CN108287073B - Resonance band selection method based on singular value component frequency domain spectrum - Google Patents
Resonance band selection method based on singular value component frequency domain spectrum Download PDFInfo
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- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract
The invention discloses a resonance band selection method based on a singular value component frequency domain spectrum, and relates to the technical field of bearing test methods. The method comprises the following steps: carrying out FFT frequency domain transformation on a fault bearing signal acquired by an acceleration sensor; determining the number of frequency spectrum divided areas according to the number of the main frequencies of the signal frequency spectrum; constructing a Hankel matrix of the collected fault bearing signals, and performing singular value decomposition on the matrix to obtain singular value components; and selecting the components for envelope demodulation analysis, and determining the center frequency and the bandwidth of the components by the maximum value of the kurtosis of the envelope spectrum. The method not only can adaptively select the optimal resonance band, but also can improve the signal to noise ratio, can improve the diagnosis accuracy to a great extent, and lays a good foundation for the subsequent fault diagnosis of the bearing.
Description
Technical Field
The invention relates to the technical field of bearing testing methods, in particular to a resonance band selection method based on singular value component frequency domain spectrum
Background
In many rolling bearing fault diagnosis methods, the resonance demodulation technology is widely applied due to the accuracy, but in the method, the setting of the parameters of the band-pass filter requires abundant professional knowledge and a great deal of experience accumulation, so that the popularization of the resonance demodulation in engineering application is limited. In addition, noise in the vibration signal of the rolling bearing also seriously affects the accuracy of resonance demodulation fault diagnosis, and in order to suppress noise and improve the signal-to-noise ratio, the signal is often required to be subjected to noise elimination processing.
Document 1(MCFADDEN P D, SMITH J D. vibration monitoring of rolling e 1-element bearing by the high-frequency response technique; a view [ J ]. Int J. Tribology,1984,17(2):3-10.) proposes that resonance demodulation techniques are widely used because of their high accuracy. However, since the resonant frequency band needs to be determined by subjective experience in band pass filtering, the resonant frequency band cannot be selected adaptively, which makes the extraction of fault features have a great subjective factor. Document 2(Antoni J, Randall R B. the spectral signals [ J ] for the optimization of non-statistical signals, 2006, 20(2):282 + 307) proposes the concept of kurtosis map for better optimization of the filter parameters and considers the spectral kurtosis as a short-time Fourier transform window width function. However, such kurtosis map is inconvenient to apply in practical engineering, and is too time-consuming and energy-consuming. The wavelet denoising method proposed in the document 3 (Guobaifei, Gaoshiming, Zhang Qiang, Signal denoising by using wavelet threshold method [ J ]. Shandong university school newspaper (Nature science edition), 2001,36 (3); 306-. The empirical mode decomposition noise reduction method used in document 4(HUANG N E, SHEN Z, LONG S R, et al, the empirical mode decomposition and the Hilbert spectrum for nonlinear time series analysis [ J ]. proceedings of Royal Society Lon-don: A,1998.454(1971): 903-995.) can decompose the signal into different frequency bands and then convert it into a stationary signal for further analysis, although it does not need to consider the selection of reference thresholds and basis functions, but it presents a certain frequency aliasing problem.
Disclosure of Invention
The invention aims to solve the technical problem of providing a resonance band selection method based on a singular value component frequency domain spectrum, which not only can adaptively select an optimal resonance band, but also can improve the signal to noise ratio and the accuracy of subsequent fault diagnosis.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a resonance band selection method based on singular value component frequency domain spectrum is characterized by comprising the following steps:
1) acquiring vibration information protected by a fault bearing by using an acceleration sensor, and performing FFT frequency domain transformation on a fault bearing signal acquired by the acceleration sensor;
2) dividing the frequency spectrum into n regions according to the number of main frequencies, namely the number of peak values, of the frequency spectrum of the signal;
3) constructing the collected fault bearing signals into a Hankel matrix with n +1 line numbers, and performing singular value decomposition on the matrix to obtain n +1 singular value components;
4) and selecting the nth component for envelope demodulation analysis, and determining the central frequency and bandwidth of the component by the maximum value of the kurtosis of the envelope spectrum.
