CN104009948B - Blind source separation method based on improved artificial bee colony algorithm - Google Patents

Abstract

The invention discloses a blind source separation method based on an improved artificial bee colony algorithm. The method includes the following steps that an observation signal X(k)=[x[1](k), x[2](k),..., x[M](k)]<T> is obtained by a source signal S(k)=[s[1](k), s[2](k),..., s[M](k)]<T> through a nonsingular hybrid matrix A; the obtained observation signal X (k) is sent to a preprocessing filter, and an output signal Z(k) of the preprocessing filter is obtained; the output signal Z(k) of the preprocessing filter is sent to a separation matrix W(k), and a separation signal Y(k) is obtained; an initial optimized separation matrix Wopt (0) of the W(k) is obtained through the improved artificial colony algorithm; after the initial optimized separation matrix Wopt (0) of the W(k) is obtained, the W(k) is updated. According to the method, the improved artificial bee colony algorithm is adopted for optimizing the blind source separation method NGA based on natural gradient so that the initial optimized separation matrix can be obtained, and then signal separation is performed through the initial optimized separation matrix. The method is low in convergence speed and small in crosstalk error and has wide application prospect in the aspects of wireless communication, image processing, voice signal processing and the like.

Description

A kind of blind source separation method based on improvement artificial bee colony algorithm

Technical field

The present invention relates to signal processing technology field, particularly a kind of blind source separating side based on improvement artificial bee colony algorithm Method.

Background technology

Bss (blind source separation, blind source separating) is the research topic that current field of signal processing is risen One of, its main task is in the case that unknown source signal and hybrid mode are unknown, the letter only receiving by sensor Number recover source signal.In blind separating method, to self-adaptive blind source separation method, when Signal separator is carried out using larger step size When, fast convergence rate, but separating property is poor；During using less step-length, preferable separating property can be kept, but convergence rate Slowly.In addition to step factor, initially-separate matrix is also the factor of an impact constringency performance.In prior art, initially-separate square Battle array randomly selects, and the convergence rate that can lead to separation process is slow, the problems such as be easily absorbed in Local Extremum.

Abc (artificial bee colony, artificial bee colony algorithm) is that a kind of swarm intelligence of imitation bee colony behavior is excellent Change method, it be mainly characterized by carry out odds relatively by treating Solve problems, using bee colony individuality local optimal searching ability, by Colony finds out problem globally optimal solution to be solved, fast convergence rate.In Traditional Man ant colony algorithm, a army of bees is divided into and drawing Lead honeybee, follow honeybee and investigation honeybee 3 class, lead honeybee, follow honeybee for the exploitation in nectar source, investigation honeybee avoids nectar source species very few；Seek Excellent process is mainly finds nectar source nectar amount highest nectar source position, and each position represents a solution of problem to be solved, bee colony The high nectar source of nectar amount is constantly looked for by search, eventually finds nectar amount highest nectar source position, the i.e. optimum of optimization problem Solution；However, lead honeybee and follow honeybee search nectar source location updating formula be

θ_ij=θ_ij+φ_ij(θ_ij-θ_kj)i≠k；

In formula, i ∈ { 1,2 ..., n }, j ∈ { 1,2 ..., d }, i ≠ k, θ_ijFor i-th new nectar source jWei position, θ_ijTable Show i-th green molasses source jWei position, θ_kjRepresent k-th nectar source jWei position, φ_ijProduce for i-th green molasses source jWei position Raw random number, span is [- 1,1], and it is to control θ_ijWith θ_kjBetween interference size, with θ_ijWith θ_kjDifference reduce, To position θ_ijDisturbance equally reduce, therefore φ_ijAdaptively reduce.After leading honeybee to search new nectar source, new nectar source position θ_ijIt is with green molasses source position θ_ijBased on plus it with neighborhood nectar source position θ_kjDifference obtain, due to neighborhood nectar source be with Machine selects, this nectar source nectar amount possible higher than green molasses source it is also possible to lower it is impossible to the new nectar source of strict control to the overall situation The search of excellent direction, the controling power being for search procedure is not enough, and the process converging to global optimum nectar source is slower.

How to solve the deficiencies in the prior art has become an existing signal processing technology field emphasis difficult problem urgently to be resolved hurrily.

Content of the invention

The technical problem to be solved is to overcome the defect that Traditional Man ant colony algorithm and blind separating method exist, And a kind of blind source separation method based on improvement artificial bee colony algorithm is provided, the present invention first enters to Traditional Man ant colony algorithm abc Row improves, then with improved artificial bee colony algorithm, initially-separate matrix is optimized, and obtains more preferable blind separation performance.This Bright method has the little performance of fast convergence rate, crosstalk error, at aspects such as radio communication, image procossing, Speech processing All have wide practical use.

