CN112001256A - Method and system for removing power frequency interference of mixed signal - Google Patents

Method and system for removing power frequency interference of mixed signal Download PDF

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CN112001256A
CN112001256A CN202010725815.1A CN202010725815A CN112001256A CN 112001256 A CN112001256 A CN 112001256A CN 202010725815 A CN202010725815 A CN 202010725815A CN 112001256 A CN112001256 A CN 112001256A
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刘汉文
陈海滨
范波
何洋
潘子安
刘超
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Abstract

The invention discloses a method and a system for removing power frequency interference of a mixed signal, which relate to the technical field of signal processing, and the method comprises the following steps: generating a separation matrix W of the mixed signal X, analyzing the ith row vector WiThe objective function of (1); acquiring particle swarm parameters, and performing particle swarm iteration; if the iteration termination condition is met, outputting the optimal position of the population as a solution of the objective function, and calculating to obtain WiA value of (d); calculating an approximate signal of an independent source signal in the X, and eliminating the approximate signal to obtain a new mixed signal; and after the m-th separation of the approximate signal of the independent source signal, generating a new separation matrix, analyzing a new target function, calculating the ith row vector of the new separation matrix according to a particle swarm algorithm, and separating the approximate signal of another independent source signal from the new mixed signal again until the power frequency signal in the mixed signal is eliminated. The inventionThe power frequency interference removing method based on the improved particle swarm optimization independent component analysis simplifies the particle searching process, improves the iteration speed and plays a role in noise suppression.

Description

Method and system for removing power frequency interference of mixed signal
Technical Field
The invention relates to the technical field of signal processing, in particular to a method and a system for removing power frequency interference of a mixed signal.
Background
The dynamic strain signal in the durability test of the whole vehicle result is an important component of fatigue reliability analysis, and because the equipment is not firmly grounded and the power frequency interference exists in the test environment in the road test process, the power frequency component with larger components can be mixed into the dynamic strain to form a mixed signal, the beneficial information is polluted by noise to cause the condition of difficult extraction, which is not beneficial to further fatigue analysis,
the current method for inhibiting power frequency interference mainly comprises the following steps: notch filtering, adaptive filtering and independent component analysis. Notch filtering is a special band-reject filter, which ideally has only one frequency point for eliminating a given frequency in a signal. But the disadvantage is also evident, and the co-workers filtering the noise will also remove the components that are present in the stop band range and need to be preserved. And the lack of weak strain signals can cause larger errors in the results of fatigue analysis. The principle of the self-adaptive filter is to actively adjust the coefficient of the filter according to the frequency drift of power frequency interference by using a least mean square method or a least square method, thereby eliminating the power frequency interference. However, the nature of the filter is consistent with that of notch filtering, so that the filter has certain damage to non-power frequency components.
Disclosure of Invention
The invention aims to overcome the defects of the background technology, and provides a method and a system for removing power frequency interference of a mixed signal, which can effectively separate power frequency components in the signal, play a role in inhibiting noise and improve the signal-to-noise ratio.
In a first aspect, a method for removing power frequency interference from a mixed signal is provided, which includes the following steps:
generating a matrix comprising N row vectors as a hybrid signalSeparation matrix W of number X, analysis W ith row vector W in conjunction with XiThe objective function of (1);
acquiring particle swarm parameters, initializing positions of particles, and iterating through a particle swarm algorithm;
if the iteration termination condition is met, outputting the optimal position Gbest of the population as a solution of the objective function, and calculating to obtain WiA value of (d);
according to the WiCalculating an approximate signal of an independent source signal in X, and eliminating the approximate signal in X to obtain a mixed signal containing N-1 independent source signals;
after the approximate signal of an independent source signal is separated for the mth time, a matrix containing N-m row vectors is generated to serve as a separation matrix of the new mixed signal based on the new mixed signal obtained after separation, a new objective function is analyzed, the ith row vector of the new separation matrix is calculated according to a particle swarm algorithm, and the approximate signal of another independent source signal is separated again from the new mixed signal until the power frequency signal in the mixed signal is eliminated.
According to the first aspect, in a first possible implementation manner of the first aspect, before the step of "generating a matrix including N row vectors as the separation matrix W of the mixed signal X", the method includes the following steps:
the test signal is centered and whitened to obtain a preprocessed mixed signal X, and the test signal is synthesized by N independent source signals.
