LU502454B1 - A Bearing Fault Identification Method and System Based on EEMD Sparse Decomposition - Google Patents

Abstract

Disclosed is a bearing fault identification method and system based on EEMD sparse decomposition. The method comprises the steps of firstly obtaining a bearing vibration signal and converting it into an electric signal; decomposing the electric signal by using an EEMD method to obtain multiple IMF components and a remainder; performing sparse processing on the multiple IMF components; and calculating the energy entropy of the bearing vibration signal by using the IMF component subjected to overall averaging by using the EEMD method, and identifying the bearing fault type in combination with the energy distribution condition. As an effective self- adaptive algorithm, the method of the present invention is especially used for decomposition of non-stationary signal processing. For each independent IMF component, it has the scale characteristics of the signal and has the characteristics that change with it.

Description

A Bearing Fault Identification Method and System Based on EEMD Sparse

Decomposition LUS02454

Technical field

The present invention relates to the field of signal and information processing. Specifically, it relates to a bearing fault identification method and system based on EEMD sparse decomposition.

Background technique

Large-scale bearings running for a long time under harsh working conditions are often under high load, high temperature, high pressure and high humidity, strong electromagnetic interference and strong coupling conditions. Material aging, high temperature and high pressure, sudden load effect, design defects, especially abnormal vibration factors in the running process will cause irreversible damage accumulation to the bearings. At the same time, the normal operation of the whole bearing is seriously affected by the fault, and in most cases, it is caused by the abnormal operation of some key parts, which not only causes permanent damage to the bearing, but also brings huge economic losses. How to ensure the stable, reliable and safe operation of the bearing has become a hot issue that needs to be paid attention to during the operation and maintenance of the bearing.

Because vibration signals directly represent the dynamic characteristics of faulty bearings, which leads to their sensitivity to faults, they are widely used to detect bearing faults. At present, the fault diagnosis of large mechanical bearings mainly focuses on collecting the vibration state parameters of equipment operation to realize condition monitoring and fault diagnosis. By analysing the changes of various parameters of the mechanical vibration signal, such as the time domain, frequency domain and amplitude domain, the mechanical fault is judged and the early warning is implemented. At the same time, the fault feature extraction methods have developed from conventional methods (such as fast Fourier transform, power spectrum estimation, time-frequency analysis and axis trajectory) to higher levels (angle domain analysis, holographic spectrum and fractal dimension). For example, the holographic spectrum theory that integrates the amplitude, frequency, phase, angular momentum and other information of mechanical vibration to conduct research and judgment is of great significance to improve the diagnostic level of mechanical fault.

Inventive content

The present invention provides a bearing fault identification method and system based on

EEMD sparse decomposition. The signals are processed according to the law that the signal frequency changes with time, and EEMD sparse decomposition method is adopted as an effective adaptive algorithm to decompose the non-stationary signal processing. For each independent IMF component, it has the scale characteristics of signals and the characteristics LU502454 that change with it. In order to further clarify the difference between fault and non-fault events, the key research for independent IMF components is carried out, and then the energy distribution of fault vibration signals in different frequency bands is analysed according to the characteristic distribution of IMF, and then it is compared with the energy distribution in normal state. At the same time, the classification of fault behaviour is determined by means of the judgment method of energy entropy.

The technical scheme of the present invention to solve the above technical problems is as follows:

In the first aspect, the present invention provides a bearing fault vibration signal feature extraction and identification method, which comprises the following steps.

Step 100: the bearing vibration signal is obtained and converted it into an electrical signal;

Step 200: Gaussian white noise with a certain amplitude is added to the electric signal and

EMD decomposition is performed on the electrical signal added with white noise to obtain multiple IMF components and a remainder;

Step 300: sparse processing is performed on multiple IMF components;

Step 400: a pre-set number of iterations are performed on steps 200 and 300. In each iteration, the added Gaussian white noise is different Gaussian white noises with equal root mean squares, and then the IMF components of the same order in the iteration results are calculated on the overall average:

Step 500: the energy entropy of the bearing vibration signal is calculated by using the IMF component after the overall average, and the bearing fault type is identified in combination with the energy distribution condition.

