CN106778694A - A kind of gear transmission noises analysis method based on set empirical mode decomposition and SVMs - Google Patents

A kind of gear transmission noises analysis method based on set empirical mode decomposition and SVMs Download PDF

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CN106778694A
CN106778694A CN201710036850.0A CN201710036850A CN106778694A CN 106778694 A CN106778694 A CN 106778694A CN 201710036850 A CN201710036850 A CN 201710036850A CN 106778694 A CN106778694 A CN 106778694A
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陈洪芳
孙衍强
石照耀
王亚韦
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Beijing University of Technology
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Abstract

A kind of gear transmission noises analysis method based on set empirical mode decomposition and SVMs, the fluctuation of different time scales or trend in gear transmission noises signal are disassembled step by step to come first with set empirical mode decomposition method, one group of intrinsic mode functions IMF is obtained.To the useful component of gear transmission noises signal for extracting, found from set empirical mode decomposition result and be reconstructed comprising nibbling frequency component, and Synchronous time average is carried out with the swing circle of gear, and do time continuation treatment and turn the unrelated signal of frequency with gear to weaken.The characteristic parameter for the treatment of backgear actuating signal is calculated, and chooses one group of characteristic parameter for differing greatly as characteristic vector.It is divided into two groups using characteristic vector as sample, two groups of numbers of samples are equal, respectively as training sample and test sample.The present invention artificially need not be participated in excessively, it is ensured that the accuracy of analysis；Intelligent analysis method based on SVMs, the recognition accuracy to transmission properties is high and quick.

Description

A kind of gear transmission noises based on set empirical mode decomposition and SVMs point Analysis method
Technical field
The present invention relates to a kind of gear transmission noises analysis method, be based particularly on set empirical mode decomposition (EEMD) and The gear transmission noises analysis method of SVMs (SVM).Belong to gear transmission noises measurement and fault diagnosis field.
Background technology
Gear transmission noises signal analysis, is mainly used in Gear Fault Diagnosis.Analysis process is applied to non-stationary signal Denoising, useful signal is extracted, the field such as signature analysis and Intelligent Recognition.Signal denoising and useful signal are extracted and are directly connected to spy Levy the correctness of analysis and Intelligent Recognition.
Traditional signal spectral analysis method, is mainly based upon Fast Fourier Transform (FFT), or based on time series models Analysis of spectrum, the precondition of both approaches assumes that signal is stable.But for gear drive process, signal often right and wrong It is stable or nonlinear, if still define data and being steady or linearly being calculated, the analysis result of mistake can be obtained.In order to The non-stationary fault characteristic signals of gear are extracted, Gearbox vibration signal is launched in time-frequency domain plane, observe m- frequency at that time Rate variation characteristic, is the important research direction of Gear Fault Diagnosis, and conventional method has a wavelet transformation, empirical mode decomposition and Wigner-Ville conversion etc..Wang and McFadden utilizes the local feature of wavelet transformation analysis vibration signal, wavelet transformation The signal of large scale and small yardstick can be simultaneously adapted to, distributed and local fault is able to detect that, but wavelet analysis is relied on In the selection of basic function, the difficulty of analysis is increased, be additionally present of temporal resolution and frequency resolution can not be while reach most Good problem.The method based on empirical mode decomposition (EMD) that Huang et al. is proposed is applied among Gear Fault Diagnosis, but There is a problem of natural mode of vibration Boundary Distortion.Wigner-Ville distribution is a kind of bilinearity distribution, double in its calculating process Linear distribution can cause the cross term interference between different components to be difficult to frequency spectrum.
A kind of patent name " gear transmission noises analysis method based on Fourier Transform of Fractional Order and SVMs (application number：Patent of invention 201510053013X) ", it is proposed that carry out gear event using the method for Fourier Transform of Fractional Order Hinder the extraction of feature and be trained identification using support vector machine method.Gear transmission noises signal is in a certain specific fraction Rank Fourier transform domain shows energy accumulating characteristic, can retain the useful signal component relevant with failure；Though the method has Having many special performances cannot but characterize signal local feature, and this causes certain for the feature extraction of gear distress signal Limitation.
Set empirical mode decomposition (Ensemble empirical mode decomposition, EEMD) be directed to through Test a kind of not enough noise assistance data for proposing of mode decomposition (Empirical mode decomposition, EMD) method Analysis method.Its core concept is the characteristic that make use of white noise that there is frequency-flat to be distributed, and white noise is added on signal After so that primary signal is provided with continuity on different time scales, changes the distribution character of extreme point, so that effectively The modal overlap phenomenon of EMD presence is avoided, the ambient noise signal unrelated with failure can be efficiently separated, retained relevant with failure Useful signal component.
