CN104679981A - Vibration signal noise reduction method based on variable-step-length LMS-EEMD - Google Patents

Abstract

The invention discloses a vibration signal noise reduction method based on variable-step-length LMS-EEMD. The method includes: acquiring an initial noise reduction signal according to an original signal; decomposing the initial noise reduction signal, and selecting an IMF component needed in noise reduction; acquiring a final noise reduction signal according to the original signal and the selected IMF component. By the method, the defects of complex operation process, high noise pollution and weak noise reduction capability in the prior art can be overcome, and simple operation process, low noise pollution and strong noise reduction capability are achieved.

Description

A kind of vibration signal noise-reduction method based on variable step size LMS-EEMD

Technical field

The present invention relates to communication technical field, particularly, relate to a kind of vibration signal noise-reduction method based on variable step size LMS-EEMD.

Background technology

Owing to being subject to the restriction of various observation condition and environmental factor, in observation data, inevitably there is the impact of various noise.Especially white noise.More very, the observation signal be present in complex environment has the characteristic of low signal-to-noise ratio.Therefore, noise reduction is a vital task of data preprocessing phase.

The noise-reduction method that non-stationary signal is conventional has, method based on wavelet and wavelet packets analysis has multiple dimensioned and many resolution characteristics, to non-stationary signal noise reduction, more effective than traditional filtering noise-reduction method, but the method noise reduction is limited to wavelet basis function, threshold value, the choosing of Decomposition order, and needs certain priori ^[1].Empirical mode decomposition (EMD) ^[2]be a kind of novel adaptive signal processing method, be very suitable for non-linear, non-stationary signal, overcoming wavelet analysis needs certain priori and small echo coupling defect.But EMD method important defect is exactly modal overlap ^[3], make the distorted signals after noise reduction.On the basis of the modal overlap phenomenal research that Wu etc. run in decomposing EMD, propose set empirical mode decomposition (EEMD) ^[4]method.A non-stationary signal is decomposed by EEMD, can obtain several stable intrinsic mode functions (IMF).The intrinsic mode functions that the method obtains effectively overcomes the problem of modal overlap in EMD decomposition.Decompose through EEMD the physical connotation that the intrinsic mode function obtained can disclose original signal, make the physical essence of each IMF more clear ^[5], thus make the signal effect after noise reduction ideal, but run into the signal of low signal-to-noise ratio, the high frequency intrinsic mode functions of the dye noise cancellation signal under the impact of anomalous event, EEMD being decomposed has occurred that white noise in various degree pollutes.Based on LMS sef-adapting filter, algorithm does not simply need priori.But it is during for wider band signal, bad during noise reduction fashion ^[6], the method is not strong for head end points noise reduction capability.

Realizing in process of the present invention, inventor finds at least to exist in prior art the defect such as the large and noise reduction capability of operating process complexity, noise pollution is weak.

Summary of the invention

The object of the invention is to, for the problems referred to above, propose a kind of vibration signal noise-reduction method based on variable step size LMS-EEMD, to realize the advantage that operating process is simple, noise pollution is little and noise reduction capability is strong.

For achieving the above object, the technical solution used in the present invention is: a kind of vibration signal noise-reduction method based on variable step size LMS-EEMD, comprising:

A, according to original signal, obtain initial de-noising signal;

B, initial de-noising signal to be decomposed, choose required IMF component in noise reduction process;

C, according to original signal and the IMF component chosen, obtain final de-noising signal.

Further, described step a, specifically comprises:

(1) choose original signal x (t), white noise 0.8*randn (size (t)) and dye noise cancellation signal z (t), initialization forward-direction filter weights, the setting initial step length factor;

(2) set filter order and number of run;

(3) variable step size LMS sef-adapting filter noise reduction is carried out to dye noise cancellation signal z (t);

(4) more square e (n) is minimum is together convergence direction, and find after search that namely start convergence upgrades step factor, formula is as follows:

$\mathrm{mu}=\frac{{\mathrm{mu}}_0}{1+\left(\frac{n}{100}\right)};$

Wherein n is the iterations of signaling point, and scope is from 1 to 1024; Mu is the step factor of n-th, and n is natural number;

(5) iteration is until signal length is n, obtains initial de-noising signal y (t).

