CN111709116B - Blind signal decomposition method based on similarity measurement - Google Patents
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Abstract
The invention discloses a blind signal decomposition method based on similarity measurement, which decomposes a blind signal compounded with multi-path source signals by adopting binary variational mode decomposition, adaptively separates out source signals in a mixed signal, combines a tree decomposition method with the similarity measurement, separates out other modes mixed in the current mode signal, finally obtains a pure sub-signal by superposition, and removes noise components according to the correlation degree of the source signals and an observation signal, solves the problem that the prior algorithm needs secondary decomposition, enhances the capability of separating anti-noise interference, can effectively separate out the source signals in the mixed signal, overcomes the problems of end effect and mode aliasing existing in EMD method decomposition, and has good anti-noise performance and signal separation capability.
Description
Technical Field
The method belongs to the field of blind signal processing, and particularly relates to a blind signal decomposition method based on similarity measurement.
Background
The unknown signals in which the source signals are mixed with each other are called "blind signals". In actual production and life, many observed signals obtained through digital sampling are blind signals mixed by multiple source signals in a system, such as underwater acoustic signals, electroencephalogram signals and the like. Each source signal constituting a blind signal reflects state information of a certain process of the observation system. Therefore, if these individual source signals can be recovered from a composite signal in which several signals are mixed, it is important to determine the coordination of the observation system components and to obtain the interaction relationship between them.
Blind signal separation is the separation or recovery of individual source signals from a received composite signal, respectively. Blind signal separation is a fundamental problem in signal processing. How to represent a complex signal as a combination of a series of individual signals is an essential core problem in signal processing. The difference between the signals is largely contained in the "frequencies" of the signals, and different source signals can be separated from the composite signal according to different frequencies. Classical signal separation algorithms include wavelet decomposition and Empirical Mode Decomposition (EMD). Wavelet decomposition can realize high-low frequency separation of signals according to frequency, but the decomposition effect is influenced by the selected wavelet basis and the decomposition layer number; the EMD method can adaptively decompose a signal into a plurality of Intrinsic Mode components (IMFs), but the EMD method has the defects of modal aliasing, endpoint effect and the like, so that the decomposition result is unstable and not unique, and the separation performance is affected. The ensemble empirical mode decomposition and the complete ensemble empirical mode decomposition can alleviate the mode aliasing problem to a certain extent, but simultaneously, the calculation amount is greatly increased, and the endpoint effect problem still exists.
Disclosure of Invention
The invention aims to provide a blind signal decomposition method based on similarity measurement to overcome the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a blind signal decomposition method based on similarity measurement comprises the following steps:
step 1), collecting blind signals as initial source signals to be decomposed;
step 2), carrying out binary variation modal decomposition on the initial source signal to be decomposed to obtain a first signal component, a second signal component and a first residual signal;
if the similarity between the first signal component and the second signal component is larger than or equal to the modal similarity evaluation threshold, superposing the first signal component and the second signal component into a modal signal; if the similarity between the first signal component and the second signal component is smaller than a modal similarity evaluation threshold, the first signal component and the second signal component are used as new source signals to be decomposed and are placed into a signal set to be decomposed after being numbered again, if modal signals with the similarity of the first residual signals being larger than or equal to a residual matching evaluation threshold exist in the modal signal set, the modal signals are overlapped with the first residual signals and are re-encoded and are placed into the modal signal set, and if the similarity of the first residual signals and the residual matching evaluation threshold does not exist in the modal signal set, the first residual signals are placed into the residual signal set;
if the similarity between the modal signal superposed by the first signal component and the second signal component and the first residual signal is greater than or equal to a residual matching evaluation threshold, the initial source signal to be decomposed is a modal signal and does not need to be decomposed;