It is necessary a kind of gear transmission noises analysis based on set empirical mode decomposition and SVMs of invention for this Method, effectively extracts fault characteristic information, improves the efficiency and precision of gear transmission noises measurement and fault diagnosis.
The content of the invention
The gear transmission noises signal analysis method of technology, it is therefore an objective to provide a kind of based on set empirical mode decomposition and branch Gear transmission noises measurement and the method for diagnosing faults of vector machine combination are held, enables rapidly to enter gear in production scene Row signal analysis simultaneously judges the quality and fault type of gear accordingly.This method has the spies such as high precision, quick and intelligent and high-efficiency Point.
To achieve the above objectives, the present invention is adopted the following technical scheme that and is achieved：
Fig. 3 be gear transmission noises experimental bench, including driving wheel, driven pulley, entering spindle case, output main spindle box, accelerate Degree sensor 1, acceleration transducer 2, data collecting card and PC.Entering spindle case, output main spindle box correspond to be provided with respectively Driving wheel, driven pulley；Acceleration transducer 1 is installed in the entering spindle X-direction of entering spindle case, and acceleration transducer 2 is pacified On output major axis X direction loaded on output main spindle box, acceleration transducer 1, acceleration transducer 2 connect with data collecting card Connect, data collecting card is connected with PC.Collect input, ambient noise w contained by output main shaft respectively using data collecting card Mixed signal s (t) of (t) and gear transmission noises signal x (t) is transported to PC carries out data processing, and t is the sampling time.
A kind of gear transmission noises analysis method based on set empirical mode decomposition and SVMs, including following steps Suddenly：
Step one：Gear transmission noises signal x (t) are gathered using acceleration transducer, superposition white Gaussian noise carries out many Secondary empirical mode decomposition.There is the statistical nature of frequency-flat distribution using white Gaussian noise, by adding equal amplitude every time Different white noises change the extreme value point feature of signal, the corresponding IMF for being obtained to multiple empirical mode decomposition afterwards (Intrinsic Mode Function, i.e. intrinsic mode function) carries out population mean to offset the white noise of addition.EEMD points Solution step is as follows:
1) initialization population mean number of times M.
2) numerical value amplitude is added to the white noise for adding, and makes i=1.
3) a white noise n for given amplitudeiT () is added in primary signal x (t), to produce a new signal, i.e.,
xi(t)=x (t)+ni(t) (1)
Wherein, niT () represents i ＆ lt additive white noise sequence；
xiT () represents the additional noise signal of i ＆ lt experiment, i=1,2 ..., M.
4) to the signal x of gained NoiseiT () carries out EMD decomposition respectively, obtain the form of the respective IMF sums such as following formula, I.e.
Wherein, ci,jT () is to decompose j-th IMF for obtaining after i ＆ lt adds white noise；
ri,jT () is survival function, the average tendency of representation signal；J is the quantity of IMF.
5) repeat step (3) and step (4) are carried out M times, and the white noise signal for adding amplitude different is decomposed every time, so that it may To the set of IMF, i.e.,
[{c1,j(t)},{c2,j(t)},…,{ci,j(t)},…,{cM,j(t)}] (3)
Wherein, j=1,2 ..., J.
6) using the principle that the assembly average of uncorrelated sequence is zero, above-mentioned corresponding IMF is carried out into ensemble average fortune Calculate, obtain the final IMF after EEMD, i.e.,
7) final result that EEMD is decomposed is
Wherein, r (t) is residual components.
Step 2：Original noise signal has been resolved into one group of more single component of time scale by step one, In the corresponding IMF that repeatedly set empirical mode decomposition is obtained, when the frequency of two noise sources is very close, frequency ratio is less than When 0.5, EEMD methods cannot be distinguished, it is therefore desirable to improve the resolution ratio of EEMD.In view of the process that EEMD is decomposed It is to be based on the principle that upper level high fdrequency component obtains low frequency component, therefore the IMF component construction high frequencies for needing to be finely divided Signal g (t), and construct following two signals：
x+(t)=x (t)+g (n) (6)
x-(t)=x (t)-g (n) (7)
Two signals of above-mentioned construction carried out with EEMD respectively decompose to obtain z+(t) and z-(t), by (z+(t)+z-(t))/2 As final result, this makes it possible to the high-frequency signal for eliminating addition, simultaneously effective the close signal of frequency is separated.Choose The appropriate meshing frequency comprising gear and its frequency multiplication or obvious IMF is distinguished to noise signal for different gear distresses It is reconstructed, i.e.,
Wherein, cj,kT () is k-th component that j-th IMF subdivision is obtained.
