CN105275833A - CEEMD (Complementary Empirical Mode Decomposition)-STFT (Short-Time Fourier Transform) time-frequency information entropy and multi-SVM (Support Vector Machine) based fault diagnosis method for centrifugal pump - Google Patents

Abstract

The invention provides a CEEMD (Complementary Empirical Mode Decomposition)-STFT (Short-Time Fourier Transform) time-frequency information entropy and multi-SVM (Support Vector Machine) based fault diagnosis method for a centrifugal pump. The method comprises the following steps: 1, preprocessing the fault data of the centrifugal pump; 2, extracting fault features; 3, performing dimensionality reduction for the fault features; 4, automatically recognizing a fault mode through a multi-SVM classifier. Vibration signals of the centrifugal pump have the characteristics of being non-stable and low in repeatability and reproducibility, so that some traditional time domain or frequency domain based analysis methods cannot timely reflect the running conditions of a system. The CEEMD is a self-adaptive signal decomposition method and can decompose the signals into a series of intrinsic mode functions; the STFT is a time-frequency analysis method and can analyze non-stable signals; the time-frequency information entropy is a metric of the signal time-frequency distribution complexity and can reflect the fault information hidden in the signals. According to the method, the CEEMD, the STFT and the information entropy method are combined; the method is applied to the actual diagnosis experiment, and the data analysis result shows that the method is high in diagnosis accuracy.

Description

A kind of centrifugal pump fault diagnostic method based on CEEMD-STFT Time-Frequency Information entropy and multi-SVM

Technical field

The present invention relates to the technical field of centrifugal pump fault diagnosis, be specifically related to a kind of centrifugal pump fault diagnostic method based on CEEMD-STFT (complete integrated empirical mode decomposition-Short Time Fourier Transform) Time-Frequency Information entropy and multi-SVM (multi-category support vector machines).

Background technique

Over nearly 20 years, along with the develop rapidly of science and technology, Diagnosis Technique is ripe gradually, and it is as a New borderline subjects, flourish in integration engineering field.As a kind of basic measures ensureing equipment safety operation, fault diagnosis can the initial failure development level of effective HERALD equipment, judges the reason that fault is formed, analyzes inducement and also propose countermeasure and suggestion, existing hidden danger is processed, to avoid or the generation of minimizing accident.After entering 21 century, along with the development of science and technology, the progress of industrial production technology, modern comfort is to complex structure, intensive, and high degree automatically, multifunctional direction develops.The problem once equipment breaks down, its predetermined function not only can reduce, and probably can lose, even cause serious accident, and even the loss that cannot retrieve.

Centrifugal pump, as a kind of key equipment, is widely used in petrochemical industry, metallurgy, machinery, electric power and defense industrial sector.Along with the raising of development in science and technology and modern industrial equipment automaticity, the contact between each equipment is also more and more tightr, and speed up, continization, maximization, centralization and automation are just becoming the direction of centrifugal pump development.The complex structure of centrifugal pump, under being operated in the mal-condition of high temperature, high speed, adds the impact of various enchancement factor, easily various mechanical failure occurs, its function is reduced.Once centrifugal pump breaks down in production system, will chain reaction be caused, seriously can cause the paralysis of device damage and even production system, cannot normally work, cause tremendous economic to lose to enterprise and society.Therefore, the fault diagnosis technology of research centrifugal pump is very important, has substantial economics to social progress and economic development, is one of important subject of science and technology and industrial development.

In rotating machinery, status information of equipment is hidden in rotor oscillation signal, the information of the various exception of the equipment that contains or fault, and vibration parameters is the important indicator extracting fault signature.For the rotating machinery of running continuously, can gather the oscillating signal of its running state of reflection, in non-stop-machine situation, adopt Method of Vibration Diagnosis to realize monitoring and fault diagnosis; To static device and engineering structure, apply external artificial stimulation, play dynamic effect, then according to reflecting the response of behavioral characteristics, analyzing and diagnosing, and then the object reaching faut detection.Research practice before shows, using the monitoring and fault diagnosis basis of oscillating signal as large-scale operational outfit, can reach the object to equipment failure and diagnosis, thus save a large amount of maintenance expenses, obtain significant economic benefit.

Summary of the invention

The technical problem to be solved in the present invention is: centrifugal pump vibration signal has features such as containing much information, non-stationary, reproducibility are not good, makes some analytical methods based on conventional Time-domain or frequency domain cannot reflect the operation conditions of system in time.

