CN112098088B - Rolling bearing fault diagnosis method based on KICA-fractal theory - Google Patents

Rolling bearing fault diagnosis method based on KICA-fractal theory Download PDF

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CN112098088B
CN112098088B CN202010835601.XA CN202010835601A CN112098088B CN 112098088 B CN112098088 B CN 112098088B CN 202010835601 A CN202010835601 A CN 202010835601A CN 112098088 B CN112098088 B CN 112098088B
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CN112098088A (en
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王晓东
杨创艳
吴建德
马军
李卓睿
李祥
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Kunming University of Science and Technology
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Abstract

The invention relates to a rolling bearing fault diagnosis method based on a KICA-fractal theory, and belongs to the technical field of mechanical fault diagnosis. EMD decomposition is carried out on signals to obtain k IMF components, and first m IMF component reconstruction data containing main fault information are selected; performing KICA modeling analysis on the reconstructed vibration signal data to obtain independent component IC, and monitoring T corresponding to IC2And SPE statistics realize early warning on abnormal signals; then, extracting the characteristics of the correlation dimension and the box dimension of the independent component IC; and finally, matching and identifying the fractal quantity of each fault, and judging a fault diagnosis result. The invention can send out fault early warning in time, can effectively extract the fault characteristics of the rolling bearing, realizes reliable diagnosis of the fault of the rolling bearing and ensures the normal operation of equipment.

Description

Rolling bearing fault diagnosis method based on KICA-fractal theory
Technical Field
The invention relates to a rolling bearing fault diagnosis method based on a KICA-fractal theory, and belongs to the technical field of mechanical fault diagnosis.
Background
The rolling bearing has the advantages of simple structure, convenient manufacture, long service life, stable operation and the like, is a universal mechanical part which is most widely applied in various rotating machines, and the performance (including the precision, the reliability, the service life and the like) of the whole machine is often directly influenced by whether the running state of the rolling bearing is normal or not. Therefore, the research on the fault detection and diagnosis technology of the rolling bearing has important theoretical research value and practical application significance for avoiding major accidents, reducing the loss of manpower and material resources, changing and maintaining physique and the like.
The rolling bearing has complex operation condition, the vibration signal of the rolling bearing is a complex, non-steady and nonlinear signal, and the EMD algorithm aims to decompose a signal with poor performance into a group of eigenmode functions with better performance. Each decomposed IMF component contains local characteristic signals of different time scales of the original signal, and the empirical mode decomposition has a denoising function at the same time, so that the method is a self-adaptive algorithm. KICA (kernel independent component analysis) is also a method for processing the nonlinear problem, the end point effect and modal aliasing of EMD can be eliminated, and in addition, the independent component obtained by the method is beneficial to the extraction of fractal dimension characteristic quantity.
Different faults of the rolling bearing usually originate from different dynamics principles, and are often greatly damaged due to power instability, the information in the aspect is sometimes difficult to obtain by the existing commonly used spectrum analysis method, and the number of independent variables required by describing a power system can be quantitatively given by utilizing the fractal dimension of chaotic mechanics, so that the fault diagnosis can be carried out on the rolling bearing through the fractal dimension.
Disclosure of Invention
The invention aims to solve the technical problem of providing a rolling bearing fault diagnosis method based on a KICA-fractal theory, which is based on a vibration signal generated when a rolling bearing is in fault, and is combined with KICA modeling analysis, the fractal theory and T2And the fault early warning system designed by SPE statistics realizes fault diagnosis of the rolling bearing, and provides an effective rolling bearing fault diagnosis method.
The technical scheme of the invention is as follows: a rolling bearing fault diagnosis method based on a KICA-fractal theory comprises the following specific steps:
step 1: EMD decomposition is carried out on original vibration signals of the rolling bearing in different fault states to obtain k IMF components, correlation coefficients of the IMF components and the original signals are calculated, and the first m IMF components containing main fault information of the rolling bearing are selected to be reconstructed to obtain reconstructed data.
Step 2: modeling and analyzing the reconstructed vibration signal data through KICA (kernel Independent Component analysis) to obtain IC (Independent Component), and monitoring T corresponding to the IC2Whether the SPE statistic exceeds a normally set control limit or not is judged, and the detection of the abnormal signal is realized;
step 3: performing fractal fault feature extraction on the obtained independent component IC, and extracting the correlation dimension and the box dimension of the independent component IC;
step 4: and matching the extracted correlation dimension and box dimension with each fault correlation dimension and box dimension of historical training, outputting a recognition result, and judging a fault diagnosis result.