In the second aspect, the present invention provides a bearing fault identification system based on EEMD sparse decomposition, wherein the system comprises: pre-processing module, obtaining bearing vibration signals and convert them into electrical signals;

EEMD sparse decomposition module, adding a certain amplitude of Gaussian white noise to the electrical signal, and performing EMD decomposition on the electrical signal added with white noise to obtain multiple IMF components and a remainder; performing sparse processing on multiple IMF components; and performing a pre-set number of iterations. In each iteration, the added white Gaussian noise is different white Gaussian noise with equal root mean square, and then the IMF components of the same order in the iteration results are calculated on the overall average. classification and identification module, using the overall averaged IMF component to calculate the energy entropy of the bearing vibration signal, and identifying the bearing fault type in combination with the energy distribution condition.

In the third aspect, the present invention provides an electronic device, comprising:

a memory for storing a computer software program; LU502454 a processor for reading and executing the computer software program stored in the memory to realize the bearing fault identification method based on EEMD sparse decomposition described in the first aspect of the invention.

In the fourth aspect, the present invention provides a computer readable storage medium, in which a computer software program for realizing the bearing fault identification method based on EEMD sparse decomposition according to any one of the first aspects of the present invention is stored.

The beneficial effects of the present invention are as follows. After obtaining the vibration signal, the EMD decomposition is carried out, and then the IMF components obtained by EMD decomposition are sparsely processed. Referring to the sparse processing method in image processing, the multiple IMF components obtained by EMD decomposition are refined. The fault features contained in IMF components are used for overall average. The feature that the frequency presents uniform distribution after the white noise is added is used to avoid the occurrence of this problem and obtain the real property of time-frequency. The added white noise component can also achieve complete noise reduction under the same-order IMF calculation of the overall mean value. However, there is no linear relationship between the actual decomposition effect and the increment of iteration times, so the selection of iteration times should be based on the experimental results. Compared with similar methods, this method can achieve better denoising and more refined processing for vibration signals.

Description of drawings

Fig.1 is a flowchart of the method provided by the embodiment of the present invention.

Fig.2 is a time domain and frequency domain diagram of a bearing fault vibration signal at a motor speed of 1200 r/min according to an embodiment of the present invention.

Specific implementation mode

The principle and features of the present invention will be described below with reference to the accompanying drawings. The embodiment is only used to explain the present invention, but not to limit the range of the present invention.

Fig. 1 is a bearing fault vibration signal feature extraction and identification method provided by the embodiment of the present invention, including the following steps:

Step 100: the bearing vibration signal is obtained and converted it into an electrical signal

OF

Step 200: Gaussian white noise with a certain amplitude is added to the sparsely processed electric signal and EMD decomposition is performed on the electrical signal added with white noise to obtain multiple IMF components and a remainder;

Step 300: sparse processing is performed on multiple IMF components;

The process of sparse processing is to use high amplitude and low amplitude dictionaries LU502454 {AA} to reconstruct the electrical signal y) and get the reconstructed signal x(#).

Specifically, it includes the following contents:

The electrical signal y(t)is restored to a low amplitude sample y, (1) with the same size as the high amplitude component of the target by using the cubic interpolation process;

S group of high pass filter is used to filter the low amplitude sample y, OF

The high pass filtered y, (1) is decomposed into overlapping component blocks with dimension xn , and the corresponding high amplitude feature .} is obtained, and the sparse coefficient is calculated as follows. i [ye — 4a], st. le, <T,

Sparse coefficient {ois obtained based on OMP method.

High amplitude component block x, = A,¢, is obtained by using high amplitude dictionary {4,}and sparse coefficient {e, } The high amplitude component blocks are spliced and the overlapped parts are averaged,

Combined with the low amplitude component y, (¢) obtained by interpolation, the high amplitude component is reconstructed: “1 x) = OEY x

Where, R, represents the feature extraction matrix of the component block.

In this step, referring to the sparse processing method in image processing, the multiple

IMF components obtained after EMD decomposition are refined to identify the fault features contained in the IMF components.

Before sparse processing, it is necessary to build a super complete dictionary A. The dictionary learning process is as follows:

The IMF component with larger amplitude il, (=1,2,3,4,5... J) is selected from the IMF component set; The IMF component Z} with smaller amplitude is obtained by fuzzy and down sampling method, and then Z} is reconstructed based on the cubic interpolation process. The

IMF component with smaller amplitude is interpolated with the same size as the IMF component with larger amplitude, and the IMF component with smaller amplitude y/ is obtained with the same size as the IMF component with larger amplitude. The three differences are piecewise interpolation. Compared with cubic spline interpolation, the interpolation polynomial value at the node is equal to the interpolation function value at the node. However, cubic spline interpolation 502454 also needs to know the derivative of the interpolation polynomial at some nodes, which is difficult to realize in practical application. The process of cubic interpolation is as follows.