The technical solution used in the present invention is: a kind of centrifugal pump fault diagnostic method based on CEEMD-STFT Time-Frequency Information entropy and multi-SVM, and the step of the method is as follows:

The first step, centrifugal pump fault data prediction;

Second step, fault signature extracts: first, use CEEMD decomposition method, pretreated signal adaptive is decomposed into a series of mode component (IMFs), mode component arranges from high to low by frequency, radio-frequency component includes main fault message, extracts top n IMF component and is further analyzed; Secondly, Short Time Fourier Transform (STFT) is done respectively to this N number of IMF component, extracts N number of time-frequency matrix comprising fault signature Time-Frequency Information respectively; Finally, according to the definition of Time-Frequency Information entropy, extract the Time-Frequency Information entropy of these time-frequency matrixes, so far, obtain a N be made up of N number of multiple dimensioned Time-Frequency Information entropy and tie up fault feature vector;

3rd step, fault signature dimension about subtracts;

4th step, identifies fault mode automatically with multi-SVM classifier: first, fault signature File is divided into training data and test data two-part; Secondly, use training data training multi-class support vector machine (multi-SVM) model, obtain the parameter of model; Finally, test data is input in the sorter model trained, goes out fault mode label corresponding to this characteristic by model prediction, complete fault diagnosis.

Wherein, in first step centrifugal pump fault data prediction, for improving quality and the efficiency of follow-up data process, removing the abnormal data in initial data, and being normalized.

Wherein, in second step, extraction top n IMF component is further analyzed middle N and is specially 6.

Wherein, in 3rd step, for improving the efficiency of computing, the degree of accuracy of pattern recognition and robustness, dimension must be carried out to characteristic vector and about subtracting, use principal component analysis (PCA) method to carry out dimensionality reduction to 6 dimensional feature vectors, obtain 3 dimensional feature vectors being convenient to visual analyzing.

The present invention's advantage is compared with prior art:

(1), the present invention uses CEEMD method to carry out adaptive decomposition to signal and get top n mode component carrying out subsequent analysis, the modal overlap problem that can effectively suppress EMD to decompose, thus contributes to extracting multiple dimensioned intrinsic malfunction feature;

(2), the present invention carries out STFT to top n mode component and analyzes the time-frequency characteristics comprising a large amount of fault message that can effectively extract in non-stationary mode component;

(3), the time-frequency distributions complexity of the present invention's application Time-Frequency Information entropy measure signal different scale, carry out fault diagnosis in this, as characteristic vector, diagnostic accuracy is high, and robustness is good.

Accompanying drawing explanation

Fig. 1 is the diagnostic flow chart of a kind of centrifugal pump fault diagnostic method based on CEEMD-STFT Time-Frequency Information entropy and multi-SVM of the present invention;

Fig. 2 is EMD algorithm flow chart;

Fig. 3 is the definition of Time-Frequency Information entropy;

Fig. 4 is the Optimal Separating Hyperplane in linear separability situation;

Fig. 5 is centrifugal pump data acquistion system;

Fig. 6 is front 6 IMF components of each fault mode, wherein, Fig. 6 (a) is nominal situation, Fig. 6 (b) is bearing inner ring fault, Fig. 6 (c) is outer race fault, Fig. 6 (d) is bearing roller fault, and Fig. 6 (e) is impeller failure;

Fig. 7 is the sound spectrograph of the IMF1 component of each fault mode, wherein, Fig. 7 (a) is nominal situation, Fig. 7 (b) is bearing inner ring fault, Fig. 7 (c) is outer race fault, Fig. 7 (d) is bearing roller fault, and Fig. 7 (e) is impeller failure;

Fig. 8 is fault feature vector dendrogram.

Embodiment

The present invention is further illustrated below in conjunction with accompanying drawing and specific embodiment.

1, based on the introduction of the centrifugal pump fault diagnostic method embodiment of CEEMD-STFT Time-Frequency Information entropy and multi-SVM

1.1 based on the flow process of the centrifugal pump fault diagnostic method of CEEMD-STFT Time-Frequency Information entropy and multi-SVM

The fault diagnosis flow scheme that this method proposes as shown in Figure 1, comprises data prediction, feature extraction, dimension altogether and about subtracts and pattern recognition 5 major components, specific as follows:

The first step, data prediction.For improving quality and the efficiency of follow-up data process, removing the abnormal data in initial data, and being normalized.