In the Step1, the concrete steps are as follows:
step1.1: EMD decomposition is carried out on the original vibration signal, and the original vibration signal is decomposed into k modal components IMF1,IMF2,IMF3,…,IMFkThe EMD decomposition specifically includes:
step1.1.1: reading an original time domain signal to be processed, assigning the original time domain signal to a sequence x (t) to be processed, extracting all maximum value points and minimum value points of the original time domain signal, respectively connecting the maximum value points and the minimum value points by a cubic spline curve to form an upper envelope line and a lower envelope line, enabling all data points of the signal to be positioned between the two envelope lines, and calculating an envelope mean value m (t) ═ E (t) (E)1+E2) (v) obtaining a signal difference sequence u (t) x (t) -m (t);
step1.1.2: detecting whether u (t) meets the condition of basic modal component requirement:
1) the number of extreme points and the number of zero-crossing points must be equal or differ by at most one in the entire data set;
2) the envelope means formed by local maxima and minima are both equal to zero;
step1.1.3: the sequence of signal difference values u (t) obtained by subtracting the upper and lower envelope mean values m (t) from the sequence x (t) is x (t) -m (t).
Step1.1.4: the first eigenmode function is denoted c1(t)＝u1(t) obtaining the residue r1(t)＝x(t)-c1(t) adding r1Repeating the above steps as new original data until the nth residue rn(t) if it is less than the given value or becomes a monotonic function, the EMD decomposition process is ended to obtain
Figure BDA0002639592760000021
The original signal consists of the eigenmode functions and the residual terms at these n different scales.
Step1.2: k modal components IMF obtained by computational decomposition1,IMF2,IMF3,…,IMFkSelecting the first m IMF components containing the main fault information of the bearing to reconstruct the correlation coefficient of the original signal to obtain reconstructed data, wherein the specific steps of the reconstructed data are as follows:
step1.2.1: according to Rxci(t)＝E[x(t)ci(t+τ)]Quantitatively calculating the correlation magnitude of k IMF components generated by EMD decomposition and an original vibration signal;
step1.2.2: and selecting the first m IMF components containing the main fault information of the bearing to reconstruct data.
In step2, the specific working principle of the KICA modeling analysis is as follows:
firstly, setting a normal working condition data matrix X as [ X ]1,x2,…,xn](n is the number of samples of data) by introducing a non-linear function
Figure BDA0002639592760000022
Transforming X to high-dimensional mapping space to obtain
Figure BDA0002639592760000023
Function in general
Figure BDA0002639592760000024
Is unknown and therefore performs a non-linear transformation by means of the kernel matrix K, the transformation of which can be represented
Figure BDA0002639592760000025
For data
Figure BDA0002639592760000026
Center normalization is performed and the kernel matrix becomes
Figure BDA0002639592760000031
In the formula, E is an n-dimensional constant matrix with 1/n of each element.
To pair
Figure BDA0002639592760000032
Performing eigenvalue decomposition
Figure BDA0002639592760000033
Obtaining the first m features lambda1,λ2,...,λmAnd its corresponding feature vector alpha1,α2,...,αmThen whitening the data to obtain
Figure BDA0002639592760000034
Wherein Λ ═ diag (λ)1,λ2,...,λm)，H＝[α1,α2,...,αm]Then further acquiring independent component IC;
the core idea is that original input data is mapped into a high-dimensional feature space to perform independent component analysis, namely whitened KPCA (kernel principal component analysis) and ICA (independent component analysis) are added, and finally, the independent components of the original data are obtained.
Step2.1: performing KICA on reconstructed data, mapping signals to a high-dimensional space by using a nonlinear function of a regenerated kernel Hilbert space as a contrast function, searching a minimum value of the contrast function in the space by using a kernel analysis method so as to obtain an optimal unmixing matrix, and separating and extracting source signals from observation sample signals, wherein the method comprises the following steps of:
step2.1.1: inputting observation data x1,x2,…,xnAnd determines the kernel function K (x, s). And realizing nonlinear transformation of the input space and the feature space by utilizing the kernel function.
Step2.1.2: and (4) centralizing and whitening the observation data to enable the observation data to be zero mean and unit variance vectors.
Step2.1.3: computing raw independent data s using cholesky decomposition1,s2,…,snOf the Gram matrix k1,k2,…,knWherein s isi＝wxiAnd W is a unmixing matrix.