Using x'(t) as final characteristic information, the noise that its direct reaction is caused because gear distress is different Difference.
Step 3：Synchronous time average (Time synchronous averaging, TSA) is carried out to above-mentioned result Processed with continuation.
Synchronous time average passes through comb filter equivalent to making signal so that different from detection object cycle vibration letters Number remitted its fury.Synchronous time average algorithm it is critical only that " synchronization " that concrete implementation method is：The weight obtained to step 2 Structure signal data does FFT and obtains turning frequency f, so as to calculate the synchronous cycle (1/f), with this cycle by the number of reconstruction signal According to being divided into (t0F) part, t0It it is the data total time of reconstruction signal, a cycle that last group is not enough is cast out；To each section Data do resampling to put at equal intervals, obtain one group of new data；It is average to this group of data investigation.
Step 4：Calculate its signal characteristic parameter.In the Time-domain Statistics index of gear transmission noises, be divided into have dimension and Dimensionless index.Having dimension characteristic value includes：It is maximum, minimum value, peak-to-peak value, average, mean square deviation, variance, degree of skewness, high and steep Degree, average amplitude and root amplitude etc..Dimensionless signature analysis value includes：Kurtosis index, waveform index, peak index, pulse Index and margin index.Their computing formula is as follows
Peak-to-peak value：Xppv=Xmax-Xmin (9)
Average：
Variance：
Mean square deviation：
Root-mean-square value：
Degree of skewness：
Kurtosis：
Average amplitude：
Root amplitude：
Waveform index：
Peak index：
Pulse index：
Domain degree index：
Kurtosis index：
Wherein, x (n)：Amplitude of the signal in sample point；
Xmax：The maximum of signal amplitude；
Xmin：The minimum value of signal amplitude；
N：Total length of data；
The average value of signal；
M0：The mode or median of signal；
σ：The standard deviation of signal；
Peak-to-peak value represents noise sound peak, therefore reacts (such as certain rotating speed, load) tooth under certain conditions The size of noise is taken turns, if gear necessarily causes the great variety of peak-to-peak value because certain reason occurs colliding with or impacts.So making Can be to showing that the exceptions with transient surge signal such as peeling or scar are preferably represented with peak-to-peak value.
The noise signal amplitude of normal gear meets standardized normal distribution, if there is obvious defect, the change of its variance, And skew direction and degree change, then can be indicated well with kurtosis and degree of skewness.
Because noise instantaneous value is continually changing over time, so representing the size of this change using virtual value.Letter Number mean-square value illustrate the intensity of signal, its square root is referred to as root-mean-square value, also referred to as virtual value, is signal averaging energy One kind expression.Because virtual value is to temporal average, if so gear has face crack, can be made using virtual value Appropriate evaluation.
Step 5：Structural feature vector.According to the characteristic vector result of calculation of step 4 different type gear signal, therefrom The gear feature value composition characteristic vector that there is significant difference is selected, for recognizing gear distress type.
Step 6：The characteristic vector obtained in step 5 is divided into two groups as sample, and the number of two groups of samples is identical, respectively As training sample and test sample, classified using SVMs, principle of classification is as shown in Figure 1.SVMs Kernel function uses Gaussian radial basis function, is classified with the software kit LIBSVM for returning using SVM pattern-recognitions, using particle Group's optimization (PSO) optimization LIBSVM disaggregated models, the SVM correction parameters after being optimized.
Further, the key step of particle group optimizing method optimization SVM parameters is as follows：
1. the Population Size of initialization particle cluster algorithm, maximum evolutionary generation T, generate m particle at random in search space, The initial position and initial velocity of each particle are determined at random；Initialize the error penalty parameter c and Gaussian kernel of SVMs Parameter g.
2. the SVMs parameter of initialization is set up into corresponding model for SVM algorithm, using the model to inspection Sample is predicted classification, and the fitness value of each particle is calculated according to fitness function.
3. using the initial fitness value of particle as its individual optimal solution, it is compared with global optimum target function value, If the initial adaptive value of particle is better than optimal objective function value, using the former as current optimal objective function value, continue to seek Look for globally optimal solution.