when the similarity between the modal signal superposed by the first signal component and the second signal component and the residual signal is smaller than a residual matching evaluation threshold value, if the similarity between the modal signal superposed by the first signal component and the second signal component and the residual signal in the modal signal set is greater than or equal to the modal matching evaluation threshold value, the modal signal and the modal signal superposed by the first signal component and the second signal component are recoded and placed in the modal signal set, otherwise, the modal signal superposed by the first signal component and the second signal component is coded and placed in the modal signal set;
when the similarity between the modal signal and the residual signal superposed by the first signal component and the second signal component is smaller than a residual matching evaluation threshold, if the modal signal set has a modal signal the similarity of which with the first residual signal is greater than or equal to the residual matching evaluation threshold, superposing the modal signal and the first residual signal, recoding and putting the superposed modal signal and the first residual signal into the modal signal set, otherwise, putting the first residual signal into the residual signal set;
step 3), repeating step 2) to sequentially carry out binary variation modal decomposition on the modal signals in the signal set to be decomposed until the signal set to be decomposed is an empty set;
step 4), overlapping all residual signals in the residual signal set to form a discrimination signal, if the maximum mutual information coefficient of the discrimination signal and the initial source signal to be decomposed is greater than or equal to the modal screening threshold value, taking the discrimination signal as a new source signal to be decomposed, and repeating the steps 2) to 4) until the maximum mutual information coefficient of the discrimination signal formed by overlapping all the residual signals in the residual signal set and the initial source signal to be decomposed is smaller than the modal screening threshold value;
and step 5), the modal signal in the modal signal set, the maximum mutual information coefficient of which with the initial source signal to be decomposed is greater than or equal to the modal screening threshold value, is the separation result of the initial source signal to be decomposed.
Further, in step 1), a blind signal is obtained through digital sampling and is used as an initial source signal to be decomposed.
Further, in step 2), performing iterative update on the initial source signal to be decomposed until a convergence condition is satisfied, and stopping iteration to obtain a first signal component, a second signal component and a first residual signal.
Further, the specific steps of iteratively updating the initial source signal to be decomposed until a convergence condition is met and stopping iteration are as follows: separately initializing modal parameters
Center frequency
And lagrange multiplier
Then iteratively calculating and updating modal parameters:
wherein k is the {1,2}, and alpha is a bandwidth constraint factor;
and (3) updating the center frequency calculation:
update to Lagrange multiplier calculation
Wherein tau is a constraint term for constraining the reconstructed signal to be equal to the original signal;
if the iteration error satisfies the formula (4), stopping the iteration to obtain a first signal component m 11 (t), the second signal component and the first residual signal, otherwise, continuing the iteration until equation (4) is satisfied;
further, the similarity is calculated by using a Pearson correlation coefficient.
Further, the first signal component m i1 (t) and a second signal component m i2 The Pearson correlation coefficient between (t) can be calculated by the following formula:
where E is the mathematical expectation, cov is the covariance, and σ is the standard deviation.
Further, a discrimination signal C f The maximum mutual information coefficient between the source signal f (t) to be decomposed and the source signal f (t) to be decomposed is calculated by the following formula:
given i and j, for the discrimination signal C f And a scatter diagram formed by the source signals f (t) to be decomposed is subjected to i-column and j-row gridding, the maximum mutual information value (MI) is obtained, and further, the maximum mutual information value is defined on two probability distributions X and Y, wherein X belongs to X, Y belongs to Y, and the mutual information is
Then normalizing the maximum mutual information value, selecting the maximum value of the mutual information under different scales as the maximum mutual information coefficient value,
in the above formula, a and B are the numbers of the division grids in the X and Y directions, respectively, and the size of B is 0.6 th power of the data amount.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention relates to a blind signal decomposition method based on similarity measurement, which decomposes a blind signal compounded with multi-channel source signals by adopting binary variational modal decomposition, adaptively separates out source signals in a mixed signal, combines a tree decomposition method with the similarity measurement, separates out other modes mixed in the current mode signal, finally obtains a pure sub-signal by superposition, and removes noise components according to the correlation degree of the source signals and an observation signal, solves the problem that the prior algorithm needs secondary decomposition, enhances the separated anti-noise interference capability, can effectively separate out the source signals in the mixed signal, overcomes the end effect and aliasing problem existing in EMD method decomposition, and has good anti-noise performance and signal separation capability.