Step2.1.4: defining the characteristic value as the formula lambda (K)1,K2,...,Km) Maximum eigenvalue
Figure BDA0002639592760000035
Abbreviated as Krα＝λDkα
Step2.1.5: calculating an objective function
Figure BDA0002639592760000036
Step2.1.6: repeating steps step2.1.3 and step2.1.5 until c (W) is the minimum value when the algorithm converges, so as to obtain the optimal unmixing matrix W, and further obtaining a group of independent source signals according to s ═ W × x.
Step2.2: calculating T of independent component IC2The SPE statistic combines the control limit to make early warning judgment, and the method comprises the following specific steps:
step2.2.1: computing T of independent components IC of training data2And SPE statistic as control limit, and calculating T of new sample independent component IC2And SPE statistics, where T2The statistic reflects the degree of deviation of each independent component from the model on the variation trend and the amplitude, and the SPE statistic describes the degree of deviation of the measured value of the input variable to the independent component IC model;
step2.2.2: judging T of new sample2And SPE
And (5) whether the statistic exceeds the normally set control limit or not, and giving an alarm for the fault vibration signal.
In Step3, the feature extraction module specifically includes:
calculating the fractal dimension of the feature extraction module, wherein the algorithm is as follows:
the generalized dimension is given by the formula:
Dq＝-limlgKq(ε)/logε
in the formula:
Figure BDA0002639592760000041
Kqreferred to as generalized entropy, q is a scale index. Thus, the variation with q can be obtained
The box dimension when q is 0,
Figure BDA0002639592760000042
the correlation dimension when q is 2,
Figure BDA0002639592760000043
according to the invention, the q values are 2 and 0, so that the correlation dimension and the box dimension of the rolling bearing can be obtained, and the extraction of fault characteristics is realized.
In the Step4, the concrete steps are as follows:
step4.1. fault type matching identification: if the correlation dimension can reflect the fault type, matching and identifying the fault signal;
and if the correlation dimension of the vibration signal can not reflect the fault characteristics of the vibration signal, matching and identifying the reconstructed vibration signal by further combining the box dimension.
And step4.2, checking whether the fault is eliminated, if the fault is eliminated, returning to the box dimension and the correlation dimension, updating the features to serve as matching features of fault identification, and otherwise, performing shutdown processing.
The invention has the beneficial effects that: the method combines the fractal theory with EMD and KICA to diagnose the fault of the rolling bearing, can effectively carry out matching identification on the fault of the bearing, judges the fault type, and simultaneously monitors T2And SPE statistics to judge the health and abnormity of the running state of the rolling bearing, and timelyAnd fault early warning is sent out, the fault characteristics of the rolling bearing can be effectively extracted, the reliable diagnosis of the fault of the rolling bearing is realized, and the normal operation of equipment is ensured.
Drawings
FIG. 1 is a basic framework of the present invention;
FIG. 2 is a time domain waveform diagram of the IMF component of the normal vibration signal;
FIG. 3 is a time domain waveform diagram of an outer ring vibration signal IMF component;
FIG. 4 is a time domain waveform diagram of an inner ring vibration signal IMF component;
FIG. 5 is a time domain waveform diagram of an IMF component of a rolling body vibration signal;
FIG. 6 is a plot of normal vibration signal correlation coefficients;
FIG. 7 is a graph of outer ring vibration signal correlation coefficients;
FIG. 8 is a graph of inner ring vibration signal correlation coefficients;
FIG. 9 is a graph of a correlation coefficient of a rolling element vibration signal;
FIG. 10 is a schematic block diagram of a KICA modeling analysis;
FIG. 11 shows a refined spectrum of the outer ring vibration signal;
FIG. 12 shows a refined spectrum of the inner ring vibration signal;
FIG. 13 is a detail chart of rolling element vibration signal;
FIG. 14 Normal State T2Comparing the SPE with the graph;
FIG. 15 outer ring and Normal State T2Comparing the SPE with the graph;
FIG. 16 inner circle and Normal State T2Comparing the SPE with the graph;
FIG. 17 Rolling elements and Normal State T2Comparing the SPE with the graph;
FIG. 18 is a plot of a correlation dimension fit of a normal vibration signal;
FIG. 19 is a plot of a fit of the correlation dimensions of the outer ring vibration signal;
FIG. 20 is a plot of a fit of the correlation dimensions of the inner ring vibration signal;
FIG. 21 is a graph fitted with the correlation dimension of the rolling element vibration signal.
Detailed Description
The invention is further described with reference to the following drawings and detailed description.