Second step, fault signature extracts.First, use CEEMD decomposition method, pretreated signal adaptive is decomposed into a series of mode component, mode component arranges from high to low by frequency, radio-frequency component includes main fault message, and therefore we extract front 6 IMF components and are further analyzed; Secondly, Short Time Fourier Transform (STFT) is done respectively to these 6 IMF components, extract the time-frequency matrix comprising fault signature Time-Frequency Information; Finally, according to the definition of Time-Frequency Information entropy, extract the Time-Frequency Information entropy of 6 time-frequency matrixes.So far, we obtain a fault feature vector be made up of 6 multiple dimensioned Time-Frequency Information entropys.

3rd step, fault signature dimension about subtracts.For improving the efficiency of computing, the degree of accuracy of pattern recognition and robustness, dimension must be carried out to characteristic vector and about subtracting.We use primary coil to divide (PCA) method to carry out dimensionality reduction to 6 dimensional feature vectors, obtain 3 dimensional feature vectors being convenient to visual analyzing.

4th step, identifies fault mode automatically with multi-SVM classifier.First, fault signature File is divided into training data and test data two-part; Secondly, use training data training multi-class support vector machine (multi-SVM) model, obtain the Optimal Parameters of model; Finally, test data is input in the sorter model trained, goes out fault mode label corresponding to this characteristic by model prediction, complete fault diagnosis.

1.2 based on the feature extraction of CEEMD-STFT Time-Frequency Information entropy

1.2.1 complete integrated empirical mode decomposition (CEEMD) principle

1.2.1.1 empirical mode decomposition (EMD)

Empirical mode decomposition (Empiricalmodedecomposition, EMD) Time Series is become a series of and be called as intrinsic mode function (Intrinsicmodefunction, IMF) simple component signal, a simple component signal represents the oscillating function that is similar to the most basic the most general harmonic function.Each IMF has different frequency components, to contain in signal by being up to minimum frequency component, has the potential of instruction different faults information.They need meet two conditions:

The first, in signal, extreme point is identical with the number of Zero Crossing Point or differ one at the most; The second, for any point on signal, the average of the envelope defined respectively by local maximum and local minimum is zero.For oscillation data, first condition is very necessary with the restriction of the stringent condition of satisfied calculating instantaneous frequency, namely provides the oscillation frequency of signal at specific time point.The upper lower envelope of second conditional request IMF, to relative to time shaft Local Symmetric, makes signal can modulate along with the IMF decomposed out.

EMD is based on following 3 hypothesis:

(1) signal has a minimum and a maximum (Non-monotonic function) at least;

(2) time difference between continuous threshold point defines characteristic time scale;

(3) if only have flex point and do not have extreme point, data will by differential, then applies EMD method and by the component integration that obtains to obtain final result.

The decomposition process of EMD method is by the composition of signal highest frequency, and the frequency range of decomposing the IMFs obtained one by one reduces successively.Decomposition method by cubic spline interpolation build burst local maximum and local minimizing envelope, in calculating lower envelope average and remove from primary signal.And remaining official post same procedure is repeated till the average envelope at each point place reasonably goes to zero, resulting in first IMF.From primary signal, deduct first IMF, use identical screening method to decomposite other IMF one by one, stop when residual signals amplitude is very little or become dullness decomposing.Accordingly, we can sum up corresponding arthmetic statement:

(1) initialization: r ₀(t)=x (t), i=1;

(2) i-th intrinsic mode function IMF is asked _i=c _i(t):

(a) initialization: h ₀(t)=r _i-1(t), j=1;

B () finds out h _j-1whole Local Extremum of (t);

(c) application cubic spline interpolation interpolation fitting h respectively _j-1t the very big and minimum point of (), tries to achieve lower envelope e ₊(t) and e _-(t), and calculate its average $m_{j-1}\left(t\right)=\frac{1}{2}\[e_{+}\left(t\right)+e_{-}\left(t\right)\];$

D () therefrom deducts the average of envelope, try to achieve h _j(t)=h _j-1(t)-m _j-1(t);

E () judges whether the condition of convergence meets, if meet, have c _i(t)=h _i(t); If do not meet, make j=j+1, return step (2);

(3)r _i(t)＝r _i-1(t)-c _i(t)；

If r _it the extreme point number of (), more than 1, orders i=i+1, return step (2), otherwise decomposed.

Fig. 2 gives the flow chart of EMD algorithm.

