CN102854015B - Diagnosis method for fault position and performance degradation degree of rolling bearing - Google Patents

Abstract

The invention discloses a diagnosis method for the fault position and the performance degradation degree of a rolling bearing, belonging to the technical field of fault diagnosis for bearings, and solving the problems of low accuracy of diagnosis for fault position and performance degradation degree, and high time consumption of training existing in an intelligent diagnosis method for a rolling bearing in the prior art. A white noise criterion is added in the disclosed integrated empirical mode decomposition method, so that artificial determination for decomposition parameters can be avoided, and the decomposition efficiency can be increased; and via the disclosed nuclear parameter optimization method based on a hypersphere centre distance, the small and effective search region of nuclear parameters in a multi-classification condition can be determined, so that training time is reduced, and the final state hypersphere model of a classifier is given. The intelligent diagnosis method based on parameter-optimized integrated empirical mode decomposition and singular value decomposition, and combined with a nuclear parameter-optimized hypersphere multi-class support vector machine based on the hypersphere centre distance is higher in identification rate compared with the existing diagnosis method. The diagnosis method disclosed by the invention is mainly applied to intelligent diagnosis on the fault position and the performance degradation degree of the rolling bearing.

Description

A kind of rolling bearing fault position and performance degradation degree diagnostic method

Technical field

The present invention relates to a kind of rolling bearing fault position and performance degradation degree diagnostic method, belong to bearing failure diagnosis technical field.

Background technology

Rolling bearing is the critical piece of numerous rotating machineries, its operation not in the same time, fault degree is different.Existing rolling bearing fault diagnosis generally concentrates on determining of abort situation (interior ring, outer shroud, rolling body), the diagnosis of performance degradation degree is the new research direction proposing recently, and it is the brand-new expansion to existing fault diagnosis technology from theory and method.

Recently, some performance degradation degree diagnostic methods are suggested and are subject to increasing concern.The scholars of winconsin university and University of Michigan have proposed based on performance degradation diagnostic methods such as Cerebellar Model Articulation Controller, logistic regression, self-organizing feature figure neural network, hidden Markov models; The people such as Qiu [QIU H, LEE J, LIN J, et al.Robust performance degradation assessment methods for enhanced rolling element bearing prognostics[J] Advanced Engineering Informatics, 2003,17:127-140.] set up the appraisal procedure that rolling bearing performance based on optimal wavelet wave filter and s self-organizing feature map is degenerated; The people such as Kang [KANG P J, BIRTWHISTLE D.Condition assessment of power transformer on load tap changers using wavelet analysis and self-organizing map:field evaluation[J] IEEE Transactions on Power Delivery, 2003,18 (1): 78-84.] utilize wavelet analysis and Self-organizing Maps to realize Condition Assessment for Power Transformer; A kind of bearing performance degradation diagnosis method based on wavelet packet and Support Vector data description has also been proposed in prior art, the method adopts wavelet packet to extract feature and sets up intelligent evaluation model, with Support Vector data description, calculate test mode vector to the distance of the centre of sphere, and then tracing trouble degree.There is on this basis scholar to propose again a kind of based on the decomposition of Lifting Wavelet bag and fuzzy C-average bearing performance Diagnosis of degradation degree method.The energy that is decomposed node by Lifting Wavelet bag forms proper vector.The normal data with proving an abortion for setting up assessment models, utilize FCM to carry out identifying and diagnosing as training sample.Empirical mode decomposition (Empirical Mode Decomposition, EMD) method is applicable to analyzing non-linear, non-stationary signal [Liu Lijun, Wang Qi, Yankee is own, Deng. the method for diagnosing faults based on EMD and Spectrum Correction [J] Chinese journal of scientific instrument, 2011,32 (6): 1278-1283.].EMD carries out feature extraction in conjunction with AR model to rotor fault, rolling bearing performance degree of degeneration and has obtained better effects [CHENG J S, YU D J, YANG Y.A fault diagnosis approach for roller bearings based on EMD method and AR model[J] Mechanical Systems and Signal Processing, 2006,20:350-362.; Kang Shouqiang, Wang Yujing, Yang Guangxue, etc. Fault Diagnosis of Roller Bearings [J] Proceedings of the CSEE based on empirical mode decomposition and hypersphere multi-class support vector machine, 2011,31 (14): 96-102.].

Svd (Singular Value Decomposition, SVD) is a kind of effective algebraic characteristic extracting method.The singular value of matrix is the inherent feature of matrix, has good stability.Based on EMD, in conjunction with the feature extracting method of the rolling bearing fault position vibration signal of SVD, obtained certain application.

In the feature extracting method of above-mentioned diagnosis, itself comes with some shortcomings EMD, and in order to suppress the pattern aliasing of EMD, Wu and Huang propose a kind of set empirical mode decomposition (Ensemble EMD, EEMD) method.EEMD method has solved the problem that pattern is obscured preferably, but its result depends on the amplitude size and these 2 parameters of population mean number of times that adds noise.Wu and Huang have only provided the relation between these 2 parameters, and generally these 2 parameters need artificially according to experience, to set, and for different signals, lack reliability and adaptivity.Document [old summary, slander sunshine, He Zhengjia, Deng. research [J] XI AN JIAOTONG UNIVERSITY Subject Index of population mean empirical mode decomposition and 1.5 dimension spectral methods, 2009,43 (05): 94-98.] proposed a kind of criterion that adds white Gaussian noise in EEMD method, added the amplitude coefficient of white noise to be determined by amplitude standard deviation and the original signal amplitude standard deviation ratio of the effective radio-frequency component of original signal, conventionally got 1/4 of this ratio and just can effectively avoid pattern to obscure; In intelligent method for classifying, support vector machine (Support Vectors Machine, SVM) shows unique advantage and good application prospect in solving small sample problem, and has good generalization ability.For multicategory classification problem, document [Zhu Meilin, Liu Xiangdong, Chen Shifu. by the support vector machine of spherical structure, solve many classification problems [J] Nanjing University journal: natural science edition, 2003,39 (2): 153-158.] a kind of many sorting algorithms of support vector machine of spherical structure have been proposed.On this basis, have scholar to propose again a kind of hypersphere multi-class support vector machine algorithm of the decision rule based on new, its experimental result shows that this algorithm can obtain the better classifying quality of hypersphere multi-class support vector machine algorithm than standard.Document [Kang Shouqiang, Wang Yujing, Yang Guangxue, Deng. the Fault Diagnosis of Roller Bearings [J] based on empirical mode decomposition and hypersphere multi-class support vector machine. Proceedings of the CSEE, 2011,31 (14): 96-102.] further provide classifying rules when training sample set is combined into empty set in critical area, and improved hypersphere multi-class support vector machine has been applied in the multiclass fault diagnosis of rolling bearing, obtained better effects.Yet, to Kernel-parameter Selection Problem in many classification situation of hypersphere multi-class support vector machine, must artificially determine in advance the interval of parameter search, it is very large to the consumption of learning time.

Summary of the invention

The present invention exists the rate of correct diagnosis of abort situation and performance degradation degree lower in order to solve rolling bearing intelligent diagnosing method of the prior art, training time consumes large problem, and then a kind of rolling bearing fault position and performance degradation degree diagnostic method are provided.

