CN109948286B - Signal decomposition method based on improved empirical wavelet decomposition - Google Patents
Signal decomposition method based on improved empirical wavelet decomposition Download PDFInfo
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Abstract
The invention relates to a signal decomposition method based on improved empirical wavelet decomposition, comprising the following steps: and (3) performing Fourier power spectral density spectral line calculation on the fault signal, selecting a plurality of thresholds with different sizes, removing the interference component spectral values, decomposing the fault signal based on a new spectral line, and screening an optimal threshold, an optimal decomposition result and modal components containing abundant fault characteristic information by using fault characteristic energy ratio information. Under the interference background, the invention can still effectively and optimally decompose the modal components containing abundant fault characteristic information, eliminate interference, inhibit modal aliasing and excessive decomposition phenomena, obtain ideal decomposition results, make up the deficiency of EWT and enrich theoretical methods of modal decomposition.
Description
Technical Field
The invention relates to a fault signal processing method of rotary machinery, in particular to a signal decomposition method based on improved empirical wavelet decomposition.
Background
The rotary machines such as hydraulic pumps, hydraulic motors, bearings, gears, rotors and the like are widely applied to various important industrial fields, and the working environments facing the rotary machines tend to severe working conditions such as high temperature, high pressure, high speed, heavy load and the like, so that the deterioration of the health state of the rotary machines is accelerated, and the intelligent fault diagnosis of the rotary machines is of great significance. The vibration form and the transmission path of the rotating machinery fault are very complex, the fault signal has the characteristics of nonlinearity, non-stationarity and the like, and the fault signal is easy to be interfered by equipment such as noise, background noise, electromagnetism and the like. Therefore, how to effectively extract the modal components with rich fault feature information and suppress interference becomes a key problem.
The disadvantages of wavelet transform are: none of the following principles and criteria are adopted to select a proper wavelet basis function to be accurately matched with the morphological characteristics of the signals; once the basis function is determined, it will not change during decomposition according to morphological features of the signal, resulting in it not being truly adaptive; again, while the wavelet has the function of a "mathematical microscope", once the basis functions and scale factors are determined, its resolution is then determined; finally, as with the limitations of short-time Fourier transforms, wavelet transforms, while having multi-scale and multi-resolution capabilities, require that the signal within the wavelet window must be approximately stationary (pseudo stationary).
Conventional empirical mode decomposition has the disadvantages of: such as modal aliasing, which cannot effectively separate the modal functions of a specific time scale based on the morphological characteristics of the signal, so that different modal components appear in the same decomposition result, or decompose the same modal component into a plurality of decomposition results; for example, the end effect causes divergence of the data edges of the modal components, and in the iteration process, the edge divergence gradually pollutes inwards, and as the number of iterations increases, the data sequence is severely distorted, so that modal aliasing and false components appear.
In view of the above problems, gilles in paper Empirical Wavelet Transform proposes a new approach to nonlinear and nonstationary signal processing, i.e., empirical wavelet decomposition (Empirical Wavelet Transform, EWT), which combines the advantages of both wavelet transformation and empirical mode decomposition. The EWT can decompose a multi-mode signal into the sum of a plurality of amplitude-modulated signals with tightly-supported spectrums by dividing the Fourier amplitude spectrum and establishing a wavelet quadrature basis in each division interval. However, in the interference background, the device cannot effectively decompose modal components containing abundant fault characteristic information, and modal aliasing and excessive decomposition are most likely to occur.
Disclosure of Invention
Aiming at the problem that the mode containing abundant fault characteristic information cannot be effectively decomposed through EWT under the interference background, the invention provides a signal decomposition method based on improved empirical wavelet decomposition (Improved Empirical Wavelet Transform, IEWT), which has wider use conditions and more obvious decomposition effect.
The technical scheme adopted for solving the technical problems is as follows:
a signal decomposition method based on improved empirical wavelet decomposition comprising the steps of:
(1) Power density spectrum determination
Calculating a power density spectrum of the fault signal;
(2) Power density spectrum based thresholding
Eliminating spectrum values smaller than the threshold value in the power density spectrum of the fault signal by utilizing different threshold values to obtain a new spectrum value sequence;
(3) Fault signal decomposition processing
Dividing the power density spectrum into N continuous intervals within the range of [0 pi ], establishing a wavelet orthogonal basis in each interval, and decomposing a fault signal into the sum of N modal components;
(4) Optimal decomposition result screening
And solving the characteristic energy ratio of each component in the decomposition results corresponding to each threshold, comparing and analyzing the maximum characteristic energy ratio and the next largest characteristic energy ratio in each decomposition result, and screening out the maximum comparison result based on the maximum comparison value of all the decomposition results, wherein the decomposition result corresponding to the maximum comparison value is the optimal decomposition result, the corresponding threshold is called the optimal decomposition threshold, and the modal component corresponding to the maximum characteristic energy ratio contains the most abundant fault characteristic information.
