CN101729157A - Method for separating vibration signal blind sources under strong noise environment - Google Patents

Abstract

The invention discloses a vibration signal blind source separation algorithm in a strong noise environment. The method of the present invention is as follows: the first step, for a group of given noise-containing mixed signals, the mixed signal is denoised by the time-delay autocorrelation method, and the mixed signal after denoising is obtained; the second step is for the first step The obtained mixed signal is subjected to de-averaging and robust whitening preprocessing to further reduce the influence of the noise signal on the separation result; the third step is to calculate the second-order and fourth-order cumulants of the initial separation signal, and use the second-order and fourth-order cumulants The sum of the diagonal elements of the cumulant matrix is used as the cost function, and by maximizing the cost function, the cumulant matrices are jointly approximated to be diagonalized, and the separation of independent source signals is realized, thereby obtaining an orthogonal separation matrix. The present invention combines the existing noise reduction method with a blind separation algorithm to realize the separation of mixed signals in a strong noise environment, and has the advantages of better separation effect and faster convergence speed than the existing algorithm, and the noise reduction effect is not limited by threshold setting.

Description

Method for separating vibration signal blind sources under a kind of strong noise environment

Technical field

The present invention relates to the isolation technics of aliasing vibration signal, the aliasing vibration signal under especially a kind of strong noise environment separates technology.

Background technology

Aliasing vibration signal blind under the strong noise environment separates, because of its more near actual conditions, be the signal of interest processing method of identification signal of vibrating and small-signal, become related scientific research mechanism, and various countries scholar's research focus.

Existing method is mostly based on such fact: ignoring under the situation of noise, utilizing optimal method the optimization of independence criterion to be realized the separation of Instantaneous Mixtures.Vibration signal is as a kind of signal with time structure, the diagonal element quadratic sum that can adopt second order cumulant matrix usually is as cost function, this cost function of optimization is realized the separation of mixed signal, and its complexity is low, computational speed is fast, but noise signal is not had robustness.Having utilized the Higher Order Cumulants of noise signal based on the JADE algorithm of fourth order cumulant matrix is zero characteristic, realize the separation of mixed signal by each fourth order cumulant matrix of associating approximate diagonalization, because it has utilized Higher Order Cumulants, its complexity is big, computational speed is slow, responsive to the open country value, and only the white Gaussian coloured noise is had robustness.

At the aliasing signal that contains noise, consider to utilize the wavelet de-noising method that signals and associated noises is carried out noise reduction earlier, reducing the influence of noise signal, and then the aliasing signal behind the noise reduction is separated separating effect.Yet in the wavelet de-noising method, choosing of threshold values is most important, selects the improper algorithm that will cause to lose efficacy.

Summary of the invention

The present invention seeks at the defective that prior art exists provide a kind of proposition under strong noise environment, have good separating property, faster separating rate, the strong aliasing vibration signal of noise robustness is separated algorithm.

The present invention adopts following technical scheme for achieving the above object:

The method for separating vibration signal blind sources of a kind of strong noise environment of the present invention is characterized in that, this method may further comprise the steps:

(1), one group of given mixed signal that contains noise is carried out noise reduction process through autocorrelation method, then the mixed signal after the autocorrelation method noise reduction process is realized the secondary noise reduction through the time delay method, obtain the mixed signal x (t) behind the noise reduction, wherein t is a time series;

(2), the mixed signal x (t) behind the described noise reduction of step (1) is gone additive white Gaussian among the mixed signal x (t) behind average and the described noise reduction of steady whitening pretreatment filtering;

Described sane whitening pretreatment method is as follows:

(A) the mixed signal x (t) behind the calculating noise reduction is at time delay τ _jUnder covariance matrix C _x(τ _j), and with covariance matrix C _x(τ _j) be adjusted into:

$M_x\left({\mathrm{\τ}}_j\right)=\frac{1}{2}[C_x\left({\mathrm{\τ}}_j\right)+C_x^T\left({\mathrm{\τ}}_j\right)]$

In the following formula, τ _jRepresent j time delay, j=1,2 ..., J, J are the time delay number and are natural number that T represents transpose of a matrix, with M _x(τ _j) be configured to a combinatorial matrix M, and carry out singular value decomposition, that is:

M＝[M _x(τ ₁)，…，M _x(τ _J)]

M＝U∑V ^T

In the following formula, U is the orthogonal matrix identical with the Metzler matrix dimension; ∑ is the diagonal matrix of being made up of the singular value of M; V is an orthogonal matrix;

(B) picked at random parameter matrix α=[α ₁..., α _j..., α _J], α wherein _jJ the vector of expression parameter matrix α is for time delay τ _j, calculate:

f _j＝U ^TM _x(τ _j)U

Carrying out linear combination has:

$F=\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{\mathrm{\α}}_j{f}_j$

When matrix F satisfies orthotropicity, then forward step (D) to, otherwise forward step (C) to;

(C) adjust parameter matrix α according to the pairing characteristic vector u of the minimal eigenvalue of matrix F, that is:

$\mathrm{\α}=\mathrm{\α}+\frac{{[u^T{f}_{1}u...u^T{f}_{J}u]}^T}{\left|\right|[u^T{f}_{1}u...u^T{f}_{J}u]\left|\right|}$

Go to step (B) then, satisfy orthotropicity up to matrix F;

(D) the parameter matrix α that utilizes step (C) to obtain calculates objective matrix C, and it is made characteristic value decomposition, that is:

$C=\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{\mathrm{\α}}_j{M}_x\left({\mathrm{\τ}}_j\right)$

C＝RDR ^T

In the formula, D is the diagonal matrix of being made up of the characteristic value of objective matrix C, the R eigenvectors matrix that each characteristic value characteristic of correspondence vector is formed of serving as reasons;

(E) try to achieve albefaction matrix Q=D ^-1/2R ^T, whitened signal is z (t)=Qx (t).

(3), calculate the second order and the fourth order cumulant of initially-separate signal, with the diagonal element quadratic sum of second order and fourth order cumulant matrix as cost function;

Described initially-separate signal is as follows:

Initial quadrature separation matrix is W, then initially-separate signal y (t)=Wz (t);

(4), by cost function in the maximization steps (3), realize the associating approximate diagonalization of each second order and fourth order cumulant matrix, the quadrature separation matrix P that obtains making the mixed signal of the described filtering additive white Gaussian of step (2) to separate, thus separation matrix H and separation signal s (t) obtained; H=PQ wherein, s (t)=Hx (t).

The blind source separation method of described a kind of strong noise environment is characterized in that described quadrature separation matrix P adopts the Givens rotary process to try to achieve.

The invention has the beneficial effects as follows that the present invention is the algorithm that the aliasing vibration signal blind separates under a kind of strong noise environment, comprise noise reduction, sane preliminary treatment, structure cost function, optimize cost function and find the solution 4 steps of separation matrix.Before separating, fully the filtering noise signal to reduce the influence of noise signal to separating resulting, is finally realized the separation of aliasing signal under the strong noise environment.

In (1) step, the present invention has adopted time delay auto-correlation noise-reduction method, when this method of use is carried out noise reduction to the aliasing signals and associated noises, can realize the secondary noise reduction and not need to be provided with threshold values, and auto-correlation processing can keep the periodicity useful information in the vibration signal, remove noise aperiodic at random, the feasibility of its noise reduction has obtained affirming of people in the industry.Therefore, with the effective noise signal in the filtering aliasing signals and associated noises of this method.

In (2) step, the present invention is directed to the aliasing signal behind the noise reduction in (1) step, propose to utilize the additive white Gaussian in the sane preprocess method filtering aliasing signal, further reduce the influence of noise to separating resulting.

In (3) step, taken all factors into consideration advantage based on second order cumulant and fourth order cumulant algorithm, with the quadratic sum of the diagonal element of second order cumulant and fourth order cumulant matrix as cost function, make algorithm the convergence speed fast and insensitive, and avoided second order cumulant algorithm and can not separate deficiency with same spectrum architecture signals to the open country value than the fourth order cumulant algorithm.

In (4) step, the present invention utilizes optimal method that cost function is carried out optimization, realizes the associating approximate diagonalization of second order cumulant and fourth order cumulant, therefore realizes the separation of aliasing signal.

Therefore, the existing algorithm of the present invention has: under the strong noise environment good separating effect and stable, be not subjected to threshold values that the advantage of restriction is set, and have the characteristic of fast convergence rate for the separation of a plurality of aliasing signals.

Description of drawings

Fig. 1 is a method flow diagram of the present invention.

Embodiment

Be elaborated below in conjunction with the technical scheme of accompanying drawing to invention:

In conjunction with the accompanying drawings enforcement of the present invention is made and being further specified.Fig. 1 is a method flow diagram of the present invention, and as shown in Figure 1, this algorithm comprises following four steps.

Step 1: for one group of given mixed signal that contains noise, at first mixed signal is made auto-correlation processing, remove then after the auto-correlation processing signal time delay be zero and the time delay maximum near part, to realize the secondary noise reduction, obtain the mixed signal behind the noise reduction.Be specially:

With the auto-correlation noise-reduction method noisy aliasing signal is carried out noise reduction, the auto-correlation function of signal x (t) is defined as:

$R_x\left(\mathrm{\τ}\right)=\underset{L\→\∞}{\lim }\frac{1}{L}{\∫}_0^{L}x\left(t\right)x(t+\mathrm{\τ})\mathrm{dt}---\left(1\right)$

Wherein, L is the cycle of signal x (t), and τ is a delay parameter.

