CN102930149A - Sensor network sensing information denoising processing method based on principal component analysis (PCA) and empirical mode decomposition (EMD) - Google Patents

Abstract

The invention discloses a sensor network sensing information denoising processing method based on principal component analysis (PCA) and empirical mode decomposition (EMD). The method comprises the following steps of: performing EMD on a sensing signal to obtain K intrinsic mode function (IMF) components imfk (t) for characterizing time scale and remainder terms; extracting detailed signal information in imf1, calculating energy W[1] of the noise contained in the imf1, and calculating energy of other layers according to W[1]; and performing PCA decomposition on imfk (t), selecting the previous H principal components in a proper number for reconstructing and denoising according to a ratio of the energy of the noise contained in the imfk(t) to obtain the denoised detailed signal information; and accumulating all the denoised detailed signal information and remainder terms to obtain the denoised signals. The method is simple and good in denoising effect.

Description

Sensor network perception information denoising method based on PCA and EMD

Technical field

The present invention relates to remove the disposal route of noise, refer to particularly a kind of sensor network perception information denoising method based on PCA and EMD.

Background technology

Wireless sensor network is the information of Real-Time Monitoring, perception and processing monitored area collaboratively, and these information are sent to the user.Owing to being subject to the impact of monitoring of environmental, can contain a large amount of noises in the perception information, these noises can cause and can't analyze exactly monitoring information as not rejecting, and badly influence the correctness of subsequent treatment.Therefore, how to being carried out effective denoising by the perception information of noise pollution to obtain more accurately measurement value sensor, be a problem demanding prompt solution.

Wavelet analysis has good time frequency analysis characteristic, is widely used in signal denoising, but when using wavelet transformation to signal denoising, needs the number of plies of chosen in advance wavelet basis and decomposition.Existing studies show that, select different wavelet basiss under the same terms and decompose the number of plies, very large on the denoising result impact, the particularly selection of wavelet basis function, denoising result is had conclusive impact, and this has brought very large inconvenience to utilizing small echo to carry out signal denoising.

EMD (Empirical mode decomposition), it is empirical mode decomposition, overcome to a certain extent the deficiency of wavelet transformation, it is the adaptive decomposition algorithm that a kind of complete data that the people such as Huang proposes drives, can become data decomposition to have in a group of physical significance and accumulate mode function (Intrinsic mode function, IMF) component.Compare with wavelet transformation, the basis function among the EMD and decomposition level do not need given in advance, but obtain adaptively by the mode of iteration according to characteristics of signals, and substrate can change with the different of signal with decomposition level.Existing Signal denoising algorithm based on EMD mainly is divided into three major types at present: the first kind is the partial reconfiguration Denoising Algorithm, select part high-frequency I MF by certain rule in these class methods, the high-frequency I MF that selects is used as pure noise directly removes, then cumulative remaining IMF is to realize denoising; Equations of The Second Kind is direct threshold denoising method, in these class methods will based on wavelet transformation soft/hard value filtering thought is directly used among the EMD, and the method for IMF coefficients by using threshold denoising is processed, each layer IMF after processing add up with the realization denoising; The 3rd class is based on the threshold denoising method of modality unit, consider the characteristic that EMD decomposes in these class methods, with the modality unit between two zero crossings among the IMF as the fundamental analysis object, as the threshold process feature, take modality unit as unit IMF is carried out threshold process to realize denoising with the modality unit amplitude.

Above-mentioned algorithm is the EMD denoising good thinking is provided, and has obtained preferably denoising effect, but still has some problems.As: in the partial reconfiguration Denoising Algorithm, the high-frequency I MF that selects directly removed as noise and directly cumulative to remaining IMF, cause after the denoising the more and noise of signal detail information dropout not remove fully; In direct threshold denoising method, do not consider the inherent characteristic that EMD decomposes, destroyed the integrality of modality unit during denoising, affected the effect of denoising; In the threshold denoising method based on modality unit, take into account the resolution characteristic of EMD, do not destroyed the integrality of built-in oscillation among the IMF during denoising, improved noise remove ability and signal detail hold facility, compare with other two kinds of methods, obtained better denoising effect.But in the threshold denoising method based on modality unit, still have two problems to be difficult to solve: the one, the threshold value of modality unit determines it is a difficult problem, often adopts wavelet threshold in the existing algorithm or rule of thumb selects threshold value, does not have perfect threshold value choice criteria; The 2nd, in the algorithm extreme value is directly removed less than the modality unit of threshold value, and extreme value directly keeps greater than the modality unit of threshold value.But noise is distributed among the whole IMF, therefore little threshold value modality unit is directly removed, and can cause part signal information to be lost; And directly keep having a few in the large threshold value modality unit not processed, can cause the noise can not be by complete removal.