According to the first possible implementation manner of the first aspect, in a second possible implementation manner of the first aspect, the whitening the centered test signal includes:
whitening the test signal Z after the centralization to obtain a mixed signal X, wherein the whitening calculation formula is as follows:
Figure BDA0002601620190000021
wherein Q is E [ ZZ ]T]E is the expectation of multiplication of Z and its transpose, B is the eigenvalue diagonal matrix of Z.
In a third possible implementation form of the first aspect as such or according to the first aspect, the analysis W ith row vector W in combination with X is performediThe "step of the objective function" includes the steps of:
assuming that the probability density function of X is p (X), the entropy of X, H (X), is: h (X) ═ E (ln (p) (X)) - [ p (X)) lnp (X) dx, the negative entropy j (X) of X is: j (x) ═ H (x)gauss) -H (X), wherein XgaussIs a Gaussian random vector with the same variance as X;
negative entropy j (x) is expressed approximately as: j (x) ═ E (g (u)) -E (g (o)))]2Where o is a Gaussian variable with zero mean and unit variance, u is a random variable with zero mean and unit variance, g (-) is any non-quadratic kernel function, and E is expectation;
analyzing With row vector WiThe objective function of (2): minL (W)i)＝[E(g(WiX))-E(g(o))]2And i is 1,2, … n, wherein n is the total number of row vectors of the separation matrix W.
According to the first aspect, in a fourth possible implementation manner of the first aspect, the step of "obtaining particle swarm parameters and initializing positions of particles" includes the following steps:
obtaining particle swarm parameters, wherein the particle swarm parameters comprise a swarm size Q, a maximum iteration number Iter, a swarm search space and a maximum inertia weight omegaendMinimum inertial weight ωstartMaximum learning factor cmaxAnd a minimum learning factor cmin；
Generating a particle swarm according to the particle swarm parameters, and randomly initializing the positions of the particles in the swarm search space, wherein the initial position Z of the jth particle0(j)＝Wi(j) The optimal position for the jth particle initialization is Pbest0(j) The optimal position of the population is
Figure BDA0002601620190000031
Initial learning factor c10＝cmax、c20＝cmin。
According to a fourth possible implementation manner of the first aspect, in a fifth possible implementation manner of the first aspect, the step of "optimizing fixed-point iterative optimization by using an improved particle swarm" includes the following steps:
the updated position of the jth particle after the t +1 th iteration is: zt+1(j)＝ω(t)Zt(j)+c1tr1t(Pbestt(j)-Zt(j))+c2tr2t(Gbest0-Zt(j) In a batch process), wherein,
Figure BDA0002601620190000041
Figure BDA0002601620190000042
rand、r1tand r2tIs [0, 1]]Random numbers are generated randomly again in each iteration;
the optimal position Pbest of the particle after the t +1 iteration of the jth particlet+1(j)＝min{Z0(j)，Z1(j)，…，Zt+1(j) The optimal position of the population Gbest is min { Pbest ═ min }t+1(1)，Pbestt+1(2)，…，Pbestt+1(Q)}。
According to the first aspect, in a sixth possible implementation manner of the first aspect, the iteration termination condition is: the iteration times reach preset times, or the difference value between the optimal position of the current iteration population and the optimal position of the last iteration population is less than or equal to a preset difference value.
In a seventh possible implementation form of the first aspect, the "re-separating the approximate signal of the further independent source signal from the new mixed signal" step includes the following steps:
ypis an approximate signal, X, of an independent source signal obtained by the p-th calculationpIs the new mixed signal, X, obtained after p separationpM < th > signal of
Figure BDA0002601620190000043
Comprises the following steps:
Figure BDA0002601620190000044
in an eighth possible implementation manner of the first aspect, after the step of "separating again the approximate signal of the further independent source signal from the new mixed signal", the method further comprises the following steps:
after an approximate signal of an independent source signal is separated every time, analyzing the frequency spectrum of the separated mixed signal;
and when the main frequency is concentrated in a preset frequency range, judging that the power frequency signal is eliminated.
In a second aspect, a mixed signal power frequency interference removing system is provided, which is capable of executing the above method.
