CN106023981A - Standard-particle-swarm-optimization-algorithm-based active noise control method - Google Patents

Abstract

The invention relates to the active noise control field, especially to a standard-particle-swarm-optimization-algorithm-based active noise control method. The method comprises: (1), according to a practical noise control problem, an iterative learning active noise control system is established; (2), on the basis of a transfer function of a generalized secondary channel, a fitness calculation formula with an independent variable being a learning filter parameter is designed; (3), a standard particle swarm optimization algorithm is established based on an IIR filter mathematical model; and (4), an optimal performance filter parameter is searched by using the standard particle swarm optimization algorithm. According to the invention, the method has the following advantages: firstly, the method is simple and is easy to realize and repeated noises can be eliminated effectively; (2), the designed iterative learning active noise control system employs a frequency domain method to describe the system and the IIR filter to realize the learning filter, and the parameters of the IIR filter are designed by using the quantum particle swarm optimization algorithm, so that the stability and robustness are high and the convergence speed is fast.

Description

Active noise controlling method based on standard particle colony optimization algorithm

Technical field

The present invention relates to active noise controlling field, particularly relate to active noise control based on standard particle colony optimization algorithm Method processed.

Background technology

Active noise controlling (ANC) was proposed in 1936 with the form of patent by Germany Lueg Paul the earliest, existing so far The development course of more than 80 year.Its principle is to be artificially generated one to carry out with noise with noise constant amplitude, same to frequency, anti-phase sound Destructive interference, thus reach the purpose of noise reduction or noise elimination.Active noise control system as it is shown in figure 1, in figure d (n) be noise, Also referred to as main sound source；U (n) is to control input；X (n) is the secondary sound source acoustical signal in cancellation region；E (n) is residual error letter Number；P (z) is the transmission function of control system, it is possible to being referred to as broad sense secondary channel, it not only includes secondary sound source to cancellation district Secondary channel between territory, the system of further comprises is input to the process that secondary sound source produces.Our purpose is intended to according to residual error Signal and control signal update control signal by adaptive mode makes residual signals gradually reduce.When noise has repetition spy Property, this problem is just seen as being a track following problem.We can utilize ILC method that noise is carried out each Study, makes secondary sound source gradually be similar to anti-phase main sound source and carries out interfering cancellation with main sound source, make residual signals reduce.Along with certainly The maturation of the ANC technology of adaptive filtering technology, the ANC technology of filtering least mean-square error (FxLMS) algorithm has obtained widely Application.But this versatility technology widely, also brings the problem in some performances: (1) is for having repeat property Noise, FxLMS-ANC cannot utilize the particularity of its noise to carry out noise reduction；(2) at those, anti-acoustic capability had ultimate attainment requirement In application background, FxLMS-ANC is the most helpless, continuous along with the development of modern control theory and New Control Theory Occurring, ANC has had the developing direction that some are new.Wherein, ANC technology based on iterative learning control theory has repetition in process The application of characteristic noise has the highest researching value.

Iterative learning control (ILC) is proposed in 1978 first by Japanese scholars Uchiyama, and it is by recycling elder generation The information that front experiment obtains obtains the control input that can produce desired output track, controls quality to improve.With traditional Unlike control method, iterative learning control can process the dynamical system that uncertainty is at a relatively high in a very simplified manner, And only need less priori and amount of calculation, and there is strong adaptability, the advantage such as be easily achieved, it is often more important that, he disobeys Rely the mathematical models in controlled device, be that one produces optimal control signal in iterative learning mode, make system output to the greatest extent The control algolithm of ideal value may be approached.Iterative learning control relies on its exclusive control mode, non-linear, complicated for solving The high accuracy Trajectory Tracking Control problem that degree is high, be difficult to model has big advantage.It has become raising and has carried out repeatability fortune Make the tracking accuracy of system and elimination system repeats the effective way of interference, be the important component part of modern control theory.