1.2.1.2 integrated empirical mode decomposition (EEMD)

The statistics that the people such as Flandrin decompose white noise experiment by EMD shows, white noise decomposites its equally distributed each frequency component through EMD regularity, and EMD shows its effective binary filter group characteristic.By utilizing the binary filter group characteristic of EMD method, we can set its cutoff frequency, reach the effect of compartment break signal, reduce the impact of modal overlap to a certain extent.But this threshold value is excessive by subjective impact, chooses and too smallly filtering can have the signal of practical significance, cannot recovering signal nature; If choose excessive, can be disturbed by other insignificant frequency components, make result distortion.Huang etc. artificially solve modal overlap problem and propose intermittent test (IntermittencyTest), and namely choose chopper frequency in advance, the IMF upper cycle limit after decomposition is fixed, and frequency drops on particular range.The adaptive characteristic of EMD has been run counter in this test, and needs have suitable understanding just can select suitable yardstick to data information.Based on above problem, Wu and Huang proposes overall experience mode decomposition (EnsembleEmpiricalModeDecomposition, EEMD), EMD algorithm is improved, by adding white Gaussian noise in primary signal before decomposition, utilize the frequency spectrum uniform distribution properties of white Gaussian noise, effectively solve modal overlap problem.

EEMD adds white Gaussian noise to primary signal, regard the combination of useful signal and noise as one totally, according to the equally distributed characteristic of white noise spectrum, the signal component of different scale is made automatically to be distributed to suitable reference yardstick, and utilize zero mean noise characteristic, after repeatedly adding general average, noise is cancelled out each other.The ratio of the white Gaussian noise that EEMD needs chosen in advance to add and add the number of times of general average.If totalling average time is n, then can produce n same percentage, the different white Gaussian noise realized, this n white noise to be added to respectively in n primary signal and to carry out EMD decomposition, the n group IMF obtained being added general average and namely obtains the final result that EEMD decomposes.Add the impact that IMF that general average makes to obtain decreases modal overlap phenomenon, the signal of Different time scales is no longer dissolved in same IMF.

We can be following three steps the arthmetic statement of EEMD:

(1) x is generated ⁱ[n]=x [n]+w ⁱ[n], wherein w ⁱ[n], i=1 ..., I is that the difference of white Gaussian noise realizes;

(2) each x ⁱ[n], i=1 ..., I decomposes the mode obtaining them by EMD wherein k=1 ..., K represents rank number of mode;

Specify for a kth mode of x [n], thus obtain corresponding average be:

1.2.1.3 complete integrated empirical mode decomposition (CEEMD)

The core concept of EEMD is that the mode obtaining after with the addition of the primary signal EMD of white Gaussian noise carries out adding general average, and this decomposition method solves the modal overlap problem of EMD.But it have also been introduced new problem, the reconstruction signal containing residual noise realization different from signals with noise may produce different mode quantity, and the summation of IMF does not perfectly reconstruct primary signal.Based on above problem, within 2011, Torres proposes a kind of variant of EEMD algorithm, can add a specific noise, and calculate a unique residual error to obtain each mode at the every one-phase decomposed.

CEEMD (Completeensembleempiricalmodedecomposition) is the same with EEMD, is also a kind of noise householder method.Wherein, the acquiring method of first IMF is identical with EEMD method.Definition operator E _j(.), when a given signal, tries to achieve a jth mode by EMD.W ⁱthe white Gaussian noise of the zero-mean having unit variance, ε _kcoefficient allows to select signal to noise ratio in each stage.If x is target signal, then the step of CEEMD is as described below:

First, use different noise to realize by EMD repetitive assignment process I time, calculated population mean value is also defined as the IMF of target signal x ₁.That is,

${\mathrm{IMF}}_1=\frac{1}{I}\underset{i=1}{\overset{I}{\Σ}}{E}_1(x+{\mathrm{\ϵ}}_0{w}^i)---\left(1\right)$

Then, calculate single order residual error,

r ₁＝x-IMF ₁(2)

Continue decomposition and realize r ₁+ ε ₁e ₁(w ⁱ), wherein i=1 ..., I, until first the IMF condition meeting them, and to define population mean be second IMF:

${\mathrm{IMF}}_2=\frac{1}{I}\underset{i=1}{\overset{I}{\Σ}}{E}_1(r_1+{\mathrm{\ϵ}}_1{E}_1\left(w^i\right))---\left(3\right)$