Compared with the prior art, the invention provides a method and a system for removing power frequency interference of a mixed signal based on improved particle swarm optimization Independent Component Analysis (ICA). The method simplifies the particle search process, improves the iteration speed, and overcomes the defect that the traditional FASTICA method is easy to converge on a local minimum value. The power frequency component in the signal can be effectively separated, the effect of inhibiting noise is achieved, and the signal to noise ratio is improved.
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FIG. 1 is a schematic flow chart of an embodiment of a method for removing power frequency interference from a mixed signal according to the present invention;
FIG. 2 is a time domain plot of measured dynamic strain;
FIG. 3 is a frequency domain curve corresponding to the measured dynamic strain time domain curve;
FIG. 4 is a time domain plot of a manually constructed power frequency reference source;
FIG. 5 is a time domain plot of another artificially constructed power frequency reference source;
fig. 6 is a noise reduction result of a frequency domain curve corresponding to the actually measured dynamic strain time domain curve.
Detailed Description
Reference will now be made in detail to the present embodiments of the invention, examples of which are illustrated in the accompanying drawings. While the invention will be described in conjunction with the specific embodiments, it will be understood that they are not intended to limit the invention to the embodiments described. On the contrary, it is intended to cover alternatives, modifications, and equivalents as may be included within the spirit and scope of the invention as defined by the appended claims. It should be noted that the method steps described herein may be implemented by any functional block or functional arrangement, and that any functional block or functional arrangement may be implemented as a physical entity or a logical entity, or a combination of both.
In order that those skilled in the art will better understand the present invention, the following detailed description of the invention is provided in conjunction with the accompanying drawings and the detailed description of the invention.
Note that: the example to be described next is only a specific example, and does not limit the embodiments of the present invention necessarily to the following specific steps, values, conditions, data, orders, and the like. Those skilled in the art can, upon reading this specification, utilize the concepts of the present invention to construct more embodiments than those specifically described herein.
Referring to fig. 1, an embodiment of the present invention provides a method for removing power frequency interference from a mixed signal, including the following steps:
generating a matrix comprising N row vectors as a separation matrix W for the mixed signal X, analyzing the ith row vector W in combination with XiThe objective function of (1);
acquiring particle swarm parameters, initializing positions of particles, and iterating through a particle swarm algorithm;
if the iteration termination condition is met, outputting the optimal position Gbest of the population as a solution of the objective function, and calculating to obtain WiA value of (d);
according to the WiCalculating an approximate signal of an independent source signal in X, and eliminating the approximate signal in X to obtain a mixed signal containing N-1 independent source signals;
after the approximate signal of an independent source signal is separated for the mth time, a matrix containing N-m row vectors is generated to serve as a separation matrix of the new mixed signal based on the new mixed signal obtained after separation, a new objective function is analyzed, the ith row vector of the new separation matrix is calculated according to a particle swarm algorithm, and the approximate signal of another independent source signal is separated again from the new mixed signal until the power frequency signal in the mixed signal is eliminated.
In particular, the independent components areThe basic principle of analysis is as follows: suppose there are n statistically independent random signals S ═ S1，S2，…，Sn]Called source signal, is linearly combined in some way to obtain m new random signals X ═ X1，X2，…，Xn]Called the mixed signal, i.e.: x is the number ofi＝ai1s1+ai2s2+…+ainsnI 1,2, …, m, the model can be simplified as: AS, a is a mixing matrix, and ICA (independent component analysis) aims to find a separation matrix W to perform the best approximate recovery of source signals from a mixed signal when independent source signals S and a are unknown, that is: and Y is WX and S.
In this embodiment, a mixed signal X to be separated is obtained, where the mixed signal X includes N independent source signals. Randomly generating a matrix containing N row vectors as a separation matrix W of the mixed signal X, wherein the number of the row vectors is the same as that of the independent signal sources, the number of the column vectors is not specifically limited, and analyzing the ith row vector W by combining XiThe objective function of (1). And acquiring particle swarm parameters, initializing the positions of the particles, and iterating through a particle swarm algorithm. If the iteration termination condition is met, outputting the optimal position Gbest of the population as a solution of the objective function, and calculating to obtain WiThe value of (c). According to WiCalculate an approximate signal of an independent source signal in X, e.g., based on Y ═ WX from WiThe value of (a) is used to calculate an approximation signal for an independent source signal, and the approximation signal is removed in X to obtain a mixed signal containing N-1 independent source signals.