H (x) = a; (x) f, + OA XS ir + B(x) f] + Ba (x) fa 5 The basis function value of cubic interpolation is: x—x. x—x, a (x) = ( —)'(+2—)

X; = Xl Xin X, x—x x—x 0,0) = P 0425)

Xi =; XX 2

X Xen

B(x) = be (x — x,) xX; a Xi 2

X—X,

Bra) = — (Xu)

Xa 7X

The pre-processing process needs to filter the information of the low-frequency part in the high amplitude component set of IMF to ensure that the dictionary can fully express the characteristic information of this part. The differential recording method can be used for processing as follows: e/ = yi - yl. For the low amplitude component set of the IMF, the pre- processing process needs to process the features of the high-frequency part of the set. Here, S group of high-pass filter is used to extract the high-frequency features. High-frequency features can be represented as /, Oy. Through this pre-processing process, the IMF high amplitude component and low amplitude component can be decomposed into component blocks with overlapping dimension xn , and then K component blocks can be randomly obtained to construct IMF high amplitude component and low amplitude component samples wp} (1.2,.,K).

Based on the IMF high amplitude component and low amplitude component samples wp} and the obtained training dictionaries {AA}, combined with the pre-processing process: p; € R"*, pi € R™", itis first given the forms p" = i pt... pl}, p'= pl, ph P!}

Then the dictionary training process of IMF high amplitude component is: min le” —A 0]. 4,.0 |p st. (Jul <1, Vk

Similarly, the dictionary training process of IMF low amplitude component is:

min lp -A0|. LU502454 st. (Jul <1, Vk _ € 1 1 I

Combining the above two dictionary training processes and using — and pry as dictionary n n training weights, the dictionary training process of IMF high and low amplitude components can be expressed as: ; Ly a 2. lu, 2 an ~{p -4,0, +—|p 40), sit. la], <7, Vk

The above formula can be simplified as: . 2

P-A min |P-40}; 7) si. (duo <I, Vk

Parameters in the formula are: 1 1 nid Nr

P= ; ‚ A= 1 (8) ! ! ——p —— A nS nS

Solving Formula (8) directly will result in an extremely high degree of freedom for the solution of dictionary A, and will increase the demand for the sample size of dictionary A, which will increase the calculation amount of sample reconstruction. In order to reduce the degree of freedom in the training process of dictionary A, the method used is to sparse represent dictionary Ae RH It A= AZ, Z eR"”" represents a sparse matrix, where A, € RS" is the basic dictionary, and the nonzero number of matrix column elements needs to be less than T1, that is, assuming that all atoms in the dictionary can be selected as the sparse representation of A, . Based on the above assumption, the dictionary training process described in Formula (7) can be expressed as: . 2 min [|P—4,20] + (lacs vk (9) © Zn wv

In the formula, Z, matches the j column elements of matrix Z, , and then the optimal solution process of problem (9) can be carried out in two steps: (1) Fix the sparse matrix Z, and update the sparse representation of the coefficient matrix Q; (2) Fix the sparse matrix Q and update the sparse matrix Z. First, fix the sparse matrix Z, and then the optimization process of

Formula (9) is:

min — AZ pi |p = 474, cap} 4502454 st. a, <T,

The OMP method is selected to solve the optimization problem of Formula ( 10 ). Secondly, the sparse coefficient Q is determined, and the optimization process of Formula ( 9 ) is as follows : min |P-AZOÏ in [PA ol (11) si. 12], <1, Vj

Assume g, is the j" column of the sparse matrix Q, then: 2 2 Mr — — 2

P- 4,20]; = PAS =]E, - 47,4]. (12)

J= F

In the formula, E, = P- A, > 2,4, k#j

The optimization update process of Formula (11) can be expressed as: 2 min ||. —4,z4, | z | 1745, I: (13) st. |<

If §,q; =1 is satisfied, then: ~ |? ~ ~

IE, — 42,4, = Tr((e, — 407,4, Xe, — 407,4, ) = 1r(ETE,)-217(q ET Az, )+ T7(G G2 AT Az) =Tr(E"E,)=27 ET A2, +2 AT Az, ~ 2 ~ ~ =|EG, 4: | +Tr(ETE )-G, EEG

In the formula, Tr(e) is the trajectory expression of the matrix. Since the value of

Tr(FTE,)-7, EE," is independent of the element z,, in the case of satisfying §,g, =1, the optimization process of Formula (13) can be modified as: min zz, Az]. 7; F (14) st. |<

Formula (14) is a sparse coding form and can be solved based on the OMP method. Based on the above two steps, the sparse matrix Z can be obtained, and then the high amplitude and low amplitude dictionaries {4,,4,} can be obtained.

