CN105910701B - Characteristic of rotating machines vibration signal blind separating method and device are corrected based on short sample spectra - Google Patents
Characteristic of rotating machines vibration signal blind separating method and device are corrected based on short sample spectra Download PDFInfo
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Abstract
The invention discloses a kind of characteristic of rotating machines vibration signal blind separating methods and device based on the correction of short sample spectra, method includes: to meet to give a threshold value in the frequency sequence obtained after merging, all exist and there is only the frequencies that a subscript meets the first expression formula, then the frequency corresponds to a candidate effective model；The set that candidate effective model is formed identifies single source module in candidate effective model set as input；K- mean cluster based on DB index is carried out to single source module, obtains the estimation of hybrid matrix；Restore source signal by the estimation of hybrid matrix, observation signal.Device includes: that vibrating sensor, analog-to-digital conversion device, microcontroller and output driving and its display module by the inter-process of dsp chip obtain the estimation of hybrid matrix；The source signal finally restored by output driving and its display module display.The present invention solves the problems, such as blind source separating of the characteristic of rotating machines vibration signal in the seldom overdetermination of number of samples.
Description
Technical field
The present invention relates to characteristic of rotating machines vibration signal blind separation field more particularly to it is a kind of based on short sample spectra correction
Characteristic of rotating machines vibration signal blind separating method and device, it is in number of samples seldom that the present invention solves characteristic of rotating machines vibration signal
Blind source separating problem in the case of overdetermination.
Background technique
As most important mechanical type in big machinery system, rotating machinery occupies very big ratio in modern project application
Weight.Due to hugeization of modern mechanical system, the development trend of fining, automation, rotatory mechanical system is often required to work and exists
In rugged environment, thus lead to the generation often of failure.Rotating machinery breaks down, and often leads to the broken of entire mechanical system
The reduction, such as the quality of production, operational safety etc. of bad either working performance.
Blind source separating (Blind Source Separation, BSS) refers to the feelings in the channel information of unknown hybrid system
Under condition, from observation the problem of recovery source signal.Blind source separating problem is widely used in machine diagnostic signal processing[1-4], language
Sound identification[5]And wireless communication[6]Equal fields.It is well known that rotary part (gear, bearing etc.) is Modern Large tool system
In most common, most critical component[7].However due to the influence of live factors (such as: multiple miniature motors are fixed on
On same structure or multiple mechanical breakdowns occur simultaneously etc.), the observation signal obtained from sensor tends not to reflect
The real work state of specific rotary part.At the same time, in engineering practice, these observation signals are often by environmental disturbances
(such as ambient noise, other mechanical systems etc.).Therefore BSS can using and it is necessary to as the pre- of the different source signal characteristics of extraction
Processing method[8], basis is provided for mechanical Fault Monitoring of HV and diagnosis.
Under normal conditions, due to working while multiple rotors in machinery, the vibration signal of rotating machinery is often by multiple
Period harmonic components are constituted.Different mechanical breakdown types, the vibration signal of generation have different spectrum signatures.Such as: turn
Son misaligns in generated vibration signal, and main feature is that there are apparent second harmonics[9]；Gear is in pinion stand
Loosen the harmonic components (being even up to 20 subharmonic sometimes) usually generated higher than 10 times；Oil whip failure always generates
Close to the subharmonic ingredient of half harmonic wave[10]。
In order to reduce loss caused by failure accident, there is an urgent need to improve response speed in fault detection and diagnosis at the scene
Degree, to find mechanical breakdown in time.The most direct solution of quick response be using the observation signal of short time as far as possible come
Fault detection and diagnosis is carried out, i.e., carries out field failure detection and diagnosis using short sample signal.
However, existing BSS method is difficult to meet the requirement of short sample as preprocessing means.Such as: rotating machinery event
The BSS algorithm independent component analysis (Independent Component Analysis, ICA) of most mainstream in barrier diagnosis[11].Perhaps
Mostly based on the method for ICA[12,13], and based on method (such as second order ICA for improving ICA[14], Nonlinear ICA[15], kernel ICA[3]Etc.) have been introduced into fault identification and analysis.
In the implementation of the present invention, discovery at least has the following disadvantages in the prior art and deficiency by inventor:
ICA usually generates uncertain solution when being provided solely for the observation of short sample.This is because, ICA be it is a kind of based on pair
The optimization algorithm of an objective function derived from fourth order cumulant kurtosis.As the fourth order cumulant of random signal, kurtosis
Calculating need to consume great amount of samples to guarantee that it is stablized and accurate.Other are based on statistical method, such as: it is based on the tetradic
The FOOBI (Fourth Order Cumulant-based Blind Identification) of analysis[16], equally can be in short sample
Poorer performance is presented in the case of this.
