CN113310684A - Gearbox fault feature extraction method based on scale space and improved sparse representation - Google Patents

Gearbox fault feature extraction method based on scale space and improved sparse representation Download PDF

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CN113310684A
CN113310684A CN202110427692.8A CN202110427692A CN113310684A CN 113310684 A CN113310684 A CN 113310684A CN 202110427692 A CN202110427692 A CN 202110427692A CN 113310684 A CN113310684 A CN 113310684A
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毛一帆
许飞云
胡建中
贾民平
黄鹏
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Southeast University
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Abstract

The invention relates to a gearbox fault feature extraction method based on scale space and improved sparse representation, which comprises the following steps of: dividing an original signal into a plurality of frequency band component signals taking each step of meshing frequency of the gear as the center according to frequency bands by using a scale space; constructing a noiseless DCT dictionary for the frequency band component signals; constructing an observation dictionary for carrying out sparse decomposition on the frequency band component signals, wherein the observation dictionary comprises a noise-containing DCT dictionary obtained by adding noise signals to atoms of a noiseless DCT dictionary in an iterative process of an orthogonal matching pursuit algorithm based on a singular value decomposition algorithm; selecting the optimal atoms in the observation dictionary by taking the fusion index of the minimum variance and the inner product as a criterion; performing sparse reconstruction on the frequency band component signals by utilizing an observation dictionary based on an orthogonal matching pursuit algorithm; the demodulation spectrum analysis then extracts the gearbox fault signature frequency. The method is used for extracting the fault characteristics of the gearbox, and has higher time-frequency resolution and reconstruction precision compared with other methods.

Description

Gearbox fault feature extraction method based on scale space and improved sparse representation
Technical Field
The invention relates to the technical field of rotary machine vibration signal analysis, in particular to a gearbox fault feature extraction method based on scale space and improved sparse representation.
Background
As one of the rotating machines commonly used in industrial scenes, a gear box having a fixed gear ratio, a large driving torque and a compact structure has been widely used in various machines. The gearbox usually works under severe conditions and is easy to malfunction, so that the gearbox fault diagnosis method has important practical significance for fault diagnosis research of the gearbox. However, the vibration signal measured in practical engineering is always nonlinear and non-stationary, and is affected by the coupling effect of multiple transmission paths among components, and strong background noise and interference source signals are doped in the vibration signal, so that the fault feature extraction of the gearbox is extremely complicated and difficult. Therefore, how to effectively recover the gearbox fault characteristic information under the strong background noise and the interference source signal is worthy of deep research.
In recent years, a variety of nonlinear, non-stationary signal decomposition and analysis methods have emerged. Empirical Mode Decomposition (EMD) is a typical adaptive time-frequency analysis method, and has good time-frequency aggregation without constructing any basis function matching signal components. However, EMD has defects of modal aliasing, end point effect and the like, lacks necessary mathematical theory and has complex model. In order to solve the problem of EMD modal aliasing, methods such as Ensemble Empirical Mode Decomposition (EEMD) are proposed in sequence, but these methods cannot completely compensate the defects of EMD. Nonparametric time-frequency analysis methods based on EMD Decomposition theory, such as Variational Mode Decomposition (VMD) and other methods, are proposed successively by people, and reference can be made to [ yellow ramification, forest establishment brightness, Liu Yang tide, yellow morning light ]. high-speed train journal box bearing fault diagnosis [ J ] based on adaptive VMD, vibration and impact, 2021, 40 (03): 240-245]. However, the VMD algorithm is very dependent on determining the number of mode components (IMFs) and the corresponding center frequency determination and setting of the band bandwidth.
In the prior art, patents related to sparse decomposition include a gear fault detection method (202010732900.0) based on an improved sparse decomposition algorithm, and the method for selecting the optimal atom from an over-complete dictionary adopts the principle of maximum inner product, and when signal noise of the atom is large, the selected atom is not the local optimal atom. The invention discloses a gearbox fault diagnosis method (201810532020.1) of sparse regularization filtering and adaptive sparse decomposition, which is used for filtering an original vibration signal, needs to determine parameters of a filter and cannot realize adaptive decomposition of an algorithm.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a gearbox fault feature extraction method based on scale space and improved sparse representation, and aims to solve the problems of low time-frequency resolution and low reconstruction accuracy.