The present invention is to solve above-mentioned technical problem to employ the following technical solutions:

According to a kind of blind source separation method based on improvement artificial bee colony algorithm proposed by the present invention, comprise the steps:

Step one, source signal s (k)=[s₁(k),s₂(k),…,s_m(k)]^tObserved through nonsingular hybrid matrix a Signal x (k)=[x₁(k),x₂(k),…,x_m(k)]^t: x (k)=as (k)；Wherein s_mK () is m-th component of source signal s (k), x_mK () is m-th component of observation signal x (k), k is time serieses, and subscript t represents conjugate transpose, and m is positive integer, a be m × M ties up matrix；

Step 2, observation signal x (k) obtaining step one are sent into pre-processing filter and are obtained its output signal z (k)；Tool Body is: first carries out centralization pretreatment to observation signal x (k), that is,Wherein e represents mathematic expectaion, Again to centralization pre-processed resultsCarry out output signal z (k) that whitening processing obtains pre-processing filter: z (k)=vx K (), wherein v are whitening matrix；

Step 3, output signal z (k) of the pre-processing filter obtaining step 2 deliver to separation matrix w (k), obtain Separate signal y (k): y (k)=w (k) x (k)；Wherein y (k) is m × 1 dimensional vector, is an estimation of source signal s (k), its point Amount is separate, and separation matrix w (k) is dimension of m m；

Step 4, the initial optimization separation matrix w by improving artificial bee colony algorithm acquisition w (k)_opt(0)；Specific as follows:

(401) artificial bee colony initialization: randomly generate 2n position, take n therein as nectar source position, n is just whole Number；Position vector θ in i-th nectar source_iCorresponding to initially-separate matrix w (0), i=1,2 ..., n, position vector θ_iFor d Dimension, and d=m (m-1)/2；Maximum cycle is iter_max, iter_maxIt is the integer more than or equal to zero；

(402) with position vector θ in i-th nectar source_iRepresent initially-separate matrix w (0), then by initially-separate matrix w (0) obtain initially-separate signal

(403) obtain initially-separate signalKurtosis and nectar source nectar amount；

SignalKurtosis be defined as

$j\left(\tilde{y}\right(k\left)\right)=\underset{i=1}{\overset{n}{\&sigma;}}|e\left({\tilde{y}}_i^4\right(k\left)\right)-3e^2\left({\tilde{y}}_i^2\right(k\left)\right)|;$

In formula,For signalI-th component, signalKurtosisIt is to solve for initial optimization separation square Battle array w_opt(0) object function；

By signalKurtosis be defined as i-th nectar source nectar flow function, that is,

$f\left({\mathrm{\&theta;}}_i\right)=j\left(\tilde{y}\right(k\left)\right);$

In formula, θ_iInitially-separate matrix w (0) corresponding to separation matrix w (k)；

(404) lead honeybee search nectar source and calculate nectar amount: lead honeybee to select one according in neighborhood pasture in memory New nectar source position, that is,

$\left\{\begin{array}{cc}{\mathrm{\&theta;}}_{ij}={\mathrm{\&theta;}}_{ij}& i=k\\ {\mathrm{\&theta;}}_{ij}={\mathrm{\&theta;}}_{ij}+{\mathrm{\&phi;}}_{ij}({\mathrm{\&theta;}}_{ij}-{\mathrm{\&theta;}}_{kj})& i\&notequal;k\end{array}\right.;$

In formula, i ∈ { 1,2 ..., n }, j ∈ { 1,2 ..., d }, θ_ijFor i-th new nectar source jWei position, θ_ijRepresent i-th Individual green molasses source jWei position, θ_kjRepresent k-th nectar source jWei position；φ_ijFor i-th green molasses source jWei position produce with Machine number, span is [- 1,1]；

After leading honeybee to search new nectar source, by nectar source nectar flow function described in step (403)To count Calculate new nectar source nectar amount, lead honeybee to determine the choice in green molasses source using greedy selection mechanism, if the nectar amount in new nectar source is high In or be equal to green molasses source nectar amount, lead honeybee just to accept new nectar source and abandon green molasses source, otherwise, lead honeybee still to keep to green molasses The collection of source nectar；

(405) follow honeybee select nectar source: when all lead honeybee to complete search procedure after, follow honeybee according to lead honeybee provide Nectar source nectar amount selects nectar source in roulette mode, and nectar source selected probability calculation formula is

$p\left({\mathrm{\&theta;}}_i\right)=\frac{f\left({\mathrm{\&theta;}}_i\right)}{\underset{i=1}{\overset{n}{\&sigma;}}f\left({\mathrm{\&theta;}}_i\right)};$

Follow the maximum nectar source of honeybee select probability as i-th new nectar source, then this nectar source jWei position θ_ijBy following honeybee The location updating formula of oneself is updated；

(406) search bee reconnaissance stage: if i-th nectar source nectar amount that search bee searches in reconnaissance stage is constant, Lead honeybee to become search bee accordingly, enter the search bee stage, and randomly generate i-th that i-th new nectar source replacement is abandoned Green molasses source, i-th randomly generating new nectar source jWei position is calculated by following equation, that is,

θ_ij=θ_ijmin+rand(0,1)(θ_ijmax-θ_ijmin)；

In formula, rand (0,1) is equally distributed random number between (0,1), θ_ijmaxWith θ_ijminIt is respectively θ_ijValue model Enclose upper and lower limit；

(407) when the cyclic process of (403)-(406) has reached maximum cycle iter_maxWhen, then record now nectar Amount highest nectar source position vector, output nectar amount highest nectar source position vector θ, to obtain initially-separate matrix w (0) Initial optimization separation matrix w_opt(0)；Otherwise, (403) are gone to；

Step 5, obtain the initial optimization separation matrix w of w (k) in (407)_opt(0), after, w (k) is updated.

