CN114235396A - Gear reducer fault feature extraction method - Google Patents

Gear reducer fault feature extraction method Download PDF

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CN114235396A
CN114235396A CN202111417628.8A CN202111417628A CN114235396A CN 114235396 A CN114235396 A CN 114235396A CN 202111417628 A CN202111417628 A CN 202111417628A CN 114235396 A CN114235396 A CN 114235396A
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李波
石剑钧
洪涛
谢晓梅
李学生
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a method for extracting fault characteristics of a gear reducer, belongs to the field of signal processing, and particularly relates to a method for extracting fault characteristics. The invention provides a method for extracting fault characteristics of a gear reducer, aiming at the defects of a method for extracting fault characteristics of high-nonlinearity and high-non-stationarity vibration signals with multi-vibration-source interference on the gear reducer. Aiming at the problem that the fault characteristics of the gear reducer cannot be effectively extracted in the existing method, the method establishes an optimization objective function fusing correlation coefficients, frequency spectrum similarity and kurtosis, obtains an optimal punishment factor of decomposition of each layer by using a wolf optimization algorithm, carries out modal decomposition on the vibration signal of the gear reducer according to the optimal punishment factor of each layer, and more effectively extracts the fault characteristics of the gear reducer.

Description

Gear reducer fault feature extraction method
Technical Field
The invention relates to the field of digital signal processing, in particular to a fault feature extraction method for a high-nonlinearity and high-instability reducer vibration signal.
Background
Currently, cranes play an increasingly important role in various industrial fields. Particularly, the crane cannot be detached in the occasions of carrying large equipment and articles, construction operation of an overhead bridge, material moving in high-rise construction and the like. Statistical data shows that 85% of cranes are bridge gears, and China has insufficient research on monitoring the gear state, so once an accident occurs to the crane, the loss is huge.
The gear reducer is used as an indispensable bearing and transmission part of the crane, and is in a high-load operation state for a long time due to variable operation conditions, so that the probability of failure is high. Therefore, the fault condition of the crane is accurately judged mainly through the dynamic response of the gear reducer.
The gear reducer belongs to a rotary machine, and for the rotary machine, the machine set is generally not suitable to be disassembled to check faults. The reducer has a typical characteristic that a machine generates abnormal sound and abnormal vibration, and the vibration signal of the reducer contains abundant fault information of the crane reducer. Generally, the failure causes of the machine are different, the generated information is also different, and the failure characteristics of the machine can be extracted according to the characteristics of the vibration signal of the machine.
There are various current research methods for extracting the fault characteristics of the gear reducer, wherein the main methods are wavelet decomposition and modal decomposition. Wavelet decomposition has the characteristic of time-frequency local change analysis, and is widely applied to extraction of fault features of the speed reducer, but due to the difficulty in selection of wavelet bases, the effect of improper extraction is very poor. Empirical Mode Decomposition (EMD) is used as a recursive time-frequency processing algorithm, can adaptively decompose signals from high frequency to low frequency, and has wide application in the aspect of bearing fault feature extraction. However, in the process of calculating the envelope, the EMD algorithm amplifies the envelope estimation error due to multiple recursive decomposition, and may be accompanied by phenomena such as modal aliasing, endpoint effect, and false impulse.
Because the working environment of the gear is complex, the vibration signal of the bearing of the speed reducer has nonlinear and non-stable characteristics due to the interference of multiple vibration sources, and therefore, the fixed single decomposition layer number and punishment factor cannot be well adapted to the decomposition of the signal.
Disclosure of Invention
The invention provides a fault feature extraction method for a gear reducer, aiming at the defects of a fault feature extraction method for a vibration signal with high nonlinearity and high non-stationarity of multi-vibration-source interference on the gear reducer. Aiming at the problem that the fault characteristics of the gear reducer cannot be effectively extracted in the existing method, the method establishes an optimization objective function fusing correlation coefficients, frequency spectrum similarity and kurtosis, obtains an optimal punishment factor of decomposition of each layer by using a wolf optimization algorithm, carries out modal decomposition on the vibration signal of the gear reducer according to the optimal punishment factor of each layer, and more effectively extracts the fault characteristics of the gear reducer.