Further, choose original signal x (t), white noise 0.8*randn (size (t)) described in and with in the operation of dye noise cancellation signal z (t), specifically comprise:

Choosing amplitude-modulation frequency-modulation signal is: x (t)=(1+0.2sin (60 π t)) cos (60 π t+0.5sin (30 π t))+sin (240 π t), noise to be average be 0 amplitude be 0.5 white noise 0.8*randn (size (t)); Namely contaminating noise cancellation signal is:

x(t)＝(1+0.2sin(60πt))cos(60πt+0.5sin(30πt))+sin(240πt)+0.8*randn(size(t))。

Further, described to dye noise cancellation signal z (t) carry out in the operation of variable step size LMS sef-adapting filter noise reduction, the concrete steps of carrying out variable step size LMS sef-adapting filter noise reduction are as follows:

1) by input signal, by producing output signal after the digital filter of Parameter adjustable, output signal and wanted signal being compared, obtains error signal; Adjust with by the parameter of adaptive algorithm to wave filter, the object of adjustment makes error signal minimum: X (n)=[x (n), x (n-1) ..., x (n-M+1)];

The weight vectors of sef-adapting filter is: W (n)=[W _n1, W _n2, W _n3..., W _nM] ^t;

The output of corresponding sef-adapting filter is: $y\left(n\right)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{W}_{i}x(n-i+1)=W{\left(n\right)}^{T}X\left(n\right);$

Y (n) relative to the error of wanted signal d (n) is: e (n)=d (n)-W (n) ^tx (n);

Square error e should be made according to minimum mean square error criterion MSE ²n () is for minimum;

2) iterative equation of LMS algorithm is: W (n+1)=W (n)+2 μ e (n) X (n); Wherein, μ is the constant of control convergence speed, is called step factor, and e (n) is error signal; Restrain after ensureing iteration, namely μ must meet:

0<μ<1/λ _max；

Wherein, λ _maxfor list entries x (n) autocorrelation matrix R _xxeigenvalue of maximum.

Further, described step b, specifically comprises:

(1) set empirical mode decomposition EEMD is carried out again to initial de-noising signal y (t) obtained;

(2) choose the white noise meeting default amplitude-modulation frequency-modulation signal, carry out 50 EMD and decompose;

(3) the IMF component obtained again weighted mean obtain average after IMF component.

Further, described initial de-noising signal y (t) to obtaining carries out the operation of gathering empirical mode decomposition EEMD again, specifically comprises:

1) repeatedly add in original signal have that average is 0, standard deviation be the white noise of constant namely:

x _i(t)＝x(t)+n _i(t)；

In formula: be the signal adding white Gaussian noise i-th time;

2) carry out set empirical mode decomposition EEMD respectively to decompose, the IMF component obtained and i residual volume.Be wherein after adding white Gaussian noise i-th time, decompose the jth IMF component obtained;

3) 1 is repeated) and 2) M time, the average statistical of incoherent random series is utilized to be the principle of 0, the IMF component of above-mentioned correspondence is carried out population mean computing, eliminate and repeatedly add the impact of white Gaussian noise on true IMF component, finally obtaining the IMF component after gathering empirical mode decomposition EEMD is:

$c_j\left(t\right)=\frac{1}{M}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{r}_i;$

Finally obtaining the residual volume after gathering empirical mode decomposition EEMD is r (t):

$r\left(t\right)=\frac{1}{M}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{r}_i;$

In formula: c _ja t jth IMF component that () obtains for carrying out set empirical mode decomposition EEMD to original signal x (t); When M is larger, the IMF component of corresponding white noise and will 0 be tending towards; The result reconstructed after now gathering empirical mode decomposition EEMD is:

x(t)＝Σ _jc _j(t)+r(t)；

In formula: r (t) is final residual volume, and M is natural number.

Further, described step c, specifically comprises:

(1) utilize original signal x (t) to carry out signal reconstruction with the correlation coefficient ρ of each IMF component;

(2) choosing the IMF component that related coefficient meets predetermined threshold value is effective value, obtains final de-noising signal x (t).

Further, the described original signal x (t) that utilizes carries out the operation of signal reconstruction with the correlation coefficient ρ of each IMF component, specifically comprises:

When choosing IMF component, the correlativity according to IMF component and original signal judges, carries out self-adapting reconstruction; The formula of the related coefficient of IMF component and original signal is:

${\mathrm{\&rho;}}_{\mathrm{xy}}=\frac{\mathrm{cov}(x,y)}{\sqrt{E\left(x\right)}\sqrt{E\left(y\right)}};$

Wherein cov (x, y) is covariance function, and E is expectation function; The span of correlation coefficient ρ is-1<=ρ <=1;

The computing formula of signal to noise ratio (S/N ratio) (SNR) is:

$\mathrm{SNR}=10{\log }^{\frac{P_s}{P_n}};$

Wherein, P _sfor the power of original signal, P _nfor the noise power of signal;

Root-mean-square error R reflects the error of de-noising signal and original signal, and its computing formula is:

$R=\sqrt{\frac{1}{n}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(s\left(i\right)-x\left(i\right))}^2};$

Wherein, s (i) is original signal, and x (i) is the signal after noise reduction.