5) And calculating a specific resonance band value according to the center frequency and the bandwidth.
The further scheme is as follows: the method for determining the number of the lines of the Hankel matrix comprises the following steps:
dividing the frequency spectrum into n regions according to the number of main frequencies, namely the number of peak values, of the signal frequency spectrum, wherein the number of lines of a Hankel matrix is n + 1; constructing a Hankel matrix with N +1 rows on the basis of a phase space reconstruction theory for vibration signals x (i) (i is 1,2, … N) containing fault information, wherein the matrix form is as follows:
in the formula: n is the length of a fault bearing signal, and N +1 is the number of rows of the matrix;
carrying out singular value decomposition on a Hankel matrix formed by fault bearing signals, wherein the decomposition formula is as follows:
wherein: a is a Hankel matrix formed by signals, U is an m-order orthogonal matrix, V is an n-order orthogonal matrix, and sigma is diag1,σ2,…σr) Is a diagonal matrix of order r, and σiIs the non-zero singular value of matrix a, 0 is a zero matrix;
removing the zero singular values in equation (1), the singular values of a can be decomposed into reduced component form, as follows:
in the formula: u. ofi、viThe ith column vector of U, V, respectively;
the singular value component of n +1 obtained after decomposition is consistent with the line number of the Hankel matrix; the frequency spectrum of each singular value component only reflects a part of frequency bands, the component frequency spectrum in the front order reflects a frequency band with lower frequency, the component frequency spectrum in the back order reflects a frequency band with higher frequency, and the frequency bands of the singular value component frequency spectrums are sequentially arranged from low to high according to the sequence of the singular value components.
The further technical scheme is that the method for selecting the singular value component corresponding to the resonance band according to the method comprises the following steps:
the number of the Hankel matrix lines is consistent with the number of singular value components obtained after singular value decomposition, and in n +1 singular value components, the nth component is a component corresponding to a resonance band; the frequency bands of the singular value component frequency spectrums are sequentially arranged from low to high according to the order of the singular value components, and the n +1 th component is a part with unobvious high-frequency vibration and cannot reflect the resonance condition, so the nth component is selected as the component corresponding to the resonance band.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: 1) the method utilizes the singular value component frequency spectrum rule to select the resonance band, can effectively remove low-frequency interference, and generally selects the optimal resonance band. 2) In the method, the resonance band in the vibration signal is determined by adopting frequency domain analysis, and the self-adaptive effect can be achieved for different bearing band-pass filters. 3) The method adopts singular value decomposition to obtain components, the singular value decomposition has a denoising effect, the influence of noise can be eliminated, vibration signals are highlighted, and the accuracy of subsequent fault diagnosis is improved to a great extent.
Drawings
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a method according to an embodiment of the invention;
FIG. 2 is a time domain plot of a faulty bearing signal in an embodiment of the present invention;
FIG. 3 is a frequency spectrum diagram of a fault bearing signal in an embodiment of the present invention;
FIG. 4 is a graph of a first singular value component spectrum according to an embodiment of the present invention;
FIG. 5 is a second graph of the spectrum of a singular value component in accordance with an embodiment of the present invention;
FIG. 6 is a third graph of the spectrum of a singular value component according to an embodiment of the present invention;
FIG. 7 is a diagram of a fourth spectrum of singular value components in an embodiment of the present invention;
FIG. 8 is a graph of the spectral kurtosis of the singular value components corresponding to a resonance band in an embodiment of the present invention;
FIG. 9 is a time domain diagram of singular value components corresponding to a resonance band in an embodiment of the present invention;
FIG. 10 is a diagram of the singular value envelope corresponding to the resonance band in an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Generally, as shown in fig. 1, the present invention discloses a resonance band selection method based on a singular value component frequency domain spectrum, which includes the following steps:
1) acquiring vibration information protected by a fault bearing by using an acceleration sensor, and performing FFT frequency domain transformation on a fault bearing signal acquired by the acceleration sensor;
2) dividing the frequency spectrum into n regions according to the number of main frequencies, namely the number of peak values, of the frequency spectrum of the signal;
3) constructing the collected fault bearing signals into a Hankel matrix with n +1 line numbers, and performing singular value decomposition on the matrix to obtain n +1 singular value components;
4) and selecting the nth component for envelope demodulation analysis, and determining the central frequency and bandwidth of the component by the maximum value of the kurtosis of the envelope spectrum.