Summary of the invention
The present invention provides it is a kind of based on short sample spectra correction characteristic of rotating machines vibration signal blind separating method and device,
The present invention only needs given shorter observation sample, can be obtained preferable source signal recovery effects, helps to improve rotating machinery
The quick response of monitoring and fault diagnosis system, described below:
A kind of characteristic of rotating machines vibration signal blind separating method based on the correction of short sample spectra, the method includes following steps
It is rapid:
It obtains to meet in the frequency sequence after merging and gives a threshold value, all exist and there is only a subscripts to meet first
The frequency of expression formula, then the frequency corresponds to a candidate effective model；
The set that candidate effective model is formed identifies single source module in candidate effective model set as input；
K- mean cluster based on DB index is carried out to single source module, obtains the estimation of hybrid matrix；
Restore source signal by the estimation of hybrid matrix, observation signal.
First expression formula specifically:
Wherein,For Frequency Estimation collection；For frequency；ε is threshold value.
The set that candidate effective model is formed identifies single source module in candidate effective model set as input
Specifically:
1) amplitude vector of single source module is parallel with some column vector of hybrid matrix；
2) phase vectors of single source module have phase equalization, i.e. the element of phase vectors meets following formula:
Wherein, 1≤r, l≤M, r ≠ l；ξ > 0 is threshold value；C is permutation and combination operation；For pth*Single source module phase to
R-th of element in amount；For pth*First of element in single source module phase vectors；p*For the subscript of single source module；M is observation
The number of signal.It is described that the K- mean cluster based on DB index is carried out to single source module, obtain the estimation of hybrid matrix specifically:
Clusters number is initialized as I=2, single source module is agglomerated into I class using K- means Method, and calculate DB and refer to
Number；
I=I+1 is enabled, and is clustered again, DB index is sought；Meet D until searching out II<DI-1, and DI<DI+1, then I can be used as
The estimation of source signal number N, and matrix composed by cluster centre, the estimation as hybrid matrix.
The frequency sequence obtained after merging specifically:
Spectrum Correction is done to each observation signal respectively, obtains several Frequency Estimation set；
Frequency Estimation set is mixed, is arranged according to ascending order, the frequency sequence after merging is obtained.
It is described that Spectrum Correction is done respectively to each observation signal, obtain several Frequency Estimation set specifically:
Observation signal is done and adds Hanning window L point DFT transform, obtains observation frequency spectrum；
The position for collecting all peak values of observation frequency spectrum, calculates the ratio of peak value and its secondary peak, obtains intermediate parameters:
According to the intermediate parameters estimate frequency shift (FS): by the frequency shift (FS) obtain Frequency Estimation, Amplitude Estimation and
Phase estimation.
A kind of characteristic of rotating machines vibration signal blind separation device based on the correction of short sample spectra, described device include: vibration
Sensor, analog-to-digital conversion device, microcontroller and output driving and its display module,
The collected multichannel observation signal x (t) of vibrating sensor samples to obtain sample by the analog-to-digital conversion device
Sequence enters the dsp chip in the form of Parallel Digital input, handles, mixed by the internal algorithm of the dsp chip
Close the estimation of matrix；The source signal finally restored by the output driving and its display module display.
The microcontroller is specially dsp chip.
The beneficial effect of the technical scheme provided by the present invention is that: the first, with other blind separating method (such as fast-ICA) phases
Than the present invention can realize that high-precision source signal restores under conditions of short sample is observed, and the observation of short sample extremely meets
The requirement of mechanical detection and the quick response of diagnosis in reality.
The second, the introduced Spectrum Correction technology of the present invention is extremely good at the extraction of harmonic information, thus is especially suitable for
In the processing of characteristic of rotating machines vibration signal, because the failure of characteristic of rotating machines vibration signal is often related to harmonic information.
Third, BSS method proposed by the invention can accurately estimate source signal by improved K- means Method
Number, and when being applied to rotating machinery signal processing, source signal number is also usually unknown, thus the present invention and practical application
It is more in line with.
4th, different from the method (such as fast-ICA, FOOBI, etc.) based on statistical property, the present invention is not required to random first
Beginning process is also not required to successive ignition, thus stability with higher and lower complexity, so that rotating machinery shakes
The analysis of dynamic signal is relatively reliable, more efficient.
Detailed description of the invention
Fig. 1 is the flow chart of the characteristic of rotating machines vibration signal blind separating method corrected based on short sample spectra；
Fig. 2 is the detail flowchart of the characteristic of rotating machines vibration signal blind separating method corrected based on short sample spectra；
Fig. 3 is the schematic diagram that the long sample of fast-ICA composite signal (L=400) restores signal；
Fig. 4 is the schematic diagram that the long sample of composite signal of the present invention (L=400) restores signal；
Fig. 5 is the schematic diagram that the short sample of fast-ICA composite signal (L=70) restores signal；
Fig. 6 is the schematic diagram that the short sample of composite signal of the present invention (L=70) restores signal；
Fig. 7 is the schematic diagram that fast-ICA actual vibration Chief Signal Boatswain sample (L=400) restores signal；
Fig. 8 is the schematic diagram that actual vibration Chief Signal Boatswain sample (L=400) of the present invention restores signal；
Fig. 9 is the schematic diagram that the short sample of fast-ICA actual vibration signal (L=70) restores signal；
Figure 10 is the schematic diagram that the short sample of actual vibration signal (L=70) of the present invention restores signal；
Figure 11 is the structural schematic diagram of the characteristic of rotating machines vibration signal blind separation device corrected based on short sample spectra；
Figure 12 is the flow chart inside DSP.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, embodiment of the present invention is made below further
Ground detailed description.