As a kind of scheme optimizing further based on the blind source separation method improving artificial bee colony algorithm of the present invention, In described step 5, w (k) is updated as the following formula:

W (k+1)=w (k)+μ [i-f (y (k)) y^t(k)]w(k)；

In formula, i represents unit matrix, and μ is step-length, and f (y (k)) is nonlinear activation primitive, and f (y (k))=2tanh (y (k)), tanh represents hyperbolic tangent function.

As a kind of scheme optimizing further based on the blind source separation method improving artificial bee colony algorithm of the present invention, The location updating formula following honeybee oneself in described (405) is；

θ_ij=η θ_ij+κ·φ_ij·(θ_ij-θ_kj)；

In formula, η represents dynamic forgetting factor, and κ is the Dynamic Neighborhood factor；

Dynamically forgetting factor is

η=γ [ω₂-(2/(1+exp(-α(iter/iter_max))^β)-0.77)(ω₂-ω₁)]；

In formula, γ is a constant, ω₁、ω₂, α, β be constant；Iter is cycle-index, iter_maxFor largest loop time Number；Exp represents the exponential function with e as bottom；

The Dynamic Neighborhood factor is

κ=γ [ω₃+(2/(1+exp(-α(iter/iter_max))^β)-1.2)(ω₄-ω₃)]；

In formula, γ is a constant, ω₃And ω₄For constant；

When nectar source nectar amount is higher than neighborhood nectar source nectar amount, γ ＜ 1；Conversely, γ ＞ 1.

The present invention adopts above technical scheme compared with prior art, has following technical effect that the inventive method will be divided From signal kurtosis as Traditional Man ant colony algorithm abc nectar source nectar flow function, in Traditional Man ant colony algorithm abc with Improve with honeybee search strategy, obtain improved artificial bee colony algorithm iabc；In iabc, lead honeybee and follow honeybee using not Carry out nectar source search with search strategy, overcome and lead honeybee in Traditional Man ant colony algorithm abc and follow honeybee same search strategy Search procedure is brought to control hypodynamic problem；The inventive method adopts improved artificial bee colony algorithm iabc to based on ladder naturally The blind source separation method nga of degree is optimized, and has the little performance of fast convergence rate, crosstalk error.The inventive method is wireless The aspects such as communication, image procossing, Speech processing all have wide practical use.

Brief description

Fig. 1 is for adaptive blind source separation system structural representation.

Fig. 2 is source signal figure: the source signal figure of (a) first via voice signal, the source signal of (b) second road voice signal Figure, the source signal figure of (c) the 3rd road voice signal.

Fig. 3 is mixed signal figure: the mixed signal figure of (a) first via voice signal, the mixing of (b) second road voice signal Signal graph, the mixed signal figure of (c) the 3rd road voice signal.

Fig. 4 is the inventive method separation signal graph: the separation signal graph of (a) second road voice signal, (b) first via voice The separation signal graph of signal, the separation signal graph of (c) the 3rd road voice signal.

Fig. 5 is the convergence curve of the inventive method.

Specific embodiment

Below in conjunction with the accompanying drawings technical scheme is described in further detail:

As shown in figure 1, it is a kind of as shown in Figure 1 based on the blind source separation method principle improving artificial bee colony algorithm.In Fig. 1, Source signal s (k)=[s₁(k),s₂(k),…,s_m(k)]^tFor m source signal unknown and independent of each other；X (k)=[x₁(k),x₂ (k),…,x_m(k)]^tFor the observation signal of nonsingular hybrid matrix a, wherein s_mK () is m-th component of source signal s (k), x_m K () is m-th component of observation signal x (k), k is time serieses, and subscript t represents conjugate transpose；M is positive integer；A is m × m Dimension matrix；Z (k) is the output signal of pre-processing filter；W (k) is separation matrix, and y (k) is to separate signal.

The present invention is using improvement artificial bee colony algorithm, initially-separate matrix w (0) of separation matrix w (k) to be optimized, To obtain more preferable separating property.The technical scheme below present invention being provided is described in detail.

