CN102854015A - 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 the bearing failure diagnosis technical field.

Background technology

Rolling bearing is the critical piece of numerous rotating machineries, and in the different moment of its operation, fault degree is different.Existing rolling bearing fault diagnosis generally concentrates on determining of abort situation (interior ring, outer shroud, rolling body), performance degradation degree diagnosis is the new research direction that proposes recently, and it is to the brand-new expansion of existing fault diagnosis technology on theory and the 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 of degenerating based on the rolling bearing performance of optimal wavelet wave filter and s self-organizing feature map; 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 the prior art, the method adopts wavelet packet to extract feature and sets up the intelligent evaluation model, calculate the test mode vector to the distance of the centre of sphere with Support Vector data description, and then the tracing trouble degree.There is on this basis the scholar to propose again a kind of C-average bearing performance Diagnosis of degradation degree method of decomposing and bluring based on the Lifting Wavelet bag.The energy that is decomposed node by the Lifting Wavelet bag forms proper vector.Data normal and that prove an abortion are used for setting up assessment models as training sample, utilize FCM to carry out identifying and diagnosing.Empirical mode decomposition (Empirical Mode Decomposition, EMD) method is fit to analyze non-linear, non-stationary signal [Liu Lijun, Wang Qi, Yankee is own, Deng. based on method for diagnosing faults [J] Chinese journal of scientific instrument of EMD and Spectrum Correction, 2011,32 (6): 1278-1283.].EMD carries out feature extraction in conjunction with the 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. based on Fault Diagnosis of Roller Bearings [J] Proceedings of the CSEE of 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 preferably stability.Obtained certain application based on EMD in conjunction with the feature extracting method of the rolling bearing fault position vibration signal of SVD.

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.The 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 to set according to experience, lack reliability and adaptivity for different signals.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 the EEMD method, the amplitude coefficient that namely adds white noise is determined by amplitude standard deviation and the original signal amplitude standard deviation ratio of the effective radio-frequency component of original signal, usually gets 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 the multicategory classification problem, document [Zhu Meilin, Liu Xiangdong, Chen Shifu. the support vector machine with spherical structure solves 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 the scholar to propose again a kind of hypersphere multi-class support vector machine algorithm based on new decision rule, 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. based on the Fault Diagnosis of Roller Bearings [J] of 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 the 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, its consumption to learning time is very large.

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, a large amount of bearing vibration signal of collection comprise the vibration signal of rolling bearing normal condition, the vibration signal of the interior ring of rolling bearing different performance degree of degeneration, 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;

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 with it;

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

Step 3 (one), each vibration signal is carried out first EMD decompose, 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, calculate again the poor E of energy scale of this original vibration signal _o, can obtain the parameter h in the formula (5);

$0<g<\frac{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">h</figure-callout>}}{2}$

In the 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 for adding the ratio coefficient of white noise, and h is the energy ratio coefficient;

Can be pushed away by formula (5)

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

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

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

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

Step 3 (three), trying to achieve on the basis of the ratio coefficient that adds noise and these two parameters of population mean number of times, each vibration signal is carried out the EEMD decomposition obtains IMF, the IMF maximum number is n in the different vibration signals, less than the additional null vector of n; N the IMF that each vibration signal is obtained forms original feature vector matrix B=[c ₁c ₂... c _n] ^T, described original feature vector matrix is carried out 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

$S_k=\left[\begin{array}{ccccc}{\mathrm{\&lambda;}}_{k,11},{\mathrm{\&lambda;}}_{k,12},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,1n};& {\mathrm{\&lambda;}}_{k,21},{\mathrm{\&lambda;}}_{k,22},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,2n};& {\mathrm{\&lambda;}}_{k,31},{\mathrm{\&lambda;}}_{k,32},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,3n};& \&CenterDot;\&CenterDot;\&CenterDot;;& {\mathrm{\&lambda;}}_{k,{\mathrm{<figure-callout\; id="1"\; label="N\; k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{k}1},{\mathrm{\&lambda;}}_{k,{\mathrm{<figure-callout\; id="2"\; label="N\; k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{k}2},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,N_{k}n}\end{array}\right]---\left(15\right)$