To k=2 ..., K, calculates k rank residual error: r _k=r _k-1-IMF _k, then extract r _k+ ε _ke _k(w ⁱ) first IMF component, wherein i=1 ..., I, and calculate their population mean thus obtain the IMF of target signal _k+1:

${\mathrm{IMF}}_{k+1}=\frac{1}{I}\underset{i=1}{\overset{I}{\Σ}}{E}_1(r_k+{\mathrm{\ϵ}}_k{E}_k\left(w^i\right))---\left(4\right)$

Continue screening process until the residual error obtained can not be decomposed (when the extreme value of residual error is no more than at most two) again, then obtain:

$R=x-\underset{k=1}{\overset{K}{\Σ}}{\mathrm{IMF}}_k---\left(5\right)$

Wherein R is final residual error, and K is the sum of IMF.Therefore, target signal can be expressed as:

$x=\underset{k=1}{\overset{K}{\Σ}}{\mathrm{IMF}}_k+R---\left(6\right)$

Above formula shows, primary signal obtains accurate reconstruct, and the method is a complete decomposition method.

1.2.2 Short Time Fourier Transform (STFT) basic principle

The basis of classical signal frequency analysis is Fourier transformation (Fouriertransform, FT), and the Fourier transformation of definition signal x (t) is:

X(ω)＝∫x(t)e ^-iωtdt(7)

X (ω) is the frequency spectrum of x (t).In formula, t is the time, and w is angular frequency.Its inverse transformation is defined as:

x(t)＝∫X(ω)e ^iωtdω(8)

Signal is converted into frequency domain by Fourier transformation, and signal becomes again to time-domain by Fourier inversion, makes analytic signal in time and frequency become possibility, in signal analysis, has critical role.But it lacks local message, can only provide the spectrum energy of signal entirety, cannot reflected signal frequency spectrum over time.Short Time Fourier Transform (Short-timeFourierTransform, STFT) develop on the basis of Fourier transformation, during application, signal is intercepted segmentation by window, and hypothesis time window within data be stable, more respectively successively Fourier transformation is carried out to these windowed data.Then signal is x (τ), and time histories sample is that the STFT of w (τ) can be expressed as:

F(t,ω)＝∫x(τ)w(τ-t)e ^-jωtdτ(9)

Because the displacement of time histories sample w (τ) makes STFT possess local characteristics, it is the function of time, is also the function of frequency.Can be considered as certain moment t, F (t, ω) " local spectrum " in this moment.Time-frequency energy spectrum is commonly used to the time-frequency distributions describing signal, is defined as the mould of STFT, that is:

S(t,ω)＝|F(t,ω)| ²(10)

Wherein, F (t, ω) is the signal complex number spectrum obtained through STFT, and S (t, ω) is time-frequency energy spectrum.

STFT can be written as in the inverse transformation of time domain:

x(τ)＝∫∫F(t,ω)w(τ-t)e ^jωtdωdt(11)

STFT is the frequency spectrum after signal windowing, and the signal characteristic being thus positioned at the local time's window width centered by t all can show at F (t, ω).Time being added in a lot of signal analysis of window can bring us directly perceived and understandable result, in window, signal is exaggerated, and signal is suppressed outside window, thus realizes partial analysis to signal.

Spectrogram algorithm is a kind of parser obtaining signal Short Time Fourier Transform (STFT), and the two dimensional image form that it produces one-dimensional signal exports---sound spectrograph (simultaneously also can obtain numerical matrix).Sound spectrograph n service time does abscissa, and the value of energy density spectral function, as y coordinate, is expressed as the pcolor of two dimension by frequency f.The time-frequency figure of this reaction signal dynamic spectrum characteristic has important use value in signal analysis, is also referred to as " visual language ".

Some frequecny domain analysis parameter (as resonance peak, pitch period etc.) situations over time can be obtained from sound spectrograph; Can also obtain energy situation over time, pseudo-color-values (or gray value) size of each pixel of image represents the signal energy density of corresponding moment, corresponding frequencies.