4. it is updated using the speed and location updating formula of particle, obtains itself desired positions of each particle Pbest, after relatively more all particle desired positions, draws the desired positions gbest of all particles.
5. check whether to meet termination condition, if reaching the error requirements or iterations of regulation, stop iteration, it is no Then go to 2. step continuation.
Step 7：Joined as SVMs using the penalty parameter c that obtains and Gauss nuclear parameter g is optimized in step 6 Number, input training sample is trained.Many classification using " one-to-many " (one-against-rest) are classified, classification The type label of the training sample of K class failure gears as shown in Figure 2, is denoted as i, wherein i=1 by principle, and 2,3...K, Eventually pass through SVMs training and obtain certain training parameter information (including supporting vector, pull-type coefficient, network deviation Deng)；
Step 8：Test sample input SVMs is identified, is outputed test result.By the label of output result I (i=1,2,3...K) determines corresponding gear-type respectively
The present invention is new to be had the beneficial effect that：By the time frequency signal analysis method using set empirical mode decomposition, can More effectively to extract gear defects feature, and be conducive to follow-up support vector cassification.And to gear transmission noises signal Useful signal extract and characterization process, it is not necessary to it is artificial excessive to participate in, it is ensured that the accuracy of analysis；Based on support to The intelligent analysis method of amount machine, the recognition accuracy to transmission properties is high and quick.
Brief description of the drawings
Fig. 1 is support vector cassification principle.
Fig. 2 is " one-to-many " multi-classification algorithm principle.
Fig. 3 is gear transmission noises experimental bench.
Fig. 4 a are the time domain and frequency domain figure that normal gear transmission noises signal is surveyed in experiment.
Fig. 4 b are the time domain and frequency domain figure that driving wheel spot corrosion gear transmission noises signal is surveyed in experiment.
Fig. 4 c are that time domain and frequency domain figure that the driving wheel whole flank of tooth damages grating of gears signal are surveyed in experiment.
Fig. 5 is set empirical mode decomposition flow.
Fig. 6 is the EEMD decomposition results that driving wheel spot corrosion gear is surveyed in experiment.
Fig. 7 is the improvement EEMD subdivision results that driving wheel spot corrosion gear is surveyed in experiment.
Fig. 8 is the reconstruction result that gear transmission noises signal is surveyed in experiment.
Fig. 9 is the Synchronous time average and continuation result that gear transmission noises signal is surveyed in experiment.
Figure 10 is support vector cassification flow.
Figure 11 is to three kinds of hands-ons of gear-type data and the result of prediction using multi-category support vector machines.
Specific embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings, to make those skilled in the art with reference to specification text Word can be implemented according to this.
Gear transmission noises collection, normal gear, driving wheel point are carried out in experiment using experimental bench as shown in Figure 3 Erosion gear and the driving wheel whole flank of tooth damage the rotational noise signal of gear as depicted in figure 4 a-4 c, it is illustrated that show to be made an uproar by observation The mode of acoustical signal waveform or spectral line can not distinguish three kinds of defect gears, therefore be analyzed by following step：
Step one：Contain ambient noise w (t) and gear transmission noises signal x (t) to being collected using acceleration transducer Mixed signal s (t), wherein t be the sampling time.The rotational noise with driving wheel spot corrosion gear to collecting mixes letter Number, ambient noise is eliminated using set empirical mode decomposition, (normal gear and the driving wheel whole flank of tooth are damaged to extract useful signal The rotational noise mixed signal processing method of gear is same, such as following).Specific method be superposition white Gaussian noise carry out it is many Secondary empirical mode decomposition, EEMD algorithm flow charts are as shown in Figure 5.EEMD decomposition steps are as follows：
1) initialization population mean number of times M=100.
2) numerical value amplitude is added to the white noise for adding, and makes i=1.
3) a white noise n for given amplitudeiT () is added in primary signal s (t), to produce a new signal, i.e.,
si(t)=s (t)+ni(t) (1)
Wherein, niT () represents i ＆ lt additive white noise sequence；
siT () represents the additional noise signal of i ＆ lt experiment, i=1,2 ..., M.
4) to the signal s of gained NoiseiT () carries out EMD decomposition respectively, obtain the form of the respective IMF sums such as following formula, I.e.
Wherein, ci,jT () is to decompose j-th IMF for obtaining after i ＆ lt adds white noise；
ri,jT () is survival function, the average tendency of representation signal；
J is the quantity of IMF.
