CN101729157B - Method for separating vibration signal blind sources under a kind of strong noise environment - Google Patents

Abstract

The present invention discloses the vibration signal blind source separation algorithm under a kind of strong noise environment.The inventive method is as follows: the first step, for the mixed signal of one group of given Noise, carries out noise reduction, obtain the mixed signal after denoising by time delay autocorrelation method to mixed signal; Second step, goes average and sane whitening pretreatment, with further noise decrease signal on the impact of separating resulting to the mixed signal that the first step obtains; 3rd step, calculate second order and the fourth order cumulant of initially-separate signal, using the diagonal entry sum of second order and fourth order cumulant matrix as cost function, by maximizing this cost function, make each cumulant matrices joint approximate diagonalization, realize the separation of each Independent sources signal, thus obtain orthogonal separation matrix.Existing noise-reduction method is combined with blind separation algorithm by the present invention, realizes mixed signal under strong noise environment and is separated, the advantage that more existing algorithm has good separating effect, fast convergence rate and noise reduction do not arrange restriction by threshold values.

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 is separated technology.

Background technology

Aliasing vibration signal blind separation under strong noise environment, because it is closer to actual conditions, is the signal of interest processing method identifying signal of vibrating and small-signal, has become related scientific research mechanism, and the research focus of scholars.

Existing method is mostly based on such fact: when ignoring noise, utilizes optimal method to realize the separation of Instantaneous Mixtures to the optimization of independence criterion.Vibration signal is as a kind of signal with time structure, usually the diagonal element quadratic sum of second-order cumulant matrix can be adopted as cost function, this cost function of optimization realizes the separation of mixed signal, and its complexity is low, computational speed fast, but does not have robustness to noise signal.The Higher Order Cumulants that JADE algorithm based on fourth order cumulant matrix make use of noise signal is the characteristic of zero, the separation of mixed signal is realized by each fourth order cumulant matrix of joint approximate diagonalization, owing to it makes use of Higher Order Cumulants, its complexity is large, computational speed is slow, responsive to outlier, and only to white Gaussian coloured noise, there is robustness.

For the aliasing signal of Noise, consider first to utilize wavelet de-noising method to carry out noise reduction to signals and associated noises, to reduce the impact of noise signal on separating effect, and then the aliasing signal after noise reduction is separated.But in wavelet de-noising method, choosing of threshold values is most important, the improper algorithm that will cause is selected to lose efficacy.

Summary of the invention

The defect that the present invention seeks to exist for prior art provides a kind of proposition under strong noise environment, have good separating property, faster separating rate, the aliasing vibration signal strong to noise robustness is separated algorithm.

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

The blind source separation method of a kind of strong noise environment of the present invention, it is characterized in that, the method comprises the following steps:

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

(2) additive white Gaussian in the mixed signal x (t) after, the mixed signal x (t) after the noise reduction described in step (1) being removed described in average and sane whitening pretreatment filtering noise reduction;

Described sane whitening pretreatment method is as follows:

(A) the mixed signal x (t) after noise reduction is calculated at time delay τ _junder covariance matrix C _x(τ _j), and by covariance matrix C _x(τ _j) be adjusted to:

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

In above formula, τ _jrepresent a jth time delay, j=1,2 ..., J, J are time delay number and are natural number, and T represents transpose of a matrix, by 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 above formula, U is the orthogonal matrix identical with Metzler matrix dimension; ∑ is the diagonal matrix be made up of the singular value of M; V is orthogonal matrix;

(B) random selecting parameter matrix α=[α ₁..., α _j..., α _j] ^t, wherein α _jrepresent a jth vector of parameter matrix α, for time delay τ _j, calculate:

f _j＝U ^TM _x(τ _j)U

Carry out linear combination to have:

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

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

(C) the characteristic vector u corresponding to the minimal eigenvalue of matrix F adjusts parameter matrix α, that is:

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

Then go to step (B), until matrix F meets orthotropicity;

(D) when the parameter matrix α of random selecting meet orthotropicity require time, utilize selected parameter matrix to calculate objective matrix C, and Eigenvalues Decomposition done to it, that is:

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

C＝RDR ^T

When the parameter matrix α of random selecting do not meet orthotropicity require time, the parameter matrix α utilizing step (C) to obtain to calculate objective matrix C, and makes Eigenvalues Decomposition to it, that is:

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

C＝RDR ^T

In formula, D is the diagonal matrix be made up of the characteristic value of objective matrix C, and R is the eigenvectors matrix be made up of each characteristic value characteristic of correspondence vector;

(E) whitening matrix Q=D is tried to achieve ^-1/2r ^t, whitened signal is z (t)=Qx (t).