The vibration signal noise-reduction method based on variable step size LMS-EEMD of various embodiments of the present invention, owing to comprising: according to original signal, obtains initial de-noising signal; Initial de-noising signal is decomposed, chooses required IMF component in noise reduction process; According to original signal and the IMF component chosen, obtain final de-noising signal; Thus the defect that in prior art, operating process is complicated, noise pollution is large and noise reduction capability is weak can be overcome, to realize the advantage that operating process is simple, noise pollution is little and noise reduction capability is strong.

Other features and advantages of the present invention will be set forth in the following description, and, partly become apparent from instructions, or understand by implementing the present invention.

Below by drawings and Examples, technical scheme of the present invention is described in further detail.

Accompanying drawing explanation

Accompanying drawing is used to provide a further understanding of the present invention, and forms a part for instructions, together with embodiments of the present invention for explaining the present invention, is not construed as limiting the invention.In the accompanying drawings:

Fig. 1 is the principle of work schematic diagram of sef-adapting filter in the present invention;

Fig. 2 is the simulation result figure that in the present invention, variable step size LMS-EEMD adaptive filter algorithm carries out contaminating noise cancellation signal noise reduction process;

Fig. 3 is the IMF component analogous diagram of IMF component that obtains of weighted mean again in the present invention;

Fig. 4 carries out through the method for related coefficient (ρ) analogous diagram that self-adapting signal reconstruct obtains noise reduction result in the present invention;

Fig. 5 is the analogous diagram of in the present invention, pollution signal being carried out to the result after variable-step self-adaptive wave filter noise reduction;

Fig. 6 is the process flow diagram of the noise-reduction method of dye noise cancellation signal in the present invention in low signal-to-noise ratio situation;

Fig. 7 is the analogous diagram of de-noising signal y (t) in the present invention;

Fig. 8 is the e of variable step size LMS sef-adapting filter in the present invention ²(n) curve map;

Fig. 9 is the learning curve figure of variable step size LMS sef-adapting filter in the present invention;

Figure 10 be in the present invention IMF component again weighted mean obtain average after the analogous diagram of IMF component;

Figure 11 is the analogous diagram of de-noising signal x (t) final in the present invention.

Embodiment

Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described, should be appreciated that preferred embodiment described herein is only for instruction and explanation of the present invention, is not intended to limit the present invention.

According to the embodiment of the present invention, as Figure 1-Figure 11, a kind of vibration signal noise-reduction method based on variable step size LMS-EEMD is provided.

Technical scheme of the present invention is for the Denoising Problems of vibration signal in low signal-to-noise ratio situation, the progress to a certain degree that the least mean square algorithm (LMS) that should be feature according to adaptive and set empirical mode decomposition (EEMD) obtain in respective field, therefore propose a kind of new self-adaptive solution method, the method is based on variable step size LMS-EEMD adaptive filter method and utilize the character of related coefficient to highlight the periodicity of original signal and IMF component, is solved the On The Choice of IMF component in noise reduction process by the related coefficient calculating IMF component and original signal ^[7].Finally, provided the signal to noise ratio (S/N ratio) (SNR) of signal by many experiments emulation, root-mean-square error (RMSE) and related coefficient (ρ) check the superiority of this algorithm.

The principle of 1 set empirical mode decomposition (EEMD) and algorithm

1.1 empirical mode decompositions (EMD) principle

Empirical mode decomposition (EMD) is the part of core the most during whole Hilbert-Huang converts, and the quality of its decomposition result directly determines the quality of HHT result.Empirical mode decomposition (EMD) is several intrinsic mode functions components (IMF) and residual volume (RES) sum a signal decomposition.The object of decomposing is exactly that a non-stationary signal is decomposed into single-frequency components from high frequency to low frequency.These components (IMF) must meet two conditions ^[2]: a) in whole burst, extreme point and the number of zero crossing differ one or equal at the most.B) signal is about time shaft Local Symmetric, is namely all zero in the average of its upper and lower envelope of any point place of signal.Document ^[2]give empirical mode decomposition (EMD) detailed algorithm.First need the local maximum minimum point determining signal in EMD decomposable process, then use cubic spline line all local maximums and minimum point to be coupled together respectively and form upper and lower envelope, then obtain Mean curve by upper and lower envelope.In the process asking for envelope, when there is the anomalous events such as shock pulse component in signal, be bound to affect choosing of extreme point, makes extreme's distribution distortion, finally causes upper and lower envelope to be the combination of the envelope of actual signal and anomalous event.Finally by the average that this envelope calculates, then the IMF component filtered out just contains intrinsic mode functions and the anomalous event of signal, thus creates modal overlap phenomenon.Finally cause EMD not good for the noise reduction of the non-stationary signal comprising anomalous event.