5) repeat step (3) and step (4) are carried out M times, and the white noise signal for adding amplitude different is decomposed every time, so that it may To the set of IMF, i.e.,
[{c1,j(t)},{c2,j(t)},…,{ci,j(t)},…,{cM,j(t)}] (3)
Wherein, j=1,2 ..., J.
6) using the principle that the assembly average of uncorrelated sequence is zero, above-mentioned corresponding IMF is carried out into ensemble average fortune Calculate, obtain the final IMF after EEMD, i.e.,
7) final result that EEMD is decomposed is
Wherein, r (t) is residual components.
In decomposable process, end condition is directly connected to the correctness of IMF decomposition, has influence on the physical significance of its expression Authenticity.There are two end conditions in theory, i.e.,：
1) end condition of IMF is decomposed：
The difference that zero passage is counted out and extreme value is counted out is less than or equal to 1, and coenvelope line and the average of lower envelope line are 0, Then terminate.This condition embodies the property that intrinsic mode function should possess；
Standard deviation factor SD meets：0.2<SD<0.3.This condition is decomposition result of checking and last result Difference it is whether sufficiently small, i.e., whether decomposable process has reached certain consistent level.
Meet two above condition, then an IMF decomposable process terminates.
2) end condition of EEMD：
Terminate when residual components are monotonic function or extreme point only one of which.Because to carrying out residual components IMF is decomposed and can not possibly again be obtained new component.Finally decompose the IMF for obtaining and react the overall trend of signal.
It is simpler, quick in order to calculate in actual application, end condition can also by limit iterations come Reach.When setting iterations and being very high, it is considered as decomposable process and has tended to be steady, whole EEMD can terminates.EEMD points Solution result is as shown in Figure 6.
Step 2：It is more single that original noise signal has adaptively been resolved into one group of time scale by step one Component, in the corresponding IMF that repeatedly set empirical mode decomposition is obtained；Wherein IMF2 and IMF3 contains the engagement of gear frequently simultaneously Rate, but IMF3 also contains motor signal simultaneously, it is therefore desirable to the further subdivisions of IMF3, to reject the signal of motor, decompose Result is as shown in Figure 7.
Be successfully separated for motor signal come by second component obtaining of decomposition, and IMF2 and IMF3 is segmented into later the 1 component (IMF3-1) is reconstructed to signal, as shown in Figure 8.It can be caused with direct reaction because gear distress is different Noise differences.
Step 3：Synchronous time average and continuation treatment are carried out to above-mentioned result, obvious cyclophysis is embodied, Concrete methods of realizing is：
FFT is done to the reconstruction signal data that step 2 is obtained to obtain turning frequency 12.5Hz, so as to calculate synchronous week The data of reconstruction signal are divided into (12.5t by phase 0.08s with this cycle0) part (t0It is the data total time of reconstruction signal), most Later group deficiency a cycle, casts out；Resampling is done to put at equal intervals to each section of data, one group of new data is obtained；It is right This group of data investigation is average, and its result is as shown in Figure 9.
Step 4：Signal characteristic parameter is calculated, dimension characteristic value is included：Maximum, minimum value, peak-to-peak value, average, Variance, variance, degree of skewness, kurtosis, average amplitude and root amplitude, and dimensionless characteristic value：Kurtosis index, waveform index, Peak index, pulse index and margin index.
Step 5：Structural feature vector.According to the calculation of characteristic parameters result of step 4 different type gear signal, from In select exist significant difference gear feature value composition characteristic vector, for recognizing gear distress type.
Step 6：Characteristic vector to multigroup gear transmission noises data is classified using SVMs, classification stream Journey is as shown in Figure 10.Gear sample altogether by 90 groups, including 30 groups of normal gears, 30 groups of driving wheel spot corrosion gears and 30 The group driving wheel whole flank of tooth damages gear, calculates their characteristic vector.Gear sample mean is divided into two groups：Training sample and Test sample, respectively damages gear comprising 15 groups of normal gears, 15 groups of driving wheel spot corrosion gears and 15 groups of driving wheel whole flank of tooth.Branch Vector machine kernel function is held using gaussian radial basis function core (RBF) K (xi,xj)=exp (- g | | xi-xj||2)；Wherein g is constant.Punishment Factor c characterizes punishment dynamics of the SVMs to error sample.The selection of kernel functional parameter g and penalty parameter c to support to The nicety of grading of amount machine all has a great impact.Using a SVM pattern-recognitions increased income and the software kit LIBSVM for returning, adopt Optimize LIBSVM disaggregated models with particle group optimizing method, parameter optimization is carried out to penalty factor c and kernel functional parameter g, obtain SVM correction parameters after optimization.