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

Described initially-separate signal is as follows:

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

(4), by cost function in maximization steps (3), realize the joint approximate diagonalization of each second order and fourth order cumulant matrix, obtain making the orthogonal separation matrix P that the mixed signal of the described filtering additive white Gaussian of step (2) is separated, thus obtain separation matrix H and separation signal s (t); Wherein H=PQ, s (t)=Hx (t).

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

The invention has the beneficial effects as follows, the present invention is the algorithm of aliasing vibration signal blind separation under a kind of strong noise environment, comprise noise reduction, sane preliminary treatment, structure cost function, optimize cost function solve separation matrix 4 steps.Before being separated, abundant filtering noise signal, with the impact of noise decrease signal on separating resulting, finally realizes the separation of aliasing signal under strong noise environment.

In (1) step, present invention employs time delay auto-correlation noise-reduction method, when using the method to carry out noise reduction to aliasing signals and associated noises, secondary noise reduction can be realized and do not need to arrange threshold values, and auto-correlation processing can retain the periodicity useful information in vibration signal, remove random noise aperiodic, the feasibility of its noise reduction has obtained the affirmative of people in the industry.Therefore, can noise signal effectively in filtering aliasing signals and associated noises by the method.

In (2) step, the present invention is directed to the aliasing signal after noise reduction in (1) step, propose the additive white Gaussian utilized in sane preprocess method filtering aliasing signal, further noise decrease is on the impact of separating resulting.

In (3) step, consider the advantage based on second-order cumulant and fourth-order cumulant quantity algorithm, using 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 to outlier compared with fourth-order cumulant quantity algorithm, and avoid second-order cumulant algorithm and can not be separated the deficiency with same spectrum architecture signals.

In (4) step, the present invention utilizes optimal method to carry out optimization to cost function, realizes the joint approximate diagonalization of second-order cumulant and fourth order cumulant, therefore realizes the separation of aliasing signal.

Therefore, the more existing algorithm of the present invention has: good separating effect under strong noise environment and stable, do not arrange restriction by threshold values advantage, and has the characteristic of fast convergence rate for the separation of multiple aliasing signal.

Accompanying drawing explanation

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

Embodiment

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

By reference to the accompanying drawings enforcement of the present invention is made and further illustrating.Fig. 1 is method flow diagram of the present invention, and as shown in Figure 1, this algorithm comprises following four steps.

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

Carry out noise reduction with auto-correlation noise-reduction method to noisy aliasing signal, 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 delay parameter.

Auto-correlation processing is carried out to reduce the random Gaussian signal in aliasing signal to noisy aliasing signal, for the impact of further noise decrease signal, carry out time delay processing to the data after auto-correlation processing, namely to remove time delay be near zero and time delay is data near maximum.The data length removed depends on the circumstances.

This 1 step also spendable noise-reduction method comprises: the methods such as wavelet de-noising method, medium filtering, but auto-correlation noise-reduction method in noise reduction process without the need to setting threshold values, the original structure of signal can not be destroyed.

Step 2: average and sane whitening pretreatment are gone to the mixed signal x (t) (wherein t is time series) after noise reduction.

The sane whitening pretreatment method that this step adopts is:

(A) mixed signal after noise reduction is calculated at different delay τ _junder covariance matrix C _x(τ _j), in order to make covariance matrix have better symmetrical structure, be adjusted to

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

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

M＝[M _x(τ ₁)，…，M _x(τ _J)](3)

M＝U∑V ^T(4)

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

(B) random selecting parameter matrix α=[α ₁..., α _j..., α _j] ^t, for each time delay τ _j, calculate

f _j＝U ^TM _x(τ _j)U(5)

Carry out linear combination to have

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

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

(C) the characteristic vector u corresponding to the minimal eigenvalue of matrix F adjusts parameter alpha, namely

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

Then go to (B), until matrix F meets orthotropicity.

(D) when the parameter matrix α of random selecting meet orthotropicity require time, utilize selected parameter matrix to calculate objective matrix C, and Eigenvalues Decomposition done to it, that is:

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

C＝RDR ^T(9)

When the parameter matrix α of random selecting do not meet orthotropicity require time, the parameter matrix α utilizing step (C) to obtain to calculate objective matrix C, and makes Eigenvalues Decomposition to it, that is:

$C=\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{\mathrm{\α}}_j{M}_x\left({\mathrm{\τ}}_j\right)---\left(10\right)$

C＝RDR ^T(11)

In formula, D is the diagonal matrix be made up of the characteristic value of objective matrix C, and R is the eigenvectors matrix be made up of each characteristic value characteristic of correspondence vector; (E) whitening matrix Q=D is tried to achieve ^-1/2r ^t, whitened signal is z (t)=Qx (t).

