Multi-source time-frequency ridge extraction method based on synchrosqueezing transform

Abstract

The application discloses a multi-source time-frequency ridge extraction method based on synchronous extraction transformation, and comprises the following steps: acquiring a gearbox time-domain vibration signal; performing variational modal decomposition filtering on the time-domain vibration signal to obtain a characteristic modal component time-domain vibration signal; performing synchronous extraction transformation time-frequency analysis on the characteristic modal component time-domain vibration signal; extracting a rotating shaft rotating frequency and a gear meshing frequency time-frequency ridge according to a local peak value search algorithm; optimizing the time-frequency ridge based on a multi-source ridge fusion method to extract a rotating frequency curve; and tracking the order of the characteristic modal component time-domain vibration signal based on the rotating frequency curve to obtain a rotating shaft fault characteristic order from an angular domain order spectrum. The method improves the frequency mutation condition and has high IF fusion precision, obtains the fault characteristic order from the order spectrum of the signal after order tracking, improves the frequency ambiguity phenomenon, and optimizes the bearing fault characteristic extraction effect.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rotating machinery condition monitoring and fault diagnosis, more particularly to a multi-source time-frequency ridge extraction method based on synchronous extraction transform. BACKGROUND

[0002] Gearbox is widely used in rotating machinery transmission and operates in harsh environment, so it is of great significance to study gearbox fault diagnosis. The change of shaft frequency of gearbox makes the signal processing method under uniform speed condition no longer applicable. The order tracking method converts time-domain non-stationary signal into angular-domain stationary signal, and extracts fault characteristic order information from angular-domain order spectrum. The order tracking method based on time-frequency analysis estimates the instantaneous frequency (IF) of shaft, avoiding the measurement accuracy problems of angle encoder disk and other data acquisition devices, and reducing the cost of gearbox online monitoring.

[0003] Many scholars have proposed effective methods to solve the problems of frequency spectrum blurring phenomenon and low IF estimation accuracy caused by variable speed and noise interference. The time-frequency ridge precision optimization problem based on time-frequency analysis (TFA) is a big difficulty in the field of variable speed.

[0004] Therefore, how to provide a time-frequency ridge extraction method capable of improving frequency blurring phenomenon and high IF fusion precision is a problem that those skilled in the art need to solve. SUMMARY

[0005] Therefore, the present application provides a multi-source time-frequency ridge extraction method based on synchronous extraction transform, which optimizes the frequency mutation and improves the IF estimation accuracy.

[0006] To achieve the above purpose, the present application adopts the following technical solutions:

[0007] The multi-source time-frequency ridge extraction method based on synchronous extraction transform comprises:

[0008] Obtaining a time-domain vibration signal of a gearbox;

[0009] Performing variational modal decomposition filtering on the time-domain vibration signal to obtain a characteristic modal component time-domain vibration signal;

[0010] Solving the synchronous extraction transform time-frequency spectrum and the synchronous extraction transform envelope time-frequency spectrum of the characteristic modal component time-domain vibration signal to obtain a gear meshing frequency spectrum line and a shaft rotation frequency spectrum line, respectively;

[0011] Extracting the shaft rotation frequency and the gear meshing frequency time-frequency ridge according to a local peak value search algorithm;

[0012] Based on the multi-source ridge line fusion method, the extraction effect of gear meshing frequency time-frequency ridge line is optimized, and the rotation frequency curve is extracted.

[0013] Based on the rotation frequency curve, the order tracking of the characteristic modal component time-domain vibration signal is performed, and the gear box bearing fault characteristic order is obtained from the angular domain order spectrum.

[0014] Preferably, the synchronous extraction transformation implementation process is:

[0015] 1) Short-time Fourier transform time-frequency spectrum

[0016] The time-frequency spectrum of the characteristic modal component time-domain vibration signal s(t) is calculated, and the short-time Fourier transform formula is as follows:

[0017]

[0018] In the formula, g(u-t) represents a movable window function;

[0019] (1) Multiply the phase factor e jωt on both sides of the formula, and the formula is as follows:

[0020]

[0021] In the formula: S(ω) represents the Fourier transform of s(t), G(ω) represents the Fourier transform of the window function g(u-t);

[0022] Let the harmonic signal with frequency ω0 be The formula is converted into the frequency domain as follows:

[0023]

[0024] In the formula: A represents the harmonic amplitude, ζ represents the frequency, and δ() represents the indicator function;

[0025] Substitute formula (3) into formula (2), and the short-time Fourier transform time-frequency spectrum formula is as follows:

[0026]

[0027] Where, G e (t,ω) represents the short-time Fourier transform time-frequency;

[0028] 2) IF estimation

[0029] The IF formula is as follows:

[0030]

[0031] In the formula: Ge(t,ω) represents the partial derivative of Ge(t,ω) with respect to t;

[0032] 3) SET time-frequency spectrum

[0033] The SET time-frequency spectrum is calculated according to the following formula:

[0034] T e (t,ω) = G e (t,ω) δ(ω-ω0(t,ω)) (6)

[0035] In the formula, δ(ω-ω0(t,ω)) represents a synchronization extraction operator, T e (t,ω) represents a SET time-frequency.

[0036] Preferably, the local peak searching algorithm is implemented as follows:

[0037] 1) Time-frequency spectrum initialization: randomly obtain n initial time points on the analysis period, and index the frequency with the maximum spectrum energy;

[0038] 2) Select the frequency with the maximum spectrum energy in the entire analysis frequency band of the current time point according to the following formula:

[0039] f(t,ω) = argmaxT e (t,ω), ω = 1, 2, …, N / 2+1 (7)

[0040] In the formula, T e (t,ω) represents a SET time-frequency spectrum, N represents an N-point fast Fourier transform, t represents a time point on a time-frequency graph, and ω represents a frequency point on the time-frequency graph.

[0041] 3) Frequency value comparison: compare the frequency with the maximum spectrum energy in the analysis frequency band of the current time point with the frequency of the previous time point, and the determination condition is as follows:

[0042] (f(t,ω) > αf(t-1,ω)) || (f(t,ω) < βf(t-1,ω)) (8)

[0043] In the formula, α and β are obtained by expert experience. If the formula (8) is not established, the frequency value corresponding to the maximum spectrum energy of the current time point is 0. The formulas (7) and (8) are cycled until the formula (8) is established, so as to obtain the frequency value of the time point.

[0044] 4) Search the frequency value corresponding to the next time point from the current time point forward and backward until the entire analysis period is searched;

[0045] 5) Redistribute to obtain the gear meshing frequency time-frequency ridge line of the global analysis period.

[0046] Preferably, the multi-source ridge line fusion method is implemented as follows:

[0047] 1) Extract 4 time-frequency ridge lines from low frequency band and high frequency resonance band of synchronous extraction transform time-frequency spectrum and synchronous extraction transform envelope time-frequency spectrum respectively;

[0048] 2) According to the fixed linear relationship between gear meshing frequency and shaft rotation frequency, and combining the structure information of synchronous extraction transform time-frequency spectrum and synchronous extraction transform envelope time-frequency spectrum, the extracted time-frequency ridge lines are preprocessed;

[0049] 3) Based on the time-frequency ridge line corresponding to the highest energy of the high frequency resonance band time-frequency spectrum as the reference, the synchronization processing is carried out;

[0050] 4) According to the frequency selection standard deviation of the fusion interval, the time-frequency ridge line with the minimum standard deviation is selected as the fusion result, the average value of the 4 time-frequency ridge lines corresponding to the non-fusion interval is calculated, and the fusion result and the time-frequency ridge line average value are redistributed to obtain the gear meshing frequency time-frequency ridge line fusion result of the global analysis period;

[0051] 5) According to the fixed linear relationship between the gear meshing frequency of the fusion result and the shaft rotation frequency, the rotation frequency curve change trend is estimated.

[0052] Preferably, the specific calculation process of the synchronization processing is:

[0053] The time-frequency ridge line synchronization processing formula is:

[0054]

[0055] In the formula, The time-frequency ridge line synchronization result is represented by k, which represents the synchronization coefficient determined by the coincidence degree of the time-frequency ridge line and the reference ridge line, and f i The low frequency band and the i-th time-frequency ridge line of the resonance frequency band are represented.

[0056] According to the above technical solution, compared with the prior art, the present application provides a multi-source time-frequency ridge line extraction method based on synchronous extraction transform, an improved multi-source ridge line fusion method improves the frequency mutation condition and has high IF fusion precision, obtains the fault characteristic order from the order spectrum of the order tracking signal, improves the frequency ambiguity phenomenon, and optimizes the bearing fault feature extraction effect. BRIEF DESCRIPTION OF DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only embodiments of the present application, and those skilled in the art can obtain other drawings according to the provided drawings without creating any creative labor.