The embodiment of the invention provides a rolling bearing fault diagnosis method based on a KICA-fractal theory, a basic block diagram is shown in figure 1, and bearing data of Kaiser Sichu university are used in the embodiment and are obtained through a constant rotating speed bench test. The test bearing is an SKF6205-2RSJEM deep groove ball bearing, the rotating speed of the bearing is 1797r/min, and the sampling frequency is 12 KHz. Four states of normal of the rolling bearing driving end, inner ring fault, outer ring fault and rolling body fault are selected for explanation.
Example 1: as shown in fig. 1, a fault diagnosis method for a rolling bearing based on a kira-fractal theory includes the following specific steps:
verifying fault vibration signal data of an outer ring of a driving end of a rolling bearing;
step1, a signal preprocessing module: EMD decomposition is carried out on the fault vibration signal of the outer ring of the driving end of the rolling bearing to obtain k IMF components, and the first m IMF components containing the main fault information of the rolling bearing are selected to reconstruct data by calculating the correlation coefficient of each IMF component and the original signal.
Step1.1: performing empirical mode decomposition on an original vibration signal, wherein the specific steps of performing empirical mode decomposition comprise:
step1.1.1: reading an original time domain signal to be processed, assigning the original time domain signal to a sequence x (t) to be processed, extracting all maximum value points and minimum value points of the original time domain signal, respectively connecting the maximum value points and the minimum value points by a cubic spline curve to form an upper envelope line and a lower envelope line, enabling all data points of the signal to be positioned between the two envelope lines, and calculating an envelope mean value m (t) ═ E (t) (E)1+E2) (v) obtaining a signal difference sequence u (t) x (t) -m (t);
step1.1.2: detecting whether u (t) meets the condition of basic modal component requirement:
1) the number of extreme points and the number of zero-crossing points must be equal or differ by at most one in the entire data set;
2) the envelope means formed by local maxima and minima are both equal to zero;
step1.1.3: the sequence of signal difference values u (t) obtained by subtracting the upper and lower envelope mean values m (t) from the sequence x (t) is x (t) -m (t).
Step1.1.4: the first eigenmode function is denoted c1(t)＝u1(t) obtaining the residue r1(t)＝x(t)-c1(t) adding r1Repeating the above steps as new original data until the nth residue rn(t) if it is less than the given value or becomes a monotonic function, the EMD decomposition process is ended to obtain
Figure BDA0002639592760000061
The original signal consists of eigenmode functions and residual terms under the n different scales; fig. 3 is a time domain waveform diagram obtained by EMD decomposition of a fault vibration signal of the outer ring of the driving end of the rolling bearing.
Step1.2: and quantitatively calculating a correlation coefficient, wherein the step of reconstructing data specifically comprises the following steps:
step1.2.1: according to Rxci(t)＝E[x(t)ci(t+τ)]Quantitatively calculating the correlation between each IMF component generated by EMD decomposition and the original vibration signal, wherein FIG. 7 is a histogram of the correlation coefficients between the first three IMF components on the outer ring and the original vibration signal;
step1.2.2: selecting the first three IMF components containing the main fault information of the outer ring fault of the rolling bearing driving end, adding the three components to obtain reconstructed data, and calculating the correlation coefficients of the first three IMF components of the outer ring fault as shown in table 1.
IMF component bearing condition IMF1 IMF2 IMF3
Normal state 0.7727 0.3544 0.3316
Outer ring 0.9906 0.0594 0.0553
Table 1: correlation coefficient of outer ring and first three IMF components in normal state
Step2, an early warning module: performing KICA modeling analysis on the reconstructed vibration signal data, and monitoring T corresponding to the independent component IC2And whether the SPE statistic exceeds the normally set control limit or not, and the detection of the abnormal vibration signal is realized.
Step2.1: the specific steps of the KICA modeling analysis are as follows:
step2.1.1: inputting observation data x1,x2,…,xnAnd determines the kernel function K (x, s). Utilizing a kernel function to realize nonlinear transformation of an input space and a feature space;
step2.1.2: centralizing and whitening the observation data to make the observation data become a zero mean value and a unit variance vector;
step2.1.3: computing raw independent data s using cholesky decomposition1,s2,…,snOf the Gram matrix k1,k2,…,knWherein s isi＝wxiW is a demixing matrix;
step2.1.4: defining the characteristic value as the formula lambda (K)1,K2,...,Km) Maximum eigenvalue: krα＝λDkα
Step2.1.5: calculating an objective function
Figure BDA0002639592760000062
Step2.1.6: repeating steps step2.1.3 and step2.1.5 until c (W) is the minimum value when the algorithm converges, so as to obtain the optimal unmixing matrix W, and further obtaining a group of independent source signals according to s ═ W × x.