Further, (2) by using a Pearson correlation coefficient as a measurement criterion, judging whether the two signals are explicitly represented by the same modal component by measuring the similarity between the two signals, and further constraining the two signals to the same mode, the problem that the performance of the existing mode number determination algorithm is influenced by mode separation order is solved, and two source signals with frequencies close to and different from the similarity of observed signals can be effectively separated.
Drawings
FIG. 1 is a flow chart of a decomposition method in an embodiment of the present invention.
Fig. 2 is a flowchart illustrating sequential decomposition of all source signals to be decomposed in a signal set to be decomposed according to an embodiment of the present invention.
FIG. 3 shows the separation result of the simulation signals according to the embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
as shown in fig. 1, a blind signal decomposition method based on similarity measurement specifically includes the following steps:
step 1), obtaining a blind signal f (t) through digital sampling as an initial source signal x (t) to be decomposed, namely x (t) = f (t); establishing a signal set M to be decomposed, a residual signal set H and a modal signal set T, and establishing a null set of the signal set M to be decomposed, the residual signal set H and the modal signal set T in an initial state;
putting the collected initial source signal x (t) to be decomposed into a signal set M to be decomposed, and forming a first source signal x to be decomposed in the signal set M to be decomposed 1 (t)；
Step 2) to-be-decomposed sources in the to-be-decomposed signal set MSignal x i (t) performing binary Variational Modal Decomposition (VMD), namely k = {1,2}, to obtain a first signal component m i1 (t), second signal component m i2 (t) and residual signal c i1 (t), t is a time independent variable, x i (t) is the ith to-be-decomposed source signal in the to-be-decomposed signal set M; the initial stage i is 1, that is, only the initial to-be-decomposed source signal x (t) is in the initial state to-be-decomposed signal set M;
if the first signal component m i1 (t) and a second signal component m i2 (t) degree of similarity δ therebetween i Greater than or equal to a modal similarity assessment threshold ρ, i.e., δ i Equal to or more than rho, the decomposition is over-decomposition, the first signal component m i1 (t) and a second signal component m i2 (t) is the same modal signal, i.e. a modal signal u is obtained i (t)＝m i1 (t)+m i2 (t); if the first signal component m i1 (t) and a second signal component m i2 (t) degree of similarity δ between i Less than the modal similarity assessment threshold ρ, the first signal component m is determined i1 (t) and a second signal component m i2 (t) renumbering as a new source signal to be decomposed, putting the new source signal into a signal set M to be decomposed, and waiting for carrying out binary Variational Modal Decomposition (VMD) in sequence; if the modal signal U exists in the modal signal set T i (t) and residual signal c i (t) similarity v ic If the residual error signal c is greater than or equal to the residual error matching evaluation threshold value gamma, the residual error signal c i (t) and the mode signal U i (t) is a modal signal, then a new modal signal U 'is obtained' i (t)＝U i (t)+c i (t) updating the mode signal U i (t), otherwise residual signal c i (t) put into the residual signal set H.