Compared with the EWT in the prior art, the invention adopting the technical scheme has the beneficial effects that:
under the interference background, the modal components containing abundant fault characteristic information can be effectively and optimally decomposed, the interference is eliminated, the modal aliasing and excessive decomposition phenomena are inhibited, and an ideal decomposition result is obtained. The defect of EWT is made up, and the theoretical method of modal decomposition is enriched.
Drawings
FIG. 1 is a time domain plot of a slipper wear fault signal;
FIG. 2 is a time domain diagram of the most abundant fault characteristic information components contained in the decomposition result of the wear fault signal of the sliding shoe obtained based on the IEWT method;
FIG. 3 is a graph of power spectral density of the most abundant fault signature information components contained in the decomposition result of the skid shoe wear fault signal based on the IEWT method;
FIG. 4 is a time domain diagram of the most abundant fault characteristic information components contained in the decomposition result of the wear fault signal of the sliding shoe based on the EWT method;
FIG. 5 is a power spectrum density diagram of the most abundant fault characteristic information components contained in the decomposition result of the wear fault signal of the sliding shoe based on the EWT method;
fig. 6 is a flow chart of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
This embodiment is described by taking a skid shoe wear failure as an example.
Referring to fig. 6, a signal decomposition method based on improved empirical wavelet decomposition (Improved Empirical Wavelet Transform, IEWT) comprises the following specific steps:
step (1), power density spectrum obtaining
And calculating a power density spectrum of the acquired discrete state fault signal f (n), wherein a spectrum value distribution sequence is marked as P.
Step (2) of threshold value elimination based on power density spectrum
The spectral values smaller than the threshold value in P are respectively removed by using L threshold values coefficient multiplied by mean (P) with different sizes to obtain L new spectral value distribution sequences P coefficient Where coefficient=1, 2, …, integer of L, mean (P) is the average spectral value. Since the interference spectrum value is generally not large, the adverse effect of the interference component spectrum information on the boundary self-adaptive segmentation is eliminated to a great extent, and thus the phenomena of modal aliasing and excessive decomposition are avoided as much as possible.
Step (3), fault signal decomposition processing
For P coefficient The following treatment is carried out: the density spectrum of the power spectrum is [0 pi ]]Since the range is divided into N consecutive segments, and n+1 boundary lines are generated, assuming that the signal has N modes, the maxima in the spectrogram are screened, and the M maxima are arranged in descending order, there are two cases:
1) M is more than or equal to N, which indicates that the method screens out sufficient maximum values and reserves the first N maximum values;
2) M < N, the number of singles in the signal is less than the number of expected components N, all maxima are preserved, and N is reset.
Any segment may be represented as Λ n ＝[ω n-1 ,ω n ],Wherein omega n Is the midpoint (omega) of two consecutive maxima n ＝0，ω N =pi). Thus from the center omega n Width T n ＝2τ n A transition section is formed.
For lambda n The windowing process is performed, and based on the Meyer wavelet method, the empirical scale function and the empirical wavelet function are shown below, respectively.
Wherein, gamma<min n [ω n+1 -ω n /ω n+1 +ω n ],β(x)＝35x 4 -8x 5 +70x 6 -20x 7 。
Wavelet transform detail coefficients W of the signal according to wavelet theory, formulas (1) and (2) x (n, t) and approximation coefficient W x (0, t) can be defined as formula (3) and formula (4):
the signal is reconstructed and the result is shown in formula (5).
From the above-mentioned available modal component f k Can be represented by the following formulas (6) and (7)
Step (4), screening the optimal decomposition result
Based on the obtained L decomposition results, each decomposition result contains a plurality of modal components, the characteristic energy ratio FER (the ratio of the energy of the fault characteristic frequency and the frequency multiplication position and the total energy of the frequency band) is obtained for each modal component of each decomposition result, and the maximum characteristic energy ratio FER of each decomposition result is obtained coefficient,max Ratio to the next largest characteristic energy FER coefficient,secondmax Comparative analysis, i.e. A coefficient ＝(FER coefficient,max -FER coefficient,secondmax )/FER coefficient,secondmax At a certain larger FER coefficient,max Find the largest A in the range coefficient Is denoted as A max ，A max The corresponding decomposition result is the optimal decomposition result, the corresponding threshold value is called the optimal threshold value, and the FER of the result coefficient,max The corresponding component is the component containing rich fault characteristic information.