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

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

Step 5 (one), with 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 the grouping i _mAll kinds of hypersphere centre ofs sphere of each multinuclear calculation of parameter to be selected between distance: detailed process is:

For k in the feature space of the hypersphere multi-class support vector machine that improves classifying rules ₁Class hypersphere centre of sphere a ^K1To k ₂Class hypersphere centre of sphere a ^K2Square distance d ²Be defined as:

${\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">d</figure-callout>}}^2=D(a^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1},a^{k_2})={\left|\right|a^{k_1}-{\mathrm{<figure-callout\; id="2"\; label="a\; k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">a</figure-callout>}}^{k_{}}\left|\right|}^2=(a^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}\&CenterDot;a^{k_1})-2(a^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}\&CenterDot;a^{k_2})+(a^{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\&CenterDot;a^{k_2})---\left(12\right)$

With the k class hypersphere centre of sphere

Bring in the formula (12), can try to achieve

${\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">d</figure-callout>}}^2=\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{\mathrm{\&alpha;}}_j^{k_1}(x_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}\&CenterDot;x_j^{k_1})-2\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{\mathrm{\&alpha;}}_j^{k_2}(x_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}\&CenterDot;x_j^{k_2})+\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{\mathrm{\&alpha;}}_j^{k_2}(x_i^{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\&CenterDot;x_j^{k_2})---\left(13\right)$

In the formula: Be the Lagrange multiplier, i=1,2 ..., N _k

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

$d=\sqrt{\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{\mathrm{\&alpha;}}_j^{k_1}k({\mathrm{<figure-callout\; id="1"\; label="x\; i\; k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">x</figure-callout>}}_{i{k}_{}}^{{}_1},x_j^{k_1})-2\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{\mathrm{\&alpha;}}_j^{k_2}k\left(x_{\mathrm{<figure-callout\; id="1"\; label="i\; k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">i</figure-callout>}}^{k_{}}{,x}_j^{k_2}\right)+\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{\mathrm{\&alpha;}}_j^{k_2}k\left({\mathrm{<figure-callout\; id="2"\; label="x\; i\; k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">x</figure-callout>}}_{i{k}_{}}^{{}_2}{,x}_j^{k_2}\right)}---\left(14\right)$

In the 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 less than the in twos number of combinations of all kinds of hyperspheres, i _m＜m (m-1)/2; If less than, execution in step D then, otherwise execution in step G;

G, find all centre of sphere spacing minimum value d that makes up in twos hypersphere _MinWith maximal value d _MaxThe time corresponding nuclear parameter value, with its optimum selection range d as nuclear parameter _Min～d _Max

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

Step 7, calculating coefficient of difference are passed 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 _pBe the element among the training sample set I in the M zone; 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 abort situation and the performance degradation degree of the abort situation of this test vibration signal and performance degradation degree and this original state hypersphere is 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:

$\left\{\begin{array}{c}{a}^k=\underset{i}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^k{x}_i^k,{\mathrm{\&alpha;}}_i^k\&NotEqual;0\\ \min {\left(R_k\right)}^2+C^k\underset{i=1}{\overset{l^k}{\mathrm{\&Sigma;}}}{\mathrm{\&epsiv;}}_i^k,s.t.{(x_i^k-a^k)}^T(x_i^k-a^k)\&le;{\left(R_k\right)}^2+{\mathrm{\&epsiv;}}_i^k\\ K(x_i^k,x_j^k)=e^{[-\frac{{(x_i^k-x_j^k)}^2}{2s^2}]}\\ {\mathrm{<figure-callout\; id="2"\; label="R\; k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">R</figure-callout>}}_k^{}=D(z^{\&prime;},a^k)=\underset{i,j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^k{\mathrm{\&alpha;}}_j^{k}K(x_i^k,x_j^k)-2\underset{i}{\mathrm{\&Sigma;}}{a}_i^{k}K(x_i^k,z^{\&prime;})+K(z^{\&prime;},z^{\&prime;})\\ \mathrm{if}\sqrt{D(z^{*},a^i)}\&le;R_i\mathrm{and\&beta;}\sqrt{D(z^{*},a^j)}<R_j\mathrm{or}\\ \mathrm{if}\sqrt{D(z^{*},a^j)}\&le;R_j\mathrm{and\&beta;}\sqrt{D(z^{*},a^i)}<R_i,\mathrm{then}{z}^{*}\mathrm{in\; region\; M}\end{array}\right.---\left(19\right)$