Traditional Man ant colony algorithm

In Traditional Man ant colony algorithm abc, a army of bees be divided into lead honeybee, follow honeybee and investigation honeybee 3 class, lead Honeybee, follow honeybee for nectar source exploitation, investigation honeybee avoid nectar source species very few；Optimization process is mainly finds nectar amount highest Nectar source, its position vector corresponds to a solution of problem to be solved.In the present invention, nectar amount highest nectar source position vector is just Initial optimization separation matrix w corresponding to separation matrix w (k)_opt(0).It is high that artificial bee colony passes through continuous search searching nectar amount Nectar source, eventually finds nectar amount highest nectar source position vector, that is, obtains optimal solution；However, leading honeybee and following honeybee search Nectar source location updating formula is

$\left\{\begin{array}{cc}{\mathrm{\&theta;}}_{ij}={\mathrm{\&theta;}}_{ij}& i=k\\ {\mathrm{\&theta;}}_{ij}={\mathrm{\&theta;}}_{ij}+{\mathrm{\&phi;}}_{ij}({\mathrm{\&theta;}}_{ij}-{\mathrm{\&theta;}}_{kj})& i\&notequal;k\end{array}\right.---\left(1\right)$

In formula, i ∈ { 1,2 ..., n }, j ∈ { 1,2 ..., d }, i ≠ k, θ_ijFor i-th new nectar source jWei position, θ_ijTable Show i-th green molasses source jWei position, θ_kjRepresent k-th nectar source jWei position, φ_ijProduce for i-th green molasses source jWei position Raw random number, span is [- 1,1], and it is to control θ_ijWith θ_kjBetween interference size, with θ_ijWith θ_kjDifference reduce, To position θ_ijDisturbance equally reduce, therefore φ_ijAdaptively reduce；After leading honeybee to search new nectar source, new nectar source position θ_ijIt is with green molasses source position θ_ijBased on plus it with neighborhood nectar source position θ_kjDifference obtain, due to neighborhood nectar source be with Machine selects, this nectar source nectar amount than green molasses source may high it is also possible to lower it is impossible to strictly control new nectar source to the overall situation The search of excellent direction, the controling power being for search procedure is not enough, and the process converging to global optimum's food source is slower.

Improve artificial bee colony algorithm iabc

In order to improve the controling power to abc search procedure, the present invention is to leading honeybee and follow honeybee and be respectively adopted different search Nectar source strategy carries out nectar source position and is updated.

Lead honeybee still to carry out nectar source location updating by formula (1), and i-th new nectar source jth dimension position of honeybee selection will be followed Put more new formula to be defined as

θ_ij=η θ_ij+κ·φ_ij·(θ_ij-θ_kj)； (2)

In formula, η represents dynamic forgetting factor, and κ is the Dynamic Neighborhood factor；

Dynamic forgetting factor is defined as

η=γ [ω₂-(2/(1+exp(-α(iter/iter_max))^β)-0.77)(ω₂-ω₁)]；

In formula, γ is a constant, ω₁、ω₂And α, β are constant；Iter is cycle-index, iter_maxFor largest loop time Number；Exp represents the exponential function with e as bottom.This formula shows, nectar source position is subject to one to increase with cycle-index iter and reduces Function is adjusted；

The Dynamic Neighborhood factor is defined as

κ=γ [ω₃+(2/(1+exp(-α(iter/iter_max))^β)-1.2)(ω₄-ω₃)]；

In formula, γ is a constant, ω₃And ω₄For constant, this formula shows, neighborhood nectar source position is subject to one with cycle-index The function that iter increases and increases is adjusted；

When nectar source nectar amount is higher than neighborhood nectar source nectar amount,_γ＜ 1；Conversely,_γ＞ 1.

Nga (natural gradient algorithm, the blind source separation method based on natural gradient)

The target of blind source separation method is to find optimum separation matrix w (k) to make output signal y (k) to each other only Vertical property is maximum, using the relation of mutual information and comentropy, the cost function of piece-rate system is defined as

$o\left(k\right)=h\left(y_m\right(k\left)\right)-ln\left|\det \left(w\right(k\left)\right)\right|=-\underset{m=1}{\overset{m}{\&sigma;}}e\left(\ln p_y\right(y_m\left(k\right)\left)\right)-ln\left|\det \left(w\right(k\left)\right)\right|---\left(3\right)$

In formula, h (y_m(k)) separate signal y m-th for separating in signal y (k)_mThe entropy of (k), p_y(y_m(k)) believe for separating M-th component y in number y (k)_mK the marginal probability density of (), e represents mathematic expectaion computing, and ln represents naturally right with e as bottom Number, det represents the determinant taking w (k)；By the more new formula that the cost function of piece-rate system obtains separation matrix w (k) it is

W (k+1)=w (k)+μ [i-f (y (k)) y^t(k)]w(k) (4)

In formula, μ represents step-length, is constant；I represents a unit matrix；The present invention takes f (y (k))=2tanh (y (k)).