If the modal signal u i (t) and residual signal c i (t) similarity v i If the residual matching evaluation threshold value gamma is larger than or equal to the residual matching evaluation threshold value gamma, the mode signal u i (t) and residual signal c i (t) is a modal signal, U i (t)＝u i (t)+c i (t), then U is added i (T) numbering and then putting the signals into a modal signal set T, wherein the source signal x to be decomposed i (t) is a modal signal U i (t)＝x i (t), no signal source doping contamination;
if the modal signal u i (t) and residual signal c i (t) similarity v i Less than the residual matching evaluation threshold gamma and the modal signal U is present in the modal signal set T i (t) and residual signal c i (t) similarity v ic Greater than or equal to the residual matching evaluation threshold gamma, the residual signal c i (t) and the mode signal U i (t) is a modal signal, then a new modal signal U 'is obtained' i (t)＝U i (t)+c i (t) updating the mode signal U i (t) in U' i (T) Replacing U in the Modal Signal set T i (t); if the modal signal U exists in the modal signal set T i (t) and mode signal u i (t) similarity v iu If the value is larger than or equal to the mode matching evaluation threshold xi, the mode signal U is i (t) and the mode signal U i (t) is a modal signal, then a new modal signal U 'is obtained' i (t)＝U i (t)+u i (t) updating the mode signal U i (t) in U' i (T) replacing U in the set of modal signals T i (t) of (d). Initial state, only one source signal x to be decomposed i (T) and the set of modal signals T is empty, so there is no need to apply the modal signals u i (T) comparing with the modal signals in the set of modal signals T, thus directly comparing the modal signal u with the set of modal signals T i (T) renumbering and placing the renumbered signals into a modal signal set T; if the modal signal u i (t) and residual signal c i (t) degree of similarity v i Less than the residual matching evaluation threshold gamma and the modal signal U in the set of modal signals T i (t) and residual signal c i (t) degree of similarity v iu Are all less than the residual matching evaluation threshold value gamma, the residual signal c is transmitted i (t) putting the mode signal u into the residual signal set H i (t) renumbering to U i (T) putting the modal signal set T into the modal signal set T; the specific decomposition is shown in fig. 2;
step 3), repeating the step 2) to decompose the source signal x to be decomposed in the signal set M to be decomposed i (t) sequentially carrying out binary variation modal decomposition, and separating the decomposed modal signals from the signals to be separatedRemoving the solution signal set until the signal set M to be decomposed is an empty set, namely finishing all the source signals x to be decomposed i (t) the binary variational modal decomposition is completed, and the source signal to be decomposed no longer appears;
step 4), all residual signals c in the residual signal set H are established i (t) discrimination signal C f I.e. all residual signals in the residual signal set are superposed to form a discrimination signal,
calculating a discrimination signal C f Maximum mutual information coefficient with initial source signal x (t) to be decomposed
If it is used
Then the signal C will be discriminated f As a new source signal to be decomposed, repeating the steps 2) to 4) until the maximum mutual information coefficient of the discrimination signal formed by superposing all residual signals in the residual signal set and the initial source signal to be decomposed is obtained
And theta is a mode screening threshold value, and all residual signals in the final residual signal set H are removed. Will discriminate the signal C f When the signal is used as a new source signal to be decomposed, the signal set M to be decomposed and the residual signal set H are empty;
step 5), sequentially calculating modal signals U in the modal signal set T i (t) maximum mutual information coefficient with the original source signal x (t) to be decomposed
If there is U i (T) is e.t, such that
The modal signal U is removed from the set of modal signals T i (t); if all the modal signals U in the modal signal set T i (t) maximum mutual information coefficient MIC with initial source signal x (t) to be decomposed (s(t),f(t)) And (4) the similarity measurement-based binary variational decomposition method is ended so far, and the modal signals in the modal signal set T are the separation result of the initial source signal x (T) to be decomposed.
And carrying out binary variational modal decomposition on the initial source signal to be decomposed, setting a modal decomposition number K =2, carrying out iterative updating on the initial source signal to be decomposed until a convergence condition is met, and stopping iteration to obtain a first signal component, a second signal component and a first residual signal.
The specific steps of carrying out iterative update on the initial source signal to be decomposed until the iterative error meets the convergence condition and stopping iteration are as follows: separately initializing modal parameters
Center frequency
And lagrange multiplier
Then iteratively calculating and updating modal parameters:
wherein k is an element {1,2}, and alpha is a bandwidth constraint factor;
and (4) updating the center frequency calculation:
update to Lagrange multiplier calculation
Wherein tau is a constraint term for constraining the reconstructed signal to be equal to the original signal;
determining a convergence condition: stopping the iteration if the iteration error satisfies the formula (4), namely the iteration error is smaller than the allowable error epsilon, and the allowable error epsilon is constant, so as to obtain the first signal component m 11 (t), the second signal component and the first residual signal, otherwise continuing the iteration until equation (4) is satisfied;
the similarity of the signals is calculated by adopting a Pearson correlation coefficient; e.g. the first signal component m i1 (t) and a second signal component m i2 The Pearson correlation coefficient between (t) can be calculated by the following formula:
where E is the mathematical expectation, cov is the covariance, σ is the standard deviation.