1.2.3 Time-Frequency Information entropy

The mathematical definition of entropy of information is: establish p (p ₁, p ₂..., p _n) be a uncertain probability distribution, k is arbitrary constant, is generally taken as 1, then the entropy of information that this distribution has is defined as:

$s\left(p\right)=-k\underset{i=1}{\overset{N}{\Σ}}{p}_i{\mathrm{lnp}}_i---\left(12\right)$

The size of entropy of information can be used for describing the average uncertainty degree of probability system.If the probability that in a certain probability system, a certain event produces is 1, the probability that other events produce is 0, after being calculated from formula (12), the entropy of information s=0 of this system, because of but a certainty annuity, uncertainty is 0.If in a certain system, its probability distribution is uniform, then in expression system each event produce probability equal, the entropy of information of this system has maximum value, namely this system uncertainty maximum.Theoretical according to this, the most uncertain probability distribution has maximum entropy, and information entropy reflects the uniformity of its probability distribution.

The time-frequency distributions of signal is the energy changing describing signal each frequency place within the sampling time, and the time-frequency distributions of same centrifugal pump under different operating state is often different, in order to this difference degree of quantitative description, is incorporated in time-frequency distributions by information entropy theory.The difference of unlike signal in time-frequency distributions shows as the difference of the energy distribution of fritter time-frequency fragments different on time-frequency plane, the uniformity of each time-frequency district energy distribution then reflects the difference of state of runtime machine, and entropy of information is the tolerance of probability distribution uniformity coefficient.As shown in Figure 3, time-frequency plane is divided into the time-frequency block of N number of area equation by us, and the energy in every block is W _i(i=1 ..., N), the energy of whole time-frequency plane is A, carries out energy normalized, obtain q to every block _i=W _i/ A (i=1 ..., N), so just have the initial normalizing condition of according calculation entropy of information, copies the formula of entropy of information, and the formula of the Time-Frequency Information entropy of signal is defined as:

$s\left(q\right)=-\underset{i=1}{\overset{N}{\Σ}}{q}_i{\mathrm{lnq}}_i---\left(13\right)$

1.3 based on the pattern recognition of multi-category support vector machines (multi-SVM)

1.3.1 support vector machine basic theories

The core of support vector machine (SVM) is structure optimal hyperlane.Its basic thought may be summarized to be: input vector is mapped to a high-dimensional feature space by the Nonlinear Mapping (kernel function) first selected in advance by certain, then in feature space, optimal separating hyper plane is found, two class data points correctly can be separated by as much as possible, make two class data point distance classification faces separately farthest (as shown in Figure 4) simultaneously.

1.3.2 two category support vector machines

Suppose to there is training sample { x _i, y _i, i=1,2 ..., l; x _i∈ R ⁿ, y _i∈ {-1,1}; L is sample number, and n is input dimension.When linear separability, have an Optimal Separating Hyperplane, two class samples separated completely:

<w.x _i>+b＝0(14)

Solving Optimal Separating Hyperplane is exactly find the weight w of given training sample and the optimum value of threshold value b, therefore can be summed up as following quadratic programming problem:

$\left\{\begin{array}{cc}min& \frac{1}{2}\left|\right|w|{|}^2\\ s.t.& y_i\left(<w.x_i>+b\right)\&GreaterEqual;0,i=1,2,...,l.\end{array}\right.---\left(15\right)$

By solving the dual problem of above-mentioned quadratic programming, corresponding optimum a can be found ^*, a ^*the sample of ≠ 0 correspondence is called support vector.The positive component selected and calculate accordingly obtaining decision function is thus:

$F\left(x\right)=\mathrm{sgn}\&lsqb;\underset{i=1}{\overset{l}{\&Sigma;}}{a}_i^{*}{y}_i<x_i.x>+b^{*}\&rsqb;---\left(16\right)$

In linearly inseparable situation, slack variable ξ can be introduced _iwith punishment parameter C, this pattern (2) just becomes:

$\left\{\begin{array}{c}\begin{array}{cc}min& \frac{1}{2}\left|\right|w|{|}^2+C\underset{i=1}{\overset{l}{\&Sigma;}}{\mathrm{\&xi;}}_i,\\ s.t.& y_i\left(<w.x_i>+b\right)\&GreaterEqual;1-{\mathrm{\&xi;}}_i,\end{array}\\ {\mathrm{\&xi;}}_i\&GreaterEqual;0,i=1,2,...,l.\end{array}\right.---\left(17\right)$

For linearly inseparable problem, by introducing a nonlinear mapping function sample is mapped to certain higher dimensional space, is translated into linear classification problem in attribute space.As long as function K is (x _i, x) meet Mercer condition, can as kernel function, and according to Mercer condition, adopt in optimal classification surface different in Product function K (x _i, x) just can realize the linear classification of a certain nonlinear transformation.Introduce after kernel function, above various in inner product can replace by kernel function.