The technical scheme adopted by the invention is as follows:
a gearbox fault feature extraction method based on scale space and improved sparse representation, the method comprising:
step one, obtaining a gear box vibration original signal required to be decomposed;
dividing the original signal into a plurality of frequency band component signals taking each step of meshing frequency of the gear as the center according to frequency bands by using a scale space;
constructing a noiseless DCT dictionary for the frequency band component signals;
fourthly, constructing an observation dictionary for performing sparse decomposition on the frequency band component signals, wherein the observation dictionary comprises the following steps:
adding a noise signal to each atom of the noiseless DCT dictionary in an iteration process based on an orthogonal matching pursuit algorithm to obtain a noisy DCT dictionary, wherein the noisy DCT dictionary is combined with the noiseless DCT dictionary to form the observation dictionary; the noise signal is obtained according to a singular value decomposition algorithm;
meanwhile, selecting the optimal atoms in the observation dictionary by taking the fusion index of the minimum variance and the inner product as a criterion;
performing sparse reconstruction on the frequency band component signals by using the observation dictionary based on an orthogonal matching pursuit algorithm to obtain reconstructed decomposition components;
and sixthly, selecting the decomposition component with the maximum correlation with the frequency band component signal according to the Pearson correlation coefficient criterion to perform demodulation spectrum analysis so as to extract the fault characteristic frequency of the gearbox.
The further technical scheme is as follows:
in the second step, performing cyclic convolution on the frequency spectrum of the original signal by using a Gaussian kernel function to obtain a local minimum value of the frequency spectrum so as to obtain a progressive difference of a scale space layer, and taking the progressive difference as a scale space curve; calculating a division frequency point set of a pre-estimated frequency band aiming at the scale space curve, and obtaining a plurality of cut-off frequency bands with bandpass filtering according to the frequency point set; and finally, dividing the original signal into a plurality of frequency band components by using band-pass filtering according to the cut-off frequency band.
In the fourth step, the noise signal to be added to the atoms of the noiseless DCT dictionary in each iteration of the orthogonal matching pursuit algorithm is calculated by using a singular value decomposition algorithm, including:
calculating a singular value difference spectrum of the frequency band component signal according to a singular value decomposition algorithm;
utilizing the singular value difference spectrum to complete reconstruction of corresponding useful signals according to effective singular values;
and obtaining the noise signal according to a residual signal of the current orthogonal matching pursuit algorithm and the useful signal.
In the fourth step, a fusion index of the minimum variance and the inner product is used as a criterion for selecting the optimal atom in the observation dictionary during each iteration of the orthogonal matching pursuit algorithm, and the expression of the fusion index is as follows:
Figure BDA0003029231240000021
in the formula
Figure BDA0003029231240000022
Respectively frequency band component signal and atomic signal in the observation dictionaryAnd N is the length of the signal.
And in the fifth step, sparse reconstruction is carried out on the frequency band component signals by utilizing the observation dictionary based on an orthogonal matching pursuit algorithm, and a reconstruction residual error is calculated to obtain a reconstructed decomposition component.
The sixth step specifically comprises: calculating a pearson correlation coefficient for each of the decomposition components with the frequency band component signals; selecting the decomposition component corresponding to the maximum Pearson correlation coefficient, and solving a Hilbert envelope demodulation spectrum of the decomposition component; constructing a new analytic signal by using the decomposed components and the Hilbert transformed envelope demodulation spectrum corresponding to the decomposed components; and carrying out modular operation on the analytic signal to obtain an envelope signal, carrying out Fourier transform on the envelope signal to obtain a corresponding envelope spectrum, calculating the fault characteristic frequency of a gear in the gear box, and obtaining a diagnosis result by combining the envelope spectrum.
The invention has the following beneficial effects:
the method is used for decomposing the vibration signal by combining the scale space and the improved sparse representation, the noise of the signal is reduced in the decomposition process, the obtained component can reflect the physical significance of the signal, the method is applied to extracting the fault feature of the gearbox, and the time-frequency resolution and the reconstruction accuracy are higher compared with other methods. The method has the following specific advantages:
1) according to the invention, the signals are preprocessed by adopting the scale space and the band-pass filtering, the upper and lower limit cut-off frequency points of the frequency band taking the gear meshing frequency of each order as the center in the vibration signal frequency spectrum are calculated according to the scale space, and then a plurality of frequency band components taking the gear meshing frequency as the center are obtained by combining the band-pass filtering, so that the obtained components can eliminate the modal aliasing phenomenon, and a good foundation is laid for extracting the fault characteristics of the subsequent gearbox.