Wherein:

Be the Lagrange multiplier, i=1,2 ..., N _kS is nuclear parameter;

It is the proper vector of certain signal of k class;

Be the slack variable of introducing, z ' is the support vector on the 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, obtain proper vector according to the feature extracting method identical with the study part signal, 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 that represents 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 then to diagnose to be out of order position and performance degradation degree.

The invention has the beneficial effects as follows:

The present invention has proposed to add in the EEMD method criterion of white Gaussian noise on the basis of analyzing the EEMD theoretical method, namely optimized definite method of EEMD desired parameters.And the EEMD that adopts Optimal Parameters sets up eigenvectors matrix in conjunction with the feature that SVD extracts the bearing vibration signal.Characteristics for the hypersphere multi-category support vector machines, derive again between the hypersphere centre of sphere apart from computing formula, the optimum selection range of hypersphere multi-class support vector machine nuclear parameter is determined the distance between the hypersphere centre of sphere in proposition as segregation index, it is large that larger hypersphere centre of sphere spacing represents the degree of separating between class and the class, then the hypersphere centre of sphere spacing according to maximum finds 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 simultaneously rolling bearing fault position and different performance degree of degeneration, proposed rolling bearing different conditions vibration signal is carried out the method for diagnosing faults of feature extraction and intelligent classification.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, the adding white noise can be according to criterion in the proposition empirical mode decomposition method.A series of intrinsic mode functions after decomposing are obtained the singular value of each state in conjunction with svd, and the 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, the adding white noise criterion in the set empirical mode decomposition method of proposition can be avoided artificially determining resolution parameter, improves its decomposition efficiency; The Optimization Method of Kernel Parameter based on hypersphere centre of sphere spacing that proposes can be determined 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, based on empirical mode decomposition and autoregressive model, the diagnostic method discrimination in conjunction with the hypersphere multi-class support vector machine is high again than existing for 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.

Description of drawings

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 among Fig. 1, Fig. 3 is the EEMD exploded view (mentioning among the present invention) of energy criteria method parameters, Fig. 4 is the EEMD exploded view (mentioning in the 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 is that (horizontal ordinate represents parameter beta for the parameter beta of control M area size and the relation of discrimination, the parameter beta span is 0～1, for ease of observing, only provide 0.8～1 scope; Ordinate represents discrimination (precision)).

Embodiment

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

Step 1, a large amount of bearing vibration signal (data) of collection comprise the vibration signal of rolling bearing normal condition, the vibration signal of the interior ring of rolling bearing different performance degree of degeneration, 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;

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 with it;

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

Step 3 (one), each vibration signal is carried out first EMD decompose, 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, calculate again the poor E of energy scale of this original vibration signal _o, can obtain the parameter h in the formula (5);

$0<g<\frac{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">h</figure-callout>}}{2}$

In the 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 for adding the ratio coefficient of white noise, and h is the energy ratio coefficient;

Can be pushed away by formula (5)

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

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

In the EEMD method, adding white noise need satisfy condition:

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

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

In the EEMD algorithm, the amplitude that adds white noise in the original signal is excessive, can produce the false mode component in the decomposable process; If it is too small to add the amplitude of noise, might be not enough to cause that the Local Extremum of original signal changes, can not the solution pattern obscure problem; Satisfy above two conditions, key is for any discontinuous signal, and what one of how to confirm effectively added white noise in the 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 is referring to formula (5) and formula (6);

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

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

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

By formula (7) as seen, 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 the g value too hour, might 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 of the adding white noise that proposes to calculate the ratio coefficient that adds white noise by original signal first, 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 again;

In the 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 when not having enough extreme points in the signal, decomposition will stop; If extreme point distribution interval is inhomogeneous in the 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 have the equally distributed statistical property of frequency, make the signal that adds behind the noise have continuity at different scale, change the extreme point characteristic of signal by the different white noises of the equal amplitude of each adding, the corresponding IMF that afterwards EMD is repeatedly obtained carries out the white noise that population mean is offset adding again, so not only can obtain the impact that has the IMF of physical significance but also eliminated noise, effectively solution pattern is obscured problem;

The EEMD decomposition step is as described below:

(1) initialization population mean number of times L;

(2) add the numerical value amplitude for the white noise that adds, and make i _E=1;

(3) the white noise of a given amplitude

Be added on the original signal x (t), to produce a new signal

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

In the formula,

Represent i _EThe subadditive white noise sequence,

Represent i _EThe additional noise signal of inferior test, i _E=1,2 ..., L;

(4) to the signal of gained Noise

Carry out respectively EMD and decompose, 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 the formula, Be i _EDecompose the i that obtains behind the inferior adding 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, and the set that the different white noise signal of each decomposition adding amplitude obtains IMF is

$\{\left({\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">c</figure-callout>}}_{1,j_E}\left(t\right)\right),\left({\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">c</figure-callout>}}_{2,j_E}\left(t\right)\right),...,\left(c_{M,j_E}\left(t\right)\right)\}$

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 the ensemble average computing, obtains the final IMF behind the EEMD, namely

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

In the formula,

I _EThe IMF that individual employing EEMD decomposes, i _E=1,2 ..., L, j _E=1,2 ..., J.

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

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

Be provided with the real matrix B of the capable L row of K, can do following decomposition to it, be referred to as svd, namely

B=UEV ^TIn the formula, U=[u ₁... u _K] ∈ R ^{K * K}, U ^TU=I, V=[v ₁... v _L] ∈ R ^{L * L}, V ^TV=I, I are unit matrixs, 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 namely is called matrix B;

According to matrix theory as can be known, the singular value of matrix is the inherent feature of matrix, and it has preferably stability, and namely when little change occured matrix element, the singular value of matrix changed 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 the pattern-recognition, constant rate, and it can portray the feature of eigenvectors matrix B effectively; Therefore, the eigenvectors matrix that forms by the IMF after EEMD is decomposed carries out svd, and the singular value that obtains 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

$S_k=\left[\begin{array}{ccccc}{\mathrm{\&lambda;}}_{k,11},{\mathrm{\&lambda;}}_{k,12},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,1n};& {\mathrm{\&lambda;}}_{k,21},{\mathrm{\&lambda;}}_{k,22},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,2n};& {\mathrm{\&lambda;}}_{k,31},{\mathrm{\&lambda;}}_{k,32},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,3n};& \&CenterDot;\&CenterDot;\&CenterDot;;& {\mathrm{\&lambda;}}_{k,{\mathrm{<figure-callout\; id="1"\; label="N\; k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{k}1},{\mathrm{\&lambda;}}_{k,{\mathrm{<figure-callout\; id="2"\; label="N\; k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{k}2},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&lambda;}}_{k,N_{k}n}\end{array}\right]---\left(15\right)$

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

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

Step 5 (one), with 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;

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

If testing feature vector z is not included in the M zone, then

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

If z is included in the M zone and set I is sky, then

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

If z is included in the M zone and set I is not sky, then

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

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

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

If Z so ^*Be positioned at the M zone;