Summary of the invention

The object of the invention is to overcome above-mentioned the deficiencies in the prior art and provides a kind of based on PCA(Principal component analysis, based on principal component analysis (PCA)) and the sensor network perception information denoising method of EMD, the method can further improve the denoising ability of EMD, effectively eliminates the noise in the perception information.

Realize that the technical scheme that the object of the invention adopts is: a kind of sensor network perception information denoising method based on PCA and EMD may further comprise the steps:

Perceptual signal x (t) is carried out EMD decompose, x (t) is decomposed into K IMF component imf that characterizes time scale _k(t) and remainder r _K, wherein (k=1,2 ..., K);

Utilize " 3 σ rule ", extract imf ₁In signal detail information imf ₁ ^d

Calculate

The energy W[1 of institute's Noise], again according to W[1] calculating imf _k(t) the energy W[k of institute's Noise in (k 〉=2)];

To imf _k(t) carry out PCA and decompose, and according to imf _k(t) ratio of contained noise energy in is selected front H principal component of suitable number Be reconstructed denoising, obtain the signal detail information after the denoising

Signal detail information after cumulative whole denoisings

With remainder r _K, obtain the signal after the denoising

In technique scheme, described perceptual signal x (t) carries out EMD by following formula and decomposes:

Imf wherein _k=y _k+ n _k, y _kExpression does not have contaminated original signal, n _kExpression institute Noise, and

In technique scheme, described

By following formulas Extraction:

${\mathrm{imf}}_1^d\left[i\right]=\left\{\begin{array}{cc}{\mathrm{imf}}_1\left[i\right],& \mathrm{ifabs}\left(\mathrm{imf}\right[i\left]\right)\&GreaterEqual;3{\mathrm{\&sigma;}}_1\\ 0,& \mathrm{ifabs}\left({\mathrm{imf}}_1\right[i\left]\right)<3{\mathrm{\&sigma;}}_1\end{array}\right..$

In the following formula, 1≤i≤M, M are imf ₁Length; Noise variance HH represents imf ₁The high-frequency sub-band wavelet coefficient.

In technique scheme, described

The energy W[1 of institute's Noise] calculate by following formula:

$W\left[1\right]=({\mathrm{imf}}_1-{\mathrm{imf}}_1^d){({\mathrm{imf}}_1-{\mathrm{imf}}_1^d)}^T=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\left({\mathrm{imf}}_1\right[i]-{\mathrm{imf}}_1^d[i\left]\right)}^2.$

In technique scheme, described imf _k(t) the energy W[k of institute's Noise in (k 〉=2)] calculate by following formula:

K 〉=2; γ in the formula=0.719, ρ=2.01.

In technique scheme, described H carries out value in accordance with the following methods: if having β so that set up with lower inequality, then make H=β,

$(\underset{i=\mathrm{\&beta;}+1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i/\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i)\&le;\frac{W\left[k\right]}{\mathrm{\&epsiv;}\left({\stackrel{\&OverBar;}{X}}_k\right)}\&le;(\underset{i=\mathrm{\&beta;}}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i/\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i)$

Wherein, N is the principal component number after PCA decomposes, λ _iBe i principal component pi characteristic of correspondence value; For

Energy,

For

Expectation.

So, imf _kValue after the denoising Wherein

u _iBe eigenvalue λ _iThe characteristic of correspondence vector.