FIG. 11 is a refined spectrum of an original vibration signal of a fault of an outer ring of a driving end of a rolling bearing, a reconstructed signal after EMD preprocessing and an outer ring fault vibration signal of an independent component IC obtained by KICA modeling analysis in a range of 100-300 Hz, wherein the refined spectrum shows that EMD decomposition retains more information of the original signal, frequency resolution is improved by combining KICA modeling analysis, fault frequency is more prominent, and the independent component IC obtained by KICA is beneficial to extracting fractal characteristic quantity of the fault signal.
Step2.2: the early warning implementation steps are as follows:
step2.2.1: computing T of independent components IC of training data2And SPE statistics as control limits, and calculating T for new sample independent component IC2And SPE statistics;
step2.2.2: judging T of new sample2And whether the SPE statistic exceeds the normally set control limit or not, and alarming and prompting the vibration signal of the fault. FIG. 14 shows a normal state T2And SPE statistic to generate normal vibration signal T2The statistic and the SPE statistic are used as control limits, in fig. 15, N2048 is the boundary point between the normal vibration signal and the outer ring fault signal, and in the figure, T is the outer ring fault2And the SPE statistic obviously exceeds the control limit of the normal state vibration signal, and then fault early warning is sent out.
Step3, a feature extraction module: after receiving the alarm information, performing fractal fault feature extraction on the obtained independent component IC, and extracting the correlation dimension and box dimension of the independent component IC, as shown in Table 2, wherein the correlation dimension of the normal state vibration signal is 0.2578, the box dimension is 1.5394, the correlation dimension of the outer ring fault vibration signal independent component IC is 1.4628, and the box dimension is 1.6945, wherein the fitting curve of the correlation dimension is shown in FIG. 19, compared with the fitting curve of the correlation dimension of the normal state in FIG. 18, the correlation dimension of the outer ring is far greater than that of the rolling bearing in the normal state;
fractal dimension of bearing state Slope and intercept of the correlation dimension P (i, j) Correlation dimension D2 Box dimension D0
Is normal (0.2578，-1.5237) 0.2578 1.5394
Outer ring (1.4628，-11.0202) 1.4628 1.6945
Table 2: correlation and box dimensions of outer circle and normal state
Step4, a fault diagnosis module: and matching the extracted correlation dimension and box dimension with each fault fractal quantity of historical training, outputting a recognition result, and judging a fault diagnosis result.
Step4.1. fault type matching identification: if the correlation dimension can reflect the fault type, matching and identifying the fault signal;
and if the correlation dimension of the vibration signal can not reflect the fault characteristics of the vibration signal, matching and identifying the reconstructed vibration signal by further combining the box dimension.
And step4.2, checking whether the fault is eliminated, if the fault is eliminated, returning fractal characteristic quantity, updating the characteristic quantity to serve as matching characteristic quantity of fault identification, and otherwise, stopping the machine.
Example 2: as shown in fig. 1, a fault diagnosis method for a rolling bearing based on a kira-fractal theory includes the following specific steps:
verifying fault vibration signal data of an inner ring at a driving end of a rolling bearing;
step1, a signal preprocessing module: EMD decomposition is carried out on the vibration signal to obtain k IMF components, correlation coefficients of each IMF component and an original signal are calculated, the first m IMF components containing main fault information of the rolling bearing are selected and added to obtain reconstructed data, and the steps are as follows:
step1.1: EMD decomposition is carried out on an original time domain signal, and FIG. 4 is a time domain waveform diagram of the first three IMF components of a fault vibration signal of an inner ring at the driving end of a rolling bearing;
step1.2: and quantitatively calculating the correlation coefficient of the fault vibration signal of the inner ring at the driving end of the rolling bearing, such as the correlation coefficients of the first three IMF components of the fault vibration signal of the inner ring at the driving end of the rolling bearing calculated in the table 3, and adding the three IMF components to obtain reconstructed data, wherein the graph 8 is a histogram of the magnitudes of the correlation coefficients of the first three IMF components of the inner ring and the original vibration signal.
IMF component bearing condition IMF1 IMF2 IMF3
Normal state 0.7727 0.3544 0.3316
Inner ring 0.7874 0.5407 0.2837
Table 3: correlation coefficient of inner circle and first three IMF components under normal state
Step2, an early warning module: performing KICA modeling analysis on the reconstructed vibration signal data, and monitoring T corresponding to the independent component IC2And whether the SPE statistic exceeds the normally set control limit or not, and the abnormal vibration signal detection is realized.