Step 3: the second order and the fourth order cumulant that calculate initially-separate signal, and using 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 initially-separate signal, W is the initial orthogonal separation matrix identical with aliasing signal dimension, then y (t)=Wz (t).Second order and the fourth order cumulant of initially-separate signal are defined as respectively:

$\begin{array}{c}{C}_{\mathrm{ij}}^y=E\left(y_i{y}_j\right)\\ C_{\mathrm{ijlk}}^y=E\left(y_i{y}_j{y}_l{y}_k\right)\end{array}---\left(12\right)$

For realizing the joint approximate diagonalization of each cumulant matrices, using the quadratic sum of the diagonal element of cumulant matrices as cost function, namely

$\begin{array}{c}{\mathrm{\ψ}}_2=\underset{i\≠j}{\overset{N}{\underset{i,j=1}{\mathrm{\Σ}}}}{\left(C_{\mathrm{ij}}^y\right)}^2\\ {\mathrm{\ψ}}_4=\frac{1}{4!}\underset{\mathrm{ijlk}}{\overset{N}{\mathrm{\Σ}}}{\left(C_{\mathrm{ijlk}}^y\right)}^2\end{array}---\left(13\right)$

Wherein, N is the number of source signal.According to principle of stacking, two cost functions of formula (13) are superposed to obtain algorithm cost function of the present invention:

ψ ₂₄＝ψ ₂+ψ ₄(14)

Step 4: by maximizing this cost function, realizing the joint approximate diagonalization of each cumulant matrices, obtaining separation matrix and separation signal.

Realizing, in the process that aliasing signal is separated, generally comprising two steps: the signal namely after signal albefaction and whitening carries out orthogonal rotation transformation.Specifically be described below:

(1) to the albefaction of aliasing signal, to remove the correlation between signal, the computation complexity of subsequent step is reduced.The whitening process of this step is realized by step 2.Here do not repeat.

(2) orthogonal transform of whitened signal.Usually, maximize the cost function of formula (14), be and look for an orthogonal separation matrix P.

Here Givens rotary process is adopted to ask for an orthogonal separation matrix.

The separation matrix obtained is the product of whitening matrix and orthogonal separation matrix, i.e. H=PQ.Separation signal is s (t)=Hx (t).

Claims (2)

1. a blind source separation method for strong noise environment, is characterized in that, the method comprises the following steps:

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

(2) additive white Gaussian in the mixed signal x (t) after, the mixed signal x (t) after the noise reduction described in step (1) being removed described in average and sane whitening pretreatment filtering noise reduction;

Described sane whitening pretreatment method is as follows:

(A) the mixed signal x (t) after noise reduction is calculated at time delay τ _junder covariance matrix C _x(τ _j), and by covariance matrix C _x(τ _j) be adjusted to:

$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 above formula, τ _jrepresent a jth time delay, j=1,2 ..., J, J are time delay number and are natural number, and T represents transpose of a matrix, by 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 above formula, U is the orthogonal matrix identical with Metzler matrix dimension; ∑ is the diagonal matrix be made up of the singular value of M; V is orthogonal matrix;

(B) random selecting parameter matrix α=[α ₁..., α _j..., α _j] ^t, wherein α _jrepresent a jth element of parameter matrix α, α _jit is scalar; For time delay τ _j, calculate:

f _j＝U ^TM _x(τ _j)U

Carry out linear combination to have:

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

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

(C) the characteristic vector u corresponding to the minimal eigenvalue of matrix F adjusts parameter matrix α, 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|}$

Then go to step (B), until matrix F meets orthotropicity;

(D) when the parameter matrix α of random selecting meet orthotropicity require time, utilize selected parameter matrix to calculate objective matrix C, and Eigenvalues Decomposition done to it, that is:

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

C＝RDR ^T

When the parameter matrix α of random selecting do not meet orthotropicity require time, the parameter matrix α utilizing step (C) to obtain to calculate objective matrix C, and makes Eigenvalues Decomposition to it, that is:

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

C＝RDR ^T

In formula, D is the diagonal matrix be made up of the characteristic value of objective matrix C, and R is the eigenvectors matrix be made up of each characteristic value characteristic of correspondence vector;

(E) whitening matrix Q=D is tried to achieve ^-1/2r ^t, whitened signal is z (t)=Qx (t);

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

Described initially-separate signal is as follows:

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

(4), by cost function in maximization steps (3), realize the joint approximate diagonalization of each second order and fourth order cumulant matrix, obtain making the orthogonal separation matrix P that the mixed signal of the described filtering additive white Gaussian of step (2) is separated, thus obtain separation matrix H and separation signal s (t); Wherein H=PQ, 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 orthogonal separation matrix P adopts Givens rotary process to try to achieve.