AU2020103681A4 - Rolling Bearing Fault Diagnosis Method Based on Fourier Decomposition and Multi-scale Arrangement Entropy Partial Mean Value - Google Patents

Rolling Bearing Fault Diagnosis Method Based on Fourier Decomposition and Multi-scale Arrangement Entropy Partial Mean Value Download PDF

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AU2020103681A4
AU2020103681A4 AU2020103681A AU2020103681A AU2020103681A4 AU 2020103681 A4 AU2020103681 A4 AU 2020103681A4 AU 2020103681 A AU2020103681 A AU 2020103681A AU 2020103681 A AU2020103681 A AU 2020103681A AU 2020103681 A4 AU2020103681 A4 AU 2020103681A4
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rolling bearing
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Keqin Ding
Siqi Huang
Qingyun Liu
Haiyang Pan
Jinyu Tong
Jingde Zheng
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Anhui University of Technology AHUT
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    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00Testing of machine parts
    • G01M13/04Bearings
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    • GPHYSICS
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    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/14Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141Discrete Fourier transforms
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
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Abstract

The invention discloses a rolling bearing fault diagnosis method based on Fourier decomposition and multi-scale arrangement entropy partial mean value, and belongs to the technical field of equipment state monitoring and fault diagnosis. The method comprises the following steps: acquiring an original rolling bearing fault vibration signal to be diagnosed; decomposing the original rolling bearing fault vibration signal by using a Fourier decomposition method; calculating a multi-scale arrangement entropy partial mean value of each component; selecting the first three components with the largest multi-scale arrangement entropy partial mean value for reconstruction; performing envelope spectrum analysis on the reconstructed signal; and identifying fault characteristics according to an envelope spectrum. According to the rolling bearing fault diagnosis method provided by the invention, the complexity of each component is represented by the multi-scale arrangement entropy partial mean value, the fault characteristic frequency and the frequency doubling thereof can be effectively obtained, and the diagnosis effect is good. 1/4 Inputting original vibration signal Decomposing signal by using FDM Calculating PMMPE for each component Selecting sensitive component for reconstruction Performing envelope spectrum analysis Obtaining a diagnostic result Figure 1