Repeating the above randomly generating a new separation matrix based on a mixed signal containing N-1 independent source signals, analyzing a new objective function, calculating an ith row vector of the new separation matrix according to a particle swarm algorithm, and separating again an approximate signal of another independent source signal from the new mixed signal, wherein after the m-th separation of the approximate signal of an independent source signal, a matrix containing N-m row vectors is generated as the separation matrix of the new mixed signal. Until the power frequency signal in the mixed signal is eliminated.
The signal reconstruction quality evaluation standard comprises a signal-to-noise ratio, a minimum root mean square error and a correlation coefficient. (1) The signal-to-noise ratio is defined as follows:
Figure BDA0002601620190000071
in the formula: s (n) represents a noise reduction signal; η (n) represents a noise signal; n represents the number of signal sample points. The unit of the signal-to-noise ratio is decibel (dB), and the larger the value of the signal-to-noise ratio is, the better the noise reduction effect of the algorithm is. (2) The minimum root mean square error, which is used to compare the degree of similarity between the noise-reduced signal and the noise-free signal, is defined as:
Figure BDA0002601620190000072
in the formula: x (n) represents a noise free signal. The smaller the minimum mean square error value is, the more similar the noise reduction signal is to the signal without noise, and the better the noise reduction effect is. (3) The correlation coefficient, similar to the minimum mean square error, can also be used to compare the similarity between the reconstructed signal and the signal without noise, and the calculation formula of the correlation coefficient is:
Figure BDA0002601620190000081
the larger the correlation coefficient is, the more similar the noise reduction signal is to the signal without noise, and the better the noise reduction effect is.
Optionally, in another embodiment of the present application, before the step of generating a matrix including N row vectors as the separation matrix W of the mixed signal X, the method includes the following steps:
the test signal is centered and whitened to obtain a preprocessed mixed signal X, and the test signal is synthesized by N independent source signals.
Specifically, in this embodiment, the test signal is centered, that is, the mean value is removed, so that the influence of the data trend term on the result is reduced, and the computational complexity of the ICA method can be simplified. Then whitening the test signal after the centralization, calculating a covariance matrix of the data after the mean value is removed, decomposing the characteristic value of the matrix, accelerating the convergence speed, and finally obtaining a mixed signal X after the pretreatment, wherein the mixed signal is synthesized by a plurality of independent source signals.
Optionally, in another embodiment of the present application, the "whitening the centered test signal" step includes the following steps:
whitening the test signal Z after the centralization to obtain a mixed signal X, wherein the whitening calculation formula is as follows:
Figure BDA0002601620190000082
wherein Q is E [ ZZ ]T]E is the expectation of multiplication of Z and its transpose, B is the eigenvalue diagonal matrix of Z.
Optionally, in another embodiment of the present application, the step of analyzing the separation matrix W of the mixed signal includes the steps of:
assuming that the probability density function of X is p (X), the entropy of X, H (X), is: h (X) ═ E (ln (p) (X)) - [ p (X)) lnp (X) dx, the negative entropy j (X) of X is: j (x) ═ H (x)gauss) -H (X), wherein XgaussIs a Gaussian random vector with the same variance as X;
negative entropy j (x) is expressed approximately as: j (x) ═ E (g (u)) -E (g (o)))]2Where o is a Gaussian variable with zero mean and unit variance, u is a random variable with zero mean and unit variance, g (-) is any non-quadratic kernel function, and E is expectation;
analyzing With row vector WiThe objective function of (2): minL (W)i)＝[E(g(WiX))-E(g(o))]2And i is 1,2, … n, wherein n is the total number of row vectors of the separation matrix W.
Specifically, in this embodiment, based on the information entropy theory, an optimization objective function related to the separation matrix is derived, and the ICA separation matrix is converted into an optimization problem based on negative entropy. E is the expectation of a discrete number sequence/continuous function, g (-) is any non-quadratic kernel function, the expression of the non-quadratic kernel function is simpler, and after the approximate signal of the independent signal source is separated each time, the row vector of the separation matrix generated again is correspondingly reduced.