2) The method uses the fusion index of the minimum variance and the inner product as the criterion for selecting the optimal atoms in the dictionary during each iteration of the orthogonal matching pursuit algorithm, and simultaneously uses the noiseless DCT dictionary combined with the noisy DCT dictionary as the observation dictionary in the sparse representation, so that the optimal dictionary atoms can still be obtained in each iteration process through the orthogonal matching pursuit algorithm when the noise in the signals is large, the obtained decomposition components can better highlight the fault characteristics, and the accurate extraction of the gear fault characteristics is realized.
3) Compared with EMD and VMD signal decomposition methods, the decomposition component obtained by the invention has better time-frequency characteristics and provides higher precision for signal processing and analysis.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
FIG. 2 is a schematic diagram of a scale space in an embodiment of the invention.
FIG. 3 is a time domain waveform diagram of signal x (t) in the simulated signal 1 according to the embodiment of the present invention.
FIG. 4 is a diagram of a signal x in an emulated signal 1 according to an embodiment of the invention1(t) time domain waveform diagrams.
FIG. 5 shows a signal x in an emulated signal 1 according to an embodiment of the invention2(t) time domain waveform diagrams.
FIG. 6 is a time-frequency diagram of a signal x (t) in the simulation signal 1 according to an embodiment of the present invention.
Fig. 7 is a time domain waveform diagram of a component of the simulation signal 1 obtained by decomposition by an EMD method according to an embodiment of the present invention.
FIG. 8 is a time-frequency diagram of IMF1 and IMF2 components of the simulation signal 1 decomposed by EMD method according to the embodiment of the present invention.
Fig. 9 is a time domain waveform diagram of the component of the simulation signal 1 obtained by the VMD decomposition method in the embodiment of the present invention.
Fig. 10 is a time-domain time-frequency diagram of components obtained by decomposing the simulation signal 1 by the VMD method in the embodiment of the present invention.
FIG. 11 is a component time domain waveform diagram of an artificial signal 1 obtained by decomposition according to the method of the present application in the embodiment of the present invention.
Fig. 12 is a component time-frequency diagram obtained by decomposing the simulation signal 1 by the method of the present application in the embodiment of the present invention.
FIG. 13 shows x in simulation signal 2 according to an embodiment of the present invention1(t) true Hilbert envelope demodulation spectra.
Fig. 14 is a Hilbert envelope demodulation spectrum of the IMF1 component of the simulated signal 2 decomposed by the EMD method according to the embodiment of the present invention.
Fig. 15 is a Hilbert envelope demodulation spectrum of the IMF1 component decomposed by the VMD method of the simulated signal 2 according to the embodiment of the present invention.
Fig. 16 is a Hilbert envelope demodulation spectrum of the IMF2 component of the simulated signal 2 decomposed by the method of the present application in the embodiment of the present invention.
FIG. 17 shows the envelope demodulation spectrum characteristic frequency obtained by the methods in the embodiment of the present invention and x in the simulation signal 21(t) true characteristic frequency amplitude difference plot.
Detailed Description
The following describes embodiments of the present invention with reference to the drawings.
The application discloses a gearbox fault feature extraction method based on scale space and improved sparse representation, which refers to a flow chart shown in figure 1 and comprises the following steps:
step one, obtaining a gear box vibration original signal required to be decomposed;
step two, dividing the original signal into a plurality of frequency band component signals centering on each step of meshing frequency of the gear according to frequency bands by using a scale space, and concretely comprising the following steps:
2.1) solving a spectrum f of a vibration original signal x (t) of the gearbox, regarding the spectrum f as a group of histograms, and performing cyclic convolution on the spectrum f by using a Gaussian kernel function, wherein the formula is as follows:
Figure BDA0003029231240000041
in the formula (I), the compound is shown in the specification,
Figure BDA0003029231240000042
g (n; t) is a discrete Gaussian kernel function and t is time.