The correlation degree between the signal set of the residual signals and the source signals to be decomposed is measured by adopting a maximum Mutual Information Coefficient (MIC), and the correlation degree between the modal signals and the initial source signals to be decomposed is measured by adopting a maximum Mutual Information Coefficient (MIC); discrimination signal C such as residual signal f The maximum mutual information coefficient between the source signal f (t) to be decomposed and the source signal f (t) is calculated by the following formula:
first, given i and j, the discrimination signal C is f And a scatter diagram formed by the source signals f (t) to be decomposed is subjected to i-column and j-row gridding, the maximum mutual information value (MI) is obtained, and further, the maximum mutual information value is defined on two probability distributions X and Y, wherein X belongs to X, Y belongs to Y, and the mutual information is
Then, the maximum mutual information value is normalized, and the maximum value of the mutual information under different scales is selected as an MIC value.
In the above formula, a and B are the numbers of the division grids in the X and Y directions, respectively, and the size of B is 0.6 th power of the data amount.
In order to verify the separation effect of the present invention on the mixed signal, the simulation signal of the composite 4 source signals is adopted to perform the blind signal decomposition based on the similarity measure proposed by the present method, and the separation result is shown in fig. 3. The result shows that the blind signal decomposition based on the similarity measurement can successfully separate the source signals in the mixed signals, compared with the prior method, the method is not influenced by the separation sequence of the source signals, and the repeated secondary decomposition is not needed, so that the method has good application prospect in the separation of the multipath mixed blind signals. The method has the advantages that binary variational modal decomposition is carried out on the source signal to be decomposed, the source signal in the mixed signal is separated out in a self-adaptive mode, the problems of end effect and modal aliasing existing in EMD method decomposition are solved, and the method has good anti-noise performance and signal separation capability; (2) By using the Pearson correlation coefficient as a measurement criterion, judging whether the two signals are explicitly represented by the same modal component or not by measuring the similarity between the two signals, and further constraining the two signals to the same mode, the problem that the performance of the existing mode number determination algorithm is influenced by mode separation order is solved, and two source signals with frequencies close to and different from the similarity of observed signals can be effectively separated; the tree decomposition method is combined with the similarity measurement, other modes mixed in the current mode signal are separated, finally, pure sub-signals are obtained through superposition, noise components are removed according to the correlation degree of the source signal and the observation signal, the problem that secondary decomposition is needed in the existing algorithm is solved, and the anti-noise interference capability of separation is enhanced.
The above-mentioned contents are only for explaining the technical idea of the invention of the present application, and can not be used as the basis for limiting the protection scope of the invention, and any modifications and substitutions made on the technical solution according to the design concept and technical features proposed by the present invention are within the protection scope of the claims of the present invention.