If

Z so ^*Be positioned at the M zone;

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 the grouping i _mAll kinds of hypersphere centre ofs sphere of each multinuclear calculation of parameter to be selected between distance: detailed process is:

For k in the feature space of the hypersphere multi-class support vector machine that improves classifying rules ₁Class hypersphere centre of sphere a ^K1To k ₂Class hypersphere centre of sphere a ^K2Square distance d ²Be defined as:

${\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">d</figure-callout>}}^2=D(a^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1},a^{k_2})={\left|\right|a^{k_1}-a^{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\left|\right|}^2=(a^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}\&CenterDot;a^{k_1})-2(a^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}\&CenterDot;a^{k_2})+(a^{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\&CenterDot;a^{k_2})---\left(12\right)$

With the k class hypersphere centre of sphere

Bring in the formula (12), can try to achieve

${\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">d</figure-callout>}}^2=\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{\mathrm{\&alpha;}}_j^{k_1}(x_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}\&CenterDot;x_j^{k_1})-2\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{\mathrm{\&alpha;}}_j^{k_2}(x_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}\&CenterDot;x_j^{k_2})+\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{\mathrm{\&alpha;}}_j^{k_2}(x_i^{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}\&CenterDot;x_j^{k_2})---\left(13\right)$

In the formula:

Be the Lagrange multiplier, i=1,2 ..., N _k

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

$d=\sqrt{\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{\mathrm{\&alpha;}}_j^{k_1}k(x_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1},x_j^{k_1})-2\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{\mathrm{\&alpha;}}_j^{k_2}k\left(x_i^{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{,x}_j^{k_2}\right)+\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{\mathrm{\&alpha;}}_j^{k_2}k\left(x_i^{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{,x}_j^{k_2}\right)}---\left(14\right)$

In the 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 the feature space that higher-dimension with low VC dimension can divide; After kernel function is selected, the then unique selection of depending on kernel functional parameter of high-dimensional feature space, and distance can be used as a kind of tolerance of classification separability in the feature space between the hypersphere centre of sphere; So derive between the hypersphere centre of sphere apart from computing formula, 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 less than the in twos number of combinations of all kinds of hyperspheres, i _m＜m (m-1)/2; If less than, execution in step D then, otherwise execution in step G;

G, find all centre of sphere spacing minimum value d that makes up in twos hypersphere _MinWith maximal value d _MaxThe time corresponding nuclear parameter value, with its optimum selection range d as nuclear parameter _Min～d _Max

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

Step 7, calculating coefficient of difference are passed 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 _pBe the element among the training sample set I in the M zone; 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 abort situation and the performance degradation degree of the abort situation of this test vibration signal and performance degradation degree and this original state hypersphere is 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:

$\left\{\begin{array}{c}{a}^k=\underset{i}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^k{x}_i^k,{\mathrm{\&alpha;}}_i^k\&NotEqual;0\\ \min {\left(R_k\right)}^2+C^k\underset{i=1}{\overset{l^k}{\mathrm{\&Sigma;}}}{\mathrm{\&epsiv;}}_i^k,s.t.{(x_i^k-a^k)}^T(x_i^k-a^k)\&le;{\left(R_k\right)}^2+{\mathrm{\&epsiv;}}_i^k\\ K(x_i^k,x_j^k)=e^{[-\frac{{(x_i^k-x_j^k)}^2}{2s^2}]}\\ {\mathrm{<figure-callout\; id="2"\; label="R\; k"\; filenames="HDA00002256257100021.png,HDA00002256257100022.png"\; state="\{\{state\}\}">R</figure-callout>}}_k^{}=D(z^{\&prime;},a^k)=\underset{i,j}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_i^k{\mathrm{\&alpha;}}_j^{k}K(x_i^k,x_j^k)-2\underset{i}{\mathrm{\&Sigma;}}{a}_i^{k}K(x_i^k,z^{\&prime;})+K(z^{\&prime;},z^{\&prime;})\\ \mathrm{if}\sqrt{D(z^{*},a^i)}\&le;R_i\mathrm{and\&beta;}\sqrt{D(z^{*},a^j)}<R_j\mathrm{or}\\ \mathrm{if}\sqrt{D(z^{*},a^j)}\&le;R_j\mathrm{and\&beta;}\sqrt{D(z^{*},a^i)}<R_i,\mathrm{then}{z}^{*}\mathrm{in\; region\; M}\end{array}\right.---\left(19\right)$