2.2) while performing the convolution, record all local minima N of L (m, t)i(initial local minimum is noted as N0)；
2.3) taking the progressive difference of the scale space layers as a scale space curve, wherein the expression is as follows:
Si＝{s|Ri-1→Ri}，i＝1，2，3，…
in which s represents a radical selected from Ri-1Layer to RiThe scale length of the layer, i.e. the number of convolutions, RiIs the ith scale space layer, and Ri＝{Ni}，{NiCharacterizing the number of local minimum values, and when the number of the local minimum values changes, i is i + 1;
2.4) calculating a threshold value by an OTSU method, and selecting the first S larger than the threshold valueiThe local minimum value points contained in the frequency band estimation are used as a frequency point dividing set Fre of the estimated frequency band, a plurality of cut-off frequency bands CFs of band-pass filtering can be obtained according to the frequency point set,
Fre＝{f0，f1，…，fn}
CFs＝{[f0，f1]，[f1，f2]，…[fn-1，fn]}
wherein f is0，f1，…，fnThe upper and lower cut-off frequencies of the divided frequency band.
2.5) finally dividing the original signal x (t) into a plurality of frequency band components by using band-pass filtering according to the upper and lower limit cut-off frequencies of the cut-off frequency band obtained in 2.4): x (t) { x1(t)，x2(t)，…，xn(t)}。
The use scale space in the second step is divided into a plurality of frequency band component signals by taking each order of meshing frequency of the gear as the center according to the frequency band, wherein each order of meshing frequency refers to the frequency band formed by order division according to the size of the meshing frequency, for example, one-time meshing frequency is 150Hz, 0-200Hz is a first order meshing frequency band, 200Hz-400Hz is a second order meshing frequency band, and the like. FIG. 2 is a schematic diagram of a scale space, wherein f0，f1，…f5Are the upper and lower cut-off frequencies of each frequency band obtained through the scale space.
Constructing a noiseless DCT dictionary for the frequency band component signals;
and fourthly, constructing an observation dictionary for performing sparse decomposition on the frequency band component signals. Firstly, calculating noise signals required to be added to atoms of a noiseless DCT dictionary by using singular value decomposition and calculating each iteration of an orthogonal matching pursuit algorithm, adding the noise signals to each atom of the noiseless DCT dictionary to obtain a noisy DCT dictionary, and combining the noisy DCT dictionary with the noiseless DCT dictionary to form an observation dictionary; the method specifically comprises the following steps:
4.1) calculating the singular value difference spectrum of the frequency band component signal according to the singular value decomposition, wherein the calculation formula of the singular value difference sequence is as follows
bi＝λi-λi+1I ═ 1, 2, …, q-1, q being the number of valid singular values; in the formula ofiThe calculated ith singular value is decomposed for the singular value.
4.2) from right to left in the singular value difference spectrum, selecting a first at least single side to be compared with an adjacent peak value thereof, and determining an effective singular value corresponding to a reconstruction signal according to the position of a corresponding point of a maximum peak value with the maximum difference absolute value, thereby completing the reconstruction of a useful signal.
Figure BDA0003029231240000043
Wherein s is a reconstructed useful signal, k represents the first k useful singular values, and u and v are left and right singular value matrixes of singular value decomposition respectively;
4.3, using residual signal r (t) (x (t) in the first iteration) of the current orthogonal matching pursuit algorithm to subtract singular value decomposition to obtain useful signal s (t), thus obtaining noise signal n (t) added in the DCT dictionary under the current iteration number,
nm(t)＝rm(t)-sm(t), wherein the subscript m represents the number of iterations;
4.4) constructing an observation dictionary required by the current iteration number m by using the frequency band division frequency points obtained in the step two and n (t) obtained in the step 4.3):
Figure BDA0003029231240000051
in the formula DmAs a noiseless DCT dictionary, Dm noiseA DCT dictionary containing noise;
wherein f ═ fi：Δf：fi+1Δ f is the frequency resolution, Δ f ═ fs/N，fsIs the signal sampling frequency, and N is the signal length;
Figure BDA0003029231240000052
fiand fi+1Respectively the upper and lower cut-off frequencies of each frequency band obtained in step 2.4).
And secondly, selecting the optimal atoms in the observation dictionary based on an orthogonal matching pursuit algorithm by taking the fusion index of the minimum variance and the inner product as a criterion. As shown in fig. 1, a total iteration number M of the orthogonal matching pursuit algorithm in sparse decomposition is set, a fusion index of a minimum variance and an inner product is used as a criterion for selecting an optimal atom in an observation dictionary in each iteration of the orthogonal matching pursuit algorithm, and a fusion index expression is as follows:
Figure BDA0003029231240000053
in the formula
Figure BDA0003029231240000054
Respectively are a frequency band component signal and an atomic signal in an observation dictionary, and N is the length of the signal.