In order to solve the problems, such as that background technique and deficiency, the embodiment of the present invention propose the base in the case of short sample
In the rotating machinery blind signals separation method and device of the correction of short sample spectra, Spectrum Correction, phase equalization criterion are combined
And improved K- means Method.The present invention can also work in longer sample situation simultaneously.
Embodiment 1
A kind of characteristic of rotating machines vibration signal blind separating method based on the correction of short sample spectra, referring to Fig. 1, this method includes
Following steps:
101: obtaining and meet a given threshold value in the frequency sequence after merging, all exist and there is only a subscripts to meet
The frequency of first expression formula, then the frequency corresponds to a candidate effective model；
102: the set that candidate effective model is formed identifies the Dan Yuanmo in candidate effective model set as input
Formula；
103: the K- mean cluster based on DB index being carried out to single source module, obtains the estimation of hybrid matrix；
104: source signal is restored by the estimation of hybrid matrix, observation signal.
Wherein, the first expression formula in step 101 specifically:
Wherein,For Frequency Estimation collection；For frequency；ε is threshold value.
Wherein, the set for forming candidate effective model in step 102 identifies candidate effective model set as input
In single source module specifically:
1) amplitude vector of single source module is parallel with some column vector of hybrid matrix；
2) phase vectors of single source module have phase equalization, i.e. the element of phase vectors meets following formula:
Wherein, 1≤r, l≤M, r ≠ l；ξ > 0 is threshold value；C is permutation and combination operation；For pth*Single source module phase to
R-th of element in amount；For pth*First of element in single source module phase vectors；p*For the subscript of single source module；M is observation
The number of signal.Wherein, the K- mean cluster based on DB index is carried out to single source module in step 103, obtains hybrid matrix
Estimation specifically:
Clusters number is initialized as I=2, single source module is agglomerated into I class using K- means Method, and calculate DB and refer to
Number；
I=I+1 is enabled, and is clustered again, DB index is sought；Meet D until searching out II<DI-1, and DI<DI+1, then I can be used as
The estimation of source signal number N, and matrix composed by cluster centre, the estimation as hybrid matrix.
Wherein, the frequency sequence after the acquisition in step 101 merges specifically:
Spectrum Correction is done to each observation signal respectively, obtains several Frequency Estimation set；
Frequency Estimation set is mixed, is arranged according to ascending order, the frequency sequence after merging is obtained.
Further, Spectrum Correction is done to each observation signal respectively, obtains several Frequency Estimation set specifically:
Observation signal is done and adds Hanning window L point DFT transform, obtains observation frequency spectrum；
The position for collecting all peak values of observation frequency spectrum, calculates the ratio of peak value and its secondary peak, obtains intermediate parameters:
Frequency shift (FS) is estimated according to intermediate parameters: Frequency Estimation, Amplitude Estimation and phase estimation are obtained by frequency shift (FS).
In conclusion this method can accurately extract the harmonic characteristic parameter (frequency, amplitude and phase) of not homologous signal,
In the lower situation of FFT resolution ratio caused by short sample, Spectrum Correction has effectively resisted spectrum leakage and fence effect (for this
Technical term well known to the technical staff of field, the embodiment of the present invention do not repeat them here this) influence.Meanwhile one by frequency
Differentiate, the selection of candidate effective model, single source frequency criterion the step of the frequency screening process that constitutes can exclude harmonic wave at
Interfering with each other between point.Further, this method can carry out the number of source signal by introducing improved K- mean algorithm
Estimation, from the priori knowledge without the number to source signal.
Embodiment 2
The scheme in embodiment 1 is described in detail below with reference to specific mathematical formulae, Fig. 2, and provides we
The detailed operating process of method, as detailed below:
One, blind source separating model
1.1, Model in Time Domain
Consider N number of unknown source and the observation of the road M.It is assumed that the rotating machinery structure studied has the rigidity of height, and size
It is smaller, thus its propagation delay can be ignored[1].In the case, characteristic of rotating machines vibration signal hybrid system can be taken as i.e.