Noisy aliasing signal is carried out auto-correlation processing to reduce the random Gaussian signal in the aliasing signal, for further reducing the influence of noise signal, data after the auto-correlation processing are carried out time delay processing, promptly remove time delay and be near zero and time delay is near the maximum data.The data length of removing depends on the circumstances.

The also spendable noise-reduction method of this 1 step comprises: methods such as wavelet de-noising method, medium filtering, but the auto-correlation noise-reduction method need not to set threshold values in noise reduction process, can not destroy the original structure of signal.

Step 2: the mixed signal x behind the noise reduction (t) (wherein t is a time series) is gone average and steady whitening pretreatment.

The sane whitening pretreatment method that this step adopted is:

(A) mixed signal behind the calculating noise reduction is at different delay τ _jUnder covariance matrix C _x(τ _j), have better symmetrical structure in order to make covariance matrix, it is adjusted into

$M_x\left({\mathrm{\τ}}_j\right)=\frac{1}{2}[C_x\left({\mathrm{\τ}}_j\right)+C_x^T\left({\mathrm{\τ}}_j\right)]---\left(2\right)$

In the formula, j=1,2 ..., J (J is the time delay number and is natural number), T represents transpose of a matrix, with M _x(τ _j) be configured to a big combinatorial matrix M, and carry out singular value decomposition, promptly

M＝[M _x(τ ₁)，…，M _x(τ _J)] (3)

M＝U∑V ^T (4)

In the formula, U is the orthogonal matrix identical with the Metzler matrix dimension; ∑ is the diagonal matrix of being made up of the singular value of M; V is an orthogonal matrix.

(B) picked at random parameter matrix α=[α ₁..., α _J], for each time delay τ _j, calculate

f _j＝U ^TM _x(τ _j)U (5)

Carrying out linear combination has

$F=\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{\mathrm{\α}}_j{f}_j---\left(6\right)$

Whether judgment matrix F satisfies orthotropicity, if matrix F is a positive definite, forwards (D) so to, otherwise forwards (C) to.

(C) adjust parameter alpha according to the pairing characteristic vector u of the minimal eigenvalue of matrix F, promptly

$\mathrm{\α}=\mathrm{\α}+\frac{{[u^T{f}_{1}u...u^T{f}_{J}u]}^T}{\left|\right|[u^T{f}_{1}u...u^T{f}_{J}u]\left|\right|}---\left(7\right)$

Go to (B) then, satisfy orthotropicity up to matrix F.

(D) the parameter matrix α that utilizes (C) to obtain calculates objective matrix C, and it is done characteristic value decomposition, promptly

$C=\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{\mathrm{\α}}_j{M}_x\left({\mathrm{\τ}}_j\right)---\left(8\right)$

C＝RDR ^T (9)

In the formula, D is the diagonal matrix of being made up of the characteristic value of Matrix C, the R eigenvectors matrix that each characteristic value characteristic of correspondence vector is formed of serving as reasons.

(E) try to achieve albefaction matrix Q=D ^-1/2R ^T, whitened signal is z (t)=Qx (t).

Step 3: calculate the second order and the fourth order cumulant of initially-separate signal, and with the quadratic sum of the diagonal element of second order and fourth order cumulant matrix as cost function.Implementation procedure is as follows:

If y (t) is the initially-separate signal, W is the initial quadrature separation matrix identical with the aliasing signal dimension, then y (t)=Wz (t).The second order and the fourth order cumulant of initially-separate signal are defined as respectively:

$C_{\mathrm{ij}}^y=E\left(y_i{y}_j\right)---\left(10\right)$

$C_{\mathrm{ijlk}}^y=E\left(y_i{y}_j{y}_l{y}_k\right)$

For realizing the associating approximate diagonalization of each cumulant matrix, with the quadratic sum of the diagonal element of cumulant matrix as cost function, promptly

${\mathrm{\ψ}}_2=\underset{\underset{i\≠j}{i,j=1}}{\overset{N}{\mathrm{\Σ}}}{\left(C_{\mathrm{ij}}^y\right)}^2---\left(11\right)$

${\mathrm{\ψ}}_4=\frac{1}{4!}\underset{\mathrm{ijlk}}{\overset{N}{\mathrm{\Σ}}}{\left(C_{\mathrm{ijlk}}^y\right)}^2$

Wherein, N is the number of source signal.According to principle of stacking, with two cost functions of formula (11) superpose algorithm cost function of the present invention:

ψ ₂₄＝ψ ₂+ψ ₄ (12)

Step 4: by maximizing this cost function, realize the associating approximate diagonalization of each cumulant matrix, obtain separation matrix and separation signal.