Optionally, in another embodiment of the present application, the step of "obtaining a particle swarm parameter and initializing each particle position" includes the following steps:
obtaining particle swarm parameters, wherein the particle swarm parameters comprise a swarm size Q, a maximum iteration number Iter, a swarm search space and a maximum inertia weight omegaendMinimum inertial weight ωstartMaximum learning factor cmaxAnd a minimum learning factor cmin；
Generating a particle swarm according to the particle swarm parameters, and randomly initializing the positions of the particles in the swarm search space, wherein the initial position Z of the jth particle0(j)＝Wi(j) The optimal position for the jth particle initialization is Pbest0(j) The optimal position of the population is
Figure BDA0002601620190000091
Initial learning factor c10＝cmax、c20＝cmin。
Specifically, in this embodiment, the particle swarm algorithm is as follows: for the one-dimensional optimization problem: minf (x); defining optimization parameters: maximum iteration number Iterz, population size (also called particle number) Q, iteration parameters r1, r2, c1, c2, population search space [ -a, a ]; population initialization: x0 ═ { X1, X2, … xN }, where the optimal position of the ith particle is xi and the initial position of the population is minf (xi); the positions of the particles are iterated according to a specified formula; at the t iteration: the traversed positions of each particle of the ith are xi (1), xi (2), … xi (t); the optimal position of the ith particle is minf (xi (1), xi (2), … xi (t)), and the optimal position of the population is minf (x1, x2, … xN); and when the iteration termination condition is met, outputting the particle position corresponding to the optimal position of the population, namely the solution of the optimization problem.
Optionally, in a further embodiment of the present application, the step of "optimizing fixed point iterative optimization using improved particle swarm" includes the following steps:
the updated position of the jth particle after the t +1 th iteration is: zt+1(j)＝ω(t)Zt(j)+c1tr1t(Pbestt(j)-Zt(j))+c2tr2t(Gbest0-Zt(j) In a batch process), wherein,
Figure BDA0002601620190000101
Figure BDA0002601620190000102
rand、r1tand r2tIs [0, 1]]Random numbers are generated randomly again in each iteration;
the optimal position Pbest of the particle after the t +1 iteration of the jth particlet+1(j)＝min{Z0(j)，Z1(j)，…，Zt+1(j) The optimal position of the population Gbest is min { Pbest ═ min }t+1(1)，Pbestt+1(2)，…，Pbestt+1(Q)}。
Specifically, in this embodiment, the particle swarm updates all the particle positions, the optimal particle positions, and the optimal population position each time iteration is performed, and after each iteration, it is determined whether an iteration termination condition is satisfied, and if not, the iteration is continued until the iteration termination condition is satisfied. If the iteration termination condition is satisfied, based on WiIs analyzed, and the optimal position Gbest of the population is taken as WiThe value of (c). Similarly, the ground W for each new separation matrix is determined according to the iterative process described aboveiIteration is performed through the particle swarm to obtain a new row vector.
Optionally, in another embodiment of the present application, the iteration termination condition is: the iteration times reach preset times, or the difference value between the optimal position of the current iteration population and the optimal position of the last iteration population is less than or equal to a preset difference value.
Optionally, in a further embodiment of the present application, the "separating again an approximate signal of a further independent source signal from the new mixed signal" step comprises the steps of:
ypis an approximate signal, X, of an independent source signal obtained by the p-th calculationpIs the new mixed signal, X, obtained after p separationpM < th > signal of
Figure BDA0002601620190000112
Comprises the following steps:
Figure BDA0002601620190000111
optionally, in a further embodiment of the present application, after the step of "separating again the approximate signal of the further independent source signal from the new mixed signal", the following steps are included:
after an approximate signal of an independent source signal is separated every time, analyzing the frequency spectrum of the separated mixed signal;
and when the main frequency is concentrated in a preset frequency range, judging that the power frequency signal is eliminated.
Specifically, in this embodiment, the test signal usually contains a 50Hz power frequency interference component, and each time a signal is separated, the frequency spectrum of the signal is analyzed, and the separation of the power frequency interference can be considered when the main frequency is concentrated at about 50 Hz.
The embodiment of the invention provides a mixed signal power frequency interference removing system, which can realize the method of the embodiment.