The technical scheme of the invention is a gear reducer fault feature extraction method, which comprises the following steps:
step 1: establishing a gear reducer fault feature extraction model;
step 1.1: the vibration signal in the gear reducer work project to be processed is initially decomposed into K discrete time sequences u with limited bandwidthk(t)；
Step 1.2: u is calculated by the following formulak(t) gradient norm L2;
Figure BDA0003376189050000021
wherein, ω iskRepresenting the central fundamental frequency band, delta (t) representing the impulse impact signal,
Figure BDA0003376189050000022
calculating a partial derivative sign of the variable t;
step 1.3: establishing constraint by the condition that the sum of the central frequency and the bandwidth obtained by calculation is minimum and the bandwidth of the K discrete time sequences is required to be satisfied, and calculating the optimal solution under the current condition according to the constraint
Figure BDA0003376189050000023
Step 2: establishing an optimization target fusing correlation coefficients, time-frequency spectrum similarity and kurtosis;
step 2.1: reconstructing the optimal solution obtained in the step1 to obtain a reconstructed signal X (t), XiFor reconstructing a certain sample point of the signal X (t), the original signal is set as S (t), SiCalculating a correlation coefficient r of X (t) and S (t) for a certain sample point of an original signal S (t);
step 2.2: calculating the similarity X of the reconstructed signal X (t) and the time frequency spectrum of the original signal S (t)t-fAnd St-fAnd obtaining the similarity S of time-frequency spectrumim；
Step 2.3: calculating the kurtosis of each signal component
Figure BDA0003376189050000024
Step 2.4: if the correlation coefficient is larger than a set threshold, taking the correlation coefficient and the kurtosis as optimization targets, otherwise, taking the frequency spectrum similarity and the kurtosis as the optimization targets;
and step 3: according to the optimization target obtained in the step2, an optimal penalty factor alpha of each layer during decomposition by adopting the model in the step1 under the current condition is obtained by utilizing a Huishen optimization algorithm
And 4, step 4: optimizing the model obtained in the step (3) in the step (1), determining the optimal decomposition layer number q according to the maximum kurtosis criterion, decomposing the vibration signal of the gear reducer into q layers by adopting the optimized model to obtain q modes, carrying out Hilbert transform on the modes, solving an envelope, carrying out Fourier transform on the envelope to obtain an envelope spectrum, and obtaining the fault characteristic of the reducer according to the envelope spectrum.
Further, the specific method of step 1.3 is as follows:
step 1.3.1: establishing the following constraint variational model:
Figure BDA0003376189050000031
in the formula: u. ofkIs the K-th IMF modal component, f is a component of the original signal;
step 1.3.2: after the constraint model is converted into a non-variational constraint problem through the following Lagrange function, the central frequency corresponding to the optimal solution of the formula (5) is obtained
Figure BDA0003376189050000032
And bandwidth
Figure BDA0003376189050000033
Figure BDA0003376189050000034
Figure BDA0003376189050000035
In the formula:
Figure BDA0003376189050000036
is expressed by uk、ωkλ is a Lagrangian function of an extremum of the independent variable,
Figure BDA0003376189050000037
Figure BDA0003376189050000038
means for determining the sum of
Figure BDA0003376189050000039
α is a secondary penalty factor, λ (t) is a lagrange factor, f (t) represents the original signal;
step 1.3.3: seeking saddle points of the variation problem by introducing an alternative multiplier direction algorithm, and then updating the central frequency of each order of IMF signals
Figure BDA00033761890500000310
And bandwidth
Figure BDA00033761890500000311
The following formula:
Figure BDA00033761890500000312
Figure BDA00033761890500000313
in the formula:
Figure BDA00033761890500000314
is the current residual
Figure BDA00033761890500000315
As a result of the filtering of (a),
Figure BDA00033761890500000316
for the center of gravity of the power spectrum of the current mode, it will be
Figure BDA00033761890500000317
Obtaining real part by performing inverse FFT
Figure BDA00033761890500000318
Step 1.3.4: updating lambda (t) by adopting the following formula;
Figure BDA00033761890500000319
recycling steps 1.3.2 to 1.3.4 until
Figure BDA00033761890500000320
ε represents the set threshold.