[0058] Figure 1 The drawings are the method flowchart provided by the present application. DETAILED DESCRIPTION

[0059] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the protection scope of the present application.

[0060] The embodiments of the present application disclose a multi-source time-frequency ridge extraction method based on synchronous extraction transform, as shown in Figure 1 The method comprises the following steps:

[0061] Step 1: Obtain a gearbox time-domain vibration signal.

[0062] Step 2: Perform variational mode decomposition (VMD) filtering on the time-domain vibration signal to obtain a characteristic modal component time-domain vibration signal, so as to prevent noise interference from affecting the time-frequency resolution of a time-frequency spectrum of the vibration signal.

[0063] Step 3: Perform synchronous extraction transform (SET) time-frequency analysis on the characteristic modal component time-domain vibration signal.

[0064] SET is a time-frequency analysis method with high time-frequency resolution and no parameterization, and the method is good in noise robustness under low signal-to-noise ratio. The implementation process of SET is as follows:

[0065] 1) Short-time Fourier transform time-frequency spectrum

[0066] The time-frequency spectrum of the time-domain vibration signal s(t) is calculated, and the short-time Fourier transform formula is as follows:

[0067]

[0068] In the formula, g(u-t) represents a movable window function.

[0069] (1) Multiply a phase factor e jωt on both sides of the formula, and the formula is as follows:

[0070]

[0071] In the formula: represents the Fourier transform of s(t), represents the Fourier transform of the window function g(u-t);

[0072] Let a harmonic signal with a frequency of ω0 be The conversion into the frequency domain is as follows:

[0073]

[0074] Where A represents the harmonic amplitude, ζ represents the frequency, and δ() represents the indicator function.

[0075] Substitute equation (3) into equation (2), the short-time Fourier transform time-frequency spectrum formula is as follows:

[0076]

[0077] 2) IF estimation

[0078] The IF formula is as follows:

[0079]

[0080] Where: Ge(t,ω) represents the partial derivative of Ge(t,ω) with respect to t.

[0081] 3) SET time-frequency spectrum

[0082] The synchronization extraction operator (SEO) removes the energy dispersion coefficient, and the time-frequency coefficient on the time-frequency ridge is retained. The SET spectrum formula is as follows:

[0083] T e (t,ω) = G e (t,ω) δ(ω-ω0(t,ω)) (6)

[0084] Where δ(ω-ω0(t,ω)) represents the synchronization extraction operator, T e (t,ω) represents the SET time-frequency.

[0085] Step 4: Extract the shaft rotation frequency and gear meshing frequency time-frequency ridge according to the local peak value search algorithm, which is specifically:

[0086] 1) Time-frequency spectrum initialization, randomly obtain n initial time points on the analysis period, and index the frequency with the maximum spectrum energy;

[0087] 2) Select the frequency with the maximum spectrum energy in the entire analysis frequency band of the current time point, and the formula is as follows:

[0088] f(t,ω) = argmaxT e (t,ω), ω = 1,2,...,N / 2+1 (7)

[0089] Where T e (t,ω) represents the SET time-frequency spectrum, N represents the N-point fast Fourier transform, t represents the time point on the time-frequency graph, and ω represents the frequency point on the time-frequency graph.

[0090] 3) Frequency value comparison: compare the frequency with the maximum spectrum energy in the current time analysis frequency band with the frequency at the previous time, and the judgment condition is as follows:

[0091] (f(t, ω) > αf(t-1, ω)) || (f(t, ω) < βf(t-1, ω)) (8)

[0092] wherein: α, β are obtained by expert experience, used to determine the search for the maximum energy frequency value within the frequency limit of the previous time point corresponding to the energy peak value of the time point. If (8) is not established, the frequency value corresponding to the maximum spectral energy of the current time point is 0, and the process of (7) and (8) is repeated until (8) is satisfied, so as to obtain the frequency value of the time point;

[0093] 4) Search the frequency value corresponding to the next time point from the current time point forward and backward until the entire analysis period is searched;

[0094] 5) Redistribute the gear meshing frequency time-frequency ridge line of the global analysis period.