Description

1/4
Inputting original vibration signal
Decomposing signal by using FDM
Calculating PMMPE for each component
Selecting sensitive component for reconstruction
Performing envelope spectrum analysis
Obtaining a diagnostic result
Figure 1
Rolling Bearing Fault Diagnosis Method Based on Fourier Decomposition and
Multi-scale Arrangement Entropy Partial Mean Value
TECHNICAL FIELD
[01] The invention belongs to the technical field of equipment state monitoring and fault diagnosis, and particularly relates to a rolling bearing fault diagnosis method based on Fourier decomposition (FDM) and multi-scale arrangement entropy partial mean (PMMPE).
BACKGROUND
[02] Rolling bearing is an important component of many rotating machinery in modern industry, and is also one of the most vulnerable components in the machine. According to statistics, 30% of the faults of rotating machinery are caused by bearing. Once the rolling bearing fails, the normal operation of the equipment can be influenced, so that the machine can generate violent vibration and interference noise, even great economic loss and large safety accidents can be caused. Therefore, the research of rolling bearing state monitoring and fault diagnosis has important engineering application value and theoretical significance for ensuring the stable operation of equipment and the safe production of enterprises.
[03] Due to the time-frequency joint distribution information of nonlinear and non-stationary signals are provided, the time-frequency analysis method has been widely used in the field of fault diagnosis of bearings, gears, etc., but the typical Empirical Mode Decomposition (EMD) and wavelet analysis all have inherent flaws. EMD can adaptively decompose non-stationary vibration signals into several inherent modal functions distributed from high frequency to low frequency. Because EMD is a data-driven signal decomposition method, which avoids the choice of basic functions, and has been affirmed and studied by many scholars. Although EMD has been applied in the field of mechanical failure, the inherent end effect, modal aliasing and other defects limit popularization and application of EMD. The basic idea of wavelet analysis is to use a wavelet function with adjustable time window width to replace the window function in the short-time Fourier transform so that different positions in the time frequency plane have different resolutions. However, the main problem of wavelet analysis is the need to select the wavelet basis and the number of decomposition layers in advance.
SUMMARY
[04] Aiming at the defects of the existing time-frequency analysis method, the invention provides a rolling bearing fault diagnosis method based on Fourier decomposition and multi-scale arrangement entropy partial mean value. According to the method provided by the invention, aliasing among frequency domain components can be solved; and components capable of representing fault information to the maximum extent are selected through multi-scale arrangement entropy partial mean value, and diagnosis is carried out from an envelope spectrum. The method provided by the invention can effectively extract components containing rich fault information and has better diagnosis effect.
[05] The invention provides a rolling bearing fault diagnosis method based on Fourier decomposition and multi-scale arrangement entropy partial mean value, which comprises the following steps:
[06] (1) acquiring an original rolling bearing fault vibration signal to be diagnosed;
[07] (2) decomposing the fault vibration signal of the original rolling bearing by utilizing a Fourier decomposition method to obtain components;
[08] (3) calculating the partial mean value of the multi-scale arrangement entropy of each component;
[09] (4) selecting the first three components with the largest partial mean value of the multi-scale arrangement entropy for reconstruction to obtain a reconstructed signal;
[010] (5) carrying out envelope spectrum analysis on the reconstructed signal to obtain an envelope spectrum;
[011] (6) identifying fault characteristics according to the envelope spectrum.
[012] The specific steps for carrying out Fourier decomposition on the fault vibration signal of the original rolling bearing in the step (2) are as follows:
[013] The Fourier decomposition method can adaptively decompose an original signal into a plurality of Fourier inherent band functions and a sum of residual terms, wherein the Fourier inherent band functions satisfy the following conditions:
[014] 1) The Fourier inherent band function has zero mean, i. e.:
[015] 2) Any two Fourier inherent band functions are mutually orthogonal, i. e.:
[016] 3) Analytic function form of Fourier inherent band function: The Fourier inherent band function has non-negative instantaneous amplitude and instantaneous frequency, that is, a i (t);> 0, where y i (t) C oo [a, b]. Therefore, the Fourier inherent band function is the sum of the zero mean sine functions with successive bands.
[017] On the basis of defining a Fourier inherent band function, the Fourier decomposition method (FDM) steps are as follows:
[018] 1) carrying out fast Fourier transform on a complex signal x (n), namely X
[k]=FFT { [x (n) ] };
[019] 2) performing forward search, i. e. scanning the analytic function of Fourier inherent band function from low frequency to high frequency
[020] In order to obtain an analytic function of a minimum number of Fourier inherent band functions from a low frequency to a high frequency scanning, for each i=1, 2,... , M, starting from N i-1+1, increasing gradually until the maximum N i is reached, where N 0=0, N M=(N/2-1), satisfying: N i-1+1 <=N i <=(N/2-1), and:
[021] Similarly, it is possible to perform a reverse search, i. e., scanning the analytic function component of the Fourier inherent band function from high frequency to low frequency, accordingly, the upper and lower sum limits of Equation (2) are changed from N i to N i-I -1, where i=1, 2,... , M, N 0=N/2, N M=1, the search should start with N i-I -1, gradually decrease until the smallest N i is reached, satisfying: 1 <N i<=Ni-1-1-1, and the phase is a monotonically increasing function.
[022] Calculating the partial mean value of the multi-scale arrangement entropy of each component in the step (3), specifically as follows:
[023] The absolute value of skewness a' correspondingly reflects the degree of skewness. The skewness is driven by the original data, so it is not suitable to compare the degree of skewness of different data; in order to compare the skewness of different data, calculate the relative value of skewness, namely skewness: Skewness, Ske; skewness is the deviation of the arithmetic mean and the mode in standard deviation, so its value range is generally between 0 and 3; The Ske of 0 means symmetrical distribution, and the Ske of +3 and -3 means extreme right skewness and extreme left skewness, respectively;
[024] Wherein SD represents the standard deviation of the original data;
[025] According to the definition of the skewness and the relation between the skewness and the mean value, the multi-scale arrangement entropy partial mean value PMMPE is defined as follows:
[026] PMMPE=(1+|Ske(MPE)|/3)*mean(MPE) (4)
[027] In the formula, Ske (MDE) and mean (MDE) represent the skewness and mean of multi-scale dispersion entropy over - scales, respectively.
[028] According to the method, the traditional Fourier representation method of the constant amplitude and the constant frequency is expanded to the generalized Fourier representation of the time amplitude and the time-varying frequency, and the method has completeness, orthogonality, locality and self-adaptability; the multi-scale arrangement entropy partial mean value is a new complexity quantitative index, and the complexity of components can be characterized; and the method can effectively obtain the fault characteristic frequency and the frequency doubling thereof, and accurately diagnose the vibration signal of the rolling bearing.
BRIEF DESCRIPTION OF THE FIGURES
[029] Figure 1 is a schematic flow chart of the method according to the present invention;
[030] Figure 2 is a time domain waveform diagram of a fault vibration signal of an inner ring of a rolling bearing according to the present invention;