Further, the correlation coefficient calculating method in step 2.1 includes:
Figure BDA00033761890500000321
further, the method for calculating the time-frequency spectrum similarity in step 2.2 includes:
Figure BDA00033761890500000322
further, the kurtosis calculating method in step 2.3 includes:
Figure BDA0003376189050000041
the method has better extraction effect and more obvious fault characteristic frequency performance on the extraction of the fault characteristics of the speed reducer.
Drawings
FIG. 1 is a flow chart of an embodiment of the method of the present invention;
FIG. 2 is a waveform diagram of an original signal of a vibration signal of a gear reducer;
FIG. 3 is an envelope spectrum of each IMF after decomposition according to the present invention;
FIG. 4 is a flowchart of fusion of three features of Pearson correlation coefficient, time-frequency spectrum similarity and kurtosis;
FIG. 5 is an iterative graph of the gray wolf optimization algorithm;
FIG. 6 is a graph of maximum kurtosis values of IMF components versus the number of decomposition levels;
FIG. 7 is an envelope spectrum of four IMFs after decomposition according to the present invention;
FIG. 8 is an envelope spectrum of four IMFs after prior art decomposition;
Detailed Description
The following is a detailed description of the implementation routine of the present invention (fig. 1), and the present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation and a specific operation procedure are given, but the scope of the present invention is not limited to the implementation routine described below.
The gear reducer mostly works in a complex environment, and the acquired reducer data has strong nonlinearity and non-stationarity due to the influence of nonlinear factors such as load, friction, clearance and rigidity on vibration signals. The waveform diagram of the collected bearing fault vibration signal is shown in figure 2
The implementation routine can be mainly divided into the following steps:
step 1: establishing a gear reducer fault feature extraction model;
through the constructed optimal variation model, a given complex signal can be subjected to iterative computation to obtain a series of IMF signals, namely, a mode function with the minimum sum of K predicted bandwidths is mined from an original time sequence:
uk(t),k∈{1,2,…,K} (1)
step 1.1: it is assumed that the gear reducer vibration signal f to be processed can be decomposed into K bandwidth-limited discrete time sequences uk(t) the central base band corresponding to each component signal is ωk(t) and from uk(t) the obtained frequency spectrum has sparse characteristics, and the bandwidth is obtained by the following specific steps:
step 1.2: solving the central frequency band bandwidth corresponding to each component signal, firstly calculating each order IMF signal u through Hilbert transformationkAnalytic signal and single-sided spectrum of (t):
Figure BDA0003376189050000042
then the modal signal ukMultiplication by an exponential term
Figure BDA0003376189050000051
Post-will signal uk(t) center band modulated onto base band:
Figure BDA0003376189050000052
calculating the gradient norm L2 of the signal:
Figure BDA0003376189050000053
step 1.3: and establishing the following constraint variational model by calculating that the obtained center frequency and bandwidth need to meet the condition of minimum sum of bandwidths of all IMF signals:
Figure BDA0003376189050000054
in the formula: u. ofkIs the K-th IMF modal component, f is the original signal; and (3) converting the constraint model into a non-variational constraint problem through the following Lagrange function to obtain an optimal solution of the formula (5):
Figure BDA0003376189050000055
in the formula:
Figure BDA0003376189050000056
is expressed by uk、ωkλ is a Lagrangian function of an extremum of the independent variable,
Figure BDA0003376189050000057
Figure BDA0003376189050000058
means for determining the sum of
Figure BDA0003376189050000059
Alpha is a secondary penalty factor, lambda is a Lagrangian factor, delta (t) is an impulse impact signal,
Figure BDA00033761890500000510