In like manner, by solving the quadratic programming dual problem under linearly inseparable condition, the categorised decision function that can obtain under linearly inseparable condition is:

$F\left(x\right)=\mathrm{sgn}\&lsqb;\underset{i=1}{\overset{l}{\&Sigma;}}{a}_i^{*}{y}_{i}K\left(x_i,x\right)+b^{*}\&rsqb;---\left(18\right)$

At present, conventional kernel function has: linear kernel function, Polynomial kernel function, Radial basis kernel function and Sigmoid kernel function.Support vector machine proposes for two classification problems in essence, but two sorting techniques can not meet the needs of practical problem far away.Along with the continuous popularization on theoretic investigation and application, engender multi-category support vector machines.

1.3.3 multi-category support vector machines

Multi-category support vector machines algorithm is mainly by combining two category support vector machines to realize.At present, the many sorting techniques based on support vector machine mainly contain: in pairs classification, a class is to remaining class method, error correcting output codes method and determine multi-class targets functional based method etc.Conventional in practical problem is that paired classification and a class are to remaining class method.This research mainly adopts paired classification.

Suppose that training sample set is S={ (x ₁, y ₁), (x ₂, y ₂) ..., (x _l, y _l).Wherein l is training sample set scale, x _i∈ R ⁿfor n dimensional feature vector, y _i∈ 1,2 ..., k} is the grade that the i-th class sample is corresponding.

Paired classification is exactly construct a classifier f with two kinds of different classes of samples _ij(i ≠ j), the combination of two that such limit is all, just can obtain individual sub-classifier.As to the i-th class and following two classification problems of jth class solution:

$\left\{\begin{array}{c}\begin{array}{cc}\underset{{\mathrm{\&omega;}}^{i,j},b^{i,j},{\mathrm{\&xi;}}^{i,j}}{\min }& \frac{1}{2}\left|\right|w^{i,j}|{|}^2+C\&lsqb;\underset{i=1}{\&Sigma;}{\mathrm{\&xi;}}_t^{i,j}\&rsqb;,\\ s.t.& \&lsqb;(w^{i,j}.x_t)+b^{i,j}\&rsqb;-1+{\mathrm{\&xi;}}_t^{i,j}\&GreaterEqual;0,\end{array}\\ \begin{array}{cc}if& y_t=i,\end{array}\\ \&lsqb;(w^{i,j}.x_t)+b^{i,j}\&rsqb;-1+{\mathrm{\&xi;}}_t^{i,j}\&le;0,\\ \begin{array}{cc}if& y_t=j,{\mathrm{\&xi;}}_t^{i,j}\&GreaterEqual;0.\end{array}\end{array}\right.---\left(19\right)$

When the sample x of unknown category attribute is tested, use k (k-1)/2 sub-classifier to carry out attribute differentiation to it respectively, and take following temporal voting strategy: if classifier f _ijjudge that x belongs to the i-th class, then the number of votes obtained of the i-th class adds 1, otherwise the number of votes obtained of jth class adds 1, and finally see which kind of number of votes obtained is maximum, which kind of x just belongs to.

2 application cases

2.1 initial data prepare

This research institute from centrifugal pump data acquistion system as shown in Figure 5, obtains centrifugal pump vibration signal by acceleration transducer with the sample rate of 10.24kHz by data.In test, 5 kinds of common centrifugal pump fault patterns are set, i.e. nominal situation, centrifugal pump bearing inner ring fault, outer race fault, bearing roller fault and centrifugal pump impeller fault.To each fault mode, be one group with the data of 1024 sampled points, intercept 20 groups.

2.2 based on the foundation of the centrifugal pump fault diagnostic model of CEEMD-STFT Time-Frequency Information entropy and multi-SVM

2.2.1 complete integrated empirical mode decomposition (CEEMD)

CEEMD optimum configurations is as follows: noise standard difference (Nstd) 0.2, integrated number of times (Ne) 600, screening maximum iteration time (MaxIter) 5000.

To the data of each fault mode, utilize CEEMD method to carry out the decomposition of signal, extract the multi-scale information of oscillating signal, obtain a series of IMF component.Front 6 IMF components of the vibration data under these 5 kinds of fault modes of centrifugal pump nominal situation, bearing inner ring fault, outer race fault, bearing roller fault and impeller failure respectively as shown in Figure 6.