Step2.1: the KICA functional block diagram is shown in FIG. 10, and the specific steps are as follows;
step2.1.1: firstly, a KICA (kernel independent component analysis) uses a nonlinear function of a regenerated kernel Hilbert space as a contrast function to map a signal to a high-dimensional space;
step2.1.2: searching the minimum value of the contrast function in the space by using a kernel analysis method so as to obtain an optimal unmixing matrix, and observing the source signal from the observation lambda (K)1,K2,...,Km) Separating and extracting the sample signal.
FIG. 12 is a refined spectrum of an original fault signal of an inner ring at a driving end of a rolling bearing, a reconstructed signal after EMD preprocessing and an outer ring fault vibration signal of an independent component IC obtained by KICA modeling analysis in the range of 150-200 Hz, the refined spectrum shows that EMD decomposition retains more information of the original signal, frequency resolution is improved by combining with KICA, fault frequency is more prominent, and the independent component IC obtained by KICA is beneficial to extracting fractal characteristic quantity of the fault signal.
Step2.2: wherein the early warning is realized by the following steps:
step2.2.1: computing T of independent components IC of training data2And SPE statistic as control limit, and calculating T of new sample independent component IC2And SPE statistics;
step2.2.2: judging T of new sample2And whether the SPE statistic exceeds the normally set control limit or not, and alarming and prompting the vibration signal of the fault. In fig. 16, N2048 is a boundary point between the normal vibration signal and the inner ring failure signal, and T of the inner ring failure is2And the SPE statistic obviously exceeds the control limit of the normal state vibration signal, and a fault early warning is sent out at the moment.
Step3, a feature extraction module: extracting fractal fault characteristics of the obtained independent component IC, and extracting the correlation dimension and box dimension of the independent component IC, wherein in table 4, the correlation dimension of the independent component IC of the inner ring fault vibration signal is 1.8172, the box dimension is 1.6912, a fitting curve of the correlation dimension is shown in fig. 20, and compared with the fitting curve of the correlation dimension in the normal state in fig. 19, the correlation dimension of the inner ring is far larger than that of a rolling bearing in the normal state;
fractal dimension of bearing state Slope and intercept of the correlation dimension P (i, j) Correlation dimension D2 Box dimension D0
Is normal (0.2578，-1.5237) 0.2578 1.5394
Inner ring (1.8172，-13.6611) 1.8172 1.6912
Table 4: inner circle and normal state correlation dimension and box dimension
Step4, a fault diagnosis module: and matching the extracted correlation dimension and box dimension with each fault fractal quantity of historical training, outputting a recognition result, and judging a fault diagnosis result.
Step4.1. fault type matching identification: if the correlation dimension can reflect the fault type, matching and identifying the fault signal;
and if the correlation dimension of the vibration signal can not reflect the fault characteristics of the vibration signal, matching and identifying the reconstructed vibration signal by further combining the box dimension.
And Step4.2, checking whether the fault is eliminated, returning fractal characteristic quantity if the fault is eliminated, updating the characteristic quantity to serve as matching characteristic quantity of fault identification, and otherwise, stopping the machine.
Example 3: as shown in fig. 1, a fault diagnosis method for a rolling bearing based on a kira-fractal theory includes the following specific steps:
verifying fault vibration signal data of a rolling body at a driving end of a rolling bearing;
step1, a signal preprocessing module: EMD decomposition is carried out on the vibration signal to obtain k IMF components, and the first m IMF component reconstruction data containing the main fault information of the rolling bearing are selected by calculating the correlation coefficient of each IMF component and the original signal.
Step1.1: EMD decomposition is carried out on an original time domain signal, and FIG. 5 is a time domain waveform diagram of the first three IMF components of a rolling element fault vibration signal at the driving end of a rolling bearing;
step1.2: and quantitatively calculating the correlation coefficient of the fault vibration signal of the inner ring at the driving end of the rolling bearing, such as the correlation coefficients of the first three IMF components of the fault vibration signal of the inner ring at the driving end of the rolling bearing calculated in the table 5, and adding the three IMF components to obtain reconstructed data, wherein the graph 9 is a histogram of the magnitudes of the correlation coefficients of the first three IMF components of the rolling element and the original vibration signal.