The mathematical description of population optimizing algorithm is：It is defined in a D dimension optimizing space, there is the m molecular group of grain Body, wherein i-th speed of particle can be expressed as vi=(vi1,vi2,...,viD), its position is xi=(xi1,xi2,..., xiD), then the optimal position p that the i-th particle is currently searchedi=(pi1,pi2,...,piD), the optimal location for searching of whole population For particle more new formula is as follows：
vid(t+1)=ω vid(t)+c1r1(pid(t)-xid(t))+c2r2(pgd(t)-xid(t)) (6)
xid(t+1)=xid(t)+vid(t+1) (7)
If vid>VmaxWhen, take vid=Vmax；If vid<-VmaxWhen, take vid=-Vmax, wherein i=1,2 ..., m, d= 1,2,...,D.T is current iteration number of times, c1,c2It is aceleration pulse, r1,r2It is the random number between [0,1], ω is inertia power Weight.
The key step of population optimizing method (PSO) optimization SVM parameters is as follows：
1. the initialization Population Size m=20 of particle cluster algorithm, greatest iteration algebraically T=200, given birth at random in search space Into 20 particles, the initial position and initial velocity of each particle are determined at random；Local Search intensity c1=1.5, global search Intensity c2=1.7, particle optimizing speed k=0.6, it is ω=1, the error punishment ginseng of SVMs to plant group velocity coefficient of elasticity Number c Search Ranges [0.1~100] and Gauss nuclear parameter g Search Ranges [0.1~1000].
2. the SVMs parameter of initialization is set up into corresponding model for SVM algorithm, using the model to inspection Sample is predicted classification, and the fitness value of each particle is calculated according to fitness function.
3. using the initial fitness value of particle as its individual optimal solution, it is compared with global optimum target function value, If the initial adaptive value of particle is better than optimal objective function value, using the former as current optimal objective function value, continue to seek Look for globally optimal solution.
4. it is updated using the speed and location updating formula of particle, obtains itself desired positions of each particle Pbest, after relatively more all particle desired positions, draws the desired positions gbest of all particles.
5. check whether to meet termination condition, if reaching the error requirements or iterations of regulation, stop iteration, Otherwise go to 2. step continuation.
Step 7：Optimizing is carried out according to particle group optimizing method in step 6, penalty parameter c=1.97483, Gaussian kernel are obtained Parameter g=116.439.It is as SVMs parameter, wherein normal gear, driving wheel spot corrosion gear and driving wheel is complete The training sample label that portion's flank of tooth damages gear is set to " 1 ", " 2 ", " 3 ", and training sample input SVMs is utilized " one against rest " classification is trained, and finally gives certain training parameter information (including supporting vector, pull-type Coefficient, network deviation etc.).
Step 8：By 45 groups of characteristic vectors of gear transmission noises signal of test sample, (wherein No. 1-15 is normal gear The characteristic vector of rotational noise signal, No. 16-30 is the characteristic vector of driving wheel spot corrosion gear transmission noises signal, No. 31-45 Be driving wheel whole the flank of tooth damage gear transmission noises signals characteristic vector) input SVMs be identified, as a result such as Shown in accompanying drawing 9.As ordinate " 1 " in accompanying drawing 9, " 2 ", that " 3 " represent normal gear, driving wheel spot corrosion gear and driving wheel respectively is complete The portion flank of tooth damages gear these three gear-types.Circle represents the actual test collection classification to input data, and asterisk is represented to defeated Enter the prediction test set classification of data.Can be intuitive to see very much using multi-category support vector machines to three kinds of teeth by accompanying drawing 11 The result of hands-on and the prediction of categorical data is taken turns, its classification accuracy has reached 95.56%, and classifying quality is clearly.