The embodiment of the invention provides a method for removing power frequency interference from a mixed signal, wherein an actually measured dynamic strain time domain curve is shown in fig. 2, and a frequency domain curve corresponding to fig. 3 can find that obvious power frequency interference exists. Because the number of observation channels is not lower than the number of independent components when the ICA basically requires, but only one strain channel is needed in practice, two orthogonal power frequency reference sources are artificially constructed, the frequency is 50Hz, channel expansion is carried out on an actually measured signal, time domain curves are shown in fig. 4 and fig. 5, and mathematical description is as follows: r is1(t)＝Asin(2πf0t)，r2(t)＝Bcos(2πf0t), wherein A, B is any constant coefficient, if harmonic components of power frequency interference exist in the strain signal, the harmonic reference source can be constructed continuously according to the method. The constructed reference source and strain signal are used to construct new observed values X (t) ═ x (t), r1(t), r2(t)]ICA analysis was performed.
Assuming that the probability density function of the dynamic strain signal (mixed signal) X is p (X), the entropy of X is defined as follows: h (x) -E (ln (p (x))) - [ p (x)) lnp (x) dx, with negative entropy defined as: j (x) ═ H (x)gauss) -h (x), wherein: xgaus represents a gaussian random vector with x being co-variance. As can be seen from information theory, a variable with a gaussian distribution has the maximum entropy among all random variables of equal variance, and in general the negative entropy is non-negative and 0 if and only if the random variable is gaussian. Negative entropy J (x) is expressed approximately as follows: j (x) ═ E (g (u)) -E (g (o)))]2Where o is a gaussian variable with zero mean and unit variance, u is a random variable with zero mean and unit variance, and G (-) represents a non-quadratic kernel function.
Converting the independent component analysis problem composed of the 3 source signals into 3 optimization problems for solving, wherein an objective function is as follows: l (W)i)＝[E(G(WiX))-E(G(o))]21,2, · · n, wherein: wi represents the ith row element of the separation matrix W.
Noise reduction processing is performed on the mixed signal, a row vector of a separation matrix is defined as particles, the number of the particles N is 24, the position range of the particles is [ -100,100], the number of iterations is 300, ω start is 0.8, ω end is 0.4, c1 is c2 is [0.6,0.1], normalization processing needs to be performed on the obtained separation vector to ensure that the separation vector has unit energy, and the noise reduction result is shown in fig. 6.
(1) Centralization and whitening of the data; (2) determining parameters such as population scale ps, maximum iteration number Iter, inertia weight omega, learning factors C1 and C2; (3) taking a certain row vector of W of the separation matrix as a particle position, and randomly initializing the particle swarm position; (4) the initial value of the parameter is selected, and the particle position is updated as shown in the following formula: xt+1(j)＝ω(i)Xt(j)+c1ir1i(Pbesti(j)-Xi(j))+c2ir2i(Gbest0-Xi(j))，
Figure BDA0002601620190000131
Figure BDA0002601620190000132
W is an inertial weight, so that the algorithm is prevented from converging to local optimum, and the random between 0 and 1 is adopted in the common situationNumbers, C1 and C2 are learning factors for avoiding premature algorithm, and r1 and r2 are random numbers between 0 and 1. (5) Updating Pbesti, Gbest according to the particle fitness value; repeating the steps, judging whether iteration termination conditions are met, if so, outputting Gbest as a row vector of the separation matrix, and if not, continuing to iterate; if the iteration termination condition is met, a path of source signals are taken out, the path of signals are eliminated in the mixed signals by adopting a decorrelation method, yp (t) is the source signal obtained by the calculation of the p time, xpi (t) is a new mixed signal obtained after p times of separation, wherein the new mixed signal comprises N-p paths of signals, and the ith path of signals is as follows:
Figure BDA0002601620190000133
wherein i is 1,2, …, N-p. The above separation steps are repeated for the new mixed signal xp (t) until no power frequency component is contained in the signal.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (10)

1. A method for removing power frequency interference of a mixed signal is characterized by comprising the following steps:
generating a matrix comprising N row vectors as a separation matrix W for the mixed signal X, analyzing the ith row vector W in combination with XiThe objective function of (1);
acquiring particle swarm parameters, initializing positions of particles, and iterating through a particle swarm algorithm;
if the iteration termination condition is met, outputting the optimal position Gbest of the population as a solution of the objective function, and calculating to obtain WiA value of (d);
according to the WiCalculating an approximate signal of an independent source signal in X, and eliminating the approximate signal in X to obtain a mixed signal containing N-1 independent source signals;
after the approximate signal of an independent source signal is separated for the mth time, a matrix containing N-m row vectors is generated to serve as a separation matrix of the new mixed signal based on the new mixed signal obtained after separation, a new objective function is analyzed, the ith row vector of the new separation matrix is calculated according to a particle swarm algorithm, and the approximate signal of another independent source signal is separated again from the new mixed signal until the power frequency signal in the mixed signal is eliminated.