Description of drawings

Fig. 1 is the process flow diagram of the inventive method;

Fig. 2 is original Doppler signal schematic representation;

Fig. 3 is for containing noisy Doppler signal schematic representation;

Fig. 4 is the signal schematic representation after signal shown in Figure 3 adopts the denoising of Bayesian-Wavlet method;

Fig. 5 is the signal schematic representation after signal shown in Figure 3 adopts the denoising of Mode-EMD method;

Fig. 6 is the signal schematic representation after signal shown in Figure 3 adopts the inventive method denoising.

Embodiment

The present invention is described in further detail below in conjunction with the drawings and specific embodiments.

The present invention is based on the sensor network perception information denoising method (hereinafter to be referred as the PCA-EMD method) of PCA and EMD, may further comprise the steps:

Step S101: perceptual signal x (t) is carried out EMD decompose, x (t) is decomposed into K IMF component imf that characterizes time scale _k(t) and remainder r _K, namely

(k=1,2 ..., K).Wherein, imf _k=y _k+ n _k, y _kExpression does not have contaminated original signal, n _kExpression institute Noise, and

Step S 102: utilize " 3 σ rule ", extract imf ₁In signal detail information imf ₁ ^d

Actual imf ₁In still contain a certain amount of signal detail information, to imf ₁Carry out suitable processing, extract its contained signal detail information and also kept, can improve denoising effect, utilize the imf after processing ₁The energy of estimating institute's Noise among all the other IMF is also more accurate.

Because imf ₁Middle noise accounts for the overwhelming majority, and only contains a small amount of signal detail information, and the still approximate obedience zero-mean normal distribution of institute's Noise, extracts so be fit to very much adopt " 3 σ rule " to carry out detailed information.Because imf ₁Satisfy Additive noise model, i.e. imf ₁=y ₁+ n ₁

Because noise

According to " 3 σ " rule, noise n ₁Distribution satisfy P{|n ₁[i] |≤3 σ ₁}=99.73%.

Because noise n ₁Drop on [3 σ ₁, 3 σ ₁] between probability be 0.9973, and drop on 3 σ ₁Outside probability only be about 0.003.If so imf ₁The value of [i] does not drop on [3 σ ₁, 3 σ ₁] within, then can think imf ₁Appreciable error must be contained in [i], also namely signal message y must be contained ₁So, need to be kept.

So utilize " 3 σ rule ", by following formula to imf ₁Carrying out detailed information extracts:

${\mathrm{imf}}_1^d\left[i\right]=\left\{\begin{array}{cc}{\mathrm{imf}}_1\left[i\right],& \mathrm{ifabs}\left(\mathrm{imf}\right[i\left]\right)\&GreaterEqual;3{\mathrm{\&sigma;}}_1\\ 0,& \mathrm{ifabs}\left({\mathrm{imf}}_1\right[i\left]\right)<3{\mathrm{\&sigma;}}_1\end{array}\right.$

Wherein, Expression is from imf ₁The signal detail information that extracts; 1≤i≤M, M are imf ₁Length; Noise variance

HH represents imf ₁The high-frequency sub-band wavelet coefficient.

Step S103: the energy that calculates each layer IMF institute Noise.

The first step: at first pass through $W\left[1\right]=({\mathrm{imf}}_1-{\mathrm{imf}}_1^d){({\mathrm{imf}}_1-{\mathrm{imf}}_1^d)}^T=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\left({\mathrm{imf}}_1\right[i]-{\mathrm{imf}}_1^d[i\left]\right)}^2$ Calculate imf ₁The energy W[1 of institute's Noise].

Second step: at above-mentioned W[1] the basis on calculate imf by following formula _k(t) the energy W[k of institute's Noise in (k 〉=2)],

K 〉=2.γ and ρ are by lot of experimental data in the formula, utilize the method for linear regression to seek W[1] and W[k] between during funtcional relationship, the regression coefficient that calculates.γ in the present embodiment=0.719, ρ=2.01.

Step S104: to imf _k(t) carry out PCA and decompose, and according to imf _k(t) ratio of contained noise energy in is selected front H principal component of suitable number

Be reconstructed denoising, obtain the signal detail information after the denoising.