When mix, expression formula can indicate are as follows:
X (t)=As (t)+n (t) (1)
Wherein, s (t)=[s1(t),…,sn(t),…,sN(t)]TFor source signal vector, x (t)=[x1(t),…,xm
(t),…,xM(t)]TFor observation signal vector, n (t)=[n1(t),n2(t),…,nN(t)]TIt is noise vector, A is mixed moment
Battle array.Short being completed for task of sample B SS is: in the case where not knowing hybrid matrix A, only from the observation signal of a small amount of sample
x1(t)~xM(t) restore source signal s in1(t)~sN(t)。
According to the relativeness of N and M size, BSS problem can be divided into 2 types, overdetermination or positive definite situation (N≤M), and
Owe shape (N > M).The embodiment of the present invention is analyzed and is described only for overdetermination situation.
Because vibration signal originates from the rotation of mechanical part, n-th (n=1,2 ..., N) a source signal sn(t) can regard as
The combination of a series of harmonic signal:
Wherein, PnIt is frequency content number, cn,p,fn,p,θn,pIt is n-th of source signal respectively, the amplitude of p-th of frequency content,
Frequency and phase parameter.
Based on above-mentioned existing Model in Time Domain, the embodiment of the present invention is directed to a kind of BSS algorithm, merely with a small amount of observation
Sample, estimated mixing matrix A simultaneously restore source signal s1(t)~sN(t).Simultaneously, it is notable that in industrial application, source letter
Number number be often it is unknown, the embodiment of the present invention simultaneously also estimates the number of source signal.
1.2, the BSS model based on harmonic wave
Joint type (1) and (2), it is found that if observation signal xm(t) it can further be associated with, then may be used with harmonic parameters
Pass through parameter cn,p,fn,p,θn,pEstimate hybrid matrix A.
Because real signal includes the both sides band spectral line of conjugation, by source signal sn(t) it rewrites are as follows:
Wherein,For signal the right with corresponding time-domain signal；When corresponding to the left side band for signal
Domain signal, andMeet following expression formula:
As certain frequency content fn,pFar from flip-flop, only consider that the time-domain signal of one of sideband spectral line (is only examined herein
Consider band time-domain signal on the right of signalWhen, so that it may include whole spectrum informations.Again with formula (1) simultaneous, the frequency domain of BSS can be obtained
Model:
Wherein,For half sideband of the right side of the frequency spectrum of observation signal x (t)；For half sideband of the right side of signal spectrum；f
For source signal and observation signal frequency domain independent variable.It is apparent from, the Fourier transform of complex exponential signal is an impulse function ' δ
(·)'.Therefore, n-th (1≤n≤N) a source signal sn(t) half sideband of the right sideFourier transform expression formula are as follows:
Wherein, δ () is impulse function.
Hybrid matrix A is expressed as to the form [a of column vector1,…,aN], formula (6), which are substituted into formula (5), to be obtained:
Wherein,For m (1≤m≤M) a observation signal xm(t) right half composes.
In order to estimate each column a of hybrid matrix A1~aN, consider such a special frequency contentIt only goes out
A present source signal is (without loss of generality, it is assumed that appear in n-th of source signal sn(t)), and other source signals without containing this frequency
Rate ingredientThat is the frequency contentMeet following requirement:
Wherein,For in addition to n-th of source signal sn(t) other than,P-th of frequency content in a source signal；PnFor
The frequency content number of n-th of source signal；PnIt isThe frequency content number of a source signal.
Then for frequency contentFormula (7) becomes
Wherein,The spectral peak for composing ingredient for right halfCorresponding frequency domain vector；It is seen for m-th
Survey signal xm(t) spectral peak of right half spectrumSpectrum value.From formula (9) as can be seen that and frequency contentCorresponding frequency domain to
AmountWith hybrid matrix vector anIn parallel.Therefore, as long as being collected into sufficiently more single source modulesIt can estimate mixed moment
All column vectors of battle array A.
1.3, the difficulty of short sample blind separation
Notice that formula (7) is the ideal Fourier transform model of BSS, frequency f therein is a continuous variable.So
And ideal Fourier transform is not achievable in practice, because this needs infinite more sample.Work as in practical application
In, ideal Fourier transform is by Discrete Fourier Transform (the Digital Fourier of L point (number that L is observation signal sampling point)
Transform, DFT) it replaces.In DFT, frequency f only allows for frequency resolution Δ f (Δ f=fs/ L, fsFor sampling speed
Rate) integral multiple.
However, the frequency f of n-th of source signaln,pIt tends not to be exactly equal to DFT frequency resolution Δ f=fsThe integer of/L
Times, this will lead to the impulse function δ (f-f of formula (7)n,p) ideal sampling result can not be obtained.This deviation is equally reflected in
Observation signal xm(t) DFT frequency spectrumOn, that is, there is spectrum leakage phenomenon.
Without loss of generality, by n-th of source signal sn(t) frequency content fn,pIt is defined as the integral multiple of frequency resolution Δ f
kn,pWith small several times δn,pSum, expression formula is as follows:
fn,p=(kn,p+δn,p)Δf,kn,p∈Z+ ,δp∈(-0.5,0.5] (10)
Wherein, Z+For positive integer.