is the derivation sign of the variable t; seeking a saddle point of the variation problem by introducing an alternative multiplier direction algorithm, and then updating the center frequency and the bandwidth of each order of IMF signals, wherein the following formula is as follows:
Figure BDA00033761890500000511
Figure BDA00033761890500000512
in the formula:
Figure BDA00033761890500000513
is the current residual
Figure BDA00033761890500000514
The filtering result of (1);
Figure BDA00033761890500000515
is the power spectrum center of gravity of the current modality; finally will be
Figure BDA00033761890500000516
Obtaining real part by performing inverse FFT
Figure BDA00033761890500000517
The specific algorithm process is as follows:
(1) initializing omegak、ukα, λ and N;
(2) when N is N +1, the algorithm starts to carry out iterative calculation;
(3) update ω from equations (5) and (6)kAnd ukK is a predetermined number of decomposition layers;
(4) λ is updated by:
Figure BDA00033761890500000518
(5) repeating the steps (3) and (4) until the termination condition is met:
Figure BDA0003376189050000061
substituting the reducer vibration signal acquired in the step1 into the algorithm, and decomposing the bearing fault vibration signal data to obtain the envelope spectrum of each component as shown in fig. 3, it can be observed that after the analysis by an unoptimized model, each IMF generates large noise, the noise suppression in the decomposition process is not obvious, the frequency components after the decomposition are almost concentrated in low frequency, the noise interference of the frequency band is large, and the fault frequency characteristic cannot be effectively observed.
Step 2: establishing an optimization objective function fusing the correlation coefficient, the similarity of the time-frequency spectrum and the kurtosis;
step 2.1: reconstructing the optimal solution obtained in the step1 to obtain a reconstructed signal X (t), XiFor reconstructing a certain sample point of the signal X (t), the original signal is set as S (t), SiCalculating a correlation coefficient r of X (t) and S (t) for a certain sample point of an original signal S (t):
Figure BDA0003376189050000062
r can also be represented by (X)i,Si) And estimating the standard fraction mean value of the sample points to obtain an expression equivalent to the formula:
Figure BDA0003376189050000063
wherein
Figure BDA0003376189050000064
And sigmaXAre respectively paired with XiThe standard fraction, the sample mean value and the sample standard deviation of the sample, wherein N is the signal sampling length;
step 2.2: method for obtaining frequency spectrum X of reconstructed signal by using Hilbert-Huang transformt-fAnd the original signal time spectrum St-fThe temporal spectral similarity is:
Figure BDA0003376189050000065
step 2.3: calculating the kurtosis of each intrinsic mode component after decomposition, and taking the maximum kurtosis:
Figure BDA0003376189050000066
step 2.4: after decomposing the vibration signal of the reducer, respectively calculating the maximum kurtosis value of each component after decomposing the signal, the correlation coefficient and the time-frequency spectrum similarity of the reconstructed signal X (t) and the original signal S (t), and fusing the three characteristics, wherein fig. 4 is a fusion flow chart of the correlation coefficient, the time-frequency spectrum similarity and the kurtosis.
And step 3:
optimizing by using a gray wolf optimization algorithm to obtain a penalty factor alpha with optimal decomposition under the current condition;
the position of each wolf individual represents the value of the current penalty factor alpha, X beta and X gamma represent the three wolfs with the optimal position of the current wolf group, the fitness value of each wolf individual represents the function value of the optimization objective function in the step3, and the position of the prey is the optimal solution. The grey wolf population predation position updating formula is as follows:
D＝|c·Xp(t)-X(t)| (15)
X(t+1)＝Xp(t) -A. D (16) wherein: c. a is a coefficient; xp is prey location; x is the gray wolf position. c. The determination formula of A is as follows:
c＝2·r1 (17)
A＝2·a·r2-a (18) wherein: r is1And r2Is [0,1 ]]The random number of (2); a is a convergence factor and linearly decreases from 2 to 0 with the number of iterations.