IMF component bearing condition IMF1 IMF2 IMF3
Normal state 0.7727 0.3544 0.3316
Rolling body 0.7874 0.5407 0.2837
Table 5: correlation coefficient of rolling element and first three IMF components of normal state
Step2, an early warning module: performing KICA modeling analysis on the reconstructed vibration signal data, and monitoring T corresponding to the independent component IC2And whether the SPE statistic exceeds the normally set control limit or not, and the detection of the abnormal vibration signal is realized.
Step2.1: the KICA functional block diagram is shown in FIG. 10, and the specific steps are as follows;
step2.1.1: firstly, mapping a signal to a high-dimensional space by using a nonlinear function of a regenerative nuclear Hilbert space as a contrast function by the KICA;
step2.1.2: searching the minimum value of the contrast function in the space by using a kernel analysis method so as to obtain an optimal unmixing matrix, and observing the source signal from the observation lambda (K)1,K2,...,Km) Separating and extracting the sample signal.
FIG. 13 is a refined spectrum of an original fault signal of a rolling element at a driving end of a rolling bearing, a reconstructed signal after EMD preprocessing and an outer ring fault vibration signal of an independent component IC obtained by KICA modeling analysis in a range of 100-300 Hz, wherein the refined spectrum shows that EMD decomposition retains more information of the original signal, frequency resolution is improved by combining with KICA, fault frequency is more prominent, and the independent component IC obtained by KICA is beneficial to extracting fractal characteristic quantity of the fault signal.
Step2.2: wherein the early warning is realized by the following steps:
step2.2.1: computing T of independent components IC of training data2And SPE statistic as control limit, and calculating T of new sample independent component IC2And SPE statistics;
step2.2.2: judging T of new sample2And whether the SPE statistic exceeds the normally set control limit or not, and alarming and prompting the vibration signal of the fault. In fig. 17, N2048 is a boundary point between a normal oscillation signal and a rolling element failure signal, and T is a rolling element failure2And the SPE statistic exceeds the control limit of the normal state vibration signal, and a fault early warning is sent out at the moment.
Step3, a feature extraction module: performing fractal fault feature extraction on the obtained independent component IC, and extracting the correlation dimension and box dimension of the independent component IC, wherein in table 6, the correlation dimension of the independent component IC of the rolling element fault vibration signal is 0.6079, the box dimension is 1.5644, the fitting curve of the correlation dimension is shown in fig. 21, and compared with the fitting curve of the correlation dimension in the normal state in fig. 18, the fitting curve of the correlation dimension of the rolling element and the normal state is very close;
fractal dimension of bearing state Slope and intercept of the correlation dimension P (i, j) Correlation dimension D2 Box dimension D0
Is normal (0.2578，-1.5237) 0.2578 1.5394
Rolling body (0.6079，-4.1282) 0.6079 1.5644
Table 6: correlation and box dimensions of rolling elements and normal states
Step4, a fault diagnosis module: and matching the extracted correlation dimension and box dimension with each fault fractal quantity of historical training, outputting a recognition result, and judging a fault diagnosis result.
Step4.1. fault type matching identification: if the correlation dimension can reflect the fault type, matching and identifying the fault signal;
and if the correlation dimension of the vibration signal can not reflect the fault characteristics of the vibration signal, matching and identifying the reconstructed vibration signal by further combining the box dimension.
And step4.2, checking whether the fault is eliminated, if the fault is eliminated, returning fractal characteristic quantity, updating the characteristic quantity to serve as matching characteristic quantity of fault identification, and otherwise, stopping the machine.
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit and scope of the present invention.

