge, and the adjacent sub-band respectively, and max means taking the maximum value; The combined sub-band corresponding to the maximum RK value after combined reconstruction is selected as the optimized demodulation band. The optimized demodulation band is expressed as: Where N m is the number of merged sub-bands, f c is the center frequency, b w is the bandwidth, RK ri [x w ] represents the RK value corresponding to the merged sub-band, and k represents the retrieval of the sub-band.

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