The present invention solves the problems of the technologies described above the technical scheme of taking to be: the method for the invention is to realize according to following steps:

Step 1, gather a large amount of bearing vibration signals, comprise vibration signal, the vibration signal of rolling bearing outer shroud different performance degree of degeneration, the vibration signal of rolling bearing rolling body different performance degree of degeneration of ring different performance degree of degeneration in the vibration signal, rolling bearing of rolling bearing normal condition;

Step 2, the vibration signal of above-mentioned various states is divided into study part signal and part of detecting signal according to the mode of x times of cross-validation method;

Step 3, feature extraction: adopt the EEMD of Optimal Parameters first study part signal to be carried out to feature extraction in conjunction with the method for SVD, detailed process is:

Step 3 (one), each vibration signal is first carried out to EMD decomposition, obtain a plurality of IMF components, will obtain the radio-frequency component of first IMF component as this vibration signal, then calculate the poor E of energy scale of first IMF _h, then calculate the poor E of energy scale of this original vibration signal _o, can obtain the parameter h in formula (5);

$0<g<\frac{h}{2}$

In formula, wherein, E _nfor adding white noise energy standard deviation, E _ofor the energy scale of original vibration signal poor, E _hpoor for the energy scale of the radio-frequency component of vibration signal, g is the ratio coefficient that adds white noise, and h is energy ratio coefficient;

By formula (5), be can be derived from

$0<E_n<\frac{1}{4}{E}_h$

Step 3 (two), obtain the population mean number of times L in EEMD method, according to formula (7), try to achieve population mean number of times L,

$e=\frac{g}{\sqrt{L}}$

In formula, e is the signal decomposition relative error of expectation, and g is the ratio coefficient that adds white noise, and L is the population mean number of times in EEMD method;

Step 3 (three), add on the ratio coefficient of noise and the basis of these two parameters of population mean number of times trying to achieve, each vibration signal is carried out to EEMD and decompose and obtain IMF, in different vibration signals, IMF maximum number is n, is less than the supplementary null vector of n; The n that each vibration signal is obtained IMF forms original feature vector matrix B=[c ₁c ₂... c _n] ^t, described original feature vector matrix is carried out to svd, the singular value that svd is obtained is described as proper vector [λ ₁, λ ₂..., λ _n];

Step 4, structural attitude vector matrix: the proper vector [λ of all learning signals of each state of rolling bearing ₁, λ ₂..., λ _n] constitutive characteristic vector matrix S _k

$S_k=\left[\begin{array}{ccccc}{\mathrm{\&lambda;}}_{k,11},{\mathrm{\&lambda;}}_{k,12},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,1n};& {\mathrm{\&lambda;}}_{k,21},{\mathrm{\&lambda;}}_{k,22},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,2n};& {\mathrm{\&lambda;}}_{k,31},{\mathrm{\&lambda;}}_{k,32},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,3n};& \&CenterDot;\&CenterDot;\&CenterDot;;& {\mathrm{\&lambda;}}_{k,N_{k}1},{\mathrm{\&lambda;}}_{k,N_{k}2},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,N_{k}n}\end{array}\right]---\left(15\right)$

In formula, k=1,2 ..., m, represents the different faults position of rolling bearing and the state of performance degradation degree; N _kit is the number of k class state learning signal;

The hypersphere multi-class support vector machine that step 5, utilization improve classifying rules is to the eigenvectors matrix S obtaining in step 4 _kcarry out preliminary classification, obtain each state original state hypersphere of rolling bearing; Adopt the method for hypersphere centre of sphere spacing maximum to carry out nuclear parameter optimization to improving the hypersphere multi-class support vector machine of classifying rules, i.e. definite kernel parameter most preferred range; Detailed process is:

Step 5 (one), by all kinds of eigenvectors matrix S _kbe input in the hypersphere multi-class support vector machine that improves classifying rules, according to all kinds of eigenvectors matrixs, determine the centre of sphere of all kinds of hyperspheres, make each state k form a hypersphere, and then obtain the original state hypersphere of all kinds of abort situation and performance degradation degree;

The process of step 5 (two), definite kernel parameter most preferred range is:

A, determine that the total class of learning sample counts m;

B, be divided into m (m-1)/2 group;

C, setting cycle index initial value i _m=1;

D, utilize formula (14) to grouping i _mall kinds of hypersphere centre ofs sphere of each multinuclear calculation of parameter to be selected between distance: detailed process is:

For improving k in the feature space of hypersphere multi-class support vector machine of classifying rules ₁class hypersphere centre of sphere a ^k1to k ₂class hypersphere centre of sphere a ^k2square distance d ²be defined as:

$d^2=D(a^{k_1},a^{k_2})={\left|\right|a^{k_1}-a^{k_2}\left|\right|}^2=(a^{k_1}\&CenterDot;a^{k_1})-2(a^{k_1}\&CenterDot;a^{k_2})+(a^{k_2}\&CenterDot;a^{k_2})---\left(12\right)$

By the k class hypersphere centre of sphere bring in formula (12), can try to achieve

$d^2=\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_1}(x_i^{k_1}\&CenterDot;x_j^{k_1})-2\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_2}(x_i^{k_1}\&CenterDot;x_j^{k_2})+\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_2}{\mathrm{\&alpha;}}_j^{k_2}(x_i^{k_2}\&CenterDot;x_j^{k_2})---\left(13\right)$

In formula: for Lagrange multiplier, i=1,2 ..., N _k;

For nonlinear situation, directly in formula (13), bring corresponding kernel function k (x, y) into, between class and class, hypersphere centre of sphere distance computation formula is converted to:

$d=\sqrt{\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_1}k(x_i^{k_1},x_j^{k_1})-2\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_2}k\left(x_i^{k_1}{,x}_j^{k_2}\right)+\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_2}{\mathrm{\&alpha;}}_j^{k_2}k\left(x_i^{k_2}{,x}_j^{k_2}\right)}---\left(14\right)$

In formula (14): j=1 ..., N _k, i=1 ..., N _k;

E, obtain maximum hypersphere centre of sphere spacing d _maxcorresponding nuclear parameter value;

F, judgement cycle index i _mwhether be less than the combination of two number of all kinds of hyperspheres, i _m< m (m-1)/2; If be less than, perform step D, otherwise execution step G;

G, find the centre of sphere spacing minimum value d of all combination of two hyperspheres _minwith maximal value d _maxtime corresponding nuclear parameter value, the optimum selection range d using it as nuclear parameter _min～d _max;

Step 6, to separating part of detecting signal in step 2, adopt the feature extracting method identical with learning part signal to obtain proper vector z=[λ ₁, λ ₂..., λ _n];

Step 7, calculating coefficient of difference, pass judgment on test signal condition; Obtain optimum penalty coefficient, nuclear parameter value and M regional dynamics parameter beta:

Based on all kinds of original state hyperspheres and the optimum selection range d of nuclear parameter _min～d _max, obtain the proper vector z=[λ of test signal ₁, λ ₂..., λ _n] and each original state hypersphere between three coefficient of difference be: and D _mI(z, x _p);

Each alphabetical implication: D (z, a in three coefficient of difference formula ^k) represent that test vector z is to k class hypersphere centre of sphere a ^kdistance square, R _kbe the radius of k class ball, x _pfor the element in training sample set I in M region; D _mI(z, x _p) represent that test vector z is to x _pdistance square;