In realizing the aliasing signal separating process, generally comprise two steps: i.e. signal albefaction reaches carries out the quadrature rotation transformation to the signal after the albefaction.Specifically be described below:

(1) to the albefaction of aliasing signal,, reduces the computation complexity of subsequent step to remove correlation between signals.The albefaction process of this step is realized by step 2.Here do not give unnecessary details.

(2) orthogonal transform of whitened signal.Usually, the cost function of maximization formula (12) is and looks for a quadrature separation matrix P.Here adopt the Givens rotary process to ask for a quadrature separation matrix.

The separation matrix that obtains is the product of albefaction matrix and quadrature separation matrix, i.e. H=PQ.Separation signal is s (t)=Hx (t).

Claims (2)

1. the method for separating vibration signal blind sources under the strong noise environment, it is characterized in that, this method may further comprise the steps: (1), one group of given mixed signal that contains noise is carried out noise reduction process through autocorrelation method, then the mixed signal after the autocorrelation method noise reduction process is realized the secondary noise reduction through the time delay method, obtain the mixed signal x (t) behind the noise reduction, wherein t is a time series;

(2), the mixed signal x (t) behind the described noise reduction of step (1) is gone additive white Gaussian among the mixed signal x (t) behind average and the described noise reduction of steady whitening pretreatment filtering;

Described sane whitening pretreatment method is as follows:

(A) the mixed signal x (t) behind the calculating noise reduction is at time delay τ _jUnder covariance matrix C _x(τ _j), and with covariance matrix C _x(τ _j) be adjusted into:

$M_x\left({\mathrm{\τ}}_j\right)=\frac{1}{2}[C_x\left({\mathrm{\τ}}_j\right)+C_x^T\left({\mathrm{\τ}}_j\right)]$

In the following formula, τ _jRepresent j time delay, j=1,2 ..., J, J are the time delay number and are natural number that T represents transpose of a matrix, with M _x(τ _j) be configured to a combinatorial matrix M, and carry out singular value decomposition, that is:

M＝[M _x(τ ₁)，…，M _x(τ _J)]

M＝U∑V ^T

In the following formula, U is the orthogonal matrix identical with the Metzler matrix dimension; ∑ is the diagonal matrix of being made up of the singular value of M; V is an orthogonal matrix;

(B) picked at random parameter matrix α=[α ₁..., α _j..., α _J], α wherein _jJ the vector of expression parameter matrix α is for time delay τ _j, calculate:

f _j＝U ^TM _x(τ _j)U

Carrying out linear combination has:

$F=\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{\mathrm{\α}}_j{f}_j$

When matrix F satisfies orthotropicity, then forward step (D) to, otherwise forward step (C) to;

(C) adjust parameter matrix α according to the pairing characteristic vector u of the minimal eigenvalue of matrix F, that is:

$\mathrm{\α}=\mathrm{\α}+\frac{{[u^T{f}_{1}u...u^T{f}_{J}u]}^T}{\left|\right|[u^T{f}_{1}u...u^T{f}_{J}u]\left|\right|}$

Go to step (B) then, satisfy orthotropicity up to matrix F;

(D) the parameter matrix α that utilizes step (C) to obtain calculates objective matrix C, and it is made characteristic value decomposition, that is:

$C=\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{\mathrm{\α}}_j{M}_x\left({\mathrm{\τ}}_j\right)$

C＝RDR ^T

In the formula, D is the diagonal matrix of being made up of the characteristic value of objective matrix C, the R eigenvectors matrix that each characteristic value characteristic of correspondence vector is formed of serving as reasons;

(E) try to achieve albefaction matrix Q=D ^-1/2R ^T, whitened signal is z (t)=Qx (t).

(3), calculate the second order and the fourth order cumulant of initially-separate signal, with the diagonal element quadratic sum of second order and fourth order cumulant matrix as cost function;

Described initially-separate signal is as follows:

Initial quadrature separation matrix is W, then initially-separate signal y (t)=Wz (t);

(4), by cost function in the maximization steps (3), realize the associating approximate diagonalization of each second order and fourth order cumulant matrix, the quadrature separation matrix P that obtains making the mixed signal of the described filtering additive white Gaussian of step (2) to separate, thus separation matrix H and separation signal s (t) obtained; H=PQ wherein, s (t)=Hx (t).

2. the blind source separation method of a kind of strong noise environment according to claim 1 is characterized in that described quadrature separation matrix P adopts the Givens rotary process to try to achieve.

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