Standard particle colony optimization algorithm (PSO-W) proposes on the basis of standard particle colony optimization algorithm (PSO).PSO Algorithm is a kind of overall situation intelligent optimization algorithm proposed in nineteen ninety-five by American scholar Kennedy and Eberhart, is used for solving Optimization problem miscellaneous.It utilizes a group particle to scan for optimal solution, and each particle can be according to the search of self Experience and the overall situation search experience update self search speed and evaluate current location fitness be next step search provide Individual experience and overall situation experience, finally search out globally optimal solution.PSO algorithm parameter is few, it is achieved get up relatively simple.For terrible To more preferable convergence, PSO-W algorithm makes particle can scan in the space of whole feasible solution, has more than PSO Good global convergence and search capability.

Summary of the invention

The present invention in place of overcoming the deficiencies in the prior art, provide active noise control based on standard particle colony optimization algorithm Method processed, the method is passed through design learning wave filter, parameters optimization algorithm, active noise controlling device can be made main audio source tracking Speed ability and error performance reach optimal.

The present invention reaches above-mentioned purpose by the following technical programs: active noise control based on standard particle colony optimization algorithm Method processed, the active noise control system based on standard particle colony optimization algorithm implementing the inventive method runs on department of computer science On system, including transmission function P (z), learning filters Q (z) and the G (z) of broad sense secondary channel, wherein Q (z)=1, G (z) by Iir filter realizes, and z is the variable of the z domain representation of system function；Comprise the following steps:

(1) according to transmission function P (z) of broad sense secondary channel, the tap coefficient number of iir filter, Qi Zhongfen are selected Number of parameters in son is l, and the number of parameters in denominator is r；

(2) according to the frequency response function P (e that the transmission function of known linear time-invariant system is corresponding^jω), obtain one Fitness function expression formula:

Wherein:

e_n(e^jω)=[1, e^-jω,...,e^-jωl]^T (2)

e_d(e^jω)=[e^-jω,e^-2jω,...,e^-jωr]^T (3)

φ=[a₁,a₂,...,a_r]^T (4)

ψ=[b₀,b₁,...,b_l]^T (5)

e^jωFor the frequency domain representation after time domain to the Laplace transform of complex frequency domain, ω is frequency, and φ, ψ are the reality of wave filter Coefficient vector, wherein []^TRepresent vector transposition, e_n(e^jω), e_d(e^jω) it is two complex function vectors.

(3) parameter of established standards particle swarm optimization algorithm；Concrete parameter has: total search algebraically N；Total number of particles M；Grain Son is equally distributed random number in obedience [0,1] at the speed v of search volume flight, accelerator coefficient c1, c2, r1, r2；

(4) filter coefficient vector is initializedThe fitness value of all individualitiesThe filter coefficient vector Pbest of individual potential optimum_i(0), i=1,2 ..., M, complete The filter coefficient vector gbest (0) of the potential optimum of office, search algebraically n=0；

(5) next generation's search, n=n+1 are entered；Calculate the fitness value of all individualities:

Relatively individual current fitness value and global optimum's fitness value of individual previous generation, if individuality work as prospective adaptation Degree global optimum's fitness value more than previous generation, then update current fitness value with global optimum's fitness value, and with overall The filter coefficient vector of potential optimum updates the filter coefficient vector of current individualIf it is individual Current fitness value less than global optimum's fitness value of previous generation, then retain the fitness value of previous generation and the complete of previous generation The potential optimal filter coefficients vector gbest of office_i(n)=gbest_i(n-1), then with individual current fitness value and previous generation Individual adaptive optimal control angle value compares, if individual current fitness value is more than previous generation individuality adaptive optimal control angle value, then with individual Body adaptive optimal control angle value updates current fitness value, and updates current individual with the filter coefficient vector of individual potential optimum Filter coefficient vector:

See whether the coefficient vector of wave filter reaches final condition, the most then update the speed of particle flight and wave filter Coefficient vector, enters next iteration.

Renewal flying speed of partcles v and filter coefficient vector:

(6) step (5) is repeated, until reaching the maximum search algebraically set；Export the wave filter system of overall potential optimum Number is as filter coefficient.

As preferably, described broad sense secondary channel includes system and is input to process and the secondary sound source that secondary sound source produces The process of the secondary channel between cancellation region.