1.2 set empirical mode decomposition (EEMD) principles

In order to overcome the modal overlap phenomenon that EMD decomposes, WU in 2008 etc. have put forward set empirical mode decomposition (EEMD) on the basis that EMD decomposes, the essence of its algorithm superposes white Gaussian noise in original signal, carry out several times EMD decomposition, get the average of IMF component as net result.This algorithm utilizes the statistical property of white Gaussian noise, make the signal after adding noise have continuity on different frequency yardstick, use the zero mean characteristic of white noise, through multiple averaging simultaneously, white noise is cancelled out each other, thus suppresses the impact eliminating white noise even completely.

1.3 set empirical mode decomposition (EEMD) algorithms

EEMD specific algorithm step is as follows:

A) repeatedly add in original signal have that average is 0, standard deviation be the white noise of constant namely:

x _i(t)＝x(t)+n _i(t)；

In formula: be the signal adding white Gaussian noise i-th time.The size and the number of times that add white Gaussian noise directly can affect the discomposing effect that signal EEMD avoids modal overlap.The equal-sized white noise of general selection dye noise cancellation signal, number of times is the bigger the better under the limited conditions ^[8].

B) EMD decomposition is carried out respectively, the IMF component obtained and i residual volume.Be wherein after adding white Gaussian noise i-th time, decompose the jth IMF obtained.

C) repeat a) and b) M time.Utilize the average statistical of incoherent random series to be the principle of 0, the IMF of above-mentioned correspondence is carried out population mean computing, eliminate and repeatedly add the impact of white Gaussian noise on true IMF, the IMF finally obtained after EEMD decomposition is:

$c_j\left(t\right)=\frac{1}{M}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{r}_i;$

The residual volume finally obtained after EEMD decomposition is r (t):

$r\left(t\right)=\frac{1}{M}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{r}_i;$

In formula: c _jt () decomposes for carrying out EEMD to original signal x (t) the jth IMF component obtained.When M is larger, corresponding white noise IMF's and will 0 be tending towards.The result that now EEMD reconstructs after decomposing is:

x(t)＝Σ _jc _j(t)+r(t)；

In formula: r (t) is final residual volume.Any one signal x (t) can be resolved into several IMF components and 1 residual volume sum, eigenmode component c by EEMD method _j(t) (j=1,2 ...) composition of representation signal different frequency range from high to low, therefore be also called single-frequency components.

2 sef-adapting filters (LMS) principle and algorithm

2.1 sef-adapting filter principles

The ultimate principle of auto adapted filtering is exactly that the result utilizing previous moment to obtain filter parameter automatically regulates the filter parameter of now " with adaptation signal and noise the unknown or time dependent statistical property " thus realizes optimal filtering.Therefore " sef-adapting filter has self-control and tracking power ^[10].The General Principle structure of sef-adapting filter, as shown in Figure 1.Be input signal in Fig. 1, by producing output signal after the digital filter of Parameter adjustable, output signal and wanted signal compared, obtains error signal.Adjust with by the parameter of adaptive algorithm to wave filter, the object of adjustment makes error signal minimum.

2.2LMS adaptive filter algorithm

The ultimate principle of auto adapted filtering is exactly the filter parameter utilizing the result of previous moment acquisition filter parameter automatically to regulate now, thus realizes optimal filtering.Therefore " sef-adapting filter has self-control and tracking power ^[10].The General Principle structure of sef-adapting filter, as shown in Figure 1.Be input signal in Fig. 1, by producing output signal after the digital filter of Parameter adjustable, output signal and wanted signal compared, obtains error signal.Adjust with by the parameter of adaptive algorithm to wave filter, the object of adjustment makes error signal minimum.

X(n)＝[x(n),x(n-1),...,x(n-M+1)]；

The weight vectors of sef-adapting filter is: W (n)=[W _n1, W _n2, W _n3..., W _nM] ^t.

The output of corresponding sef-adapting filter is: $y\left(n\right)=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{W}_{i}x(n-i+1)=W{\left(n\right)}^{T}X\left(n\right).$

Y (n) relative to the error of wanted signal d (n) is: e (n)=d (n)-W (n) ^tx (n).