Referring to fig. 2, 3, 4 and 5, in this embodiment, the IEWT method and the EWT method in the prior art are based on decomposing the skid shoe wear fault signal respectively to obtain 8 modal components and 53 modal components, and selecting the modal component containing the most abundant fault feature information in the optimal decomposition result. Fig. 2, which contains the most abundant fault signature modal components, clearly presents the periodic impact signature based on the IEWT, while fig. 4, which contains the most abundant fault signature modal components, also clearly presents the periodic impact signature based on the EWT, its spectral value is much smaller than that obtained based on the IEWT; the morphological characteristic information of fig. 2 containing the most abundant fault characteristic information modal components obtained based on IEWT and the morphological characteristic information of the skid shoe wear fault primary signal in fig. 1 have high similarity, and the morphological characteristic information of fig. 4 containing the most abundant fault characteristic information modal components obtained based on EWT and the morphological characteristic information of the skid shoe wear fault primary signal in fig. 1 are much more similar. The modal component results obtained based on the IEWT optimal decomposition clearly show the spectral lines at the skid shoe wear failure characteristic frequency 171.5Hz and the frequency doubling thereof, and although the modal component results obtained based on the EWT and containing the most abundant failure characteristic information clearly show the spectral lines at the skid shoe wear failure characteristic frequency 171.5Hz and the frequency doubling thereof, the spectral values are much smaller than those obtained based on the IEWT.
The foregoing is merely a specific embodiment of the present invention, and it should be noted that, although the present invention has been described in detail with reference to this embodiment, it will be apparent to those skilled in the art that several modifications and adaptations of the present invention can be made without departing from the spirit and scope of the invention.
Claims (1)
1. A signal decomposition method based on improved empirical wavelet decomposition is characterized in that,
the method comprises the following specific steps:
step (1), power density spectrum obtaining
Calculating power density spectrum of collected discrete state fault signal f (n), and distributing sequence of spectrum values
Denoted as P;
step (2) of threshold value elimination based on power density spectrum
The spectral values smaller than the threshold value in P are respectively removed by using L threshold values coefficient multiplied by mean (P) with different sizes to obtain L new spectral value distribution sequences P coefficient Wherein coefficient=1, 2, …, integer of L, mean (P) is the average spectral value; since the interference spectrum value is not large, the adverse effect of the interference component spectrum information on the boundary self-adaptive segmentation is eliminated to a great extent, so that the modal aliasing and excessive segmentation are avoided as much as possibleSolving a phenomenon;
step (3), fault signal decomposition processing
For P coefficient The following treatment is carried out: the density spectrum of the power spectrum is [0 pi ]]Since the range is divided into N consecutive segments, and n+1 boundary lines are generated, assuming that the signal has N modes, the maxima in the spectrogram are screened, and the M maxima are arranged in descending order, there are two cases:
1) M is more than or equal to N, which indicates that the method screens out sufficient maximum values and reserves the first N maximum values;
2) M < N, the number of single modes in the signal is smaller than the expected number N of components, all maxima are reserved, and N is reset;
any one of the segments can be represented asWherein omega n Is the midpoint (omega) of two consecutive maxima n ＝0，ω N Pi), thus from the center ω n Width T n ＝2τ n Forming a transition section;
for lambda n Windowing is carried out, and based on a Meyer wavelet method, an empirical scale function and an empirical wavelet function are respectively shown as follows;
wherein, gamma<min n [ω n+1 -ω n /ω n+1 +ω n ],β(x)＝35x 4 -8x 5 +70x 6 -20x 7 ；
Wavelet transform detail coefficients W of the signal according to wavelet theory, formulas (1) and (2) x (n, t) and approximation coefficient W x (0, t) can be defined as formula (3) and formula (4):
reconstructing the signal, wherein the result is shown as a formula (5);
from the above-mentioned available modal component f k Can be represented by the following formulas (6) and (7)
Step (4), screening the optimal decomposition result
Based on the obtained L decomposition results, each decomposition result contains a plurality of modal components, the characteristic energy ratio FER (the ratio of the energy of the fault characteristic frequency and the frequency multiplication position and the total energy of the frequency band) is obtained for each modal component of each decomposition result, and the maximum characteristic energy ratio FER of each decomposition result is obtained coefficient,max Ratio to the next largest characteristic energy FER coefficient,secondmax Comparative analysis, i.e. A coefficient ＝(FER coefficient,max -FER coefficient,secondmax )/FER coefficient,secondmax At a certain larger FER coefficient,max Find the largest A in the range coefficient Is denoted as A max ，A max The corresponding decomposition result is the optimal decomposition result, the corresponding threshold value is called the optimal threshold value, and the FER of the result coefficient,max The corresponding component is the component containing rich fault characteristic information.
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| CN110795843B (en) * | 2019-10-24 | 2024-03-29 | 北京建筑大学 | Method and device for identifying faults of rolling bearing |
| CN113111618B (en) * | 2021-03-09 | 2022-10-18 | 电子科技大学 | Analog circuit fault diagnosis method based on improved empirical wavelet transform |
| CN113554103B (en) * | 2021-07-28 | 2022-05-27 | 大连海天兴业科技有限公司 | Fault diagnosis algorithm for rolling bearing of train running gear |
| CN115146672A (en) * | 2022-06-20 | 2022-10-04 | 中国人民解放军96963部队 | Dense-frequency modal separation reconstruction method and device |
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