When sample length L becomes smaller, DFT frequency resolution Δ f is bigger, and DFT frequency spectrum becomes rougher, i.e., fence effect is tighter
Weight.Due to the effect of fence effect, the ignored small several ' δ of formula (10)n,pThe value of Δ f ' will become much larger, this will lead to
DFT spectral peak position of spectral line (i.e. DFT frequency estimation,) and the deviation of actual frequency can be bigger.
In order to overcome this problem, the embodiment of the present invention introduces Spectrum Correction to obtain accurate harmonic parameters estimation.
Two, based on the BSS of Spectrum Correction
2.1, Spectrum Correction
In order to remove the influence of huge deviation caused by spectrum leakage brought by short sample and fence effect, the present invention
Embodiment introduces ratio spectrum correction method[17]。
Ratio spectrum correction method estimates frequency deviation using spectral peak and its adjacent maximum spectral line, recycles frequency deviation to frequency
Frequency, amplitude and the phase of rate ingredient are corrected.To each road observation signal Xm(k), m=1,2 ... M carry out Spectrum Correction, often
A observation signal can all be corrected after harmonic parameters, it may be assumed that Frequency Estimation collectionAmplitude Estimation collectionEstimate with phase
Meter collection
After the harmonic parameters corrected, for a frequency contentSuch as formula (8) and formula (9) it is found that only when the frequency
Rate ingredient is pertaining only to a source signal, and when being not belonging to other source signals, harmonic parameters can be used to estimate the column vector of A.Therefore,
Before estimated mixing matrix, it is necessary to filter out single source module.
2.2, single derived components screening
Single derived components screening is divided into three steps: frequency merges, candidate effective model selects, single source module criterion.
2.2.1, frequency merge
It is worth noting that, influenced by noise, interference and correction method itself precision, even the same frequency content,
Its result from all observations by Spectrum Correction estimation can still have slight difference.Therefore, it need to be merged by frequency and be walked
Suddenly the different estimations of the same frequency content are merged, to obtain more accurate Frequency Estimation, and is combined into each
The amplitude vector and phase vectors of frequency content.If the Frequency Estimation set that M is observed is merged into a big collection, and by liter
Sequence arrangement, then the different estimations of the forenamed same frequency content must tend to shape since there is only little differences
At a cluster.It is assumed that a total of P cluster forms (the wherein frequency content of the corresponding merging of each cluster), it without loss of generality, will
The element definition of p-th of cluster is(ΓpIt is the element number of the cluster).The then ΓpA element should be by it
ValueIt replaces, to achieve the effect that merging, equal value expression are as follows:
2.2.2, candidate effective model selection
Theoretically, as long as being free of zero in the element of hybrid matrix A, as can be seen that institute's active signal owns from formula (1)
Frequency content should be included in the observation signal of the road M simultaneously.Thus, the frequency content that those do not include by all observation signals is often
For pseudo frequency ingredient, it is likely that generated by the interference between noise or frequency content.Can be found by many experiments, this pseudo frequency at
Divide often amplitude very little, and not parallel with the column vector of hybrid matrix A.In order to exclude pseudo frequency ingredient, it is necessary to select (certain
In error range) candidate pattern of the frequency that includes by all observation signals as subsequent step.
In practical operation, it is assumed that small threshold epsilon > 0, for certain frequency content after mergingIf to each
Observation signal xm(t) Frequency Estimation collectionIn the presence of and there is only a subscriptMeet
Then certain frequency contentCandidate effective frequency can be taken as.Meanwhile according to formula (9), using candidate pattern at M
Amplitude and phase parameter in observation signal construct the candidate effective model vector being shown below
Wherein,For the number of candidate effective model.After the selection of candidate effective frequency, under the number for merging frequency
It drops toIt is a.
2.2.3, single source module criterion
In rotating machinery fault analysis, multiple source signals can usually occur while including that the same frequency content is (i.e. heavy
Folded frequency) the case where.Obviously, this frequency content is not able to satisfy formula (8), thus, it can not obtain the conclusion of formula (9), i.e. this kind
Frequency content will be not parallel with the column vector of hybrid matrix A, can not be used to estimated mixing matrix A.Thus, overlaid frequency should be gone
It removes, to guarantee the estimated accuracy of hybrid matrix A.
It is assumed that in candidate effective frequency,It is the frequency content in single source, i.e. frequency contentMeet formula (8), by formula (9)
As can be seen thatAll phases both from the same frequency contentPhase, thusEvery phase
Position must be with uniformity, i.e., is equal within a certain error range, and frequency contentCorresponding pattern vectorComposition
Set of patternsFor single source module collection (p*For the subscript of single source module, P*For the number of single source module).