Determining the position X of three wolfs from the formulas (4) and (5)α(t+1)、Xβ(t+1)、Xγ(t +1), then determining the positions of other wolfs in the population by the positions of the three wolfs:
Figure BDA0003376189050000071
the optimization method by utilizing the gray wolf optimization algorithm comprises the following steps:
step 1: setting the values of initial parameters a and A, C of a gray wolf optimization algorithm;
step 2: is calculated to
Figure BDA0003376189050000072
As the position of the ith gray wolf, a range of 100 to 8000 is taken. Randomly initializing the positions of N wolf individuals in the wolf population;
step 3: comparing the position X of each wolfiAs a penalty factor [ alpha ]1,α2,…,αK]Decomposing the signal, calculating according to the formulas (12), (13) and (14) to obtain a fitness value, and recording the optimal three wolf individual positions X alpha, X beta and X gamma;
step 4: updating the positions of other wolf individuals by the formula (19), and updating the values of the parameters A, C and a by the formulas (17) and (18);
step 5: the loop iteration is switched to Step3 until an iteration termination condition is reached;
an iterative graph of the grayish optimization algorithm to find the best penalty factor is shown in fig. 5.
And 4, step 4:
the optimal number of decomposition levels is determined according to the maximum kurtosis criterion, fig. 6 is the relationship between the maximum kurtosis and the number of decomposition levels, and the optimal number of decomposition levels is determined to be 4 according to fig. 6. And (3) improving the model in the step (1) by utilizing the optimal parameters obtained in the step (3) to obtain a fault feature extraction method based on the gear reducer, decomposing the vibration signal of the gear reducer to obtain 4 modes, carrying out Hilbert transform on the modes, solving the envelope of the modes, carrying out Fourier transform on the envelope to obtain an envelope spectrum of the envelopes, and obtaining the fault feature of the gear reducer according to the envelope spectrum.
Fig. 7 is an envelope spectrum of four decomposed IMFs of the present invention, and it can be seen from the IMF4 envelope spectrum of fig. 7 that there are significant spectral peaks at the fault frequency and at 2-5 multiples thereof, which shows that the fault characteristic frequency is extracted, which proves the effectiveness of the method proposed herein, and the spectrogram is cleaner at the fault frequency and at the multiples thereof and has less interference.
As shown in fig. 8, after the conventional decomposition, although a spectrum peak can be seen in an IMF4 envelope spectrogram at a fault characteristic frequency and at 2-3 multiples thereof, the spectrum peak is not very obvious and is greatly interfered by surrounding noise frequencies, and the spectrum peak is not substantially seen at 4 multiples and at more than 4 multiples, so that the required fault characteristic is also suppressed due to an excessively severe suppression effect, and the fault characteristic information contained in the signal cannot be effectively represented.