2.2.2 Short Time Fourier Transform (STFT)

In this research, STFT optimum configurations is as follows: frame length (window) 512, slip length (noverlap) 510, discrete Fourier transform length (nfft) 512 (equal with window length), sample frequency fs=10.24kHz generates sound spectrograph.

The time-frequency matrix (sound spectrograph) of each fault mode as shown in Figure 7.

2.2.3 Time-Frequency Information entropy (SFIE) is extracted

The optimum configurations of Time-Frequency Information entropy is: time-frequency block length 64, wide by 64, horizontal sliding 32, straight skidding 32 (unit is 1 row or 1 row).

Extract 6 dimension Time-Frequency Information entropys as fault feature vector to the time-frequency matrix of each fault mode, result is as shown in table 1.

Table 1 fault feature vector File

2.2.4 characteristic dimension about subtracts

For improving degree of accuracy and the robustness of fault diagnosis, we do dimension to above-mentioned 6 dimension fault signature Time-Frequency Information entropys and about subtract, and obtain 3 dimension fault feature vectors as shown in table 2.Fig. 8 intuitively illustrates the Clustering Effect of the fault feature vector extracted, and as shown in Figure 6, the centrifugal pump fault feature extracting method originally researched and proposed has extracted faulty intrinsic feature, has good classification performance.

Fault feature vector File after table 2 dimensionality reduction

2.2.5 based on the pattern recognition of multi-SVM

In this research, we adopt multi-SVM as classifier to realize the automatic identification of fault mode.First, training data and test data is divided into by extracting the fault signature File obtained; Secondly, training data training multi-SVM classifier is adopted; Finally, with the faulty tag of the sorter model identification test data trained, and Fault Identification accuracy rate is obtained.

The classification results of test data is as shown in table 3.

Table 3 test data classification results

The present invention comprehensive CEEMD adaptive decomposition, STFT time frequency analysis and information entropy theory propose a kind of new centrifugal pump fault feature extracting method, are then automatically to identify that fault mode adopts multi-SVM as fault grader.The method of proposition is applied to experimental analysis, and result shows the Fault-Sensitive information that the method can extract centrifugal pump, has high diagnostic accuracy and good robustness.

Claims (4)

1., based on a centrifugal pump fault diagnostic method of CEEMD-STFT Time-Frequency Information entropy and multi-SVM, it is characterized in that: the step of the method is as follows:

The first step, centrifugal pump fault data prediction;

Second step, fault signature extracts: first, use CEEMD decomposition method, pretreated signal adaptive is decomposed into a series of mode component (IMFs), mode component arranges from high to low by frequency, radio-frequency component includes main fault message, extracts top n IMF component and is further analyzed; Secondly, Short Time Fourier Transform (STFT) is done respectively to this N number of IMF component, obtains N number of time-frequency matrix comprising fault signature Time-Frequency Information respectively; Finally, according to the definition of Time-Frequency Information entropy, extract the Time-Frequency Information entropy of these time-frequency matrixes, so far, the N obtaining being made up of the Time-Frequency Information entropy of this N number of different scale ties up fault feature vector;

3rd step, fault signature dimension about subtracts;

4th step, identifies fault mode automatically with multi-SVM classifier: first, fault signature File is divided into training data and test data two-part; Secondly, use training data training multi-category support vector machines (multi-SVM) model, obtain the parameter of sorter model; Finally, test data is input in the sorter model trained, goes out fault mode label corresponding to this characteristic by model prediction, complete fault diagnosis.

2. a kind of centrifugal pump fault diagnostic method based on CEEMD-STFT Time-Frequency Information entropy and multi-SVM according to claim 1, it is characterized in that: in first step centrifugal pump fault data prediction, for improving quality and the efficiency of follow-up data process, remove the abnormal data in initial data, and be normalized.

3. a kind of centrifugal pump fault diagnostic method based on CEEMD-STFT Time-Frequency Information entropy and multi-SVM according to claim 1, is characterized in that: in second step, and extract top n IMF component and be further analyzed, wherein N is specifically taken as 6.

4. a kind of centrifugal pump fault diagnostic method based on CEEMD-STFT Time-Frequency Information entropy and multi-SVM according to claim 1, it is characterized in that: in the 3rd step, for improving the efficiency of computing, the degree of accuracy of pattern recognition and robustness, dimension must be carried out to characteristic vector about to subtract, use primary coil to divide (PCA) method to carry out dimensionality reduction to this 6 dimensional feature vector, obtain 3 dimensional feature vectors being convenient to visual analyzing.