The beneficial effects of the present invention is: (1) the inventive method is simple, it is easy to accomplish, it is possible to solve repetitive noise de-noising Problem；(2) present invention designs a kind of iterative learning active noise control system, this system frequency domain method descriptive system, uses IIR Wave filter realizes learning filters, and by the parameter of standard particle colony optimization algorithm design iir filter, has the most steady Qualitative, and interference is had good robustness, the least residual error, fast convergence rate can be obtained.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of the active noise control system structural principle implementing the inventive method；

Fig. 2 is the system structure schematic diagram implementing the inventive method；

Fig. 3 is the program flow diagram of the inventive method；

Fig. 4 is the variation diagram that in the embodiment of the present invention, fitness increases with search algebraically；

Fig. 5 is noise reduction velocity factor amplitude figure on frequency domain in the embodiment of the present invention；

Fig. 6 is residual error comparison diagram before and after noise reduction in the embodiment of the present invention；

Fig. 7 is residual error power spectrum comparison diagram before and after noise reduction in the embodiment of the present invention；

Detailed description of the invention

Below in conjunction with specific embodiment, the present invention is described further, but protection scope of the present invention is not limited in This.

As in figure 2 it is shown, be the active noise control system based on standard particle colony optimization algorithm realizing the inventive method Structural representation, u_kN () is control signal, i.e. the input signal of control system；P (z) is the transmission function of broad sense secondary channel； Q (z) and G (z) is learning filters；r_kN () is the main sound source comprising random noise, main sound source on iteration axle be one strict Repeating signal, in each iteration, main sound source is all identical curve；e_kN () is residual signals, be also the output signal of system；w_k (n) and v_kN () is the observation noise comprised in learning filters input, be not reproducible interference, and k is number of iterations.By Fig. 2 it is System block diagram obtains system input u_k(n) iteration in z-transform territory more new formula:

U_k+1(z)=Q (z) [U_k(z)+W_k(z)]-G(z)[E_k(z)+V_k(z)] (10)

Owing to the active noise controlling device based on standard particle colony optimization algorithm of the present invention is to be applied to have repeatability Main sound source de-noising, main sound source is the most all identical, and main sound source also can be with the interference one of random noise React on system.By formulae express it is:

r_k(n)=x (n)+y_k(n) (11)

Wherein x (n) is main sound source, y_kN () is random noise.u_k(n) and e_kN () relation in z-transform territory is as follows:

E_k(z)=R_k(z)-P(z)U_k(z) (12)

Residual signals e can be obtained by above 2 equatioies_k(n) iteration in z-transform territory more new formula:

E_k+1(z)=[1-Q (z)] X (z)+Y_k+1(z)-Q(z)Y_k(z)-P(z)Q(z)W_k(z)+P(z)G(z)V_k(z)

+[Q(z)+P(z)G(z)]E_k(z) (13)

The condition of residual error convergence is:

$\mathrm{\&rho;}=\underset{\&ForAll;\mathrm{\&omega;}}{max}|Q\left(e^{j\mathrm{\&omega;}}\right)+P\left(e^{j\mathrm{\&omega;}}\right)G\left(e^{j\mathrm{\&omega;}}\right)|<1---\left(14\right)$

Wherein, ρ is the convergence rate factor, reflects the noise reduction speed of system, and ρ value is the least, and noise reduction speed is the fastest.In order to ask Obtain system anti-acoustic capability, i.e. residual error E during number of iterations k → ∞_∞Z the maximum of (), defines 3 intermediate variables and 1 gain becomes Amount:

$\left\{\begin{array}{c}{A}_k\left(z\right)=Y_{k+1}\left(z\right)-Q\left(z\right)Y_k\left(z\right)={\mathrm{\&xi;A}}_k^{-}\left(z\right)\\ B_k\left(z\right)=-P\left(z\right)Q\left(z\right)W_k\left(z\right)={\mathrm{\&xi;B}}_k^{-}\left(z\right)\\ C_k\left(z\right)=P\left(z\right)G\left(z\right)V_k\left(z\right)={\mathrm{\&xi;C}}_k^{-}\left(z\right)\\ D\left(z\right)=Q\left(z\right)+P\left(z\right)G\left(z\right)\end{array}\right.---\left(15\right)$