Claims (5)

1. A gear reducer fault feature extraction method comprises the following steps:
step 1: establishing a gear reducer fault feature extraction model;
step 1.1: the vibration signal in the gear reducer work project to be processed is initially decomposed into K discrete time sequences u with limited bandwidthk(t)；
Step 1.2: u is calculated by the following formulak(t) gradient norm L2;
Figure FDA0003376189040000011
wherein, ω iskRepresenting the central fundamental frequency band, delta (t) representing the impulse impact signal,
Figure FDA0003376189040000014
calculating a partial derivative sign of the variable t;
step 1.3: establishing constraint by the condition that the sum of the central frequency and the bandwidth obtained by calculation is minimum and the bandwidth of the K discrete time sequences is required to be satisfied, and calculating the optimal solution under the current condition according to the constraint
Figure FDA0003376189040000015
Step 2: establishing an optimization target fusing correlation coefficients, time-frequency spectrum similarity and kurtosis;
step 2.1: reconstructing the optimal solution obtained in the step1 to obtain a reconstructed signal X (t), XiFor reconstructing a certain sample point of the signal X (t), the original signal is set as S (t), SiCalculating a correlation coefficient r of X (t) and S (t) for a certain sample point of an original signal S (t);
step 2.2: calculating the reconstructed signal X (t) and the original signal S (t)Time-frequency spectrum similarity Xt-fAnd St-fAnd obtaining the similarity S of time-frequency spectrumim；
Step 2.3: calculating the kurtosis of each signal component
Figure FDA0003376189040000012
Step 2.4: if the correlation coefficient is larger than a set threshold, taking the correlation coefficient and the kurtosis as optimization targets, otherwise, taking the frequency spectrum similarity and the kurtosis as the optimization targets;
and step 3: according to the optimization target obtained in the step2, the optimal penalty factor alpha of each layer when the model in the step1 is adopted for decomposition under the current condition is obtained by utilizing a wolf optimization algorithm
And 4, step 4: optimizing the model obtained in the step (3) in the step (1), determining the optimal decomposition layer number q according to the maximum kurtosis criterion, decomposing the vibration signal of the gear reducer into q layers by adopting the optimized model to obtain q modes, carrying out Hilbert transform on the modes, solving an envelope, carrying out Fourier transform on the envelope to obtain an envelope spectrum, and obtaining the fault characteristic of the reducer according to the envelope spectrum.
2. The method for extracting the fault characteristics of the gear reducer according to claim 1, wherein the specific method in the step 1.3 is as follows:
step 1.3.1: establishing the following constraint variational model:
Figure FDA0003376189040000013
in the formula: u. ofkIs the K-th IMF modal component, f is a component of the original signal;
step 1.3.2: after the constraint model is converted into a non-variational constraint problem through the following Lagrange function, the central frequency corresponding to the optimal solution of the formula (5) is obtained
Figure FDA0003376189040000021
And bandwidth
Figure FDA0003376189040000022
Figure FDA0003376189040000023
In the formula:
Figure FDA0003376189040000024
is expressed by uk、ωkλ is a Lagrangian function of an extremum of the independent variable,
Figure FDA0003376189040000025
Figure FDA0003376189040000026
means for determining the sum of
Figure FDA0003376189040000027
α is a secondary penalty factor, λ (t) is a lagrange factor, f (t) represents the original signal;
step 1.3.3: seeking saddle points of the variation problem by introducing an alternative multiplier direction algorithm, and then updating the central frequency of each order of IMF signals
Figure FDA0003376189040000028
And bandwidth
Figure FDA0003376189040000029
The following formula:
Figure FDA00033761890400000210
Figure FDA00033761890400000211
in the formula:
Figure FDA00033761890400000212
is the current residual
Figure FDA00033761890400000213
As a result of the filtering of (a),
Figure FDA00033761890400000214
for the center of gravity of the power spectrum of the current mode, it will be
Figure FDA00033761890400000215
Obtaining real part by performing inverse FFT
Figure FDA00033761890400000216
Step 1.3.4: updating lambda (t) by adopting the following formula;
Figure FDA00033761890400000217
recycling steps 1.3.2 to 1.3.4 until
Figure FDA00033761890400000218
ε represents the set threshold.
3. The method for extracting the fault characteristics of the gear reducer according to claim 1, wherein the method for calculating the correlation coefficient in the step 2.1 comprises the following steps:
Figure FDA00033761890400000219
4. the method for extracting the fault characteristics of the gear reducer according to claim 1, wherein the method for calculating the time-frequency spectrum similarity in the step 2.2 comprises the following steps:
Figure FDA00033761890400000220
5. the method for extracting the fault characteristics of the gear reducer as claimed in claim 1, wherein the kurtosis calculation method in the step 2.3 is as follows:
Figure FDA00033761890400000221
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