By two characteristics for analyzing the frequency content that can sum up single source above:
1) amplitude vector of the frequency content in single source is parallel with some column vector of hybrid matrix A.
2) phase vectors of the frequency content in single source have phase equalization, i.e. the element of phase vectors meets following formula:
Wherein, 1≤r, l≤M, r ≠ l, ξ > 0 are small threshold value, and C is permutation and combination operation.
2.3, source number and the hybrid matrix estimation based on DB index
If source signal number it is known that if can use K- means Method to single source module collection obtained by upper section It is clustered and carrys out estimated mixing matrix A.However in practical engineering applications, the number ' N ' of source signal is often not
Know.For estimated mixing matrix A in the case of source signal number is unknown, and restore source signal, the embodiment of the present invention mentions
Go out based on DB index[18]Clustering is found under the premise of unknown source signal number with the clustering technique of K- means Method
Natural division.
Clusters number is set as I first, then to single source module collectionK- means Method is carried out, it will
It is polymerized to I cluster Ci, CiTo cluster resulting i-th (i=1,2 ..., I) a cluster, then
Wherein, riFor cluster after single source module subscript,For the r of i-th of clusteriA list source module, RiFor i-th of cluster
Single source module number.CiMeet following expression:
Wherein, U is to seek union operation.
For a certain specific cluster result (clusters number I), DB index can evaluate the appropriate level of the result,
Balancing method can be used as a general measurement index independently of clustering algorithm.DB index can be with is defined as:
Wherein, DIThe DB index of cluster result when for clusters number equal to I；Mi,jIt represents between the i-th cluster and jth cluster
Index of similarity；GiAnd GjRepresent the dispersion index between the i-th cluster and jth cluster.GiExpression formula be
Wherein, ciFor the cluster centre of the i-th cluster, GjExpression formula similarly, the embodiment of the present invention does not repeat them here this.
Wherein, Mi,jExpression formula be
Mi,j=| | ci-cj|| (20)
Wherein, cjFor the cluster centre of jth cluster.
It by above-mentioned discussion, is apparent from, with the element in cluster, dispersion is smaller, and the degree for representing aggregation is higher, then gathers
Class effect is better.The distance between different clusters are bigger, represent that similarity is lower, then Clustering Effect is better.Thus, for DB index
Expression formula, it can be deduced that, the result performance of cluster corresponding to DB index minimum is best.It follows that source signal number
Number estimation can seek its DB index, wherein the number of clusters of the corresponding cluster of the minimum of DB index by repeatedly being clustered to data
It can not only be used for the estimation of source signal number, and matrix composed by the cluster centre of each cluster of the clusterIt then can be used as mixing
The estimation of matrix A.
2.4, the recovery of source signal
For overdetermination situation, in the estimation for obtaining hybrid matrixAfterwards, the recovery of source signal can pass through following formula
It obtains
Wherein,The pseudo- inverse operation of hybrid matrix A is sought in expression.
3, the detailed process of the short sample rotating machinery blind signal separation provided in an embodiment of the present invention based on Spectrum Correction
It is as follows, it is described below with reference to Fig. 2:
3.1 Spectrum Correction steps
Step 1: to observation signal xm(t), m=1 ..., M are done plus Hanning window L point DFT transform, obtains observation frequency spectrum Xm
(k), k=0,1 ..., L；
Step 2: observation frequency spectrum X is collectedm(k) position of all peak values.To spectral peak(PmIt is m-th
The spectral peak number of observation), calculate peak valueAnd its ratio of secondary peak
Wherein,For the spectral line on the left of spectral peak；For the spectral line on the right side of spectral peak.
Intermediate parameters then can be obtained
Step 3: according to intermediate parametersEstimate frequency shift (FS)
Then Frequency EstimationAre as follows:
Step 4: Amplitude Estimation Then it is respectively as follows:
Wherein, angle () representative takes phase angle operation.It is corrected, obtain Frequency Estimation setAmplitude Estimation
SetAnd phase estimation set
When specific implementation, above-mentioned the step of being corrected to frequency spectrum, is known to those skilled in the art, and the present invention is implemented
Example does not repeat them here this.
3.2, single source module screening step
Step 5: by M frequency setsIt is mixed, is arranged according to ascending order, obtain P frequency cluster,
Wherein a cluster of pth (p=1 ..., P) is made of the lesser Frequency Estimation result of differenceΓpFor the cluster
Element number, the then frequency after merging are to collect all merging frequencies, the then frequency sequence after being merged shown in formula (11)
Step 6: the frequency sequence after merging is found outIt is middle to meet given small threshold epsilon > 0, for every
A m exists and there is only a subscriptsMeet the frequency of formula (12), then the frequency is candidate effective frequency, one corresponding
Candidate effective model, as shown in formula (13), whereinFor candidate effective model number.
Step 7: by candidate effective model setAs input, identified according to formula (14)In single source module mould
Formula is simultaneously denoted asMeet above formula (14) is single source module.