Square error e should be made according to minimum mean square error criterion MSE ²n () is for minimum.Namely the iterative equation of LMS algorithm is: W (n+1)=W (n)+2 μ e (n) X (n); Wherein, μ is the constant of control convergence speed, is called step factor, and e (n) is error signal.Restrain after ensureing iteration, namely μ must meet:

0<μ<1/λ _max；

Wherein, λ _maxfor list entries x (n) autocorrelation matrix R _xxeigenvalue of maximum.For variable step size sef-adapting filter specific algorithm document ^[9]provide.Feature due to LMS sef-adapting filter is that structure is simple, good stability, be easy to realize, and is therefore widely used in the fields such as System Discrimination, echo cancellor, Interference Cancellation, Signal separator.But the steady-state error of LMS algorithm and rate of convergence exist inevitable contradiction, cause result to be: little step-length can reduce imbalance, improve steady-state behaviour, but rate of convergence can be caused again to reduce, noise reduction is undesirable; Large step-length can improve convergence of algorithm speed, but imbalance is comparatively large, the possibility of error function concussion is comparatively large and steady-state behaviour will reduce.Thus good noise reduction can not be reached for the comparatively complicated amplitude-modulation frequency-modulation signal that dye is made an uproar.

The evaluation criterion of 3 de-noising signals

3.1 related coefficients (ρ), signal to noise ratio (S/N ratio) (SNR), root-mean-square error (RMSE)

Related coefficient is the concept in statistical study, can represent two seasonal effect in time series degrees of correlation in the signal.Technical scheme of the present invention mainly studies the noise reduction of signal, does not get rid of the situation occurring filtering original signal effective constituent, therefore selects related coefficient to contrast.Moreover related coefficient is in amplitude-modulation frequency-modulation signal, the otherness of true IMF component and false IMF component and noise IMF component can be strengthened.When choosing IMF component, the correlativity according to IMF component and original signal judges, thus carries out self-adapting reconstruction, and this is just more effective, convenient and accurate for choosing IMF component compared with people.The formula of related coefficient is:

${\mathrm{\&rho;}}_{\mathrm{xy}}=\frac{\mathrm{cov}(x,y)}{\sqrt{E\left(x\right)}\sqrt{E\left(y\right)}};$

Wherein cov (x, y) is covariance function, and E is expectation function.The span of correlation coefficient ρ is-1<=ρ <=1.ρ >0 represents that positive correlation ρ <0 represents that negative correlation ρ=0 represents uncorrelated. and degree of correlation between the larger explanation of the absolute value of ρ two components is higher.The applicant thinks that generally getting ρ >=0.5 is correlated with for general ^[7].

The computing formula of signal to noise ratio (S/N ratio) (SNR) is:

$\mathrm{SNR}=10{\log }^{\frac{P_s}{P_n}};$

Wherein, P _sfor the power of original signal, P _nfor the noise power of signal.Signal to noise ratio (S/N ratio) (SNR) is the bigger the better.

Root-mean-square error (RMSE) reflects the error of de-noising signal and original signal, therefore R is the smaller the better, and its computing formula is:

$R=\sqrt{\frac{1}{n}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(s\left(i\right)-x\left(i\right))}^2};$

Wherein, s (i) is original signal, and x (i) is the signal after noise reduction.

4 noise-reduction methods and the contrast of relevant emulation experiment

Technical scheme of the present invention is noisy mainly for environment, disturbs the noise reduction process of more outdoor vibration signal.So select there is limit for length, the signal of low signal-to-noise ratio in simulation process, use MATLAB2012a to carry out many experiments emulation, get N=1024 point.The new method variable step size LMS-EEMD adaptive filter algorithm selecting set empirical mode decomposition (EEMD), variable step size adaptive LMS filter set empirical mode decomposition (EEMD) and the applicant to propose respectively carries out dye noise cancellation signal noise reduction process.Utilize the evaluation criterion of collection of illustrative plates and three signals through comparing thus prove that the new method of the applicant has certain values.

Choosing amplitude-modulation frequency-modulation signal is:

x(t)＝(1+0.2sin(60πt))cos(60πt+0.5sin(30πt))+sin(240πt)

Noise to be average be 0 amplitude be 0.5 white noise 0.8*randn (size (t)).Namely contaminating noise cancellation signal is:

x(t)＝(1+0.2sin(60πt))cos(60πt+0.5sin(30πt))+sin(240πt)+0.8*randn(size(t))

Simulation result as shown in Figure 2.