In step 400, a pre-set number of iterations are performed on steps 200 and 300. In each iteration, the added Gaussian white noise is different Gaussian white noises with equal root mean squares, and then the IMF components of the same order in the iteration results are LU502454 calculated on the overall average.

The iterations in steps 200 and 300 and the overall average calculation process constitute the EEMD sparse decomposition method.

The EEMD sparse method is used as an effective adaptive algorithm to decompose the processing of non-stationary signals. For each independent IMF component, it has the scale characteristics of the signal and has the characteristics that change accordingly.

The problem of mode aliasing will appear again when using the traditional empirical mode decomposition method. In this part, the frequency of white noise is uniformly distributed after it is added, which can well avoid the problem and obtain the real attributes of time and frequency.

The added white noise component can also achieve complete noise reduction under the operation of finding the overall mean value of the same order IMF. However, there is no linear relationship between the actual decomposition effect and the increase of iteration times, so the selection of iteration times should be based on the experimental results. Compared with similar methods, this method can better achieve denoising and more refined processing for vibration signals.

However, the front-end sensor array detects different frequencies of vibration signals, and the propagation angle and orientation of the received vibration signals are random and uncertain.

In general, the vibration frequencies collected by all vibration sensors are compared each time, and more than three vibration signals with larger amplitude and lower frequency are selected for processing. The vibration frequencies measured on each sensor are different. The main vibration frequency plays an important role in signal analysis. Therefore, the principle of selecting the main vibration frequency and other component frequencies among the selected vibration waves is as follows. The vibration wave with the highest amplitude among the several vibration waves measured in the sensor is taken as the main vibration frequency and the others are taken as the components.

In step 500, the energy entropy of the bearing vibration signal is calculated by using the

IMF component after the overall average, the energy of the IMF component is characterized by

C,,andC= {C..k € R} will be used as the energy distribution of the signal. The energy entropy value is calculated by the expression H = YA lgV, , in which V,=C, /C . Then, the k=1 bearing fault type is identified according to the energy distribution condition.

Under the normal working condition of the bearing, the energy distribution of the vibration signal is uniform and fluctuates little. If there is a fault condition, resonance will be detected in the corresponding frequency band, and the energy will converge in this frequency band, and the entropy value of energy will also change accordingly.

By calculating the energy entropy value and comparing it with the data in the rolling LU502454 bearing fault energy entropy empirical database, combined with the energy distribution, the fault type can be preliminarily judged and the early warning can be made in time.

The characteristics of vibration signals of bearings under fault conditions are analysed below. When the motor speed is 1200r/min, the time and frequency domain waveforms of the fault vibration signal collected by the FBG acceleration sensor are shown in Fig. 2.

After noise reduction and conditioning of the above signals, nine IMF components and one residual component will appear after EEMD sparse decomposition. With the gradual increase of IMF components, the resulting "endpoint effect" becomes more and more obvious, and the influence on the energy situation of IMF components also increases. The superiority of

EEMD sparse method can be reflected here. By reducing the attenuation of signal energy caused by "endpoint effect”, the typical IMF characteristic components are selected and their energy distribution and entropy value are calculated to achieve the purpose.

The IMF components have both the local characteristics of the original signal and the scale characteristics of time-varying. Through theoretical analysis, it is known that the energy changes under different conditions can be mastered by comparing the energy entropy so as to determine the fault events and normal events.

Six types of fault conditions are selected and their energy entropy values are calculated, as shown in Table 1.

Table 1 Energy entropy distribution of six types of fault modes

Outer

BEHEBESa number Normal cour Six Four Six Four Six scratches scratches scratches | scratches | scratches | scratches

Energy

It can be seen from Table 1 that the energy entropy value of each working part of the bearing is the largest and stable under normal working conditions. As the fault continues to deteriorate, the energy entropy value will continue to decrease. The order of the energy entropy values under the same type of fault conditions is as follows: inner ring, outer ring and roller.

According to the analysis of this law, the energy entropy value under various fault conditions can be used as the basis for fault diagnosis.