[0095] Step 5: Optimizing the time-frequency ridge line based on the multi-source ridge line fusion method and extracting the rotation frequency curve;

[0096] 1) Extracting 4 time-frequency ridge lines from the low frequency band and high frequency resonance band of the SET time-frequency spectrum and the SET envelope time-frequency spectrum respectively; the time-domain vibration signal of the characteristic modal component filtered by VMD of the SET envelope time-frequency spectrum is first enveloped, and then the SET time-frequency analysis is performed on the enveloped signal to obtain

[0097] 2) According to the linear relationship of the gear meshing frequency and the shaft rotation frequency, and combining the structure information of the SET time-frequency spectrum and the SET envelope time-frequency spectrum, the extracted time-frequency ridge lines are preprocessed, including: according to the linear relationship of the gear meshing frequency and the rotation frequency sideband, the rotation frequency and its frequency ridge line, the frequency component of the time-frequency ridge line in the analysis period will not be suddenly changed in theory, the time period of the frequency sudden change between the multi-source time-frequency ridge lines is replaced by the ridge line without sudden change, and then the time-frequency ridge line information more consistent with the vibration characteristics of the gear box is obtained by segmenting and superimposing;

[0098] 3) Synchronization processing based on the time-frequency ridge line corresponding to the highest energy of the high frequency resonance band time-frequency spectrum as the reference:

[0099] Selecting the time-frequency ridge line f3 corresponding to the highest energy of the high frequency resonance band time-frequency spectrum as the reference for synchronization processing:

[0100] The time-frequency ridge line synchronization processing formula is:

[0101]

[0102] wherein, The time-frequency ridge line synchronization result is represented by k, and k represents the synchronization coefficient (determined by the coincidence degree of the time-frequency ridge line and the reference ridge line);

[0103] Any time point t iSynchronization frequency and the reference instantaneous frequency f3, the standard deviation formula is as follows:

[0104]

[0105] In the formula, ave represents the average of the four frequency values, σ(t i ) represents the standard deviation at any time point t i .

[0106] When the four time-frequency ridges obtained by reprocessing using the local peak search algorithm are effective curves, the standard deviations of the four synchronization frequencies are theoretically close to 0. However, in practice, the influence of the time-frequency analysis method on the time-frequency resolution and noise interference, etc. cause the four IFs to have abnormal intervals, i.e. fusion intervals. The fusion interval is determined by a rising edge τ1 and a falling edge τ2. The determination condition is as follows:

[0107]

[0108] In the formula, Δσ represents a threshold value. The threshold value is determined by the cumulative probability distribution, and the formula is as follows:

[0109]

[0110] In the formula, CPDE(Δσ(τ i )) represents the cumulative probability distribution of Δσ(τ i ), and the difference corresponding to the peak value of the cumulative probability distribution is the threshold value. The part greater than the threshold value is the fusion interval, and the time-frequency ridge with the minimum standard deviation corresponding to the frequency of the fusion interval is selected as the final fusion result. The remaining part is the non-fusion interval.

[0111] 4) The time-frequency ridge with the minimum standard deviation corresponding to the frequency of the fusion interval is selected as the fusion result, the average of the four time-frequency ridges corresponding to the non-fusion interval is calculated, and the fusion result and the average of the time-frequency ridges are redistributed to obtain the gear meshing frequency time-frequency ridge fusion result of the global analysis period;

[0112] 5) According to the transmission characteristics of the gearbox transmission chain, the change trend of the order curve is estimated.

[0113] Step 6: Order tracking is performed on the time-domain vibration signal of the feature modal component based on the order curve, and the gear box bearing fault characteristic order is obtained from the angular domain order spectrum.

[0114] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same and similar parts of each embodiment can be referred to each other. For the device disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the related parts can be referred to the method part.