Optimize blind separating method using improving artificial bee colony algorithm, the present invention obtaining is a kind of to be calculated based on improvement artificial bee colony The blind source separation method of method, comprises the steps:

Step one, source signal s (k)=[s₁(k),s₂(k),…,s_m(k)]^tObserved through nonsingular hybrid matrix a Signal x (k)=[x₁(k),x₂(k),…,x_m(k)]^t: x (k)=as (k)；Wherein s_mK () is m-th component of source signal s (k), x_mK () is m-th component of observation signal x (k), k is time serieses, and subscript t represents conjugate transpose, and m is positive integer, a be m × M ties up matrix；

Step 2, observation signal x (k) obtaining step one are sent into pre-processing filter and are obtained its output signal z (k)；Tool Body is: first carries out centralization pretreatment to observation signal x (k), that is,Wherein e represents mathematic expectaion, Again to centralization pre-processed resultsCarry out output signal z (k) that whitening processing obtains pre-processing filter: z (k)=vx K (), wherein v are whitening matrix；

Step 3, output signal z (k) of the pre-processing filter obtaining step 2 deliver to separation matrix w (k), obtain Separate signal y (k): y (k)=w (k) x (k)；Wherein y (k) is m × 1 dimensional vector, is an estimation of source signal s (k), its point Amount is separate, and separation matrix w (k) is dimension of m m；

Step 4, the initial optimization separation matrix w by improving artificial bee colony algorithm acquisition w (k)_opt(0)；Specific as follows:

(401) artificial bee colony initialization: randomly generate 2n position, take n therein as nectar source position, n is just whole Number；Position vector θ in i-th nectar source_iCorresponding to initially-separate matrix w (0), i=1,2 ..., n, position vector θ_iFor d Dimension, and d=m (m-1)/2；Maximum cycle is iter_max, iter_maxIt is the integer more than or equal to zero；

(402) with position vector θ in i-th nectar source_iRepresent initially-separate matrix w (0), then by initially-separate matrix w (0) obtain initially-separate signal

(403) obtain initially-separate signalKurtosis and nectar source nectar amount；

SignalKurtosis be defined as

$j\left(\tilde{y}\right(k\left)\right)=\underset{i=1}{\overset{n}{\&sigma;}}|e\left({\tilde{y}}^4\right(k\left)\right)-3e^2\left({\tilde{y}}_i^2\right(k\left)\right)|;$

In formula,For signalI-th component, signalKurtosisIt is to solve for initial optimization separation square Battle array w_opt(0) object function；

Because initially-separate matrix w (0) is i-th nectar source position vector θ_iFunction, thereforeIt is θ_iFunction, because AndIt is also θ_iFunction, therefore, by signalKurtosis be defined as i-th nectar source nectar flow function, that is,

$f\left({\mathrm{\&theta;}}_i\right)=j\left(\tilde{y}\right(k\left)\right);$

In formula, θ_iInitially-separate matrix w (0) corresponding to separation matrix w (k)；

(404) lead honeybee search nectar source and calculate nectar amount: lead honeybee to select one according in neighborhood pasture in memory New nectar source position, that is,

$\left\{\begin{array}{cc}{\mathrm{\&theta;}}_{ij}={\mathrm{\&theta;}}_{ij}& i=k\\ {\mathrm{\&theta;}}_{ij}={\mathrm{\&theta;}}_{ij}+{\mathrm{\&phi;}}_{ij}({\mathrm{\&theta;}}_{ij}-{\mathrm{\&theta;}}_{kj})& i\&notequal;k\end{array}\right.;$

In formula, i ∈ { 1,2 ..., n }, j ∈ { 1,2 ..., d }, θ_ijFor i-th new nectar source jWei position, θ_ijRepresent i-th Individual green molasses source jWei position, θ_kjRepresent k-th nectar source jWei position；φ_ijFor i-th green molasses source jWei position produce with Machine number, span is [- 1,1], and it is to control θ_ijWith θ_kjBetween interference size, with θ_ijWith θ_kjDifference reduce, to position θ_ijDisturbance equally reduce, therefore φ_ijAdaptively reduce；

After leading honeybee to search new nectar source, by nectar source nectar flow function described in step (403)To count Calculate new nectar source nectar amount, lead honeybee to determine the choice in green molasses source using greedy selection mechanism, if the nectar amount in new nectar source is high In or be equal to green molasses source nectar amount, lead honeybee just to accept new nectar source and abandon green molasses source, otherwise, lead honeybee still to keep to green molasses The collection of source nectar；

(405) follow honeybee select nectar source: when all lead honeybee to complete search procedure after, follow honeybee according to lead honeybee provide Nectar source nectar amount selects nectar source in roulette mode, and nectar source nectar amount is higher, and its selected probability is bigger, and nectar source is selected Probability calculation formula is

$p\left({\mathrm{\&theta;}}_i\right)=\frac{f\left({\mathrm{\&theta;}}_i\right)}{\underset{i=1}{\overset{n}{\&sigma;}}f\left({\mathrm{\&theta;}}_i\right)};$

Follow the maximum nectar source of honeybee select probability as i-th new nectar source, then this nectar source jWei position θ_ijBy following honeybee The location updating formula of oneself is updated；

(406) search bee reconnaissance stage: if i-th nectar source nectar amount that search bee searches in reconnaissance stage is constant, Lead honeybee to become search bee accordingly, enter the search bee stage, and randomly generate i-th that i-th new nectar source replacement is abandoned Green molasses source, i-th randomly generating new nectar source jWei position is calculated by following equation, that is,

θ_ij=θ_ijmin+rand(0,1)(θ_ijmax-θ_ijmin)；

In formula, rand (0,1) is equally distributed random number between (0,1), θ_ijmaxWith θ_ijminIt is respectively θ_ijValue model Enclose upper and lower limit；

(407) when the cyclic process of (403)-(406) has reached maximum cycle iter_maxWhen, then record now nectar Amount highest nectar source position vector, output nectar amount highest nectar source position vector θ, to obtain initially-separate matrix w (0) Initial optimization separation matrix w_opt(0)；Otherwise, (403) are gone to；

Step 5, obtain the initial optimization separation matrix w of w (k) in (407)_opt(0), after, w (k) is updated.