Claims (7)
1. A blind signal decomposition method based on similarity measurement is characterized by comprising the following steps:
step 1), collecting blind signals as initial source signals to be decomposed;
step 2), carrying out binary variation modal decomposition on the initial source signal to be decomposed to obtain a first signal component, a second signal component and a first residual signal;
if the similarity between the first signal component and the second signal component is larger than or equal to the modal similarity evaluation threshold, superposing the first signal component and the second signal component into a modal signal; if the similarity between the first signal component and the second signal component is smaller than a modal similarity evaluation threshold, the first signal component and the second signal component are used as new source signals to be decomposed and are placed into a signal set to be decomposed after being numbered again, if modal signals with the similarity of the first residual signals being larger than or equal to a residual matching evaluation threshold exist in the modal signal set, the modal signals are overlapped with the first residual signals and are re-encoded and are placed into the modal signal set, and if the similarity of the first residual signals and the residual matching evaluation threshold does not exist in the modal signal set, the first residual signals are placed into the residual signal set;
if the similarity between the modal signal superposed by the first signal component and the second signal component and the first residual signal is greater than or equal to a residual matching evaluation threshold, the initial source signal to be decomposed is a modal signal and does not need to be decomposed;
when the similarity between the modal signal superposed by the first signal component and the second signal component and the residual signal is smaller than a residual matching evaluation threshold, if the similarity between the modal signal superposed by the first signal component and the second signal component and the residual signal in the modal signal set is larger than or equal to the modal matching evaluation threshold, the modal signal and the modal signal superposed by the first signal component and the second signal component are superposed and then re-encoded and placed in the modal signal set, otherwise, the modal signal superposed by the first signal component and the second signal component is encoded and then placed in the modal signal set;
when the similarity between the modal signal and the residual signal superposed by the first signal component and the second signal component is smaller than a residual matching evaluation threshold, if the modal signal set has a modal signal the similarity of which with the first residual signal is greater than or equal to the residual matching evaluation threshold, superposing the modal signal and the first residual signal, recoding and putting the superposed modal signal and the first residual signal into the modal signal set, otherwise, putting the first residual signal into the residual signal set;
step 3), repeating step 2), and sequentially carrying out binary variational modal decomposition on the source signals to be decomposed in the signal set to be decomposed until the signal set to be decomposed is an empty set;
step 4), overlapping all residual signals in the residual signal set to form a discrimination signal, if the maximum mutual information coefficient of the discrimination signal and the initial source signal to be decomposed is greater than or equal to the modal screening threshold value, taking the discrimination signal as a new source signal to be decomposed, and repeating the steps 2) to 4) until the maximum mutual information coefficient of the discrimination signal formed by overlapping all the residual signals in the residual signal set and the initial source signal to be decomposed is smaller than the modal screening threshold value;
and step 5), the modal signals in the modal signal set, the maximum mutual information coefficient of which with the initial source signal to be decomposed is larger than or equal to the modal screening threshold value, are the separation results of the initial source signal to be decomposed.
2. The method according to claim 1, wherein the blind signal obtained by the step 1) is used as the original source signal to be decomposed by digital sampling.
3. The method according to claim 1, wherein in step 2), the initial source signal to be decomposed is iteratively updated until a convergence condition is satisfied, and then iteration is stopped to obtain the first signal component, the second signal component, and the first residual signal.
4. The method of claim 3, wherein iterative updating is performed on the initial source signal to be decomposed until a convergence condition is satisfied and then iteration is stoppedThe method comprises the following steps: separately initializing modal parameters
Center frequency
And lagrange multiplier
Then iteratively calculating and updating modal parameters:
wherein k is the {1,2}, and alpha is a bandwidth constraint factor;
and (4) updating the center frequency calculation:
update to Lagrange multiplier calculation
Wherein tau is a constraint term for constraining the reconstructed signal to be equal to the original signal;
stopping the iteration if the iteration error satisfies the formula (4), and obtaining a first signal component m 11 (t), the second signal component and the first residual signal, otherwise, continuing the iteration until equation (4) is satisfied;
5. the method according to claim 1, wherein the similarity is calculated using Pearson correlation coefficients.
6. A method for blind signal decomposition based on similarity measure according to claim 5, characterized in that the first signal component m i1 (t) and a second signal component m i2 The Pearson correlation coefficient between (t) can be calculated by the following formula:
where E is the mathematical expectation, cov is the covariance, σ is the standard deviation.
7. The method according to claim 1, wherein the decision signal C is a signal C f The maximum mutual information coefficient between the source signal f (t) to be decomposed and the source signal f (t) is calculated by the following formula:
given i and j, for C f And f (t) are gridded in i columns and j rows to obtain the maximum mutual information value (MI), and further defined on two probability distributions X and Y, wherein X belongs to X, Y belongs to Y, and the mutual information is
Then normalizing the maximum mutual information value, selecting the maximum value of the mutual information under different scales as the maximum mutual information coefficient value,
in the above formula, a and B are the numbers of the division grids in the X and Y directions, respectively, and the size of B is 0.6 th power of the data amount.
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