If the coefficient of difference of the proper vector of test signal and certain original state hypersphere is minimum, just illustrate that the abort situation of this test vibration signal and abort situation and the performance degradation degree of performance degradation degree and this original state hypersphere are the most close; Therefore, can judge the malfunction of test signal; When rate of correct diagnosis is the highest, determine d _min～d _maxbetween optimum nuclear parameter value, penalty coefficient C and M regional dynamics parameter beta;

Step 8, according to above-mentioned parameter: d _min～d _maxbetween optimum nuclear parameter value, penalty coefficient C and M regional dynamics parameter beta, and then obtain the end-state hypersphere model of each state under this parameter:

$\left\{\begin{array}{c}{a}^k=\underset{i}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^k{x}_i^k,{\mathrm{\&alpha;}}_i^k\&NotEqual;0\\ \min {\left(R_k\right)}^2+C^k\underset{i=1}{\overset{l^k}{\mathrm{\&Sigma;}}}{\mathrm{\&epsiv;}}_i^k,s.t.{(x_i^k-a^k)}^T(x_i^k-a^k)\&le;{\left(R_k\right)}^2+{\mathrm{\&epsiv;}}_i^k\\ K(x_i^k,x_j^k)=e^{[-\frac{{(x_i^k-x_j^k)}^2}{2s^2}]}\\ R_k^2=D(z^{\&prime;},a^k)=\underset{i,j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^k{\mathrm{\&alpha;}}_j^{k}K(x_i^k,x_j^k)-2\underset{i}{\mathrm{\&Sigma;}}{a}_i^{k}K(x_i^k,z^{\&prime;})+K(z^{\&prime;},z^{\&prime;})\\ \mathrm{if}\sqrt{D(z^{*},a^i)}\&le;R_i\mathrm{and\&beta;}\sqrt{D(z^{*},a^j)}<R_j\mathrm{or}\\ \mathrm{if}\sqrt{D(z^{*},a^j)}\&le;R_j\mathrm{and\&beta;}\sqrt{D(z^{*},a^i)}<R_i,\mathrm{then}{z}^{*}\mathrm{in\; region\; M}\end{array}\right.---\left(19\right)$

Wherein: for Lagrange multiplier, i=1,2 ..., N _k; S is nuclear parameter; it is the proper vector of certain signal of k class; for the slack variable of introducing, z ' is the support vector on hypersphere, z ^*proper vector for learning signal or test signal;

The actual field diagnosis of step 9, rolling bearing health status:

Gather actual field bearing vibration signal, according to the feature extracting method identical with study part signal, obtain proper vector, then calculate the proper vector of actual field bearing vibration signal and the coefficient of difference between each end-state hypersphere model, the rolling bearing health status representing according to end-state hypersphere model corresponding to coefficient of difference minimum value is passed judgment on the health status of on-the-spot rolling bearing: be normal condition or malfunction, as have fault to diagnose to be out of order position and performance degradation degree.

The invention has the beneficial effects as follows:

The present invention is analyzing on the basis of EEMD theoretical method, has proposed to add in EEMD method the criterion of white Gaussian noise, has optimized definite method of EEMD desired parameters.And the EEMD that the adopts Optimal Parameters feature of extracting bearing vibration signal in conjunction with SVD, set up eigenvectors matrix.Feature for hypersphere multi-category support vector machines, derive again the distance computing formula between the hypersphere centre of sphere, the distance of proposition using between the hypersphere centre of sphere determined the optimum selection range of hypersphere multi-class support vector machine nuclear parameter as segregation index, larger hypersphere centre of sphere spacing represents that degree separated between class and class is large, then according to maximum hypersphere centre of sphere spacing, find optimum nuclear parameter scope, to reduce the consumption of learning time.Thereby utilize the hypersphere multi-class support vector machine after optimizing to carry out many classification, intelligent diagnostics when finally realizing rolling bearing fault position and performance degradation degree.

In order more effectively to diagnose out rolling bearing fault position and different performance degree of degeneration, proposed rolling bearing different conditions vibration signal to carry out the method for diagnosing faults of feature extraction and intelligent classification simultaneously.The method is gathered empirical mode decomposition to each state vibration signal, but its effect depends on size and these two important parameters of population mean number of times that add noise, and therefore, what propose to add in empirical mode decomposition method white noise can be according to criterion.A series of intrinsic mode functions after decomposing are obtained to the singular value of each state in conjunction with svd, and composition characteristic vector matrix.Be entered into the hypersphere multi-class support vector machine of optimizing nuclear parameter based on hypersphere centre of sphere spacing and classify, thereby realize that rolling bearing is normal, the multimode of different faults position and performance degradation degree intelligent diagnostics simultaneously.Experimental result shows, in the set empirical mode decomposition method of proposition, adds white noise criterion, can avoid artificially determining resolution parameter, improves its decomposition efficiency; The Optimization Method of Kernel Parameter based on hypersphere centre of sphere spacing proposing, can determine in many classification situation, nuclear parameter little and the effective region of search, thereby minimizing training time.Set empirical mode decomposition and svd based on Optimal Parameters, the intelligent diagnosing method of the hypersphere multi-class support vector machine of optimizing in conjunction with the nuclear parameter of hypersphere centre of sphere spacing again than existing based on empirical mode decomposition and autoregressive model, higher in conjunction with the diagnostic method discrimination of hypersphere multi-class support vector machine.

Accompanying drawing explanation

Fig. 1 is the overall flow block diagram of the method for the invention, Fig. 2 is the specific implementation process flow diagram flow chart of step 5 in Fig. 1, Fig. 3 is the EEMD exploded view (mentioning in the present invention) of energy criteria method parameters, Fig. 4 is the EEMD exploded view (mentioning in prior art) of amplitude Criterion Method parameters, Fig. 5 is the EEMD exploded view of outer ring fault flaw detection diameter 0.18mm vibration signal, Fig. 6 is the relation of parameter penalty coefficient C and nuclear parameter s and discrimination (precision), Fig. 7 controls the parameter beta of M area size and the relation of discrimination (horizontal ordinate represents parameter beta, parameter beta span is 0～1, for ease of observing, only provide 0.8～1 scope, ordinate represents discrimination (precision)).

Embodiment

Embodiment one: as shown in Fig. 1～2, a kind of rolling bearing fault position and performance degradation degree diagnostic method described in present embodiment are realized according to following steps:

Step 1, gather a large amount of bearing vibration signals (data), comprise vibration signal, the vibration signal of rolling bearing outer shroud different performance degree of degeneration, the vibration signal of rolling bearing rolling body different performance degree of degeneration of ring different performance degree of degeneration in the vibration signal, rolling bearing of rolling bearing normal condition;

Step 2, the vibration signal of above-mentioned various states is divided into study part signal and part of detecting signal according to the mode of x times of cross-validation method;

Step 3, feature extraction: adopt the EEMD of Optimal Parameters first study part signal to be carried out to feature extraction in conjunction with the method for SVD, detailed process is:

Step 3 (one), each vibration signal is first carried out to EMD decomposition, obtain a plurality of IMF components, will obtain the radio-frequency component of first IMF component as this vibration signal, then calculate the poor E of energy scale of first IMF _h, then calculate the poor E of energy scale of this original vibration signal _o, can obtain the parameter h in formula (5);