Wherein, ξ is a constant more than 0 so thatBy this A little intermediate variables substitute into the iteration more new formula of residual signals, obtain:

$E_{k+1}\left(z\right)=(1-Q(z\left)\right)X\left(z\right)+D\left(z\right)E_k\left(z\right)+\mathrm{\&xi;}\left(A_k^{-}\right(z)+B_k^{-}(z)+C_k^{-}(z\left)\right)$

$<(1-Q(z\left)\right)X\left(z\right)+D\left(z\right)E_k\left(z\right)+3\mathrm{\&xi;}---\left(16\right)$

As k → ∞ and meet system convergence condition, the upper limit of maximum residul difference signal can be expressed as:

$E_{\mathrm{\&infin;}}\left(z\right)<\frac{1-Q\left(z\right)}{1-Q\left(z\right)-P\left(z\right)G\left(z\right)}X\left(z\right)+\frac{3\mathrm{\&xi;}}{1-Q\left(z\right)-P\left(z\right)G\left(z\right)}---\left(17\right)$

As can be seen from the above equation, maximum residul difference signal is not only affected by the parameter of learning filters, the impact being also disturbed. But interference only affects the amplitude of maximum residul difference signal, without affecting the stability of system.Along with number of iterations constantly increases, it is System meeting asymptotic convergence to fixed value, and float near this value.

It is that ξ is typically a value the least in reality application.We may be selected by learning filters Q (z)=1, so The residual signals of system just can be made to minimize.Then design learning wave filter G (z) makes ρ minimum.

Learning filters G (z) can realize with an iir filter.The transmission function of iir filter can represent For:

$G\left(z\right)=\frac{b_0+b_1{z}^{-1}+b_2{z}^{-2},\mathrm{...},+b_l{z}^{-l}}{1+a_1{z}^{-1}+a_2{z}^{-2},\mathrm{...},+a_r{z}^{-r}}---\left(8\right)$

Definition vector φ=[a₁,a₂,...,a_r] T, ψ=[b₀,b₁,...,b_l] T,Reality for wave filter Coefficient vector, wherein []^TRepresent vector transposition.Re-define two complex function vectors:

e_n(z)=[1, z^-1,...,z^-l]^T (19)

e_d(z)=[z^-1,z^-2,...,z^-r]^T (20)

The matrix form of iir filter is expressed as:

$G\left(z\right)=\frac{{\mathrm{\&psi;}}^T{e}_n\left(z\right)}{1+{\mathrm{\&phi;}}^T{e}_d\left(z\right)}---\left(21\right)$

Corresponding frequency response function can be expressed as:

$G\left(e^{j\mathrm{\&omega;}}\right)=\frac{{\mathrm{\&psi;}}^T{e}_n\left(e^{j\mathrm{\&omega;}}\right)}{1+{\mathrm{\&phi;}}^T{e}_d\left(e^{j\mathrm{\&omega;}}\right)}---\left(22\right)$

The learning filters of iterative learning active noise control system is realized, the receipts of system according to such iir filter The condition of holding back can be expressed as:

$\mathrm{\&rho;}=\underset{\&ForAll;\mathrm{\&omega;}}{max}|1+p\left(e^{j\mathrm{\&omega;}}\right)\frac{{\mathrm{\&psi;}}^T{e}_n\left(e^{j\mathrm{\&omega;}}\right)}{1+{\mathrm{\&phi;}}^T{e}_d\left(e^{j\mathrm{\&omega;}}\right)}|<1---\left(23\right)$

So, the design problem of learning filters G (z) can be attributed to a unconstrained nonlinear optimization.Ask The mathematical description of topic is as follows:

Such unconstrained nonlinear optimization can utilize standard particle colony optimization algorithm to solve.Use quanta particle The mathematical description of colony optimization algorithm design learning wave filter G (z) is as follows:

IfThen

IfThen

Wherein,Represent the i-th particle filter coefficient vector in the n-th generation,It it is i-th particle Fitness vector, pbest_iN () is the filter coefficient vector of the potential optimum of i-th particle, gbest (n) is that the overall situation is potential Optimum filter coefficient vector, n represents current search algebraically, and i represents that particle is numbered, and M represents total number of particles, always searches for algebraically N；The speed v that particle flies in search volume, accelerator coefficient c1, c2, c1=c2=1.49445, r1, r2 are for obeying in [0,1] Equally distributed random number.