In step 5, w (k) is updated as the following formula:

W (k+1)=w (k)+μ [i-f (y (k)) y^t(k)]w(k)；

In formula, i represents unit matrix, and μ is step-length, and f (y (k)) is nonlinear activation primitive, and f (y (k))=2tanh (y (k)), tanh represents hyperbolic tangent function.

(405) the location updating formula following honeybee oneself in is；

θ_ij=η θ_ij+κ·φ_ij·(θ_ij-θ_kj)；

In formula, η represents dynamic forgetting factor, and κ is the Dynamic Neighborhood factor；

Dynamically forgetting factor is

η=γ [ω₂-(2/(1+exp(-α(iter/iter_max))^β)-0.77)(ω₂-ω₁)]；

In formula, γ is a constant, ω₁、ω₂, α, β be constant；Iter is cycle-index, iter_maxFor largest loop time Number；Exp represents the exponential function with e as bottom；

The Dynamic Neighborhood factor is

κ=γ [ω₃+(2/(1+exp(-α(iter/iter_max))^β)-1.2)(ω₄-ω₃)]；

In formula, γ is a constant, ω₃And ω₄For constant；

When nectar source nectar amount is higher than neighborhood nectar source nectar amount, γ ＜ 1；Conversely, γ ＞ 1.

In order to evaluate the performance of the inventive method, using crosstalk error as evaluation index, that is,

$pi\left(c\right)=\underset{m=1}{\overset{m}{\&sigma;}}\&lsqb;\left(\underset{k=1}{\overset{m}{\&sigma;}}\frac{\left|c_{mk}\right|}{\underset{l}{\max }\left(c_{ml}\right)}-1\right)\&rsqb;+\underset{m=1}{\overset{m}{\&sigma;}}\&lsqb;\left(\underset{k=1}{\overset{m}{\&sigma;}}\frac{\left|c_{km}\right|}{\underset{l}{\max }\left(c_{lm}\right)}-1\right)\&rsqb;;$

In formula, c=wa=p λ is the overall matrix of whole system, and wherein p and λ represents a permutation matrix and right respectively Angular moment battle array, the signal after they illustrate blind source separating exists uncertain in amplitude and sequentially, and if only if p λ=i When, the signal after separating just is equal to source signal；Closer to zero, separating effect to be illustrated is better for the wherein value of pi (c).c_mkFor matrix The element of c m row kth row；c_mlElement for matrix c m row l row；c_kmElement for matrix c row k m row；c_lmFor square The element of battle array c l row m row.

For the constringency performance comparing Traditional Man ant colony algorithm abc and improve artificial bee colony algorithm iabc, utilize Two function pair Traditional Man ant colony algorithm abc of griewank and sphere and the constringency performance improving artificial bee colony algorithm iabc Tested, as shown in Table 1 and Table 2, table 1 is the test result of griewank to test result, table 2 is the test knot of sphere Really.

Table 1

Table 2

Tables 1 and 2 shows, to griewank test function, minima during abc algorithmic statement is 0.2134, converges to Minima needs iteration 92 times, and minima during iabc algorithmic statement is 0, converges to minima and need iteration 53 times；Right Sphere test function, minima during abc algorithmic statement is 9.8156e-17, converges to minima and need iteration 853 times, and Minima during iabc algorithmic statement is 1.5741e-19, converges to minima and need iteration 543 times.Therefore, the performance of iabc More superior than abc.

In order to verify the effectiveness of the inventive method (referred to as iabc+nga), divided based on the blind source of natural gradient with tradition It is comparison other from method nga, the blind source separation method (abc+nga) based on Traditional Man ant colony algorithm, carried out with matlab Emulation experiment compares.In an experiment, take m=3, at this moment separation matrix w (k) is 3 × 3-dimensional matrix, according to orthogonal matrix Matter, initially-separate matrix w (0) of separation matrix w (k) is write as a series of spin matrixs long-pending, that is,

$w\left(0\right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& {\mathrm{cos\&theta;}}_1& -{\mathrm{sin\&theta;}}_1\\ 0& {\mathrm{sin\&theta;}}_1& {\mathrm{cos\&theta;}}_1\end{array}\right]\left[\begin{array}{ccc}{\mathrm{cos\&theta;}}_2& 0& -{\mathrm{sin\&theta;}}_2\\ 0& 1& 0\\ {\mathrm{sin\&theta;}}_2& 0& {\mathrm{cos\&theta;}}_2\end{array}\right]\left[\begin{array}{ccc}{\mathrm{cos\&theta;}}_3& -{\mathrm{sin\&theta;}}_3& 0\\ {\mathrm{sin\&theta;}}_3& {\mathrm{cos\&theta;}}_3& 0\\ 0& 0& 1\end{array}\right]---\left(5\right)$