Claims (2)

1. A rolling bearing fault diagnosis method based on a KICA-fractal theory is characterized by comprising the following steps:
step 1: EMD decomposition is carried out on original vibration signals of the rolling bearing in different fault states to obtain k IMF components, correlation coefficients of each IMF component and the original vibration signals are calculated, and the first m IMF components containing main fault information of the rolling bearing are selected to be reconstructed to obtain reconstructed vibration signal data;
step 2: modeling and analyzing the reconstructed vibration signal data through KICA to obtain IC, and monitoring T corresponding to IC2Whether the SPE statistic exceeds a normally set control limit or not is judged, and the detection of the abnormal signal is realized;
step 3: extracting fractal fault features of the obtained IC, and extracting the correlation dimension and the box dimension of the IC;
step 4: matching the extracted correlation dimension and box dimension with each fault correlation dimension and box dimension of historical training, outputting an identification result, and judging a fault diagnosis result;
the Step1 is specifically as follows:
step1.1: EMD decomposition is carried out on the original vibration signal, and the original vibration signal is decomposed into k modal components IMF1,IMF2,IMF3,…,IMFkThe method specifically comprises the following steps:
step1.1.1: reading an original time domain signal to be processed, assigning the original time domain signal to a sequence x (t) to be processed, extracting all maximum value points and minimum value points of the original time domain signal, respectively connecting the maximum value points and the minimum value points by a cubic spline curve to form an upper envelope line and a lower envelope line, enabling all data points of the signal to be positioned between the two envelope lines, and calculating an envelope mean value m (t) ═ E (t) (E)1+E2) (v) obtaining a signal difference sequence u (t) x (t) -m (t);
step1.1.2: detecting whether the condition required by the basic modal component is met:
1) the number of extreme points and the number of zero-crossing points must be equal or differ by at most one in the entire data set;
2) the envelope means formed by local maxima and minima are both equal to zero;
step1.1.3: subtracting the mean value m (t) of the upper envelope and the lower envelope from the sequence x (t) to obtain a signal difference sequence u (t), wherein x (t) -m (t);
step1.1.4: the first eigenmode function is denoted c1(t)＝u1(t) obtaining the residue r1(t)＝x(t)-c1(t) adding r1Repeating the above steps as new original data until the nth residue rn(t) if it is less than the given value or becomes a monotonic function, the EMD decomposition process is ended to obtain
Figure FDA0003402028550000011
The original vibration signal consists of eigenmode functions and residual terms under the n different scales;
step1.2: k modal components IMF obtained by computational decomposition1,IMF2,IMF3,…,IMFkAnd selecting the first m IMF components containing the main fault information of the bearing for reconstruction according to the correlation coefficient of the original vibration signal to obtain reconstructed vibration signal data, wherein the reconstruction method specifically comprises the following steps:
step1.2.1: according to
Figure FDA0003402028550000012
Quantitatively calculating the correlation magnitude of k IMF components generated by EMD decomposition and an original vibration signal;
step1.2.2: selecting the first m IMF components containing the main fault information of the bearing to reconstruct vibration signal data;
the Step2 is specifically as follows:
step2.1: modeling and analyzing the reconstructed vibration signal data through KICA, mapping the signal to a high-dimensional space by using a nonlinear function of a regenerated kernel Hilbert space as a comparison function, searching a minimum value of the comparison function in the space by using a kernel analysis method so as to obtain an optimal unmixing matrix, and separating and extracting a source signal from an observation sample signal, wherein the method specifically comprises the following steps of:
step2.1.1: inputting observation data x1,x2,…,xnAnd determining a kernel function K (x, s) usingThe kernel function realizes the nonlinear transformation of the input space and the characteristic space;
step2.1.2: centralizing and whitening the observation data to make the observation data become a zero mean value and a unit variance vector;
step2.1.3: computing raw independent data s using cholesky decomposition1,s2,…,snOf the Gram matrix k1,k2,…,knWherein s isi＝wxiW is the unmixing matrix;
step2.1.4: defining the characteristic value as the formula lambda (K)1,K2,...,Km) Maximum eigenvalue:
Figure FDA0003402028550000021
abbreviated as Krα＝λDkα
Step2.1.5: calculating an objective function
Figure FDA0003402028550000022
Step2.1.6: repeating the steps step2.1.3 and step2.1.5 until the algorithm converges to enable C (W) to obtain a minimum value, so as to obtain an optimal unmixing matrix W, and further obtain a group of independent source signals according to s ═ W x;
step2.2: calculating T of IC2SPE statistics, make early warning judgement in combination with control limit, its concrete step is:
step2.2.1: computing T of independent components IC of training data2And SPE statistic as control limit, and calculating T of new sample independent component IC2And SPE statistics, where T2The statistic reflects the degree of deviation of each independent component from the model on the variation trend and the amplitude, and the SPE statistic describes the degree of deviation of the measured value of the input variable to the independent component IC model;
step2.2.2: judging T of new sample2And whether the SPE statistic exceeds the normally set control limit or not, and alarming and prompting the vibration signal of the fault.
2. The rolling bearing fault diagnosis method based on the KICA-fractal theory as claimed in claim 1, wherein Step4 specifically comprises:
step4.1: if the associated dimension characteristic quantity can reflect the fault type, matching and identifying the fault signal;
if the associated dimension characteristic quantity can not reflect the fault characteristic, matching and identifying the reconstructed vibration signal by further combining the box dimension characteristic quantity;
step4.2: and checking whether the fault is eliminated, if the fault is eliminated, returning to the box dimension and the correlation dimension, updating the feature to serve as a matching feature for fault identification, and otherwise, performing shutdown processing.
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