5) And calculating a specific resonance band value according to the center frequency and the bandwidth.
Specifically, the method comprises the following steps:
1) determining the number of lines of a Hankel matrix
Fig. 2 is a time domain diagram of a bearing fault signal, a frequency spectrum is divided into 3 regions according to the number of main frequencies, i.e., the number of peak values, in the frequency spectrogram of the signal of fig. 3, and the number of lines of a Hankel matrix is 4; constructing a Hankel matrix with 4 rows on the basis of a phase space reconstruction theory for vibration signals x (i) (i ═ 1,2, … N) containing fault information, wherein the matrix form is as follows:
in the formula: n is the length of a fault bearing signal, and 4 is the number of rows of the matrix;
carrying out singular value decomposition on a Hankel matrix formed by fault bearing signals, wherein the decomposition formula is as follows:
wherein: a is a Hankel matrix formed by signals, U is an m-order orthogonal matrix, V is an n-order orthogonal matrix, and sigma is diag1,σ2,…σr) Is a diagonal matrix of order r, and σiIs the non-zero singular value of matrix a, 0 is a zero matrix;
removing the zero singular values in equation (1), the singular values of a can be decomposed into reduced component form, as follows:
in the formula: u. ofi、viThe ith column vector of U, V, respectively;
the 4 singular value components obtained after decomposition are consistent with the line number of the Hankel matrix; 4-7 are graphs of the decomposed spectra of four singular value components, each of which has a spectrum that reflects only a portion of the frequency band and sequentially preceding component spectra that reflect lower frequency bands and sequentially succeeding components that reflect higher frequency bands, the frequency bands of the singular value component spectra being arranged in order from lower to higher in the order of the singular value components; therefore, when a Hankel matrix is constructed, a row is additionally arranged, so that the unobvious components of the high-frequency part of the vibration signal can be removed, the resonance band is highlighted, the resonance band can be well extracted, and the noise reduction effect is achieved.
2) Selecting singular value components corresponding to a resonance band
The number of the Hankel matrix lines is consistent with the number of singular value components obtained after singular value decomposition, and in 4 singular value components, the 3 rd component is a component corresponding to a resonance band. The frequency band generated by fault impact is very wide, and the natural frequency of the detection part is necessarily covered, so that the high frequency of the system is excited and the system vibrates. The frequency bands of the singular value component frequency spectrums are arranged in sequence from low to high according to the order of the singular value components, as shown in fig. 7, the 4 th component is mixed with the part at the tail of the frequency spectrum, which is not obvious in high-frequency vibration, and the resonance condition can not be reflected, so the 3 rd component shown in fig. 6 is selected as the component corresponding to the resonance band. The spectral kurtosis of the component is enveloped to obtain a spectral kurtosis diagram shown in fig. 8, the central frequency of the signal is 8800Hz, the bandwidth is 1600Hz, and the specific range of the selected resonance band is 8000 Hz-9600 Hz according to the central frequency and the bandwidth. Meanwhile, as shown in fig. 9, the singular value time domain diagram corresponding to the resonance band has fewer noise components and has obvious impact characteristics. Fig. 10 is an envelope spectrum of the corresponding singular value component of the resonance band, where the fault signature and its frequency multiplication are clearly visible with a low noise level. It can be seen that the singular value decomposition has the ability to remove noise. The method also plays the roles of suppressing noise and improving the signal-to-noise ratio when the resonance band is selected.