The relevant emulation of 4.1 set empirical mode decomposition (EEMD)

Set empirical mode decomposition (EEMD) is carried out to dye noise cancellation signal z (t).Document ^[10]if point out noise intensity have much so carry out EEMD decompose time the equirotal white noise of intensity can be selected to decompose.The white noise intensity of the amplitude-modulation frequency-modulation signal of simulating due to technical scheme of the present invention is 0.8, therefore chooses the white noise of 0.8 intensity, carries out 50 EMD and decomposes, and the IMF component that obtains of weighted mean is as shown in Figure 3 again for the IMF component obtained.

As can be seen from Figure 3 IMF2, IMF3, IMF4 are the fundamental component of original signal from high frequency to low frequency.IMF2, IMF3, IMF4 compared with EMD obviously can find out that the scope of modal overlap and intensity are all reducing and successful.But the modal overlap phenomenon of IMF still exists.Carry out self-adapting signal reconstruct through the method for related coefficient (ρ) and obtain noise reduction result as shown in Figure 4.

In Fig. 4, signal is obviously better than the noise reduction result of EMD.Also can find out according to the result of table 3 decompose no matter the signal after noise reduction is signal to noise ratio (S/N ratio) through EEMD, root-mean-square error or related coefficient be obtained for and improve significantly.As shown in table 1:

table 1

The relevant emulation of 4.2 variable step size LMS sef-adapting filters

Carry out variable step-size LMS sef-adapting filter and choose through many experiments that initial to upgrade step factor be mu ₀=0.055, LMS filter order is k=10, and number of run is 30 times.Find after search that namely start convergence upgrades step factor, formula is as follows:

$\mathrm{mu}=\frac{{\mathrm{mu}}_0}{1+\left(\frac{n}{100}\right)};$

Wherein n is the iterations of signaling point, and scope is from 1 to 1024.Mu is the step factor of n-th.Result after variable-step self-adaptive wave filter noise reduction is carried out as shown in Figure 5 to pollution signal.

Its result is significantly better than the noise reduction result of small echo, EMD, EEMD as shown in Figure 5.Also obviously can find that variable step size LMS sef-adapting filter makes after noise reduction three evaluation criterions be obtained for and significantly improves according to the result of table 2.But still there is white noise phenomenon in head end points place.As shown in table 2:

table 2

5 based on the relevant emulation of variable step size LMS-EEMD adaptive algorithm

From the Experimental comparison of Part IV, it is that any noise-reduction method is all with the limitation of self that the applicant finds.EEMD noise reduction in low signal-to-noise ratio situation is bad; The immutable step factor problem of LMS adaptive algorithm and the undesirable problem of head end points noise reduction.Variable step size LMS-EEMD adaptive algorithm is proposed for above problem technical scheme of the present invention.Its result is signal to noise ratio (S/N ratio), root-mean-square error or related coefficient all increases, for the noise-reduction method of the dye noise cancellation signal in low signal-to-noise ratio situation provides good guidance.Shown in algorithm steps process flow diagram 6.

Still choose the original signal x (t) of Part IV, white noise 0.8*randn (size (t)) and dye noise cancellation signal z (t).Carry out variable step size LMS sef-adapting filter noise reduction, choose the initial step length factor through test of many times being mu to dye noise cancellation signal z (t) ₀=0.055, LMS filter order is k=10, and number of run is 30 times.Find after search that namely start convergence upgrades step factor, formula is as follows:

$\mathrm{mu}=\frac{{\mathrm{mu}}_0}{1+\left(\frac{n}{100}\right)};$

Wherein n is the iterations of signaling point, and scope is from 1 to 1024.Mu is the step factor of n-th.

The weights of initialization forward-direction filter:

W＝[0.1642，0.1341，0.0529，-0.0624，-0.1586，-0.1932，-0.1555，-0.0599，0.0584，0.1229，0.1106]

Obtain de-noising signal y (t) as shown in Figure 7.

Signal y (t) the head end points place obtained after variable step size LMS sef-adapting filter noise reduction as can be seen from Figure 7 still has white noise not have filtering.Make the e about variable step size LMS sef-adapting filter respectively ²the learning curve figure of (n) curve map and variable step size LMS sef-adapting filter, respectively as shown in Figure 8, Figure 9.

Point left and right de-noising signal y (t) or have larger error with original signal x (t) from 0th o'clock to the 50th as can be seen from Figure 8.

Signal y (t) obtained carries out set empirical mode decomposition (EEMD) again, the white noise amplitude of the amplitude-modulation frequency-modulation signal of simulating due to technical scheme of the present invention is 0.8, therefore choose the white noise of 0.8, carry out 50 EMD decompose the IMF component that obtains again weighted mean obtain average after IMF component, as shown in Figure 10.