In formula, θ₁,θ₂,θ₃∈ [0,2 π) be three spin matrixs the anglec of rotation, θ=[θ will be solved₁,θ₂,θ₃] optimum Problem is converted into nectar source nectar amount highest nectar source position vector problem in solution artificial bee colony algorithm, as long as this problem presses step (401) it is optimized to the described process of step (407), just obtain θ=[θ₁,θ₂,θ₃] optimal solution, thus obtaining by formula (5) The initial optimization separation matrix w of initially-separate matrix w (0)_opt(0).In experiment, it is separate that No. three mike gathers Voice signal, is referred to as the first via, the second tunnel, the 3rd road source signal, and voice signal all saves as .wav file, adopts altogether As sampled point, choose matrix at 14000 pointsAs hybrid matrix, parameter ω₁=ω₃=0.2, ω₂ =ω₄=1.2, α=1.8, β=2.2；When nectar source nectar value is more than neighborhood nectar source nectar value, γ=0.8, otherwise, γ =1.2.

The constringency performance of the separation signal of source signal, mixed signal and the inventive method gained and its inventive method is bent Line, respectively as shown in Fig. 2, Fig. 3, Fig. 4 and Fig. 5.In Fig. 2, (a) is the source signal figure of first via voice signal, and (b) is the second tunnel The source signal figure of voice signal, (c) is the source signal figure of the 3rd road voice signal；In Fig. 3, (a) is first via voice signal Mixed signal figure, (b) is the mixed signal figure of the second road voice signal, and (c) is the mixed signal figure of the 3rd road voice signal；Figure 4 is the inventive method separation signal graph, and wherein (a) is the separation signal graph of the second road voice signal, and (b) believes for first via voice Number separation signal graph, (c) is the separation signal graph of the 3rd road voice signal；Fig. 4 shows, compared with the source signal shown in Fig. 2, The inventive method (iabc+nga) has obtained good separation signal；Fig. 5 shows, to traditional blind source separation method nga, step-length is One main influence factor: when μ=0.00125, nga about needs 10000 convergences of iteration；When μ=0.00175, nga About iteration 6000 times convergence, but crosstalk error is larger, separating property is poor.Compared with nga, abc+nga method performance has larger Lifting；Compared with abc+nga, the inventive method iabc+nga, in scale n=20 of step size mu=0.00125, bee colony, iter_max When=200, about 3500 convergences of iteration, convergence rate accelerates and crosstalk error diminishes, separating property improves.Therefore, originally Inventive method, improves convergence rate, reduces crosstalk error, and separating property has and is obviously improved.The inventive method is no The aspects such as line communication, image procossing, Speech processing all have wide practical use.

Technological means disclosed in the present invention program are not limited only to the technological means disclosed in above-mentioned embodiment, also include The technical scheme being made up of above technical characteristic combination in any.It should be pointed out that for those skilled in the art For, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications are also considered as Protection scope of the present invention.

Claims (2)

1. a kind of blind source separation method based on improvement artificial bee colony algorithm is it is characterised in that comprise the steps:

Step one, source signal s (k)=[s₁(k),s₂(k),…,s_m(k)]^tObtain observation signal x through nonsingular hybrid matrix a (k)=[x₁(k),x₂(k),…,x_m(k)]^t: x (k)=as (k)；Wherein s_mK () is m-th component of source signal s (k), x_m(k) It is m-th component of observation signal x (k), k is time serieses, subscript t represents conjugate transpose, and m is positive integer, and a is dimension of m m square Battle array；

Step 2, observation signal x (k) obtaining step one are sent into pre-processing filter and are obtained its output signal z (k)；Particularly as follows: First centralization pretreatment is carried out to observation signal x (k), that is,Wherein e represents mathematic expectaion, then centering Heart pre-processed resultsCarry out output signal z (k) that whitening processing obtains pre-processing filter: z (k)=vx (k), wherein V is whitening matrix；

Step 3, output signal z (k) of the pre-processing filter obtaining step 2 deliver to separation matrix w (k), are separated Signal y (k): y (k)=w (k) x (k)；Wherein y (k) is m × 1 dimensional vector, is an estimation of source signal s (k), its component phase Mutually independent, separation matrix w (k) is dimension of m m；

Step 4, the initial optimization separation matrix w by improving artificial bee colony algorithm acquisition w (k)_opt(0)；Specific as follows:

(401) artificial bee colony initialization: randomly generate 2n position, take n therein as nectar source position, n is positive integer；The Position vector θ in i nectar source_iCorresponding to initially-separate matrix w (0), i=1,2 ..., n, position vector θ_iTie up for d, And d=m (m-1)/2；Maximum cycle is iter_max, iter_maxIt is the integer more than or equal to zero；

(402) with position vector θ in i-th nectar source_iRepresent initially-separate matrix w (0), then obtained by initially-separate matrix w (0) Initially-separate signal