Through the search in some generations, population meeting asymptotic convergence is to optimum filter coefficient position.Although standard Particle swarm optimization algorithm has a good ability of searching optimum, but still has certain probabilistic search to suboptimal solution, Wo Menke To repeat repeatedly to search for, select best filter coefficient.This is the most applicable for the design application of off-line wave filter.

Existing main sound source is a signal containing 10 random frequency compositions and is attended by random noise, and signal to noise ratio is 20dB.Learning filters input in containing average be 0 variance be the observation noise of 1.The transmission function of broad sense secondary channel is:

$P\left(z\right)=\frac{0.2+0.01z^{-1}}{1-1.1z^{-1}+0.38z^{-2}-0.04z^{-3}}---\left(25\right)$

Use active noise controlling method based on standard particle colony optimization algorithm that above-mentioned main sound source is carried out denoising Processing, As shown in Figure 3；

(1) according to transmission function P (z), the tap coefficient number of iir filter, the number of parameters in its Middle molecule are selected For l=3, the number of parameters in denominator is r=5.

(2) according to the frequency response function P (e that transmission function P (z) is corresponding^jω), obtain a fitness function expression formula:

Wherein:

$P\left(e^{j\mathrm{\&omega;}}\right)=\frac{0.2+0.01e^{-j\mathrm{\&omega;}}}{1-1.1e^{-j\mathrm{\&omega;}}+0.38e^{-2j\mathrm{\&omega;}}-0.04e^{-3j\mathrm{\&omega;}}}---\left(26\right)$

e_n(e^jω)=[1, e^-jω,e^-2jω,e^-3jω]^T (27)

e_d(e^jω)=[e^-jω,e^-2jω,e^-3jω,e^-4jω,e^-5jω]^T (28)

φ=[a₁,a₂,a₃,a₄,a₅]^T (29)

ψ=[b₀,b₁,b₂,b₃]^T (30)

(3) parameter of established standards particle swarm optimization algorithm.Concrete parameter has: total search algebraically N=100；Particle is total Number M=200, accelerator coefficient c1=c2=1.49445, r1, r2 are equally distributed random number in obedience [0,1].

(4) filter coefficient vector is initializedThe fitness value of all individualitiesThe filter coefficient vector Pbest of individual potential optimum_i(0), i=1,2 ..., M, complete The filter coefficient vector gbest (0) of the potential optimum of office, search algebraically n=0.

(5) next generation's search, n=n+1 are entered.Calculate the fitness value of all individualities:

Relatively individual current fitness value and global optimum's fitness value of individual previous generation, if individuality work as prospective adaptation Degree global optimum's fitness value more than previous generation, then update current fitness value with global optimum's fitness value, and with overall The filter coefficient vector of potential optimum updates the filter coefficient vector of current individualIf it is individual Current fitness value less than global optimum's fitness value of previous generation, then retain the fitness value of previous generation and the complete of previous generation The potential optimal filter coefficients vector gbest of office_i(n)=gbest_i(n-1), then with individual current fitness value and previous generation Individual adaptive optimal control angle value compares, if individual current fitness value is more than previous generation individuality adaptive optimal control angle value, then with individual Body adaptive optimal control angle value updates current fitness value, and updates current individual with the filter coefficient vector of individual potential optimum Filter coefficient vector:

See whether the coefficient vector of wave filter reaches final condition, the most then update the speed of particle flight and wave filter Coefficient vector, enters next iteration.

Renewal flying speed of partcles v and filter coefficient vector:

(6) step (5) is repeated, until reaching the maximum search algebraically 100 set.