Claims (3)

1. a kind of gear transmission noises analysis method based on set empirical mode decomposition and SVMs, builds gear first Rotational noise experimental bench, the experimental bench include driving wheel, driven pulley, entering spindle case, output main spindle box, acceleration transducer 1, Acceleration transducer 2, data collecting card and PC；Entering spindle case, output main spindle box correspond to be provided with driving wheel, driven respectively Wheel；Acceleration transducer 1 is installed in the entering spindle X-direction of entering spindle case, and acceleration transducer 2 is installed on output main shaft On the output major axis X direction of case, acceleration transducer 1, acceleration transducer 2 are connected with data collecting card, data collecting card It is connected with PC；Collect input, ambient noise w (t) and gear drive contained by output main shaft respectively using data collecting card Mixed signal s (t) of noise signal x (t) is transported to PC and carries out data processing, and t is the sampling time；
It is characterized in that：The method comprises the steps：
Step one：Gear transmission noises signal x (t) are gathered using acceleration transducer, superposition white Gaussian noise is repeatedly passed through Test mode decomposition；There is the statistical nature of frequency-flat distribution using white Gaussian noise, by adding equal amplitude every time not Change the extreme value point feature of signal with white noise, the corresponding IMF that multiple empirical mode decomposition is obtained is carried out afterwards overall flat Offset the white noise of addition；EEMD decomposition steps are as follows:
1) initialization population mean number of times M；
2) numerical value amplitude is added to the white noise for adding, and makes i=1；
3) a white noise n for given amplitudeiT () is added in primary signal x (t), to produce a new signal, i.e.,
xi(t)=x (t)+ni(t) (1)
Wherein, niT () represents i ＆ lt additive white noise sequence；
xiT () represents the additional noise signal of i ＆ lt experiment, i=1,2 ..., M；
4) to the signal x of gained NoiseiT () carries out EMD decomposition respectively, obtain the form of the respective IMF sums such as following formula, i.e.,
x i ( t ) = &Sigma; j = 1 J c i , j ( t ) + r i , j ( t ) - - - ( 2 )
Wherein, ci,jT () is to decompose j-th IMF for obtaining after i ＆ lt adds white noise；
ri,jT () is survival function, the average tendency of representation signal；J is the quantity of IMF；
5) repeat step (3) and step (4) are carried out M times, the white noise signal for adding amplitude different are decomposed every time, so that it may obtain The set of IMF, i.e.,
[{c1,j(t)},{c2,j(t)},…,{ci,j(t)},…,{cM,j(t)}] (3)
Wherein, j=1,2 ..., J；
6) using the principle that the assembly average of uncorrelated sequence is zero, above-mentioned corresponding IMF is carried out into ensemble average computing, is obtained Final IMF after to EEMD, i.e.,
c j ( t ) = 1 M &Sigma; i = 1 M c i , j ( t ) - - - ( 4 )
7) final result that EEMD is decomposed is
x ( t ) = &Sigma; j c j ( t ) + r ( t ) - - - ( 5 )
Wherein, r (t) is residual components；
Step 2：Original noise signal has been resolved into one group of more single component of time scale by step one, multiple In the corresponding IMF that set empirical mode decomposition is obtained, when the frequency of two noise sources is very close, when frequency ratio is less than 0.5, EEMD methods cannot be distinguished, it is therefore desirable to improve the resolution ratio of EEMD；The process decomposed in view of EEMD is to be based on Upper level high fdrequency component obtains the principle of low frequency component, therefore the IMF component construction high-frequency signals g for needing to be finely divided (t), and construct following two signals：
x+(t)=x (t)+g (n) (6)
x-(t)=x (t)-g (n) (7)
Two signals of above-mentioned construction carried out with EEMD respectively decompose to obtain z+(t) and z-(t), by (z+(t)+z-(t))/2 conducts Final result, this makes it possible to the high-frequency signal for eliminating addition, simultaneously effective separates the close signal of frequency；Choose appropriate The meshing frequency comprising gear and its frequency multiplication or distinguish obvious IMF for different gear distresses noise signal carried out Reconstruct, i.e.,
x &prime; ( t ) = &Sigma; j , k c j ( t ) + c j , k ( t ) - - - ( 8 )
Wherein, cj,kT () is k-th component that j-th IMF subdivision is obtained；
Using x'(t) as final characteristic information, the difference of the noise that its direct reaction is caused because gear distress is different；
Step 3：Synchronous time average and continuation treatment are carried out to above-mentioned result；
Synchronous time average equivalent to make signal pass through comb filter so that the vibration signal different from the detection object cycle is strong Degree weakens；Synchronous time average algorithm it is critical only that " synchronization " that concrete implementation method is：The reconstruct letter obtained to step 2 Number does FFT and obtains turning frequency f, so as to calculate the synchronous cycle (1/f), with this cycle by data of reconstruction signal etc. It is divided into (t0F) part, t0It it is the data total time of reconstruction signal, a cycle that last group is not enough is cast out；To each section of data Resampling is done to put at equal intervals, one group of new data is obtained；It is average to this group of data investigation；