[031] Figure 3 is a component result obtained by decomposing a vibration signal with the Fourier decomposition method according to the present invention;
[032] Figure 4 is a graph showing the variation trend of multi-scale arrangement entropy partial means according to the present invention;
[033] Figure 5 is an envelope spectrum of the diagnosis of the method according to the invention.
DESCRIPTION OF THE INVENTION
[034] In order that the objects, technical schemes and advantages of the embodiments of the present invention will be more apparent, the technical schemes in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention.
[035] Referring to Figure 1, the rolling bearing fault diagnosis method based on Fourier decomposition and multi-scale arrangement entropy partial mean value in the embodiment comprises the following steps:
[036] (1) acquiring an original rolling bearing fault vibration signal to be diagnosed;
[037] (2) decomposing the fault vibration signal of the original rolling bearing by utilizing a Fourier decomposition method to obtain components;
[038] (3) calculating the partial mean value of the multi-scale arrangement entropy of each component;
[039] (4) selecting the first three components with the largest partial mean value of the multi-scale arrangement entropy for reconstruction;
[040] (5) carrying out envelope spectrum analysis on the reconstructed signal to obtain an envelope spectrum;
[041] (6) identifying fault characteristics according to the envelope spectrum.
[042] The method for diagnosing the fault of the rolling bearing by the Fourier decomposition and the multi-scale arrangement entropy partial mean value provided by the embodiment has the advantages of creativity in the aspect of representing the complexity of each component after decomposition, and has good recognition effect in the aspect of recognizing fault characteristic information in an envelope spectrum.
[043] The specific steps for carrying out Fourier decomposition on the fault vibration signal of the original rolling bearing in the step (2) are as follows:
[044] The Fourier decomposition method is capable of adaptively decomposing an original signal into a sum of a plurality of Fourier inherent band functions (FIBF) and a residual term, wherein the FIBF satisfy the following conditions:
[045] 1) FIBF has zero mean, i. e.:
[046] 2) Any two FIBF are mutually orthogonal, i. e.:
[047] 3) The analytic function form of FIBF (Analytic FIBF, AFIBF): the analytic function form has non-negative instantaneous amplitude and instantaneous frequency, that is, a i (t);> 0, where y i (t) E C oo [a, b]. Therefore, the FIBF is the sum of the zero mean sine functions with successive frequency bands.
[048] On the basis of defining FIBF, the Fourier decomposition method (FDM) steps are as follows:
[049] 1) carrying out fast Fourier transform on a complex signal x (n), namely X
[k]=FFT { [x (n) ] };
[050] 2) performing forward searching, i. e. scanning the AFIBF from low frequency to high frequency
[051] In order to obtain a minimum number of AFIBF from low frequency to high frequency scanning, for each i=1, 2,... , M, starting from N i-1+1, increasing gradually until the maximum N i is reached, where N 0=0, N M=(N/2-1), satisfying: N i-1+1 <N i <=(N/2-1), and:
[052] Similarly, it is possible to perform a reverse search, that is, scanning the AFIBF component from high frequency to low frequency, accordingly, the upper and lower sum limits in Equation (2) are changed from N i to N i-I-1, where i=1, 2,... , M, N 0=N/2, N M=1, the search should start with N i-I-1, gradually decrease until the smallest N i is reached, satisfying: 1 N i <=N i-I-I-1, and the phase is a monotonically increasing function.
[053] The step of calculating the partial mean value of the multi-scale arrangement entropy of the components in the step (3) is as follows:
[054] The absolute value of the skewness a' correspondingly reflects the degree of skewness. However, the skewness is driven by original data, so it is not suitable to compare the degree of skewness of different data. In order to compare the skewness of different data, calculate the relative value of the skewness, that is, the Skewness. The skewness is the deviation between the arithmetic mean and the mode in standard deviation, so its value range is generally between 0 and 3. The Ske of 0 indicates a symmetrical distribution, and the Ske of +3 and -3 indicates extreme right skewness and extreme left skewness, respectively.
[055] Where SD represents the standard deviation of the original data.
[056] According to the definition of the skewness and the relation between the skewness and the mean value, the definition of the PMMPE index provided by the invention is as follows:
[057] PMMPE=(1+|Ske(MPE)|/3)*mean(MPE) (4)
[058] In the formula, the Ske (MDE) and mean (MDE) represents the skewness and mean of multi-scale dispersion entropy over - scales, respectively.
[059] And selecting the first three components with the largest partial mean value of the multi-scale arrangement entropy for reconstruction, and performing envelope spectrum analysis on the reconstructed signal to obtain an envelope spectrum containing fault characteristic information.
[060] In order to verify the effectiveness of this method in fault diagnosis of the rolling bearing, the signal is effectively decomposed by the Fourier decomposition method, the complexity of each component is analyzed, and the effectiveness of the method is illustrated.
[061] The experimental equipment adopted in the embodiment is BVT-5 bearing vibration measuring instrument, the type of the test bearing is 6210 deep groove ball bearing, and the single point fault is arranged on the bearing by using the electric spark machining technology. After the experimental bearing is installed, the outer ring of the bearing is fixed through the radial loader and the axial loader, the outer ring is kept fixed all the time in the experimental process, and the inner ring rotates synchronously with the main shaft. The rotating speed is 1800r/min, the corresponding rotating frequency f r=30Hz, and signals are collected by an acceleration sensor, wherein the axial vibration signal is collected by a No.2 sensor, and the radial vibration signal is collected by a No.3 sensor.
[062] In the embodiment, a group of data of the fault of the inner ring of the rolling bearing is selected, the sampling frequency is 10240Hz, the characteristic frequency f i of the fault of the inner ring is calculated to be 177.21Hz, and the time domain waveform diagram is shown in Figure 2.
[063] First, performing FDM decomposition on the bearing inner ring fault vibration signal to obtain 31 components and one residual component r as shown in Figure 3, calculating a multi-scale arrangement entropy partial mean value for each decomposed component to obtain a variation trend of the partial mean value as shown in Figure 4, and extracting a sensitive component containing rich fault information according to the magnitude of the value, in which the partial mean value of the 24th, 28th and 29th components is the first three largest partial mean values. After the three components are added and reconstructed, an envelope spectrum is drawn as shown in Figure 5, and it can be seen from the figure that there is an obvious peak value at the fault characteristic frequency f i, the 2f i and 3f i just correspond to the 2 frequency and the 3 frequency multiplication of the fault characteristic frequency, and modulation side bands with intervals equal to the rotation frequency f r of 30Hz are arranged on the two sides of each frequency multiplication, which accords with the fault characteristics of the inner ring, so that the fault can be effectively diagnosed as the fault of the inner ring of the bearing.
[064] Although the invention has been described with reference to specific examples, it will be appreciated by those skilled in the art that the invention may be embodied in many other forms, in keeping with the broad principles and the spirit of the invention described herein.
[065] The present invention and the described embodiments specifically include the best method known to the applicant of performing the invention. The present invention and the described preferred embodiments specifically include at least one feature that is industrially applicable