2. The method of claim 1, wherein the step of generating a matrix comprising N row vectors as the separation matrix W of the mixed signal X is preceded by the step of:
the test signal is centered and whitened to obtain a preprocessed mixed signal X, and the test signal is synthesized by N independent source signals.
3. The method of claim 2, wherein said step of "whitening the centered test signal" comprises the steps of:
whitening the test signal Z after the centralization to obtain a mixed signal X, wherein the whitening calculation formula is as follows:
Figure FDA0002601620180000011
wherein Q is E [ ZZ ]T]E is the expectation of multiplication of Z and its transpose, B is the eigenvalue diagonal matrix of Z.
4. The method of claim 1, wherein analyzing With row vector Wy in conjunction with XiThe "step of the objective function" includes the steps of:
assuming that the probability density function of X is p (X), the entropy of X, H (X), is: h (X) ═ E (ln (p) (X)) - [ p (X)) lnp (X) dx, the negative entropy j (X) of X is: j (x) ═ H (x)gauss) -H (X), wherein XgaussIs a Gaussian random vector with the same variance as X;
negative entropy j (x) is expressed approximately as: j (x) ═ E (g (u)) -E (g (o)))]2Where o is a Gaussian variable with zero mean and unit variance, and u is zeroRandom variables for mean and unit variance, g (-) is any non-quadratic kernel function, E is expectation;
analyzing With row vector WiThe objective function of (2): min L (W)i)＝[E(g(WiX))-E(g(o))]2And i is 1,2, … n, wherein n is the total number of row vectors of the separation matrix W.
5. The method of claim 1, wherein said step of obtaining a population parameter and initializing each particle location comprises the steps of:
obtaining particle swarm parameters, wherein the particle swarm parameters comprise a swarm size Q, a maximum iteration number Iter, a swarm search space and a maximum inertia weight omegaendMinimum inertial weight ωstartMaximum learning factor cmaxAnd a minimum learning factor cmin；
Generating a particle swarm according to the particle swarm parameters, and randomly initializing the positions of the particles in the swarm search space, wherein the initial position Z of the jth particle0(j)＝Wi(j) The optimal position for the jth particle initialization is Pbest0(j) The optimal position of the population is
Figure FDA0002601620180000021
Initial learning factor c10＝cmax、c20＝cmin。
6. The method of claim 5, wherein said step of fixed point iterative optimization with improved particle swarm optimization comprises the steps of:
the updated position of the jth particle after the t +1 th iteration is: zt+1(j)＝ω(t)Zt(j)+c1tr1t(Pbestt(j)-Zt(j))+c2tr2t(Gbest0-Zt(j) In a batch process), wherein,
Figure FDA0002601620180000031
Figure FDA0002601620180000032
rand、r1tand r2tIs [0, 1]]Random numbers are generated randomly again in each iteration;
the optimal position Pbest of the particle after the t +1 iteration of the jth particlet+1(j)＝min{Z0(j)，Z1(j)，…，Zt+1(j) The optimal position of the population Gbest is min { Pbest ═ min }t+1(1)，Pbestt+1(2)，…，Pbestt+1(Q)}。
7. The method of claim 1, wherein the iteration termination condition is: the iteration times reach preset times, or the difference value between the optimal position of the current iteration population and the optimal position of the last iteration population is less than or equal to a preset difference value.
8. The method of claim 1, wherein said step of re-separating an approximation signal of a further independent source signal from said new mixed signal comprises the steps of:
ypis an approximate signal, X, of an independent source signal obtained by the p-th calculationpIs the new mixed signal, X, obtained after p separationpM < th > signal of
Figure FDA0002601620180000033
Comprises the following steps:
Figure FDA0002601620180000034
9. a method as claimed in claim 1, characterized in that the step of "separating again an approximation signal of a further independent source signal from the new mixed signal" is followed by the steps of:
after an approximate signal of an independent source signal is separated every time, analyzing the frequency spectrum of the separated mixed signal;
and when the main frequency is concentrated in a preset frequency range, judging that the power frequency signal is eliminated.
10. A mixed signal interference cancellation system for performing the method of any one of claims 1 to 9.
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