Utilizing PCA to remove imf _kDuring (k 〉=2) middle noise, the first few items principal component has comprised the principal character information of signal, and the principal component after relatively leaning on mainly is made of noise.If reach preferably denoising effect, must select front H principal component of suitable number to be reconstructed.

When the perceptual signal x (t) that is polluted by white noise after EMD decomposes, imf _kInstitute's Noise is approximate obeys the zero-mean normal distribution, and imf _k=y _k+ n _k, n _kExpectation E (n _k)=0, k 〉=2.

If $X_k={\mathrm{imf}}_k^T,$ ${\stackrel{\&OverBar;}{X}}_k={\mathrm{imf}}_k^T-E\left({\mathrm{imf}}_k^T\right)=X_k-E\left(X_k\right),$ $C_{x_k}=E\left({\stackrel{\&OverBar;}{X}}_k{\stackrel{\&OverBar;}{X}}_k^T\right)$ Be the covariance matrix of X, λ ₁〉=λ ₂〉=... 〉=λ _MBe the eigenwert of C, U=(u ₁, u ₂..., u _M) be the orthogonal matrix that the corresponding proper vector of eigenwert forms, M represents imf _kLength, obviously Institute's Noise with

Institute's Noise is identical.Suppose

Principal component after PCA decomposes is P=[p ₁, p ₂..., p _M] ^TIf, H principal component before selecting

Be reconstructed to remove

In noise, the signal after the denoising then

For: ${\widetilde{\stackrel{\&OverBar;}{X}}}_k=U\tilde{P}=(u_1,u_2,\&CenterDot;\&CenterDot;\&CenterDot;,u_M){(p_1,\&CenterDot;\&CenterDot;\&CenterDot;,p_H,0,\&CenterDot;\&CenterDot;\&CenterDot;,0)}^T=\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{u}_i{p}_i,$ This moment from

The noise of middle deletion

For: $\mathrm{\&Delta;}{\stackrel{\&OverBar;}{X}}_k={\stackrel{\&OverBar;}{X}}_k-{\widetilde{\stackrel{\&OverBar;}{X}}}_k=\underset{i=H+1}{\overset{M}{\mathrm{\&Sigma;}}}{u}_i{p}_i.$

If

With

Energy be respectively

If the H that selects can make

With

Contained noise energy W[k own] identical, namely

Then think

In noise substantially by full scale clearance, reached preferably denoising effect.Therefore, H is according to selecting following methods to carry out value in the present embodiment: if having β so that set up with lower inequality, then make H=β,

$(\underset{i=\mathrm{\&beta;}+1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i/\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i)\&le;\frac{W\left[k\right]}{\mathrm{\&epsiv;}\left({\stackrel{\&OverBar;}{X}}_k\right)}\&le;(\underset{i=\mathrm{\&beta;}}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i/\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i);$ Wherein, N is the principal component number after PCA decomposes, λ _iBe i principal component p _iThe characteristic of correspondence value,

After the principal component number H that should keep determines, according to

Obtain Signal after the denoising

Because

So imf _kValue after the denoising is: ${\mathrm{imf}}_k^d={({\widetilde{\stackrel{\&OverBar;}{X}}}_k+E\left({\mathrm{imf}}_k^T\right))}^T.$

Step S105: the signal after cumulative whole denoisings

With remainder r _K, obtain the signal after the denoising

The sensor network signal " Blocks " that the present embodiment selects four classes to have characteristic feature, " Bumps ", " Heavy sine " and " Doppler " are used for the denoising performance of explanation the inventive method as test sample book.

To above-mentioned four kinds of sensor network signals adopt respectively Wavelet-denoising Method (Bayesian-Wavelet) based on the Bayesian threshold value, based on the EMD threshold method (Mode-EMD) of modality unit with the present invention is based on PCA and EMD Denoising Algorithm (PCA-EMD) carries out denoising, when utilizing the Bayesian-Wavelet method to carry out denoising, wavelet basis is selected " db8 " small echo, decomposes the number of plies and is taken as 10; In the denoising of Bayesian-Wavelet and Mode-EMD, all adopt hard threshold method.The inventive method adopts square error MSE and signal to noise ratio snr to come the performance of appraisal procedure: signal to noise ratio (S/N ratio) is larger, and square error is less, shows that denoising effect is better.Result after the denoising is as shown in table 1, adopts the overall denoising effect of PCA-EMD method to be better than Bayesian-Wavelet method and Mode-EMD method.