Wherein:

Be the Lagrange multiplier, i=1,2 ..., N _kS is nuclear parameter;

It is the proper vector of certain signal of k class;

Be the slack variable of introducing, z ' is the support vector on the 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, obtain proper vector according to the feature extracting method identical with the study part signal, 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 that represents 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 then to diagnose to be out of order position and performance degradation degree.

Emulation experiment is carried out in feature extraction in the inventive method (step 3): simulate signal is constructed rolling bearing inner ring spot corrosion fault model take rolling bearing spot corrosion fault as example;

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

A _i=A (cos (2 π f _rT+ φ _A)+C _A) in the formula, A _iBe the amplitude of impacting, T is for impacting the cycle that occurs, f _nBe resonant frequency, f _rFor inner ring is the inner ring failure-frequency by frequency, n (t) is additive noise.

The 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 the 1.99GHz dual core processor, using Matlab software to carry out emulation on the computing machine of internal memory 1GB.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.] (the adding noise criteria called after amplitude Criterion Method of mentioning in the document) determines two important parameters in the EEMD method with the criterion (called after energy criteria method) that this paper proposes to add noise, and the decomposition result that obtains EEMD is seen Fig. 3 and Fig. 4.IMF3 from two figure as seen, obvious modulation phenomenon is arranged, the IMF3 of Fig. 3 slightly good (all can obviously be out of order from the spectral line diagnosis if IMF3 is carried out envelope demodulation), and as can be seen from Table 1, in the situation that signal to noise ratio (S/N ratio) is with to decompose relative error identical, the noise ratio value coefficient of determining based on the energy criteria method and population mean number of times are than definite little of amplitude Criterion Method.It is also few that this (gets respectively the time after average 10 times) so that decompose the used time.Therefore, the 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 are 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, the inner ring fault is damaged diameter 0.18mm, the inner ring fault is damaged diameter 0.53mm, the outer ring fault is damaged diameter 0.18mm, the outer ring fault is damaged diameter these 5 kinds of different faults positions of 0.53mm and the performance degradation degree is carried out fault diagnosis.

Take housing washer fault damage diameter 0.18mm vibration signal as example, adopt the energy criteria method to obtain and add the white noise parameter, carry out EEMD and decompose, the result is as shown in Figure 5.In the experiment, setting e is 1%, and the α that calculates is 0.104, and the population mean number of times is 108.

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

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

Adopt 8 times of cross-validation methods that 5 class Rolling Bearing Status signals are tested.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, then all sample points all are support vectors, so s value is since 0.1 value, the artificial larger span of setting, and from 0.1 to 50, search step-length 0.5.In the process of determining hypersphere, if C＞1, then C has just lost the effect of penalty coefficient; If C＜1/N can't satisfy 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 improving classifying rules and the relation of average recognition rate.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 by these figure, have namely determined end-state hypersphere disaggregated model.