3.3 based on the K- mean cluster of DB index and the recovering step of source signal
Step 8: being initialized as I=2 for clusters number, using K- means Method by single source module collectionIt is polymerized to I
Class, and its corresponding DB index D is calculated according to formula (18)~formula (20)I。
Step 9: I=I+1 is enabled, and is clustered again, DB index D is soughtI.Step 10: it is full until searching out I to repeat Step 9
Sufficient DI<DI-1, and DI<DI+1If (I=2 need to only meet DI<DI+1), then I can be used as the estimation of source signal number N, and cluster centre
Composed matrix can be used as the estimation of hybrid matrix
Step 11: the recovery of source signal can be obtained by expression formula (21).
In conclusion this method can accurately extract the harmonic parameters of not homologous signal, spectrum leakage and grid have effectively been resisted
Column effect；Meanwhile one of this method offer is selected by frequency discrimination, candidate effective model, the step of single source frequency criterion
Suddenly the frequency screening process constituted can exclude interfering with each other between harmonic components；Further, this method is improved by introducing
K- mean algorithm, the number of source signal can be estimated, from the priori knowledge without the number to source signal.
Embodiment 3
Feasibility verifying is carried out to the method in embodiment 1-2 below with reference to specific calculated result, attached drawing, it is as detailed below
Description:
Four, it tests
4.1, composite signal emulates
Consider 3 × 2 hybrid systems
Source signal expression formula is
Sampling rate fs=2000Hz considers 4 kinds of sample lengths (L=400,200,100,70).Fast-ICA is introduced to calculate
Method introduces the related coefficient for restoring signal and source signal as comparison algorithm, i.e. recovery related coefficient refers to as performance measure
Mark.Because fast-ICA algorithm statistical property signal-based, each run result are variant.In order to preferably measure
Its performance repeats experiment 1000 times, record wherein number of success, and the average value for restoring related coefficient successfully tested.
Wherein primary operation result is shown in Fig. 3~Fig. 6, and the number of success and Successful tests of 1000 experiments are flat
Restore related coefficient such as table 1.
1 composite signal number of success of table and averagely recovery related coefficient
As shown in Figure 3 and Figure 4, in the case of long sample (L=400), fast-ICA and the present invention can be accurate
Restore source signal.However, be reduced to L=70 when number of samples, i.e., in the case of short sample, by Fig. 5 and Fig. 6 it can be concluded that,
There is apparent distortion in the recovery signal of fast-ICA, and the present invention has still accurately restored source signal.
As can be known from Table 1, as the number of sample is reduced, the successful recovery number of fast-ICA sharply declines, and successfully
The average recovery related coefficient of experiment also slightly decreases, and the performance of this method remains at the ideal feelings that related coefficient is 1
Shape, and all experiments all successfully carry out.Thus, in terms of handling composite signal, this method is in short sample, performance
It is substantially better than fast-ICA.
4.2, actual vibration signal
Experiment
Still above-mentioned hybrid system is utilized, and signal is then two actual mechanical fault signals.s1It (t) is power frequency
89.6853Hz imbalance fault signal, s2It (t) is power frequency 102.8811Hz rotor misalignment fault-signal.Consider different
Sample length (L=400,200,100,70) carries out 1000 repetitions equally under sample length and tests, wherein primary operation
As a result it shows in Fig. 7~Figure 10, the number of success and Successful tests of 1000 experiments averagely restore related coefficient such as table 2.
2 actual vibration signal number of success of table and averagely recovery related coefficient
From in Fig. 7 and Fig. 8 it is found that fast-ICA and this method all can Exact recoveries under long sample (L=400) situation
Source signal.And for short sample situation (L=70), it can be clearly seen that in Fig. 9, the recovery signal of fast-ICA exists obvious
Distortion, and this method still is able to Exact recovery source signal, sees Figure 10.From Table 2, it can be seen that with number of samples from
400 drop to 70, and the performance of this method is better than fast-ICA.Further, when number of samples reduces to a certain extent,
The case where number of success appearance of fast-ICA sharply declines, and this method performance is relatively stable.In processing actual vibration signal
Aspect, for this method in short sample, performance is still substantially better than fast-ICA.
Embodiment 4
It is described below the embodiment of the invention provides a kind of device corresponding with scheme in embodiment 1 to 2: hard
Part implements figure as shown in figure 11, will pass through A/D (analog-to-digital conversion device) from the collected multichannel observation signal x (t) of vibrating sensor
Sampling obtains sample sequence x (n), enters dsp chip in the form that Parallel Digital inputs, at the internal algorithm of dsp chip
Reason, obtains the estimation of hybrid matrix；The source signal finally restored by output driving and its display module display.