Step five, based on the orthogonal matching pursuit algorithm, sparse reconstruction is carried out on each frequency band component signal by utilizing an observation dictionary to obtain n reconstructed decomposition components IMFs,
Figure BDA0003029231240000055
the reconstructed residual Res is calculated according to the following formula,
Figure BDA0003029231240000056
obtaining the final decomposition component:
Figure BDA0003029231240000057
specifically, as shown in fig. 1, in each iteration, a noise signal that needs to be added to the DCT dictionary containing noise is constructed for each decomposition component according to an orthogonal matching pursuit algorithm, a dictionary atom index selected in each iteration is obtained, a corresponding dictionary atom in the noiseless dictionary is selected according to the obtained atom index to obtain a reconstructed signal, and a result is output until the number M of loop iterations is greater than or equal to M.
And step six, selecting a decomposition component with the maximum correlation with the frequency band component signal according to a Pearson correlation coefficient criterion to perform demodulation spectrum analysis so as to extract the fault characteristic frequency of the gearbox. The method specifically comprises the following steps:
6.1) calculating each of the decomposition components
Figure BDA00030292312400000512
Pearson correlation coefficient with frequency band component signal x (t):
Figure BDA0003029231240000058
in the formula
Figure BDA0003029231240000059
Is composed of
Figure BDA00030292312400000510
The average value of the components is calculated,
Figure BDA00030292312400000511
is the average value of x (t);
6.2) selecting the decomposition component with the maximum Pearson correlation coefficient in the step 6.1)
Figure BDA0003029231240000061
And solving the Hilbert envelope demodulation spectrum of the signal, namely:
Figure BDA0003029231240000062
6.3) to decompose the components
Figure BDA0003029231240000063
As the real part, transform x by Hilberth(t) is the imaginary part, which constitutes the new analytic signal:
Figure BDA0003029231240000064
6.4) performing modulo operation on the analytic signal h (t) to obtain a decomposition component
Figure BDA0003029231240000069
Corresponding envelope signal he(t)：
Figure BDA0003029231240000065
6.5) Fourier transforming the envelope signal to obtain decomposed components
Figure BDA0003029231240000066
A corresponding envelope spectrum;
6.6) calculating the fault characteristic frequency of the gears in the gear box, and obtaining a diagnosis result by combining the envelope spectrogram.
The scheme of the present application is further illustrated by the following specific examples:
constructing a frequency-modulated simulation signal-simulation signal 1, as shown in fig. 3-6, which is a time-domain waveform diagram of the simulation signal 1, the simulation signal 1 is composed of x (t), x1(t)、x2(t) three parts:
Figure BDA0003029231240000067
the sampling frequency of the simulation signal x (t) is 1200Hz, and the number of sampling points is 1200.
Fig. 7-12 are time domain diagrams and time frequency diagrams of the simulation signal 1 processed by the EMD and VMD decomposition method and the method of the present application. In which, comparing fig. 7, 9 and 11, it can be seen that the decomposition component obtained by the method of the present application is consistent with the original simulation signal. Comparing fig. 8, fig. 10 and fig. 12, it can be seen that the component time-frequency diagram obtained by the method of the present application is consistent with the simulation signal, while the time-frequency diagram of the component obtained by the EMD and VMD decomposition methods has a divergence phenomenon and the EMD and VMD decomposition methods have a modal aliasing phenomenon.
Further verifying the effect of the method in the aspect of extracting the fault characteristics of the gearbox, constructing a fault signal of the gearbox, namely a simulation signal 2, wherein the signal component is as follows:
Figure BDA0003029231240000068
where n (t) is white Gaussian noise of-10 dB.
The sampling frequency is 1500Hz, the number of sampling points is 1500, and the gear meshing frequency is 300 Hz. The failure of the gearbox is uniform wear, and the failure characteristic frequency is f-12.5 Hz. And selecting the EMD and VMD algorithms and the component with the maximum correlation coefficient with the original signal from the decomposition components obtained by the method to perform Hilbert envelope spectrum demodulation. FIGS. 13-16 are graphs of the gearbox fault simulation signal 2 processed by EMD and VMD decomposition reconstruction demodulation and the method of the present invention as Hilbert envelope demodulation. Compared with the three methods, the spectral lines of the Hilbert envelope demodulation spectrum obtained by the application method are more prominent and clear. The extraction method provided by the application is verified to be more effective than EMD and VMD algorithms in the aspects of highlighting fault signal characteristics and improving diagnosis precision.