Table 1

MSE and the SNR of perceptual signal after three kinds of method denoisings of different signal to noise ratio (S/N ratio)s is as shown in table 1.Can find out, as SNR=5dB the time, " Doppler " signal effect after the de-noising of PCA-EMD method is relatively good, compares with the Bayesian-Wavlet method, and SNR has improved approximately 2.509, and MSE has reduced approximately 0.053; Compare with the Mode-EMD method, SNR has improved approximately 1.529, and MSE has reduced approximately 0.017.The below adopts distinct methods to carry out the denoising contrast experiment to sensor network signal in the test sample book " Doppler ".In experiment, generate signal to noise ratio (S/N ratio) and be respectively SNR=0, the test signal of 5,10,15,20dB, signal length L is taken as 1000.When Fig. 2 is SNR=5dB, test sample book Doppler original signal figure, Fig. 3 is the Doppler signal graph behind the Noise, Fig. 4 is the signal graph that adopts after the Bayesian-Wavlet method is processed signal shown in Figure 3, Fig. 5 is the signal graph that adopts after the Mode-EMD method is processed signal shown in Figure 3, and Fig. 6 is the signal graph that adopts after PCA-EMD method of the present invention is processed signal shown in Figure 3, in Fig. 4 ~ Fig. 6, curve a is original signal, and curve b is signal after the denoising.

By above-mentioned Comparison of experiment results as can be known, the overall denoising effect of PCA-EMD method that the present invention proposes is better than Bayesian-Wavelet method and Mode-EMD method, and the signal after the de-noising is more near original signal.

Claims (6)

1. sensor network perception information denoising method based on PCA and EMD is characterized in that:

Perceptual signal x (t) is carried out EMD decompose, x (t) is decomposed into K IMF component imf that characterizes time scale _k(t) and remainder r _K, k=1 wherein, 2 ..., K;

Utilize " 3 σ rule ", extract imf ₁In signal detail information

Calculate

The energy W[1 of institute's Noise], again according to W[1] calculating imf _k(t) the energy W[k of institute Noise in], k 〉=2 wherein;

To imf _k(t) carry out PCA and decompose, and according to imf _k(t) ratio of contained noise energy in is selected front H principal component of suitable number

Be reconstructed denoising, obtain the signal detail information after the denoising

Signal detail information after cumulative whole denoisings

(1≤k≤K) and remainder r _K, obtain the signal after the denoising

2. described sensor network perception information denoising method based on PCA and EMD according to claim 1 is characterized in that described perceptual signal x (t) carries out EMD by following formula and decomposes:

Imf wherein _k=y _k+ n _k, y _kExpression does not have contaminated original signal, n _kExpression institute Noise, and

3. described sensor network perception information denoising method based on PCA and EMD according to claim 2 is characterized in that utilizing " 3 σ rule ", and is described Extract by following formula:

In the formula, 1≤i≤M, M are imf ₁Length, noise variance HH represents imf ₁The high-frequency sub-band wavelet coefficient.

4. described sensor network perception information denoising method based on PCA and EMD according to claim 3 is characterized in that described

The energy W[1 of institute's Noise] calculate by following formula:

。

5. described sensor network perception information denoising method based on PCA and EMD according to claim 4 is characterized in that described imf _k(t) the energy W[k of institute's Noise in] calculate by following formula:

In the formula, γ=0.719, ρ=2.01.

6. each described sensor network perception information denoising method based on PCA and EMD according to claim 1 ~ 5 is characterized in that described H carries out value in accordance with the following methods: if having β so that set up with lower inequality, then make H=β,

Wherein, N is the principal component number after PCA decomposes, λ _iBe i principal component p _iThe characteristic of correspondence value;

For

Energy,

For Expectation; Imf _kValue after the denoising Wherein

u _iBe eigenvalue λ _iThe characteristic of correspondence vector.

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