Can find out substantially do not have mode mixing problem and high fdrequency component IMF1 to only have a small amount of white noise now from Figure 10.Key is that IMF1 component well shows y (t) head end spot noise composition.Finally utilize original signal x (t) to carry out signal reconstruction with the correlation coefficient ρ of each IMF component, get ρ >=0.5 here and be just considered as effective IMF component.Final de-noising signal x (t) obtained as shown in figure 11.

The result obtained from Figure 11 can find out that waveform presses close to original signal x (t) more, and the noise contribution of y (t) head end points is well by filtering.Evaluation criterion is as shown in table 3:

table 3

Contaminate noise cancellation signal z (t) as can be seen from Table 3 all can effectively improve through variable step size LMS-EEMD adaptive algorithm three evaluation criterions.Signal to noise ratio (S/N ratio) improves 12%, and root-mean-square error also reduces, and correlativity brings up to 0.9417.

Technical scheme of the present invention is for the noise reduction problem of low signal-to-noise ratio vibration signal, make use of the advantage that the fast convergence rate step factor of variable step size LMS adaptive algorithm is adjustable, for the amplitude-modulation frequency-modulation signal in low signal-to-noise ratio situation, can effective noise reduction, but still there is a large amount of white noises in the signal header end points place after noise reduction.Make use of again the advantage that set empirical mode decomposition (EEMD) anti-mode is folded, the white noise decompositing high frequency that can be correct, but, in low signal-to-noise ratio situation, easily occur that anomalous event makes IMF component occur slight modal overlap effect, thus cannot correctly decomposite a part of white noise and need artificial selection and identify effective IMF component.Merits and demerits for above two methods devises variable step size LMS-EEMD sef-adapting filter, and the advantage that this algorithm has above two methods also substantially overcomes their shortcoming.Thus be issued to good noise reduction in the situation of low signal-to-noise ratio.

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Last it is noted that the foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, although with reference to previous embodiment to invention has been detailed description, for a person skilled in the art, it still can be modified to the technical scheme described in foregoing embodiments, or carries out equivalent replacement to wherein portion of techniques feature.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (8)

1., based on a vibration signal noise-reduction method of variable step size LMS-EEMD, it is characterized in that, comprising:

A, according to original signal, obtain initial de-noising signal;

B, initial de-noising signal to be decomposed, choose required IMF component in noise reduction process;

C, according to original signal and the IMF component chosen, obtain final de-noising signal.

2. the vibration signal noise-reduction method based on variable step size LMS-EEMD according to claim 1, it is characterized in that, described step a, specifically comprises:

(1) choose original signal x (t), white noise 0.8*randn (size (t)) and dye noise cancellation signal z (t), initialization forward-direction filter weights, the setting initial step length factor;

(2) set filter order and number of run;

(3) variable step size LMS sef-adapting filter noise reduction is carried out to dye noise cancellation signal z (t);

(4) more square e (n) is minimum is together convergence direction, and find after search that namely start convergence upgrades step factor, formula is as follows:

$\mathrm{mu}=\frac{m_0}{1+\left(\frac{n}{100}\right)};$

Wherein n is the iterations of signaling point, and scope is from 1 to 1024; Mu is the step factor of n-th, and n is natural number;

(5) iteration is until signal length is n, obtains initial de-noising signal y (t).

3. the vibration signal noise-reduction method based on variable step size LMS-EEMD according to claim 2, it is characterized in that, described choose original signal x (t), white noise 0.8*randn (size (t)) and and dye noise cancellation signal z (t) operation in, specifically comprise:

Choosing amplitude-modulation frequency-modulation signal is: x (t)=(1+0.2sin (60 π t)) cos (60 π t+0.5sin (30 π t))+sin (240 π t), noise to be average be 0 amplitude be 0.5 white noise 0.8*randn (size (t)); Namely contaminating noise cancellation signal is:

x(t)＝(1+0.2sin(60πt))cos(60πt+0.5sin(30πt))+sin(240πt)+0.8*randn(size(t))。

4. the vibration signal noise-reduction method based on variable step size LMS-EEMD according to claim 2, it is characterized in that, described to dye noise cancellation signal z (t) carry out in the operation of variable step size LMS sef-adapting filter noise reduction, the concrete steps of carrying out variable step size LMS sef-adapting filter noise reduction are as follows:

1) by input signal, by producing output signal after the digital filter of Parameter adjustable, output signal and wanted signal being compared, obtains error signal; Adjust with by the parameter of adaptive algorithm to wave filter, the object of adjustment makes error signal minimum: X (n)=[x (n), x (n-1) ..., x (n-M+1)];