As can be seen from fig. 17, it is seen that the amplitude difference between the obtained fault feature and the actual fault feature is relatively minimum, so that the extracted fault feature is closer to the true fault feature. The effectiveness and superiority of the method in extracting the fault characteristics of the gearbox are demonstrated.

Claims (6)

1. A gearbox fault feature extraction method based on scale space and improved sparse representation is characterized by comprising the following steps:
step one, obtaining a gear box vibration original signal required to be decomposed;
dividing the original signal into a plurality of frequency band component signals taking each step of meshing frequency of the gear as the center according to frequency bands by using a scale space;
constructing a noiseless DCT dictionary for the frequency band component signals;
fourthly, constructing an observation dictionary for performing sparse decomposition on the frequency band component signals, wherein the observation dictionary comprises the following steps:
adding a noise signal to each atom of the noiseless DCT dictionary in an iteration process based on an orthogonal matching pursuit algorithm to obtain a noisy DCT dictionary, wherein the noisy DCT dictionary is combined with the noiseless DCT dictionary to form the observation dictionary; the noise signal is obtained according to a singular value decomposition algorithm;
meanwhile, selecting the optimal atoms in the observation dictionary by taking the fusion index of the minimum variance and the inner product as a criterion;
performing sparse reconstruction on the frequency band component signals by using the observation dictionary based on an orthogonal matching pursuit algorithm to obtain reconstructed decomposition components;
and sixthly, selecting the decomposition component with the maximum correlation with the frequency band component signal according to the Pearson correlation coefficient criterion to perform demodulation spectrum analysis so as to extract the fault characteristic frequency of the gearbox.
2. The method according to claim 1, wherein in the second step, the frequency spectrum of the original signal is circularly convolved by using a gaussian kernel function to obtain local minimum values of the frequency spectrum, so as to obtain progressive differences of scale space layers, and the progressive differences are used as scale space curves; calculating a division frequency point set of a pre-estimated frequency band aiming at the scale space curve, and obtaining a plurality of cut-off frequency bands with bandpass filtering according to the frequency point set; and finally, dividing the original signal into a plurality of frequency band components by using band-pass filtering according to the cut-off frequency band.
3. The method according to claim 1, wherein in the fourth step, the singular value decomposition algorithm is used to calculate the noise signal to be added to the atoms of the noiseless DCT dictionary at each iteration of the orthogonal matching pursuit algorithm, and the method comprises:
calculating a singular value difference spectrum of the frequency band component signal according to a singular value decomposition algorithm;
utilizing the singular value difference spectrum to complete reconstruction of corresponding useful signals according to effective singular values;
and obtaining the noise signal according to a residual signal of the current orthogonal matching pursuit algorithm and the useful signal.
4. The method according to claim 3, wherein in the fourth step, a fusion index of minimum variance and inner product is used as a criterion for selecting an optimal atom in the observation dictionary in each iteration of the orthogonal matching pursuit algorithm, and the expression of the fusion index is as follows:
Figure FDA0003029231230000011
in the formula, x is a group of,
Figure FDA0003029231230000021
frequency band component signals and atomic signals in the observation dictionary respectively, wherein N is the length of the signals.
5. The method according to claim 1, wherein in the fifth step, sparse reconstruction is performed on the frequency band component signals by using the observation dictionary based on an orthogonal matching pursuit algorithm, and a reconstruction residual is calculated to obtain a reconstructed decomposition component.
6. The method according to claim 1, wherein the sixth step specifically comprises: calculating a pearson correlation coefficient for each of the decomposition components with the frequency band component signals; selecting the decomposition component corresponding to the maximum Pearson correlation coefficient, and solving a Hilbert envelope demodulation spectrum of the decomposition component; constructing a new analytic signal by using the decomposed components and the Hilbert transformed envelope demodulation spectrum corresponding to the decomposed components; and carrying out modular operation on the analytic signal to obtain an envelope signal, carrying out Fourier transform on the envelope signal to obtain a corresponding envelope spectrum, calculating the fault characteristic frequency of a gear in the gear box, and obtaining a diagnosis result by combining the envelope spectrum.
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