CN116610907A - Gear vibration signal characteristic extraction method based on variational modal decomposition - Google Patents
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Abstract
A gear vibration signal characteristic extraction method based on variation modal decomposition relates to a gear vibration signal characteristic extraction method. The method comprises the following steps: step one, signal acquisition; step two, constructing a Hankel matrix of the signal, calculating a singular value kurtosis differential spectrum of the Hankel matrix, and positioning a maximum mutation point r of the differential spectrum; step three, signal denoising is carried out according to the effective order of the r positioning singular value matrix; calculating the decomposition layer number K of the VMD by using the proposed optimal K value algorithm; fifthly, screening IMF components by using a correlation and peak value principle; step six, optimizing MCKD parameters by using a dung beetle algorithm, and carrying out pulse enhancement on signals by using the optimized MCKD; and seventhly, feature extraction is achieved by using fuzzy entropy, approximate entropy and sample entropy. The invention provides a gear vibration signal characteristic extraction method which can extract the characteristics of gear vibration signals more completely. The method is suitable for extracting the characteristics of the gear vibration signals.
Description
Technical field:
the invention relates to a vibration signal characteristic extraction method.
Background field:
when the state of the gear is evaluated, because the environmental factors often cause that other interference signals are contained in the obtained gear vibration signals, some weak fault signals can be covered in noise signals, so that fault information contained in the gear vibration signals is not obvious, further, the feature extraction of the gear fault information is incomplete, and the fault diagnosis after the fault diagnosis is affected.
The invention comprises the following steps:
in order to reduce the influence of noise interference on gear fault information feature extraction and improve the accuracy of gear state evaluation, the invention provides a gear vibration signal feature extraction method based on variation modal decomposition.
The gear vibration signal characteristic extraction based on variation modal decomposition is carried out according to the following steps:
step 1, collecting gear vibration signals;
step 2, constructing a Hankel matrix of the signal, calculating a singular value kurtosis difference spectrum of the Hankel matrix, and positioning a maximum mutation position r of the difference spectrum;
step 3, reserving the first r singular values in the Hankel matrix, setting zero for other singular values, and carrying out signal denoising;
step 4, calculating the VMD decomposition layer number by using an optimal K value algorithm;
step 5, using the correlation and peak value index as the basis to screen IMF components and reconstructing signals;
step 6, selecting the optimal parameters in the MCKD by using a dung beetle optimization algorithm, and carrying out pulse enhancement on the reconstructed signal by using the optimized MCKD;
and 7, extracting features by using fuzzy entropy, approximate entropy and sample entropy to obtain a fusion feature matrix.
Further, in the second step, discretizing the collected continuous signals and constructing a Hankel matrix, wherein the matrix expression is as follows:
in formula (1), x (i) is an element in the vibration signal sequence;
further, in the second step, a singular value decomposition Hankel matrix is used and a singular value differential spectrum is calculated, so that a maximum mutation r of the singular value differential spectrum is obtained, and a singular value decomposition expression is as follows:
A＝UΣV T (2)
in formula (2), U is the left singular vector of matrix a, Σ is the singular value of matrix a, and V is the right singular vector of matrix a.
Further, the calculation method of the optimal K value algorithm in the fourth step is as follows: singular value decomposition is carried out on a Hankel matrix constructed by the original signal, a singular value kurtosis difference spectrum of the Hankel matrix is calculated, a kurtosis difference spectrum mutation position is located, and the mutation position is used as an initial K value. And decomposing the original vibration signal by using an initial K value, calculating the center frequency distance between adjacent IMF components, adding 1 to the initial K value if all the initial K values are larger than 0.1, and stopping until the distance between any adjacent IMFs is smaller than 0.1, wherein the K value is the optimal K value of the VMD.
Further, the IMF screening method in the fifth step comprises the following steps: and calculating the correlation between the IMF and the original signal and the kurtosis value of the IMF, selecting the IMF with the correlation coefficient larger than the average value and the kurtosis value larger than 3, and carrying out signal reconstruction by using the screened IMF.