(403) obtain initially-separate signalKurtosis and nectar source nectar amount；

SignalKurtosis be defined as

$j\left(\tilde{y}\right(k\left)\right)=\underset{i=1}{\overset{n}{\&sigma;}}|e\left({\tilde{y}}_i^4\right(k\left)\right)-3e^2\left({\tilde{y}}_i^2\right(k\left)\right)|;$

In formula,For signalI-th component, signalKurtosisIt is to solve for initial optimization separation matrix w_opt(0) object function；

By signalKurtosis be defined as i-th nectar source nectar flow function, that is,

$f\left({\mathrm{\&theta;}}_i\right)=j\left(\tilde{y}\right(k\left)\right);$

In formula, θ_iInitially-separate matrix w (0) corresponding to separation matrix w (k)；

(404) lead honeybee to search for nectar source calculate nectar amount: lead honeybee according to select in neighborhood pasture in memory one new Nectar source position, that is,

$\left\{\begin{array}{cc}{\mathrm{\&theta;}}_{ij}={\mathrm{\&theta;}}_{ij}& i=k\\ {\mathrm{\&theta;}}_{ij}={\mathrm{\&theta;}}_{ij}+{\mathrm{\&phi;}}_{ij}({\mathrm{\&theta;}}_{ij}-{\mathrm{\&theta;}}_{kj})& i\&notequal;k\end{array}\right.;$

In formula, i ∈ { 1,2 ..., n }, j ∈ { 1,2 ..., d }, θ_ijFor i-th new nectar source jWei position, θ_ijRepresent i-th former Nectar source jWei position, θ_kjRepresent k-th nectar source jWei position；φ_ijRandom for the generation of i-th green molasses source jWei position Number, span is [- 1,1]；

After leading honeybee to search new nectar source, by nectar source nectar flow function described in step (403)To calculate new honey Source nectar amount, leads honeybee to determine the choice in green molasses source using greedy selection mechanism, if the nectar amount in new nectar source is higher than or waits In the nectar amount in green molasses source, lead honeybee just to accept new nectar source and abandon green molasses source, otherwise, lead honeybee still to keep to green molasses source nectar Collection；

(405) follow honeybee select nectar source: when all lead honeybee to complete search procedure after, follow honeybee according to lead honeybee provide nectar source Nectar amount selects nectar source in roulette mode, and nectar source selected probability calculation formula is

$p\left({\mathrm{\&theta;}}_i\right)=\frac{f\left({\mathrm{\&theta;}}_i\right)}{\underset{i=1}{\overset{n}{\&sigma;}}f\left({\mathrm{\&theta;}}_i\right)};$

Follow the maximum nectar source of honeybee select probability as i-th new nectar source, then this nectar source jWei position θ_ijBy following honeybee oneself Location updating formula be updated；

Described follow honeybee oneself location updating formula be:

θ_ij=η θ_ij+κ·φ_ij·(θ_ij-θ_kj)；

In formula, η represents dynamic forgetting factor, and κ is the Dynamic Neighborhood factor；

Dynamically forgetting factor is

η=γ [ω₂-(2/(1+exp(-α(iter/iter_max))^β)-0.77)(ω₂-ω₁)]；

In formula, γ is a constant, ω₁、ω₂, α, β be constant；Iter is cycle-index, iter_maxFor maximum cycle； Exp represents the exponential function with e as bottom；

The Dynamic Neighborhood factor is

κ=γ [ω₃+(2/(1+exp(-α(iter/iter_max))^β)-1.2)(ω₄-ω₃)]；

In formula, γ is a constant, ω₃And ω₄For constant；

When nectar source nectar amount is higher than neighborhood nectar source nectar amount, γ ＜ 1；Conversely, γ ＞ 1；

(406) search bee reconnaissance stage: if i-th nectar source nectar amount that search bee searches in reconnaissance stage is constant, accordingly The honeybee that leads become search bee, enter the search bee stage, and randomly generate i-th green molasses that i-th new nectar source replacement is abandoned Source, i-th randomly generating new nectar source jWei position is calculated by following equation, that is,

θ_ij=θ_ijmin+rand(0,1)(θ_ijmax-θ_ijmin)；

In formula, rand (0,1) is equally distributed random number between (0,1), θ_ijmaxWith θ_ijminIt is respectively θ_ijSpan Upper and lower limit；

(407) when the cyclic process of (403)-(406) has reached maximum cycle iter_maxWhen, then record now that nectar amount is High nectar source position vector, output nectar amount highest nectar source position vector θ, to obtain the initial of initially-separate matrix w (0) Optimize separation matrix w_opt(0)；Otherwise, (403) are gone to；

Step 5, obtain the initial optimization separation matrix w of w (k) in (407)_opt(0), after, w (k) is updated.

2. according to claim 1 a kind of based on improving the blind source separation method of artificial bee colony algorithm it is characterised in that institute State w (k) in step 5 to be updated as the following formula:

W (k+1)=w (k)+μ [i-f (y (k)) y^t(k)]w(k)；

In formula, i represents unit matrix, and μ is step-length, and f (y (k)) is nonlinear activation primitive, and f (y (k))=2tanh (y (k)), tanh represents hyperbolic tangent function.