Claims (2)

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:
1. The rolling bearing fault diagnosis method based on Fourier decomposition and multi-scale arrangement entropy partial mean value, characterized in that the method comprises the following steps:
(1) acquiring an original rolling bearing fault vibration signal to be diagnosed;
(2) decomposing the original rolling bearing fault vibration signal by using a Fourier decomposition method to obtain components;
(3) calculating the partial mean value of the multi-scale arrangement entropy of each component;
(4) selecting the first three components with the largest partial mean value of the multi-scale arrangement entropy for reconstruction to obtain a reconstructed signal;
(5) carrying out envelope spectrum analysis on the reconstructed signal to obtain an envelope spectrum;
(6) identifying fault characteristics according to the envelope spectrum.
2. The rolling bearing fault diagnosis method based on Fourier decomposition and multi-scale arrangement entropy partial mean value, according to claim 1, characterized in that the step (3) is as follows:
Skew degree: Skewness, Ske is the deviation between arithmetic mean and mode in unit of standard deviation, so the value range of Ske is generally between 0 and 3; Ske is 0 to represent symmetric distribution, Ske is +3 to represent extreme right deviation and Ske is -3 to represent extreme left deviation respectively;
Wherein SD represents the standard deviation of the original data;
According to the definition of the skewness and the relation between the skewness and the mean value, the multi-scale arrangement entropy partial mean value PMMPE is defined as follows:
PMMPE=(1+|Ske(MPE)|/3)*mean(MPE) (4)
In the formula, Ske (MDE) and mean (MDE) represent the skewness and mean value of multi-scale dispersion entropy over - scales, respectively.
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