[0115] The foregoing description of the disclosed embodiments enables a person skilled in the art to make or use the application. Numerous modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein can be applied to other embodiments without the use of the inventive faculty. Therefore, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-source time-frequency ridge extraction method based on synchronous extraction transform, characterized in that, The method comprises the following steps: Obtain the time domain vibration signal of the gearbox; Perform variational modal decomposition filtering on the time domain vibration signal to obtain a characteristic modal component time domain vibration signal; Synchronously extract a transform time-frequency spectrum and a transform envelope time-frequency spectrum from the characteristic modal component time domain vibration signal to obtain a gear meshing frequency spectrum line and a shaft rotation frequency spectrum line, respectively; Extract the shaft rotation frequency and the gear meshing frequency time-frequency ridge line according to a local peak value search algorithm; Optimize the gear meshing frequency time-frequency ridge line extraction effect and extract the rotation frequency curve based on a multi-source ridge line fusion method; Track the order of the characteristic modal component time domain vibration signal based on the rotation frequency curve to obtain a gearbox bearing fault characteristic order from an angular domain order spectrum; The synchronous extraction transform implementation process is as follows: 1) Short-time Fourier transform time-frequency spectrum The time-frequency spectrum of the characteristic modal component time domain vibration signal s(t) is calculated, and the short-time Fourier transform formula is as follows: In the formula, g(u-t) represents a movable window function, t represents a time point on the time-frequency diagram, and ω represents a frequency point on the time-frequency diagram; (1) The same phase factor e on both sides of the formula jωt The formula is as follows: wherein: denotes the Fourier transform of s(t), denotes the Fourier transform of the window function g(u-t); Let the harmonic signal of frequency ω0be The conversion to the frequency domain is as follows: wherein: A denotes the harmonic amplitude, denotes the frequency, δ() denotes the indicator function; The formula (3) is substituted into the formula (2), and the short-time Fourier transform time-frequency spectrum formula is as follows: wherein G e (t, ω) denotes the short-time Fourier transform time-frequency; 2) IF estimation The IF formula is as follows: wherein: denotes the partial derivative of Ge(t, ω) with respect to t; 3) SET time-frequency spectrum The SET time-frequency spectrum is calculated, and the formula is as follows: T e (t,ω) = G e (t,ω) δ(ω - ω0(t,ω)) (6) wherein: δ(ω - ω0(t,ω)) represents a synchronization extraction operator, T e (t,ω) represents the SET time-frequency.

2. The synchronous extraction transform based multi-source time-frequency ridge extraction method according to claim 1, characterized in that, The local peak value search algorithm is implemented as follows: 1) Time-frequency spectrum initialization: n initial time points are randomly obtained on the analysis period, and the frequency with the maximum spectrum energy is indexed; 2) Select the frequency with the maximum spectrum energy in the entire analysis frequency range of the current time point, and the formula is as follows: f(t, ω) = argmaxT e (t, ω), ω = 1, 2,..., N / 2 + 1 (7) where T e (t, ω) denotes the SET time-frequency spectrum, N denotes an N-point fast Fourier transform, t denotes a time point on the time-frequency plot, and ω denotes a frequency point on the time-frequency plot. 3) Frequency value comparison: compare the frequency with the maximum spectrum energy in the current time point analysis frequency range with the frequency of the previous time point, and the judgment condition is as follows: (f(t,ω)>αf(t-1,ω))||(f(t,ω)<βf(t-1,ω)) (8) In the formula, α and β are obtained by expert experience. If the formula (8) is not established, the frequency value corresponding to the maximum spectrum energy of the current time point is 0. The formula (7) and (8) are cycled until the formula (8) is established, so that the frequency value of the time point is obtained; 4) Search the frequency value corresponding to the next time point from the current time point forward and backward until the entire analysis period is searched; 5) Redistribute the gear meshing frequency time-frequency ridge line of the global analysis period.

3. The synchronous extraction transform based multi-source time-frequency ridge extraction method according to claim 1, characterized in that, The multi-source ridge line fusion method is implemented as follows: 1) Extract four time-frequency ridge lines from the low-frequency band and the high-frequency resonance band of the synchronous extraction transform time-frequency spectrum and the synchronous extraction transform envelope time-frequency spectrum, respectively; 2) According to the fixed linear relationship between the gear meshing frequency and the shaft rotation frequency, and combining the structure information of the synchronous extraction transform time-frequency spectrum and the synchronous extraction transform envelope time-frequency spectrum, the extracted time-frequency ridge lines are preprocessed; 3) Based on the time-frequency ridge line with the highest energy in the high-frequency resonance band time-frequency spectrum as the reference, the synchronization processing is performed; 4) According to the frequency selection standard deviation of the fusion interval, the time-frequency ridge line with the minimum standard deviation is selected as the fusion result. The average value of the four time-frequency ridge lines corresponding to the non-fusion interval is calculated. The fusion result and the time-frequency ridge line average value are redistributed to obtain the gear meshing frequency time-frequency ridge line fusion result of the global analysis period; 5) According to the fixed linear relationship between the gear meshing frequency and the shaft rotation frequency of the fusion result, the change trend of the rotation frequency curve is estimated.

4. The synchronous extraction transform based multi-source time-frequency ridge extraction method according to claim 3, characterized in that, The synchronization processing specific calculation process is: The time-frequency ridge line synchronization processing formula is: In the formula, represents the time-frequency ridge synchronization result, k represents the synchronization coefficient determined by the coincidence degree of the time-frequency ridge and the reference ridge, f i represents the i-th time-frequency ridge in the low frequency band and the resonance frequency band.

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