$0<g<\frac{h}{2}$

In formula, wherein, E _nfor adding white noise energy standard deviation, E _ofor the energy scale of original vibration signal poor, E _hpoor for the energy scale of the radio-frequency component of vibration signal, g is the ratio coefficient that adds white noise, and h is energy ratio coefficient;

By formula (5), be can be derived from

$0<E_n<\frac{1}{4}{E}_h$

Generally, get g=h/4 and just can effectively avoid the pattern aliasing in signal decomposition;

In EEMD method, add white noise to satisfy condition:

(1) extreme point that the white noise adding should not affect signal radio-frequency component distributes;

(2) it is spaced apart that the white noise adding should change the extreme point of low-frequency component; The extreme point interval of low-frequency component is reduced, it is evenly distributed, the matching envelope that reduces cubic spline function is asked local mean value error;

In EEMD algorithm, in original signal, add the amplitude of white noise excessive, in decomposable process, can produce false mode component; If add the amplitude of noise too small, be likely not enough to cause that the Local Extremum of original signal changes, can not solution pattern obscure problem; Meet above two conditions, key is for any discontinuous signal, and what one of how to confirm effectively added white noise in EEMD method can be according to criterion; With a large amount of experimental study, this method has proposed to add the criterion of white noise in EEMD by analysis, i.e. energy Criterion Method, referring to formula (5) and formula (6);

Step 3 (two), obtain the population mean number of times L in EEMD method, according to formula (7), try to achieve population mean number of times L,

$e=\frac{g}{\sqrt{L}}$

In formula, e is the signal decomposition relative error of expectation, and e generally gets 1%; G is the ratio coefficient that adds white noise, and L is the population mean number of times in EEMD method;

From formula (7), if it is less to add the amplitude coefficient g of white noise, error e is less, be conducive to the raising of Decomposition Accuracy, but when g value too hour, likely be not enough to cause the variation of signal Local Extremum, thereby can not change local time's span of signal, just can not bring into play the advantage of EEMD; If L is larger, e also can reduce, but has also increased computation burden simultaneously.Therefore, generally the artificial first value of definite population mean number of times L is undesirable.Adopt the criterion that adds white noise proposing first by original signal, to calculate the ratio coefficient that adds white noise, then according to anticipation error e (generally getting 1%) is set, application of formula (7) just can obtain the value of population mean number of times L;

In EMD method, the ability that obtains having actual physical meaning IMF depends on the existence of signal extreme point and the distribution interval of extreme point; If while there is no enough extreme points in signal, decompose and will stop; If extreme point distribution interval is inhomogeneous in signal, can produce the error of fitting of the upper and lower envelope of extreme point, thus the pattern of generation aliasing.The essence of EEMD method is a kind of repeatedly empirical mode decomposition of the white Gaussian noise that superposes, utilized white Gaussian noise to there is the equally distributed statistical property of frequency, make to add the signal after noise on different scale, to there is continuity, by add the different white noises of equal amplitude to change the extreme point characteristic of signal at every turn, afterwards the corresponding IMF that repeatedly EMD obtains is carried out to population mean again and offset the white noise adding, so not only can obtain the impact that has the IMF of physical significance but also eliminated noise, solution pattern is effectively obscured problem;

EEMD decomposition step is as described below:

(1) initialization population mean number of times L;

(2) add numerical value amplitude to the white noise adding, and make i _e=1;

(3) the white noise of a given amplitude be added to original signal x (t) upper, to produce a new signal

$x_{i_E}\left(t\right)=x\left(t\right)+n_{i_E}\left(t\right)$

In formula, represent i _esubadditive white noise sequence, represent i _ethe additional noise signal of inferior test, i _e=1,2 ..., L;

(4) signal to gained Noise carry out respectively EMD decomposition, obtain IMF separately and form

$x_{i_E}\left(t\right)=\underset{j_E=1}{\overset{J}{\mathrm{\&Sigma;}}}{c}_{i_E,j_E}\left(t\right)+r_{i_E,j_E}\left(t\right)$

In formula, be i _edecompose the i obtaining inferior adding after white noise _eindividual IMF, remaining function, the average tendency of representation signal, J is the quantity of IMF;

(5) repeating step 3 and step 4 are carried out L time, each decompose the set that adds white noise signal that amplitude is different to obtain IMF and are

$\{\left(c_{1,j_E}\left(t\right)\right),\left(c_{2,j_E}\left(t\right)\right),...,\left(c_{M,j_E}\left(t\right)\right)\}$

Wherein, j _e=1,2 ..., J;

(6) utilizing the assembly average of uncorrelated sequence is zero principle, and the IMF of above-mentioned correspondence is carried out to ensemble average computing, obtains the final IMF after EEMD,

$c_{j_E}\left(t\right)=\frac{1}{L}\underset{i_E=1}{\overset{L}{\mathrm{\&Sigma;}}}{c}_{i_E,j_E}\left(t\right)$

In formula, i _ethe IMF that individual employing EEMD decomposes, i _e=1,2 ..., L, j _e=1,2 ..., J.

Step 3 (three), add on the ratio coefficient of noise and the basis of these two parameters of population mean number of times trying to achieve, each vibration signal is carried out to EEMD and decompose and obtain IMF, in different vibration signals, IMF maximum number is n, is less than the supplementary null vector of n; The n that each vibration signal is obtained IMF forms original feature vector matrix B=[c ₁c ₂... c _n] ^t, described original feature vector matrix is carried out to svd, the singular value that svd is obtained is described as proper vector [λ ₁, λ ₂..., λ _n];

About further illustrating of svd: any one real symmetry square matrix can be converted into diagonal matrix through orthogonal transformation, for arbitrary real matrix, can utilize svd to be translated into diagonal matrix;

The real matrix B that is provided with the capable L row of K, can do following decomposition to it, is referred to as svd,

B=UEV ^tin formula, U=[u ₁... u _k] ∈ R ^{k * K}, U ^tu=I, V=[v ₁... v _l] ∈ R ^{l * L}, V ^tv=I, I is a unit matrix, and E is that a K * L ties up diagonal matrix, and its main diagonal element is non-negative, and E is matrix [diag{ λ ₁, λ ₂..., λ _n}: 0] or the form of its transposition, this depends on K < L or K>=L, n=min (K, L), λ ₁>=λ ₂>=...>=λ _n>=0, λ ₁, λ ₂..., λ _nthe singular value that is called matrix B;

Known according to matrix theory, the singular value of matrix is the inherent feature of matrix, and it has good stability, and, when little change occurs matrix element, the singular value of matrix changes very little, and the singular value of matrix also has constant rate and rotational invariance simultaneously; Therefore, singular values of a matrix meets the desired stability of feature extraction and rotation in pattern-recognition, constant rate, and it can portray the feature of eigenvectors matrix B effectively; Therefore, the eigenvectors matrix consisting of the IMF after EEMD is decomposed carries out svd, and the singular value obtaining just can be portrayed the fault signature of bearing vibration signal;

Step 4, structural attitude vector matrix: the proper vector [λ of all learning signals of each state of rolling bearing ₁, λ ₂..., λ _n] constitutive characteristic vector matrix S _k