Further, the fusion mode of the feature vectors in the step six is as follows: dividing the reconstruction signal into n segments, calculating fuzzy entropy, approximate entropy and sample entropy of each segment, taking entropy value as characteristic of the reconstruction signal, fusing entropy values of all signal segments, for example, the characteristic vector of A is A= [ a ] 1 … a n ]The feature vector of B is b= [ B ] 1 … b n ]The C eigenvector is c= [ C 1 … c n ]So the fusion feature vector is f= [ a ] 1 … a n b 1 … b n c 1 … c n ]。
The principle of the invention is as follows:
the method comprises the steps of constructing a Hankel matrix of a vibration signal during feature extraction, decomposing the Hankel matrix of the vibration signal by singular values, and calculating a singular value kurtosis difference spectrum; positioning the maximum mutation position r of kurtosis spectrum, setting all elements after the r order of the diagonal line of the singular value matrix to zero, and using the singular value matrix to reconstruct vibration signals so as to finish signal denoising; calculating a preset mode number K of the VMD by using a proposed optimal K value algorithm; screening IMF by using cross correlation and kurtosis as indexes to reconstruct signals; introducing a dung beetle algorithm to optimize parameters L and M in the MCKD, and performing pulse enhancement on a reconstruction signal by using the optimized MCKD; features are extracted from different angles by using fuzzy entropy, approximate entropy and sample entropy, and fusion feature vectors are formed.
The invention has the beneficial effects that:
according to the invention, the mutation position of the singular value kurtosis difference spectrum is obtained according to the Hankel matrix of the original signal, the SVD is used for removing noise in the original signal, the proposed optimal K value algorithm is used for calculating the preset mode number K in the variation mode decomposition algorithm, and the problem that the setting of the preset mode number K depends on experience judgment in the past is solved. The invention carries out signal reconstruction according to the correlation and kurtosis value, and screens useful IMF component signals. According to the invention, an optimal combination of parameters L and M in the MCKD is found by using a dung beetle optimization algorithm, and pulse components in the reconstructed signal are enhanced by using the optimized MCKD, so that weak features can be identified during feature extraction. The invention uses three modes to extract the features from different angles to manufacture the fusion feature vector, thereby solving the problem of incomplete feature extraction caused by the single mode of feature extraction and ensuring the quality of the extracted fault features.
Description of the drawings (last):
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a reconstructed signal time domain diagram;
fig. 3 is a signal feature fusion graph.
The specific embodiment is as follows:
the invention will be further described in detail with reference to the drawings and examples below for better explaining the objects, technical solutions and advantages of the invention. The specific embodiments described herein are merely illustrative of the invention and are not intended to be limiting.
As described in connection with fig. 2 and 3, the processed reconstructed signal is more distinct than the original signal characteristics.
The gear vibration signal characteristic extraction method based on variation modal decomposition in the embodiment is carried out according to the following steps:
step one: a gearbox system built in a laboratory collects signals;
step two: constructing a vibration signal Hankel matrix, calculating singular values of the Hankel matrix by singular value decomposition, and locating a maximum mutation r by a singular value peak differential spectrum, wherein the Hankel matrix and the singular value decomposition expression are as follows:
A＝UΣV T (2)
in formula (2), U is the left singular vector of matrix a, Σ is the singular value of matrix a, and V is the right singular vector of matrix a.
Step three: performing signal denoising processing by using SVD according to r;
the signal denoising method in the third step comprises the following steps: setting elements after r orders on diagonal lines in the singular value matrix decomposed by SVD to zero, and carrying out signal reconstruction by using the singular value matrix after processing.
Step four: calculating the VMD decomposition layer number by using an optimal K value algorithm;
the optimal K value algorithm in the fourth step is as follows: setting the maximum mutation r of the original signal singular value peak differential spectrum as an initial K value, carrying out VMD decomposition on the denoising signal by using the initial K value, calculating the center frequency distance between adjacent IMFs, adding 1 to the K value when all the center frequency distances are larger than 0.1, and repeating the steps until the step is finished when the center frequency distance between any adjacent IMFs is smaller than 0.1, and obtaining the optimal K value of the VMD.
Step five: using a correlation and kurtosis principle to screen IMF components with correlation larger than the mean value and kurtosis larger than 3 for signal reconstruction;
step six: optimizing MCKD parameters by using a dung beetle algorithm and carrying out pulse enhancement on the reconstructed signals;
the MCKD parameter optimization algorithm in the step six is as follows: randomly initializing 100L, M combinations, using the sample entropy of the MCKD enhanced signal as an objective function, finding the L, M combination that minimizes the sample entropy of the MCKD enhanced result over 15 iterations, and pulse enhancing the reconstructed signal using set L, M.