Wherein, the DSP (Digital Signal Processor, digital signal processor) of Figure 10 is core devices,
During Signal parameter estimation, following major function is completed:
(1) core algorithm is called, completes the FFT transform of signal, Spectrum Correction, single derived components screening (merge comprising frequency,
Candidate components screening and single derived components identification) obtain single source module collection of signal；
(2) single source module collection is clustered using the improvement K- means Method based on DB index, obtain source number and
The estimation of hybrid matrix, and the estimation of source signal is acquired by the pseudoinverse that observation signal and hybrid matrix are estimated, and result is defeated
Out to driving and display module；
The internal processes process of DSP device is as shown in figure 12.The algorithm proposed is implanted into DSP device by the present invention, base
High-precision, low complex degree, efficient characteristic of rotating machines vibration signal blind separation are completed in this.
Figure 12 process is divided into the following steps:
1) requirement of real-time according to rotary machinery fault diagnosis, the sampling number L of setting signal are needed first；
2) secondly, CPU main controller reads sampled data from the port I/O, into internal RAM；
3) recovery of source signal finally, is carried out by treatment process Fig. 1 and Fig. 2 of the invention, and it is passed through into external display
Device is shown.
The embodiment of the present invention to the model of each device in addition to doing specified otherwise, the model of other devices with no restrictions,
As long as the device of above-mentioned function can be completed.
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It will be appreciated by those skilled in the art that attached drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention
Serial number is for illustration only, does not represent the advantages or disadvantages of the embodiments.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and
Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (5)
1. a kind of characteristic of rotating machines vibration signal blind separating method based on the correction of short sample spectra, which is characterized in that the method
The following steps are included:
Spectrum Correction is done to each observation signal respectively, obtains several Frequency Estimation set；Frequency Estimation set is mixed
It closes, is arranged according to ascending order, obtain the frequency sequence after merging；
It obtains to meet in the frequency sequence after merging and gives a threshold value, all exist and there is only a subscripts to meet the first expression
The frequency of formula, then the frequency corresponds to a candidate effective model；
The set that candidate effective model is formed identifies single source module in candidate effective model set as input；
K- mean cluster based on DB index is carried out to single source module, obtains the estimation of hybrid matrix；
Restore source signal by the estimation of hybrid matrix, observation signal；
Wherein, the set that candidate effective model is formed identifies the Dan Yuanmo in candidate effective model set as input
Formula specifically:
Find out the frequency sequence after mergingIt is middle meet give a threshold epsilon > 0, exist for each m and only
There are a subscriptsMeet the frequency of the first expression formula, then the frequency is candidate effective frequency, a corresponding effective mould of candidate
Formula vector zp；
First expression formula specifically:
Wherein,For Frequency Estimation collection；For frequency；ε is threshold value；
By candidate effective model setAs input, according toIdentificationIn single source module simultaneously
It is denoted as
Wherein, 1≤r, l≤M；ξ > 0 is threshold value；C is permutation and combination operation；For pth*R-th in single source module phase vectors
Element；For pth*First of element in single source module phase vectors；p*For the subscript of single source module；M is of observation signal
Number.
2. a kind of characteristic of rotating machines vibration signal blind separating method based on the correction of short sample spectra according to claim 1,
It is characterized in that, described carry out the K- mean cluster based on DB index to single source module, the estimation of hybrid matrix is obtained specifically:
Clusters number is initialized as I=2, single source module is agglomerated into I class using K- means Method, and calculate DB index；
I=I+1 is enabled, and is clustered again, DB index is sought；Meet D until searching out II< DI-1, and DI< DI+1, then I can be used as source
The estimation of signal number N, and matrix composed by cluster centre, the estimation as hybrid matrix.
3. a kind of characteristic of rotating machines vibration signal blind separating method based on the correction of short sample spectra according to claim 2,
It is characterized in that, described do Spectrum Correction to each observation signal respectively, several Frequency Estimation set are obtained specifically:
Observation signal is done and adds Hanning window L point DFT transform, obtains observation frequency spectrum；
The position for collecting all peak values of observation frequency spectrum, calculates the ratio of peak value and its secondary peak, obtains intermediate parameters:
Frequency shift (FS) is estimated according to the intermediate parameters: Frequency Estimation, Amplitude Estimation and phase are obtained by the frequency shift (FS)
Estimation.
4. a kind of for implementing a kind of rotation based on the correction of short sample spectra described in any claim in claim 1-3
The device of mechanical oscillation signal blind separating method, which is characterized in that
Described device includes: vibrating sensor, analog-to-digital conversion device, microcontroller and output driving and its display module,
The collected multichannel observation signal x (t) of vibrating sensor samples to obtain sample sequence by the analog-to-digital conversion device,
Enter the microcontroller in the form of Parallel Digital input, handles, mixed by the internal algorithm of the microcontroller
The estimation of matrix；The source signal finally restored by the output driving and its display module display.
5. device according to claim 4, which is characterized in that the microcontroller is specially dsp chip.
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