$S_k=\left[\begin{array}{ccccc}{\mathrm{\&lambda;}}_{k,11},{\mathrm{\&lambda;}}_{k,12},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,1n};& {\mathrm{\&lambda;}}_{k,21},{\mathrm{\&lambda;}}_{k,22},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,2n};& {\mathrm{\&lambda;}}_{k,31},{\mathrm{\&lambda;}}_{k,32},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,3n};& \&CenterDot;\&CenterDot;\&CenterDot;;& {\mathrm{\&lambda;}}_{k,N_{k}1},{\mathrm{\&lambda;}}_{k,N_{k}2},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,N_{k}n}\end{array}\right]---\left(15\right)$

In formula, k=1,2 ..., m, represents the different faults position of rolling bearing and the state of performance degradation degree; N _kit is the number of k class state learning signal;

The hypersphere multi-class support vector machine that step 5, utilization improve classifying rules is to the eigenvectors matrix S obtaining in step 4 _kcarry out preliminary classification, obtain each state original state hypersphere of rolling bearing; Adopt the method for hypersphere centre of sphere spacing maximum to carry out nuclear parameter optimization to improving the hypersphere multi-class support vector machine of classifying rules, i.e. definite kernel parameter most preferred range; Detailed process is:

Step 5 (one), by all kinds of eigenvectors matrix S _kbe input in the hypersphere multi-class support vector machine that improves classifying rules, according to all kinds of eigenvectors matrixs, determine the centre of sphere of all kinds of hyperspheres, make each state k form a hypersphere, and then obtain the original state hypersphere of all kinds of abort situation and performance degradation degree;

About improving the explanation of the hypersphere multi-class support vector machine of classifying rules: at document [Kang Shouqiang, Wang Yujing, Yang Guangxue, Deng. the Fault Diagnosis of Roller Bearings [J] based on empirical mode decomposition and hypersphere multi-class support vector machine. Proceedings of the CSEE, 2011,31 (14): 96-102.] in, describe hypersphere multi-class support vector machine in detail theoretical, and improved classifying rules on this basis, and supplemented in critical area (M region) classifying rules when training sample set is combined into empty set; New classifying rules is as follows:

If testing feature vector z is not included in M region,

$f_1\left(z\right)=\arg \underset{k=1}{\overset{m}{\min }}(D(z,a^k)-R_k^2)$

If z is included in M region and set I is sky,

$f_2\left(z\right)=\arg \underset{x_p\&Element;I}{\min }\left(\frac{\sqrt{D(z,a^k)}}{R_k}\right)$

If z is included in M region and set I is not sky,

$f_3\left(z\right)=\arg \underset{x_p\&Element;I}{\min }\left(D_{\mathrm{MI}}(z,x_p)\right)$

In formula, the implication of all parameters is referring to the above-mentioned document of mentioning;

M region is a dynamic region, by β parameter, is controlled.Training of judgement sample or test sample book z ^*whether be positioned at M region in the following way:

If z so ^*be positioned at M region;

If z so ^*be positioned at M region;

Wherein, i=1,2 ..., m, j=1,2 ..., m, and i ≠ j; The span of β is [0,1];

The process of step 5 (two), definite kernel parameter most preferred range is:

A, determine that the total class of learning sample counts m;

B, be divided into m (m-1)/2 group;

C, setting cycle index initial value i _m=1;

D, utilize formula (14) to grouping i _mall kinds of hypersphere centre ofs sphere of each multinuclear calculation of parameter to be selected between distance: detailed process is:

For improving k in the feature space of hypersphere multi-class support vector machine of classifying rules ₁class hypersphere centre of sphere a ^k1to k ₂class hypersphere centre of sphere a ^k2square distance d ²be defined as:

$d^2=D(a^{k_1},a^{k_2})={\left|\right|a^{k_1}-a^{k_2}\left|\right|}^2=(a^{k_1}\&CenterDot;a^{k_1})-2(a^{k_1}\&CenterDot;a^{k_2})+(a^{k_2}\&CenterDot;a^{k_2})---\left(12\right)$

By the k class hypersphere centre of sphere bring in formula (12), can try to achieve

$d^2=\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_1}(x_i^{k_1}\&CenterDot;x_j^{k_1})-2\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_2}(x_i^{k_1}\&CenterDot;x_j^{k_2})+\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_2}{\mathrm{\&alpha;}}_j^{k_2}(x_i^{k_2}\&CenterDot;x_j^{k_2})---\left(13\right)$

In formula: for Lagrange multiplier, i=1,2 ..., N _k;

For nonlinear situation, directly in formula (13), bring corresponding kernel function k (x, y) into, between class and class, hypersphere centre of sphere distance computation formula is converted to:

$d=\sqrt{\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_1}k(x_i^{k_1},x_j^{k_1})-2\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_2}k\left(x_i^{k_1}{,x}_j^{k_2}\right)+\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_2}{\mathrm{\&alpha;}}_j^{k_2}k\left(x_i^{k_2}{,x}_j^{k_2}\right)}---\left(14\right)$

In formula (14): j=1 ..., N _k, i=1 ..., N _k;

Support vector machine adopts kernel function that the inseparable input space of low-dimensional is mapped to and has the feature space that the higher-dimension of lower VC dimension can divide; After kernel function is selected, the unique selection of depending on kernel functional parameter of high-dimensional feature space, and hypersphere centre of sphere spacing can be used as a kind of tolerance of classification separability in feature space; So derive the distance computing formula between the hypersphere centre of sphere, utilize the optimum selection range of method definite kernel parameter of multiclass hypersphere centre of sphere spacing maximum, shorten the learning time of sorter;

E, obtain maximum hypersphere centre of sphere spacing d _maxcorresponding nuclear parameter value;

F, judgement cycle index i _mwhether be less than the combination of two number of all kinds of hyperspheres, i _m< m (m-1)/2; If be less than, perform step D, otherwise execution step G;

G, find the centre of sphere spacing minimum value d of all combination of two hyperspheres _minwith maximal value d _maxtime corresponding nuclear parameter value, the optimum selection range d using it as nuclear parameter _min～d _max;

Step 6, to separating part of detecting signal in step 2, adopt the feature extracting method identical with learning part signal to obtain proper vector z=[λ ₁, λ ₂..., λ _n];

Step 7, calculating coefficient of difference, pass judgment on test signal condition; Obtain optimum penalty coefficient, nuclear parameter value and M regional dynamics parameter beta:

Based on all kinds of original state hyperspheres and the optimum selection range d of nuclear parameter _min～d _max, obtain the proper vector z=[λ of test signal ₁, λ ₂..., λ _n] and each original state hypersphere between three coefficient of difference be: and D _mI(z, x _p);

Each alphabetical implication: D (z, a in three coefficient of difference formula ^k) represent that test vector z is to k class hypersphere centre of sphere a ^kdistance square, R _kbe the radius of k class ball, x _pfor the element in training sample set I in M region; D _mI(z, x _p) represent that test vector z is to x _pdistance square;

If the coefficient of difference of the proper vector of test signal and certain original state hypersphere is minimum, just illustrate that the abort situation of this test vibration signal and abort situation and the performance degradation degree of performance degradation degree and this original state hypersphere are the most close; Therefore, can judge the malfunction of test signal; When rate of correct diagnosis is the highest, determine d _min～d _maxbetween optimum nuclear parameter value, penalty coefficient C and M regional dynamics parameter beta;