Step 4：Calculate its signal characteristic parameter；In the Time-domain Statistics index of gear transmission noises, being divided into has dimension and immeasurable Guiding principle index；Having dimension characteristic value includes：It is maximum, minimum value, peak-to-peak value, average, mean square deviation, variance, degree of skewness, kurtosis, flat Equal amplitude and root amplitude etc.；Dimensionless signature analysis value includes：Kurtosis index, waveform index, peak index, pulse index and Margin index；Their computing formula is as follows
Peak-to-peak value：Xppv=Xmax-Xmin (9)
Average：
Variance：
Mean square deviation：
Root-mean-square value：
Degree of skewness：
Kurtosis：
Average amplitude：
Root amplitude：
Waveform index：
Peak index：
Pulse index：
Domain degree index：
Kurtosis index：
Wherein, x (n)：Amplitude of the signal in sample point；
Xmax：The maximum of signal amplitude；
Xmin：The minimum value of signal amplitude；
N：Total length of data；
The average value of signal；
M0：The mode or median of signal；
σ：The standard deviation of signal；
Peak-to-peak value represents noise sound peak, thus reaction grating of gears under certain conditions size, if gear because Certain reason occurs colliding with or impacts, and necessarily causes the great variety of peak-to-peak value；So can be to showing to peel off using peak-to-peak value Or the exception with transient surge signal such as scar is preferably represented；
The noise signal amplitude of normal gear meets standardized normal distribution, if there is obvious defect, the change of its variance, and partially Tilted direction and degree change, then can be indicated well with kurtosis and degree of skewness；
Because noise instantaneous value is continually changing over time, so representing the size of this change using virtual value；Signal Mean-square value illustrates the intensity of signal, and its square root is referred to as root-mean-square value, also referred to as virtual value, is one kind of signal averaging energy Expression；Because virtual value is to temporal average, if so gear has face crack, can be made appropriately using virtual value Evaluation；
Step 5：Structural feature vector；According to the characteristic vector result of calculation of step 4 different type gear signal, therefrom select There is the gear feature value composition characteristic vector of significant difference, for recognizing gear distress type；
Step 6：The characteristic vector obtained in step 5 is divided into two groups as sample, and the number of two groups of samples is identical, respectively as Training sample and test sample, are classified using SVMs, and principle of classification is as shown in Figure 1；SVMs core letter Number uses Gaussian radial basis function, is classified with the software kit LIBSVM for returning using SVM pattern-recognitions, excellent using population Change method optimizes LIBSVM disaggregated models, the SVM correction parameters after being optimized；
Step 7：It is defeated using the penalty parameter c and Gauss nuclear parameter g that obtain is optimized in step 6 as SVMs parameter Enter training sample to be trained；Many classification using " one-to-many " are classified, by the class of the training sample of K class failure gears Type label is denoted as i, wherein i=1, and 2,3...K, eventually pass through SVMs training and obtain training parameter information；
Step 8：Test sample input SVMs is identified, is outputed test result；By the label i (i of output result =1,2,3...K) corresponding gear-type is determined respectively.
2. a kind of gear transmission noises based on set empirical mode decomposition and SVMs according to claim 1 are divided Analysis method, it is characterised in that：The step of particle group optimizing method optimization SVM parameters, is as follows：
1. the Population Size of initialization particle cluster algorithm, maximum evolutionary generation T, generate m particle at random in search space, at random Determine the initial position and initial velocity of each particle；Initialize the error penalty parameter c and Gauss nuclear parameter of SVMs g；
2. the SVMs parameter of initialization is set up into corresponding model for SVM algorithm, using the model to test samples Classification is predicted, and the fitness value of each particle is calculated according to fitness function；
3. using the initial fitness value of particle as its individual optimal solution, it is compared with global optimum target function value, if The initial adaptive value of particle is better than optimal objective function value, then using the former as current optimal objective function value, continually look for complete Office's optimal solution；
4. it is updated using the speed and location updating formula of particle, obtains itself desired positions pbest of each particle, than After more all particle desired positions, the desired positions gbest of all particles is drawn；
5. check whether to meet termination condition, if reaching the error requirements or iterations of regulation, stop iteration, otherwise turn To 2. step continuation.
3. a kind of gear transmission noises based on set empirical mode decomposition and SVMs according to claim 1 are divided Analysis method, it is characterised in that：Training parameter information in step 7 includes supporting vector, pull-type coefficient, network deviation.
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