For bearing fault identification based on energy entropy, the preliminary judgment of bearing fault type can be realized by comparing with the threshold value in the energy entropy sub-database in the rolling bearing standard database set of Case Western Reserve University.

The rolling bearing data of Case Western Reserve University in the United States is widely concerned around the world and cited as a fault diagnosis standard database. It is also widely used for reference in China. Signals are collected through a 16-channel DAT recorder LU502454 and processed in MATLAB.

The energy entropy values calculated by selecting some typical fault features are compared with the database, and the results are shown in Table 2.

The results in Table 2 show that the energy entropy judgment method can be effectively used as the eigenvalue to judge the typical faults of rolling bearings.

Table 2 Comparison table of fault type database ~~ Energy

Energy entropy data range in the Western Reserve Judgment of

Number entropy

Rolling Bearing Database fault type value

Quter ring 1 0.06954 0.0425 ~ 0.0823 soratch

Inner ring 2 1.3072 1.3005 ~ 1.3273 scratch

The above description is only a preferred embodiment of the present invention, and it is not intended to limit the present invention. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the protection range of the present invention.

Claims (9)

1. A bearing fault identification method based on EEMD sparse decomposition, wherein the method includes the following steps. step 100: the bearing vibration signal is obtained and converted it into an electrical signal; step 200: Gaussian white noise with a certain amplitude is added to the electric signal and EMD decomposition is performed on the electrical signal added with white noise to obtain multiple IMF components and a remainder; step 300: sparse processing is performed on multiple IMF components; step 400: a pre-set number of iterations are performed on steps 200 and 300. In each iteration, the added Gaussian white noise is different Gaussian white noises with equal root mean squares, and then the IMF components of the same order in the iteration results are calculated on the overall average; step 500: the energy entropy of the bearing vibration signal is calculated by using the IMF component after the overall average, and the bearing fault type is identified in combination with the energy distribution condition.

2. The method according to claim 1, wherein the bearing vibration signal is a low frequency vibration signal not higher than 1000 Hz.

3. The method according to claim 1, wherein multiple IMF components are sparsely processed, including: — using cubic interpolation process to restore the electrical signal ¥(t)to low amplitude sample y, (1) with the same size as the target high amplitude component ; — using S group of high-pass filter to filter low amplitude sample y, (1). — decomposing the high pass filtered y, (1) into overlapping component blocks with dimension JnxJn to obtain the corresponding high amplitude feature Qi}. and calculate the sparse coefficient:

. 2 i [yi = Ae], N st. |e], <7, — obtaining sparse coefficient {en} based on OMP method;

— adopting high amplitude dictionary {4,} and sparse coefficient le} to obtain high LU502454 amplitude component block x, = A,@, ; splicing the obtained high amplitude component block, and performing mean value processing on the overlapping part; — combining the low amplitude component y, (¢) obtained by interpolation to reconstruct the high amplitude component: -1 x(1)= v,()+ ER Es k k — where R, represents the feature extraction matrix of the component block.

4. The method according to claim 1, wherein the number of iterations is 100 to 400 times in step 400.

5. The method according to claim 1, wherein the bearing fault type is identified according to the energy distribution condition, and the identification method includes a classification and identification method based on SVM.

6. The method according to claim 1, wherein the dictionary used in the sparse processing of the electrical signal is obtained through the K-SVD dictionary learning algorithm.

7. A bearing fault identification system based on EEMD sparse decomposition, wherein the system comprises: — pre-processing module, obtaining bearing vibration signals and converting them into electrical signals; — EEMD sparse decomposition module, adding a certain amplitude of Gaussian white noise to the electrical signal, and performing EMD decomposition on the electrical signal added with white noise to obtain multiple IMF components and a remainder; performing sparse processing on the multiple IMF components; and performing a pre- set number of iterations, wherein in each iteration, the added white Gaussian noise is different white Gaussian noise with equal root mean square, and then the IMF components of the same order in the iteration results are calculated on the overall average; — classification and identification module, using the overall averaged IMF component to calculate the energy entropy of the bearing vibration signal, and identifying the bearing fault type in combination with the energy distribution condition.

8. An electronic device comprising:

— a memory for storing a computer software program; LU502454 — a processor for reading and executing the computer software program stored in the memory to realize the bearing fault identification method based on EEMD sparse decomposition according to any one of claims 1 - 6.

9. A computer readable storage medium, characterized in that the storage medium stores a computer software program for realizing a bearing fault identification method based on EEMD sparse decomposition according to any one of claims 1 - 6.