The weight vectors of sef-adapting filter is: W (n)=[W _n1, W _n2, W _n3..., W _nM] ^t;

The output of corresponding sef-adapting filter is: $y\left(n\right)=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{W}_{i}x(n-i+1)=W{\left(n\right)}^{T}X\left(n\right);$

Y (n) relative to the error of wanted signal d (n) is: e (n)=d (n)-W (n) ^tx (n);

Square error e should be made according to minimum mean square error criterion MSE ²n () is for minimum;

2) iterative equation of LMS algorithm is: W (n+1)=W (n)+2 μ e (n) X (n); Wherein, μ is the constant of control convergence speed, is called step factor, and e (n) is error signal; Restrain after ensureing iteration, namely μ must meet:

0<μ<1/λ _max；

Wherein, λ _maxfor list entries x (n) autocorrelation matrix R _xxeigenvalue of maximum.

5. the vibration signal noise-reduction method based on variable step size LMS-EEMD according to any one of claim 2-4, it is characterized in that, described step b, specifically comprises:

(1) set empirical mode decomposition EEMD is carried out again to initial de-noising signal y (t) obtained;

(2) choose the white noise meeting default amplitude-modulation frequency-modulation signal, carry out 50 EMD and decompose;

(3) the IMF component obtained again weighted mean obtain average after IMF component.

6. the vibration signal noise-reduction method based on variable step size LMS-EEMD according to claim 5, is characterized in that, described initial de-noising signal y (t) to obtaining carries out the operation of gathering empirical mode decomposition EEMD again, specifically comprises:

1) repeatedly add in original signal have that average is 0, standard deviation be the white noise of constant namely:

x _i(t)＝x(t)+n _i(t)；

In formula: be the signal adding white Gaussian noise i-th time;

2) carry out set empirical mode decomposition EEMD respectively to decompose, the IMF component obtained and i residual volume.Be wherein after adding white Gaussian noise i-th time, decompose the jth IMF component obtained;

3) 1 is repeated) and 2) M time, the average statistical of incoherent random series is utilized to be the principle of 0, the IMF component of above-mentioned correspondence is carried out population mean computing, eliminate and repeatedly add the impact of white Gaussian noise on true IMF component, finally obtaining the IMF component after gathering empirical mode decomposition EEMD is:

$c_j\left(t\right)=\frac{1}{M}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{r}_i;$

Finally obtaining the residual volume after gathering empirical mode decomposition EEMD is r (t):

$r\left(t\right)=\frac{1}{M}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{r}_i;$

In formula: c _ja t jth IMF component that () obtains for carrying out set empirical mode decomposition EEMD to original signal x (t); When M is larger, the IMF component of corresponding white noise and will 0 be tending towards; The result reconstructed after now gathering empirical mode decomposition EEMD is:

x(t)＝Σ _jc _j(t)+r(t)；

In formula: r (t) is final residual volume, and M is natural number.

7. the vibration signal noise-reduction method based on variable step size LMS-EEMD according to claim 6, it is characterized in that, described step c, specifically comprises:

(1) utilize original signal x (t) to carry out signal reconstruction with the correlation coefficient ρ of each IMF component;

(2) choosing the IMF component that related coefficient meets predetermined threshold value is effective value, obtains final de-noising signal x (t).

8. the vibration signal noise-reduction method based on variable step size LMS-EEMD according to claim 7, is characterized in that, the described original signal x (t) that utilizes carries out the operation of signal reconstruction with the correlation coefficient ρ of each IMF component, specifically comprises:

When choosing IMF component, the correlativity according to IMF component and original signal judges, carries out self-adapting reconstruction; The formula of the related coefficient of IMF component and original signal is:

${\mathrm{\&rho;}}_{\mathrm{xy}}=\frac{\mathrm{cov}(x,y)}{\sqrt{E\left(x\right)}\sqrt{E\left(y\right)}};$

Wherein cov (x, y) is covariance function, and E is expectation function; The span of correlation coefficient ρ is-1<=ρ <=1;

The computing formula of signal to noise ratio (S/N ratio) (SNR) is:

$\mathrm{SNR}=10{\log }^{\frac{P_s}{P_n}};$

Wherein, P _sfor the power of original signal, P _nfor the noise power of signal;

Root-mean-square error R reflects the error of de-noising signal and original signal, and its computing formula is:

$R=\sqrt{\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(s\left(i\right)-x\left(i\right))}^2};$

Wherein, s (i) is original signal, and x (i) is the signal after noise reduction.