Step 8, according to above-mentioned parameter: d _min～d _maxbetween optimum nuclear parameter value, penalty coefficient C and M regional dynamics parameter beta, and then obtain the end-state hypersphere model of each state under this parameter:

$\left\{\begin{array}{c}{a}^k=\underset{i}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^k{x}_i^k,{\mathrm{\&alpha;}}_i^k\&NotEqual;0\\ \min {\left(R_k\right)}^2+C^k\underset{i=1}{\overset{l^k}{\mathrm{\&Sigma;}}}{\mathrm{\&epsiv;}}_i^k,s.t.{(x_i^k-a^k)}^T(x_i^k-a^k)\&le;{\left(R_k\right)}^2+{\mathrm{\&epsiv;}}_i^k\\ K(x_i^k,x_j^k)=e^{[-\frac{{(x_i^k-x_j^k)}^2}{2s^2}]}\\ R_k^2=D(z^{\&prime;},a^k)=\underset{i,j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^k{\mathrm{\&alpha;}}_j^{k}K(x_i^k,x_j^k)-2\underset{i}{\mathrm{\&Sigma;}}{a}_i^{k}K(x_i^k,z^{\&prime;})+K(z^{\&prime;},z^{\&prime;})\\ \mathrm{if}\sqrt{D(z^{*},a^i)}\&le;R_i\mathrm{and\&beta;}\sqrt{D(z^{*},a^j)}<R_j\mathrm{or}\\ \mathrm{if}\sqrt{D(z^{*},a^j)}\&le;R_j\mathrm{and\&beta;}\sqrt{D(z^{*},a^i)}<R_i,\mathrm{then}{z}^{*}\mathrm{in\; region\; M}\end{array}\right.---\left(19\right)$

Wherein: for Lagrange multiplier, i=1,2 ..., N _k; S is nuclear parameter; it is the proper vector of certain signal of k class; for the slack variable of introducing, z ' is the support vector on hypersphere, z ^*proper vector for learning signal or test signal;

The actual field diagnosis of step 9, rolling bearing health status:

Gather actual field bearing vibration signal, according to the feature extracting method identical with study part signal, obtain proper vector, then calculate the proper vector of actual field bearing vibration signal and the coefficient of difference between each end-state hypersphere model, the rolling bearing health status representing according to end-state hypersphere model corresponding to coefficient of difference minimum value is passed judgment on the health status of on-the-spot rolling bearing: be normal condition or malfunction, as have fault to diagnose to be out of order position and performance degradation degree.

Feature extraction in the inventive method (step 3) is carried out to emulation experiment: it is example that simulate signal be take rolling bearing spot corrosion fault, structure rolling bearing inner ring spot corrosion fault model;

$x\left(t\right)=\underset{i}{\mathrm{\&Sigma;}}{A}_i{e}^{-k(t-\mathrm{iT})}\sin (2\mathrm{\&pi;}{f}_n(t-\mathrm{iT})+{\mathrm{\&phi;}}_i)(\mathrm{Ut}-\mathrm{iT})+n\left(t\right)---\left(17\right)$

A _i=A (cos (2 π f _rt+ φ _a)+C _a) in formula, A _ifor the amplitude of impacting, T is for impacting the cycle occurring, f _nfor resonant frequency, f _rfor inner ring is inner ring failure-frequency by frequency, n (t) is additive noise.

Additive noise signal to noise ratio (S/N ratio) is 16dB, to simulate signal x (t) with sample frequency f _s=20kHz samples, and gathers altogether 1024 points.Be configured to 1.99GHz dual core processor, on the computing machine of internal memory 1GB, using Matlab software to carry out emulation.Adopt respectively document [old summary, slander sunshine, He Zhengjia, Deng. the research [J] of population mean empirical mode decomposition and 1.5 dimension spectral methods. XI AN JIAOTONG UNIVERSITY Subject Index, 2009,43 (05): 94-98.] (in the document, mention add noise criteria called after amplitude Criterion Method) with propose to add the criterion (called after energy criteria method) of noise to determine two important parameters in EEMD method herein, the decomposition result that obtains EEMD is shown in Fig. 3 and Fig. 4.IMF3 from two figure, there is obvious modulation phenomenon, the IMF3 of Fig. 3 slightly good (all can obviously be out of order from spectral line diagnosis if IMF3 is carried out to envelope demodulation), and as can be seen from Table 1, signal to noise ratio (S/N ratio) with decompose relative error identical in the situation that, based on the definite noise ratio value coefficient of energy criteria method and population mean number of times than definite little of amplitude Criterion Method.This makes to decompose the time used, and (getting respectively the time after average 10 times) is also few.Therefore, energy criteria method can improve the decomposition efficiency of EEMD.

Two kinds of table 1 simulate signal add the contrast of noise criteria method

The application of the inventive method and analysis

Utilize the rolling bearing experimental data in U.S. CWRU electrical engineering laboratory.The 6205-2RS deep groove ball bearing that test bearing provides for SKF, sample frequency is 12kHz.Bearing local damage (hole point) is to be made in the inside and outside circle artificial of bearing by electric discharge machine.There is the motor of 4 kinds of different loads (0,0.75,1.5,2.25kW) in every kind of state.This experiment is normal to rolling bearing, inner ring fault is damaged diameter 0.18mm, inner ring fault is damaged diameter 0.53mm, outer ring fault is damaged diameter 0.18mm, outer ring fault is damaged these 5 kinds of different faults positions of diameter 0.53mm and performance degradation degree is carried out fault diagnosis.

The housing washer fault of take damage diameter 0.18mm vibration signal is example, adopts energy criteria method to obtain and adds white noise parameter, carries out EEMD decomposition, and result as shown in Figure 5.In experiment, setting e is 1%, and the α calculating is 0.104, and population mean number of times is 108.

Each state vibration signal of rolling bearing, after EEMD decomposes, obtains one group of IMF component, and each IMF component has comprised different characteristic dimension information.By EEMD, decompose, the feature of vibration signal is just portrayed by the IMF component obtaining completely, can under different resolution, reveal, and the IMF component (high band) obtaining the at first main failure message that comprised bearing vibration signal.Therefore,, by front which floor IMF component is carried out to feature extraction, just can obtain the feature of original vibration signal.Select front 6 layers of IMF component herein, i.e. n=6 in formula (15) and (16).It is as shown in table 2 that the feature extracting method of employing based on svd tried to achieve the eigenwert of 5 kinds of state vibration signals of rolling bearing.

The eigenwert of 5 kinds of state vibration signals of table 2 rolling bearing

Adopt 8 times of cross-validation methods to test 5 class Rolling Bearing Status signals.Optimize in the hypersphere multi-class support vector machine method of nuclear parameter, select radial basis gaussian kernel function K (x _i, x _j)=exp[-(x _i-x _j) ²/ 2s ²], wherein s is nuclear parameter.If nuclear parameter s is tending towards 0, all sample point is all support vector, so s value is since 0.1 value, artificially sets larger span, from 0.1 to 50, search step-length 0.5.In determining the process of hypersphere, if C > 1, C has just lost the effect of penalty coefficient; If C < is 1/N, cannot meet this formula, this is just for penalty coefficient C defines span, i.e. 1/N≤C≤1.Therefore, C value from 0.05 to 1, step-length 0.1.Fig. 6 and Fig. 7 have provided to adopt and have optimized EEMD, svd in conjunction with fault diagnosis parameters C, s and the β of the Hypersphere Support Vector Machine method of improvement classifying rules and the relation of average recognition rate.By these figure, we can determine that the average recognition rate of 8 times of cross-validation methods when parameters C, s and β select how to be worth is the highest, have determined end-state hypersphere disaggregated model.