Result shows in figures 4-7.Fig. 4 shows, after search algebraically reached for 96 generations, fitness minimizes value 0.2412, the filter coefficient of response is close to optimal value, and 8 filter coefficients are respectively as follows:

Fig. 5 shows, after search 100 instead of, the noise reduction velocity factor of each frequency component is less than 0.04 it was confirmed use the present invention Method energy design effectively IIR learning filters, and the active noise control system being made up of this learning filters will have Noise reduction speed quickly.Within in Fig. 6 first 1.02 seconds, it is the waveform of main sound source, within latter 1.02 seconds, is the residual signals after 10 iterative learnings Waveform, contrast demonstrates that the active noise control system of the present invention can effectively reduce repetitive noise.Fig. 7 is noise reduction power spectrum chart, Noise power reduces 37dB.

It is the specific embodiment of the present invention and the know-why used described in Yi Shang, if conception under this invention institute Make change, function produced by it still without departing from description and accompanying drawing contained spiritual time, must belong to the present invention's Protection domain.

Claims (1)

1. active noise controlling method based on standard particle colony optimization algorithm, implements optimizing based on standard particle group of this method The active noise control system of algorithm runs in computer system, including transmission function P (z), the study of broad sense secondary channel Wave filter Q (z) and G (z), wherein Q (z)=1, G (z) is realized by iir filter, and z is the variable of the z domain representation of system function； This method comprises the following steps:

(1) according to transmission function P (z) of broad sense secondary channel, the tap coefficient number of iir filter is selected, in its Middle molecule Number of parameters be l, the number of parameters in denominator is r；

(2) according to the frequency response function P (e that the transmission function of known linear time-invariant system is corresponding^jω), obtain a fitness Function expression:

Wherein:

e_n(e^jω)=[1, e^-jω,...,e^-jωl]^T (2)

e_d(e^jω)=[e^-jω,e-^2jω,...,e-^jωr]^T (3)

φ=[a₁,a₂,...,a_r]^T (4)

ψ=[b₀,b₁,...,b_l]^T (5)

e^jωFor the frequency domain representation after time domain to the Laplace transform of complex frequency domain, ω is frequency, and φ, ψ are the real coefficient of wave filter Vector, wherein []^TRepresent vector transposition, e_n(e^jω), e_d(e^jω) it is two complex function vectors.

(3) parameter of established standards particle swarm optimization algorithm；Concrete parameter has: total search algebraically N；Total number of particles M；Particle exists The speed v of search volume flight, accelerator coefficient c1, c2, r1, r2 are equally distributed random number in obedience [0,1]；

(4) filter coefficient vector is initializedThe fitness value of all individualitiesThe filter coefficient vector Pbest of individual potential optimum_i(0), i=1,2 ..., M, complete The filter coefficient vector gbest (0) of the potential optimum of office, search algebraically n=0；

(5) next generation's search, n=n+1 are entered；Calculating the fitness value of all individualities, i represents i-th particle:

Relatively individual current fitness value and global optimum's fitness value of individual previous generation, if the current fitness of individuality is big In global optimum's fitness value of previous generation, then update current fitness value with global optimum's fitness value, and potential by the overall situation Optimum filter coefficient vector updates the filter coefficient vector of current individualIf individuality is current Fitness value is less than global optimum's fitness value of previous generation, then the overall situation retaining the fitness value of previous generation and previous generation is potential Optimal filter coefficients vector gbest_i(n)=gbest_i(n-1), then with the current fitness value of individuality and previous generation individuality Excellent fitness value compares, if individual current fitness value is more than previous generation individuality adaptive optimal control angle value, then with individual optimum Fitness value updates current fitness value, and updates the wave filter of current individual with the filter coefficient vector of individual potential optimum Coefficient vector:

See whether the coefficient vector of wave filter reaches final condition, the most then update the speed of particle flight and the coefficient of wave filter Vector, enters next iteration.

Renewal flying speed of partcles v and filter coefficient vector:

(6) step (5) is repeated, until reaching the maximum search algebraically set；The filter coefficient exporting overall potential optimum is made For filter coefficient.