Because artificial to set the nuclear parameter scope larger, to consume learning time longer.Optimize the method for nuclear parameter in order to verify the employing hypersphere centre of sphere spacing of proposition, determine that by the hypersphere centre of sphere spacing of calculating between 5 class samples 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], as seen comparing the people 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 the hypersphere multi-class support vector machine method of utilizing same improvement classifying rules, compare document [Kang Shouqiang based on EMD in conjunction with the diagnostic method of svd, Wang Yujing, Yang Guangxue, Deng. based on the Fault Diagnosis of Roller Bearings [J] of empirical mode decomposition and hypersphere multi-class support vector machine. Proceedings of the CSEE, 2011,31 (14): 96-102.] EMD is in conjunction with the diagnostic method of Ulrych-Clayton or Yule-Walker in, not only diagnose spent time short, and average recognition rate is also high; In conjunction with the diagnostic method of svd and method based on amplitude criterion Optimal Parameters, average recognition rate is basic identical based on the EEMD of energy criteria Optimal Parameters, but the diagnosis spent time is short.And be combined the diagnostic method of svd based on EMD and compare average recognition rate and exceed nearly 1 percentage point; Adopting the hypersphere centre of sphere spacing that proposes to optimize the method for nuclear parameter selection range, approximately is 1/9th of additive method on the training time.In addition, the par of gathering training sample among the I from table can find out that there is the space that crosses really in the classification hypersphere.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.

Table 3 method for diagnosing faults relatively

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

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

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

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

(4), carry out feature extracting method based on the EEMD of the adding white noise criterion of energy in conjunction with SVD, be the highest to the discrimination of diagnosis rolling bearing different faults position and performance degradation degree, can reach 97.61% (from table 3, can find out).

(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, approximately is 1/9th (can find out from table 3) of additive method on the training time.

Claims (2)

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

Step 1, a large amount of bearing vibration signal of collection comprise the vibration signal of rolling bearing normal condition, the vibration signal of the interior ring of rolling bearing different performance degree of degeneration, 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;

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 with it;

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

Step 3 (one), each vibration signal is carried out first EMD decompose, 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, calculate again the poor E of energy scale of this original vibration signal _o, can obtain the parameter h in the formula (5);

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

In the 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 for adding the ratio coefficient of white noise, and h is the energy ratio coefficient;

Can be pushed away by formula (5)

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

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

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

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

Step 3 (three), trying to achieve on the basis of the ratio coefficient that adds noise and these two parameters of population mean number of times, each vibration signal is carried out the EEMD decomposition obtains IMF, the IMF maximum number is n in the different vibration signals, less than the additional null vector of n; N the IMF that each vibration signal is obtained forms original feature vector matrix B=[c ₁c ₂... c _n] ^T, described original feature vector matrix is carried out 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 the formula, k=1,2 ..., m, the different faults position of expression rolling bearing and the state of performance degradation degree; N _kIt is the number of k class state learning signal;

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

Step 5 (one), with 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 the grouping i _mAll kinds of hypersphere centre ofs sphere of each multinuclear calculation of parameter to be selected between distance: detailed process is:

For k in the feature space of the hypersphere multi-class support vector machine that improves classifying rules ₁Class hypersphere centre of sphere a ^K1To k ₂Class hypersphere centre of sphere a ^K2Square distance d ²Be defined as:

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

With the k class hypersphere centre of sphere

Bring in the 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 the formula:

Be the Lagrange multiplier, i=1,2 ..., N _k

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

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

In the 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 less than the in twos number of combinations of all kinds of hyperspheres, i _m＜m (m-1)/2; If less than, execution in step D then, otherwise execution in step G;

G, find all centre of sphere spacing minimum value d that makes up in twos hypersphere _MinWith maximal value d _MaxThe time corresponding nuclear parameter value, with its optimum selection range d as nuclear parameter _Min～d _Max

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

Step 7, calculating coefficient of difference are passed 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 _pBe the element among the training sample set I in the M zone; 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 abort situation and the performance degradation degree of the abort situation of this test vibration signal and performance degradation degree and this original state hypersphere is 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:

Be the Lagrange multiplier, i=1,2 ..., N _kS is nuclear parameter;

It is the proper vector of certain signal of k class;

Be the slack variable of introducing, z ' is the support vector on the 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, obtain proper vector according to the feature extracting method identical with the study part signal, 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 that represents 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 then 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, it is characterized in that: in step 3 (two), the signal decomposition relative error e of expectation gets 1%.

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