To set nuclear parameter scope larger due to artificial, to consume learning time longer.In order to verify the employing hypersphere centre of sphere spacing of proposition, optimize the method for nuclear parameter, by the hypersphere centre of sphere spacing of calculating between 5 class samples, determine that minimum spacing and the corresponding nuclear parameter of maximum spacing are respectively 0.1 and 5.7, so the optimum selection range of nuclear parameter s is [0.1,5.7], the visible people of comparing is that the nuclear parameter scope [0.1,50] of choosing is dwindled a lot.

In table 3, provided and utilized several method to carry out the comparative result of fault diagnosis, comprise the averaging time of optimal value, training time, average recognition rate and a signal of diagnosis of C, s and β parameter.Can find out, on the basis of hypersphere multi-class support vector machine method that utilizes same improvement classifying rules, based on EMD, in conjunction with the diagnostic method of svd, compare document [Kang Shouqiang, Wang Yujing, Yang Guangxue, Deng. the Fault Diagnosis of Roller Bearings [J] based on empirical mode decomposition and hypersphere multi-class support vector machine. Proceedings of the CSEE, 2011,31 (14): 96-102.] in, EMD is in conjunction with the diagnostic method of Ulrych-Clayton or Yule-Walker, not only diagnose spent time short, and average recognition rate is also high; EEMD based on energy criteria Optimal Parameters is in conjunction with the diagnostic method of svd and the method based on amplitude criterion Optimal Parameters, and average recognition rate is basic identical, but diagnosis spent time is short.And with based on EMD, be combined the diagnostic method of svd and compare average recognition rate and exceed nearly 1 percentage point; Adopt the hypersphere centre of sphere spacing proposing to optimize the method for nuclear parameter selection range, be approximately 1/9th of additive method on the training time.In addition, the par of gathering training sample in I from table can find out that classification hypersphere exists the space that crosses really.The training time of institute's extracting method comprises the time of calculating hypersphere centre of sphere spacing and Training Support Vector Machines.The time that comprises feature extraction and classification averaging time of a test signal diagnosis.

The comparison of table 3 method for diagnosing faults

In conjunction with above-mentioned application, for the technique effect of the inventive method, further set forth again:

(1), proposed herein a kind ofly more effectively not only can and to its performance degradation degree vibration signal, carry out the method for diagnosing faults of feature extraction and intelligent classification to rolling bearing different faults position simultaneously.This can be, and maintenance personal makes reasonable judgement to each fault and processing provides important evidence, reduces servicing time, improves Enterprise Integrated competitive power.

(2), based on EMD, in conjunction with SVD, carry out feature extraction, recycling is improved diagnostic method that the hypersphere multi-class support vector machine of classifying rules classifies than high in conjunction with the diagnostic method discrimination of AR model based on EMD.

(3), the white noise criterion that adds based on energy makes to have reduced in EEMD decomposition algorithm artificial parameters, and the decomposition efficiency than the EEMD algorithm of optimizing based on amplitude criteria parameter is high, the inventive method in characteristic extraction step owing to having adopted energy criteria method, on year-on-year basis under condition, compare with the EEMD algorithm of amplitude criteria parameter optimization, required time has reduced by 1/3rd (as can be seen from Table 1).

(4) EEMD that adds white noise criterion, based on energy carries out feature extracting method in conjunction with SVD, to the discrimination of diagnosis rolling bearing different faults position and performance degradation degree, is the highest, can reach for 97.61% (as can be seen from Table 3).

(5), the hypersphere centre of sphere spacing that adopt to propose is optimized the method for hypersphere multi-class support vector machine nuclear parameter selection range, is approximately 1/9th (as can be seen from Table 3) of additive method on the training time.

Claims (2)

1. rolling bearing fault position and a performance degradation degree diagnostic method, is characterized in that: described method realizes according to following steps:

Step 1, gather a large amount of bearing vibration signals, comprise vibration signal, the vibration signal of rolling bearing outer shroud different performance degree of degeneration, the vibration signal of rolling bearing rolling body different performance degree of degeneration of ring different performance degree of degeneration in the vibration signal, rolling bearing of rolling bearing normal condition;

Step 2, the vibration signal of above-mentioned various states is divided into study part signal and part of detecting signal according to the mode of x times of cross-validation method;

Step 3, feature extraction: adopt the EEMD of Optimal Parameters first study part signal to be carried out to feature extraction in conjunction with the method for SVD, detailed process is:

Step 3 (one), each vibration signal is first carried out to EMD decomposition, obtain a plurality of IMF components, will obtain the radio-frequency component of first IMF component as this vibration signal, then calculate the poor E of energy scale of first IMF _h, then calculate the poor E of energy scale of this original vibration signal _o, can obtain the parameter h in formula (5);

$0<g<\frac{h}{2}---\left(5\right)$ In formula, wherein, E _nfor adding white noise energy standard deviation, E _ofor the energy scale of original vibration signal poor, E _hpoor for the energy scale of the radio-frequency component of vibration signal, g is the ratio coefficient that adds white noise, and h is energy ratio coefficient;

By formula (5), be can be derived from

$0<E_n<\frac{1}{4}{E}_h---\left(6\right)$

Step 3 (two), obtain the population mean number of times L in EEMD method, according to formula (7), try to achieve population mean number of times L,

$e=\frac{g}{\sqrt{L}}---\left(7\right)$

In formula, e is the signal decomposition relative error of expectation, and people is for choosing a certain concrete numerical value; G is the ratio coefficient that adds white noise, and g exists between get a certain concrete numerical value; L is the population mean number of times in EEMD method;

Step 3 (three), add on the ratio coefficient of noise and the basis of these two parameters of population mean number of times trying to achieve, each vibration signal is carried out to EEMD and decompose and obtain IMF, in different vibration signals, IMF maximum number is n, is less than the supplementary null vector of n; The n that each vibration signal is obtained IMF forms original feature vector matrix B=[c ₁c ₂c _n] ^t, described original feature vector matrix is carried out to svd, the singular value that svd is obtained is described as proper vector [λ ₁, λ ₂..., λ _n];

Step 4, structural attitude vector matrix: the proper vector [λ of all learning signals of each state of rolling bearing ₁, λ ₂..., λ _n] constitutive characteristic vector matrix S _k

$S_k=[{\mathrm{\&lambda;}}_{k,11},{\mathrm{\&lambda;}}_{k,12},...,{\mathrm{\&lambda;}}_{k,1n};{\mathrm{\&lambda;}}_{k,21},{\mathrm{\&lambda;}}_{k,22},...,{\mathrm{\&lambda;}}_{k,2n};{\mathrm{\&lambda;}}_{k,31},{\mathrm{\&lambda;}}_{k,32},...,{\mathrm{\&lambda;}}_{k,3n};{\mathrm{\&lambda;}}_{k,N_{k}1},{\mathrm{\&lambda;}}_{k,N_{k}2},...,{\mathrm{\&lambda;}}_{k,N_{k}n}]---\left(15\right)$