Claims (2)
1. A resonance band selection method based on singular value component frequency domain spectrum is characterized by comprising the following steps:
1) acquiring vibration information of a fault bearing by using an acceleration sensor, and performing FFT frequency domain transformation on a fault bearing signal acquired by the acceleration sensor;
2) dividing the frequency spectrum into n regions according to the number of main frequencies, namely the number of peak values, of the frequency spectrum of the signal;
3) constructing the collected fault bearing signals into a Hankel matrix with n +1 line numbers, and performing singular value decomposition on the matrix to obtain n +1 singular value components;
the method for determining the number of the lines of the Hankel matrix comprises the following steps:
dividing the frequency spectrum into n regions according to the number of main frequencies, namely the number of peak values, of the signal frequency spectrum, wherein the number of lines of a Hankel matrix is n + 1; measuring a vibration signal x (i) containing fault information, wherein i is 1,2.. N; based on a phase space reconstruction theory, a Hankel matrix with n +1 rows is constructed, and the matrix form is as follows:
in the formula: n is the length of a fault bearing signal, and N +1 is the number of rows of the matrix;
carrying out singular value decomposition on a Hankel matrix formed by fault bearing signals, wherein the decomposition formula is as follows:
wherein: a is a Hankel matrix formed by signals, U is an m-order orthogonal matrix, V is an n-order orthogonal matrix, and sigma is diag1,σ2,…σr) Is a diagonal matrix of order r, and σiIs the non-zero singular value of matrix a, 0 is a zero matrix;
removing zero singular values in the formula (1), and decomposing and writing the singular value of A into a reduced component form as follows:
in the formula: u. ofi、viThe ith column vector of U, V, respectively;
the singular value component of n +1 obtained after decomposition is consistent with the line number of the Hankel matrix; the frequency spectrum of each singular value component only reflects a part of frequency bands, the component frequency spectrum in the front sequence reflects a frequency band with lower frequency, the component frequency spectrum in the back sequence reflects a frequency band with higher frequency, and the frequency bands of the singular value component frequency spectrums are sequentially arranged from low to high according to the sequence of the singular value components;
4) selecting the nth component to carry out envelope demodulation analysis, and determining the central frequency and bandwidth of the component according to the maximum value of the kurtosis of an envelope spectrum;
5) and calculating a specific resonance band value according to the center frequency and the bandwidth.
2. The singular value component frequency domain spectrum-based resonance band selection method as claimed in claim 1, wherein the method for selecting the singular value component corresponding to the resonance band according to the method for determining the number of lines of the Hankel matrix is as follows:
the number of the Hankel matrix lines is consistent with the number of singular value components obtained after singular value decomposition, and in n +1 singular value components, the nth component is a component corresponding to a resonance band; the frequency bands of the singular value component frequency spectrums are sequentially arranged from low to high according to the order of the singular value components, and the n +1 th component is a part with unobvious high-frequency vibration and cannot reflect the resonance condition, so the nth component is selected as the component corresponding to the resonance band.
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| CN111611870B (en) * | 2020-04-26 | 2023-05-09 | 广东机电职业技术学院 | Fault feature identification method, system, device and medium for cold tandem mill |
| CN114486256B (en) * | 2021-08-22 | 2023-10-31 | 北京燃气绿源达清洁燃料有限公司 | CNG compressor rolling bearing fault feature extraction method |
| CN114169379B (en) * | 2022-02-07 | 2022-04-26 | 石家庄铁道大学 | Method for detecting abnormal vibration data during bearing state monitoring |
| CN115730199B (en) * | 2022-11-10 | 2023-07-21 | 天地(常州)自动化股份有限公司北京分公司 | Rolling bearing vibration signal noise reduction and fault feature extraction method and system |
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