Step seven: extracting a reconstructed signal characteristic by using a sample entropy, a fuzzy entropy and an approximate entropy to obtain a fusion characteristic;
the method comprises the steps of carrying out equidistant segmentation on a reconstructed signal, dividing the reconstructed signal into n sections, carrying out feature extraction on each section by using sample entropy, fuzzy entropy and approximate entropy, and splicing the extracted features to obtain a fusion feature vector.
Experimental results show that noise in an original signal can be removed by SVD denoising, the optimal K value algorithm can obtain reasonable preset mode numbers, the dung beetle optimization algorithm can effectively jump out the limitation of local optimization and find the optimal MCKD parameter combination, the optimized MCKD enhances weak pulse signals in a reconstructed signal, feature line vectors are extracted in different modes by using fuzzy entropy, approximate entropy and sample entropy and combined into a mixed feature vector matrix, features are extracted from different scales, the obtained feature vectors are more complete, and support is provided for gear fault diagnosis.
Claims (7)
1. The gear vibration signal characteristic extraction method based on variation modal decomposition is characterized by comprising the following specific processes:
step 1, a laboratory collects vibration signals of a gear box;
step 2, constructing a Hankel matrix of the signal, calculating a singular value kurtosis difference spectrum of the Hankel matrix, and positioning a maximum mutation position r of the difference spectrum;
step 3, reserving the first r singular values in the Hankel matrix, setting zero for other singular values, and carrying out signal denoising;
step 4, calculating the VMD decomposition layer number by using an optimal K value algorithm;
step 5, using the correlation and peak value index as the basis to screen IMF components and reconstructing signals;
step 6, selecting the optimal parameters in the MCKD by using a dung beetle optimization algorithm, and carrying out pulse enhancement on the reconstructed signal by using the optimized MCKD;
and 7, extracting features by using fuzzy entropy, approximate entropy and sample entropy to obtain a fusion feature matrix.
2. The method for extracting the gear vibration signal characteristics of the variation modal decomposition according to claim 1, wherein in the step 2, the vibration signal is constructed as a Hankel matrix, a Hankel singular value matrix is obtained by using a singular value decomposition algorithm, a singular value kurtosis differential spectrum is calculated, and a maximum mutation r of the differential spectrum is positioned.
3. The method for extracting the gear vibration signal characteristics by the variation modal decomposition according to claim 1, wherein in the step 3, the effective order of a singular value matrix is determined through the mutation position of the singular value kurtosis spectrum, the singular value after the r order of a diagonal line of the singular value matrix is set to zero, and the processed singular value matrix is used for obtaining the vibration signal after denoising.
4. The method for extracting the gear vibration signal characteristics of the variation modal decomposition according to claim 1, wherein step 4 provides an optimal K value calculation method of VMD: taking the maximum mutation position of the singular value kurtosis difference spectrum of the signal as an initial K value, carrying out VMD decomposition on the signal, calculating the center frequency distance between the decomposed adjacent IMF components, adding 1 to the K value when the center frequency distances of all the IMFs are larger than 0.1, and repeating the steps until the center distance of any adjacent IMF is smaller than 0.1, and obtaining the optimal K value at the moment.
5. The method for extracting the vibration signal characteristics of the gear decomposed by the variation mode according to claim 1, wherein the IMF components decomposed in the step 5 are subjected to signal reconstruction by using correlation and peak values as indexes, and the IMF components with correlation coefficients larger than the average value and kurtosis larger than 3 are screened.
6. The method for extracting features of vibration signals of a gear decomposed by a variation mode according to claim 1, wherein in the step 6, a dung beetle optimization algorithm is used to find the best combination of L and M in the range that the filter length L belongs to [100,500] and the shift number M belongs to [1,7], so that the effect of enhancing weak pulses in the vibration signals by MCKD is the best.
7. The method for extracting vibration signal characteristics of a gear using a variation modal decomposition according to claim 1, wherein in step 7, characteristics of the vibration signal are extracted from different angles using three different signal entropies of fuzzy entropy, approximate entropy, and sample entropy.
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