In formula, k=1,2 ..., m, represents the different faults position of rolling bearing and the state of performance degradation degree; N _kit is the number of k class state learning signal;

The hypersphere multi-class support vector machine that step 5, utilization improve classifying rules is to the eigenvectors matrix S obtaining in step 4 _kcarry out preliminary classification, obtain each state original state hypersphere of rolling bearing; Adopt the method for hypersphere centre of sphere spacing maximum to carry out nuclear parameter optimization to improving the hypersphere multi-class support vector machine of classifying rules, i.e. definite kernel parameter most preferred range; Detailed process is:

Step 5 (one), by all kinds of eigenvectors matrix S _kbe input in the hypersphere multi-class support vector machine that improves classifying rules, according to all kinds of eigenvectors matrixs, determine the centre of sphere of all kinds of hyperspheres, make each state k form a hypersphere, and then obtain the original state hypersphere of all kinds of abort situation and performance degradation degree;

The process of step 5 (two), definite kernel parameter most preferred range is:

A, determine that the total class of learning sample counts m;

B, be divided into m (m-1)/2 group;

C, setting cycle index initial value i _m=1;

D, utilize formula (14) to grouping i _mall kinds of hypersphere centre ofs sphere of each multinuclear calculation of parameter to be selected between distance: detailed process is:

For improving k in the feature space of hypersphere multi-class support vector machine of classifying rules ₁class hypersphere centre of sphere a ^k1to k ₂class hypersphere centre of sphere a ^k2square distance d ²be defined as:

$d^2=D(a^{k_1},a^{k_2})={\left|\right|a^{k_1}-a^{k_2}\left|\right|}^2=(a^{k_1}\&CenterDot;a^{k_1})-2(a^{k_1}\&CenterDot;a^{k_2})+(a^{k_2}\&CenterDot;a^{k_2})---\left(12\right)$

By the k class hypersphere centre of sphere bring in formula (12), can try to achieve

$d^2=\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_1}(x_i^{k_1}\&CenterDot;x_j^{k_1})-2\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_2}(x_i^{k_1}\&CenterDot;x_j^{k_2})+\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_2}{\mathrm{\&alpha;}}_j^{k_2}(x_i^{k_2}\&CenterDot;x_j^{k_2})---\left(13\right)$

In formula: for Lagrange multiplier, i=1,2 ..., N _k;

For nonlinear situation, directly in formula (13), bring corresponding kernel function k (x, y) into, between class and class, hypersphere centre of sphere distance computation formula is converted to:

$d=\sqrt{\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_1}k(x_i^{k_1},x_j^{k_1})-2\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_1}{\mathrm{\&alpha;}}_j^{k_2}k(x_i^{k_1},x_j^{k_2})+\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k_2}{\mathrm{\&alpha;}}_j^{k_2}k(x_i^{k_2},x_j^{k_2})}---\left(14\right)$

In formula (14): j=1 ..., N _k, i=1 ..., N _k;

E, obtain maximum hypersphere centre of sphere spacing d ' _maxcorresponding nuclear parameter value;

F, judgement cycle index i _mwhether be less than the combination of two number of all kinds of hyperspheres, i _m<m (m-1)/2; If be less than, i _m=i _m+ 1, and perform step D, otherwise execution step G;

G, find the centre of sphere spacing minimum value d of all combination of two hyperspheres _minwith maximal value d _maxtime corresponding nuclear parameter value, the optimum selection range d using it as nuclear parameter _min～d _max;

Step 6, to separating part of detecting signal in step 2, adopt the feature extracting method identical with step 3 learning part signal to obtain proper vector z=[λ ₁, λ ₂..., λ _n];

Step 7, calculating coefficient of difference, pass judgment on test signal condition; Obtain optimum penalty coefficient, nuclear parameter value and M regional dynamics parameter beta:

Based on all kinds of original state hyperspheres and the optimum selection range d of nuclear parameter _min～d _max, obtain the proper vector z=[λ of test signal ₁, λ ₂..., λ _n] and each original state hypersphere between three coefficient of difference be: and D _mI(z, x _p);

Each alphabetical implication: D (z, a in three coefficient of difference formula ^k) represent that test vector z is to k class hypersphere centre of sphere a ^kdistance square, R _kbe the radius of k class ball, x _pfor the element in training sample set I in M region; D _mI(z, x _p) represent that test vector z is to x _pdistance square;

If the coefficient of difference of the proper vector of test signal and certain original state hypersphere is minimum, just illustrate that the abort situation of this test vibration signal and abort situation and the performance degradation degree of performance degradation degree and this original state hypersphere are the most close; Therefore, can judge the malfunction of test signal; When rate of correct diagnosis is the highest, determine d _min～d _maxbetween optimum nuclear parameter value, penalty coefficient C and M regional dynamics parameter beta;

Step 8, according to above-mentioned parameter: d _min～d _maxbetween optimum nuclear parameter value, penalty coefficient C and M regional dynamics parameter beta, and then obtain the end-state hypersphere model of each state under this parameter:

$\left\{\begin{array}{c}{a}^k=\underset{i}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^k{x}_i^k,{\mathrm{\&alpha;}}_i^k\&NotEqual;0\\ \min {\left(R_k\right)}^2+C^k\underset{i=1}{\overset{l^k}{\mathrm{\&Sigma;}}}{\mathrm{\&epsiv;}}_i^k,s.t.{(x_i^k-a^k)}^T(x_i^k-a^k)\&le;{\left(R_k\right)}^2+{\mathrm{\&epsiv;}}_i^k\\ K(x_i^k,x_j^k)=e^{[-\frac{{(x_i^k-x_j^k)}^2}{2s^2}]}\\ R_k^2=D(z^{\&prime;},a^k)=\underset{i,j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^k{\mathrm{\&alpha;}}_j^{k}K(x_i^k,x_j^k)-2\underset{i}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{k}K(x_i^k,z^{\&prime;})+K(z^{\&prime;},z^{\&prime;})\\ \mathrm{if}\sqrt{D(z^{*},a^i)}\&le;R_i\mathrm{and\&beta;}\sqrt{D(z^{*},a^j)}<R_j\mathrm{or}\\ \mathrm{if}\sqrt{D(z^{*},a^j)}\&le;R_j\mathrm{and\&beta;}\sqrt{D(z^{*},a^i)}<R_i,\mathrm{then\; z}*\mathrm{in\; region\; M}\end{array}\right.---\left(19\right)$

Wherein: for Lagrange multiplier, i=1,2 ..., N _k; S is nuclear parameter; it is the proper vector of certain signal of k class; for the slack variable of introducing, z ' is the support vector on hypersphere, and z* is the proper vector of learning signal or test signal;

The actual field diagnosis of step 9, rolling bearing health status:

Gather actual field bearing vibration signal, according to the feature extracting method identical with study part signal, obtain proper vector, then calculate the proper vector of actual field bearing vibration signal and the coefficient of difference between each end-state hypersphere model, the rolling bearing health status representing according to end-state hypersphere model corresponding to coefficient of difference minimum value is passed judgment on the health status of on-the-spot rolling bearing: be normal condition or malfunction, as have fault to diagnose to be out of order position and performance degradation degree.

2. a kind of rolling bearing fault position according to claim 1 and performance degradation degree diagnostic method, is characterized in that: in step 3 (two), the signal decomposition relative error e of expectation gets 1%.