CN103218459A - Chaotic system parameter estimating method based on neighborhood information optimization algorithm - Google Patents

Abstract

The invention discloses a chaotic system parameter estimating method based on a neighborhood information optimization algorithm. According to the method, a neighborhood information sharing thought is integrated in a particle swarm optimization algorithm; the speed and the position of a particle are updated by means of tracking an individual extreme value and a neighborhood extreme value of the particle as well as a global extreme value of population; the evolution information among the particles during a search process is utilized fully; the diversity of the particles is increased; the premature convergence of the algorithm is avoided; and the method has the capabilities of high-efficiency search and global search, so that an optimum parameter estimating effect is achieved.

Description

Chaos system method for parameter estimation based on the neighborhood information optimized Algorithm

Technical field

The present invention relates to System Discrimination and intellectual technology field, be specifically related to a kind of method for parameter estimation based on the neighborhood information particle swarm optimization algorithm at chaos system.

Background technology

Chaos controlling has become the important subject in complexity science field, and has obtained broad research with synchronously since proposing the nineties in last century.Yet existing most control and method for synchronous all are to provide under the known situation of systematic parameter, and these method majorities are no longer suitable under the situation of unknown parameters.Thereby, estimate that the unknown parameter of chaos system becomes chaos controlling and needs the urgent matter of utmost importance that solves synchronously.

The generation of particle cluster algorithm (PSO) derives from the social model simulation of simplifying, and is proposed in nineteen ninety-five by Eberhart and Kennedy.Because simple, the easy realization of its algorithm, fast convergence rate have obtained extensive concern.Initial stage PSO convergence of algorithm speed is very fast optimizing, and still along with the continuation of optimizing process, easily is absorbed in local optimum in the search later stage.At this problem, scholars have provided various improvement particle cluster algorithms, as the PSO of band compressibility factor, the PSO that becomes the study factor, second order vibration PSO, mixing PSO etc.

The present invention plans to build upright a kind of simple in structure, make full use of search procedure particle neighborhood information guiding search direction, and adjust the particle neighborhood according to the time period and form, take all factors into consideration the practicable chaos system parameter estimation algorithm of computation complexity, fast convergence, effective search ability, aspect such as of overall importance.

Summary of the invention

The objective of the invention is to overcome the deficiency of elementary particle group algorithm, propose a kind of particle swarm optimization algorithm and estimate based on neighborhood information

The parameter of chaos system can be worked in coordination with switching in the searching process between neighborhood extreme value and global extremum, and can make full use of the interparticle neighborhood search mechanism of search, has the ability of effective search and global search, realizes the optimal parameter estimation effect to reach.

Technical scheme of the present invention is as follows:

A kind of chaos system method for parameter estimation based on the neighborhood information optimized Algorithm comprises the steps:

Step 1: produce T chaos discrete-time series (x (t), y (t), z (t)) by chaos system, wherein (x (t), y (t), z (t)) is the state variable of chaos system, and t is the series of discrete time series from 1 to T.

Step 2: initialization; Determine the population scale M of population, dimension size D, the particle position vector is s _i=(s _I1, s _I2..., s _ID), the velocity vector of particle correspondence is v _i=(v _I1, v _I2..., v _ID), i=1,2 ..., M, study factor c ₁=c ₂=c ₃=1.4962, maximal rate V _Max, each neighborhood particle is counted N, makes MmodN=0, iterations k=1, maximum iteration time K _Max

Step 3: the fitness function that calculates each particle; According to the discrete-time series of chaos system variable, determine the fitness function of estimated parameter correspondence, its formula is:

$e_i^k=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}\{{(x\left(t\right)-x_i^k\left(t\right))}^2+{(y\left(t\right)-y_i^k\left(t\right))}^2+{(z\left(t\right)-z_i^k\left(t\right))}^2\}$

Wherein, t is the series of discrete time series from 1 to T,

Be to obtain the pairing system state variables sequence of parameter behind the k time iteration particle group optimizing, (x (t), y (t), z (t)) real system state variable sequence for recording.

Step 4: determine the neighborhood scheme; If k＜K _Max, adopt

Construct q=M/N neighborhood; Otherwise, adopt

Construct q=M/N neighborhood, j=1,2 ..., q; First particle of each neighborhood can be accepted global information, and other particles are only accepted neighborhood information.

Step 5: the k+1 time iteration, particle are according to following formula renewal speed and position:

$v_i^{k+1}={\mathrm{wv}}_i^k+c_1{r}_1(p_i^k-s_i^k)+c_2{r}_2(p_g^k-s_i^k)Y_i+c_3{r}_2({\mathrm{pl}}_i^k-s_i^k)(1-Y_i)$

$s_i^{k+1}=s_i^k+v_i^{k+1}$

Wherein: i=1,2 ..., M, M are population size, w is an inertia weight; c ₁, c ₂, c ₃Be the study factor, r ₁, r ₂Get equally distributed random number between [0,1],

Be the desired positions of i particle experience,

Be the desired positions of all particle population experience,

Be the desired positions of all particle experience in the corresponding neighborhood of i particle, Y _iBe neighborhood learning ability function, get constant or random number between [0,1], obtain the ability of the overall situation or neighborhood knowledge with the difference particle.

Step 6: if reach maximum iteration time (k=K _Max), then optimizing finishes resulting global optimum

Be the optimized parameter value of chaos system parameter estimation; Otherwise k:=k+1 turns to step 3.

Wherein,

In the described step 2, the search population M of colony need set according to concrete problem scale; Dimension size D represents the variable number of optimization problem; The general span of the study factor is [04], also can dynamically adjust according to search procedure, for adopting fixed value for simplicity.

Useful technique effect of the present invention is:

Compare with existing various improvement particle cluster algorithms, chaos system parameter estimation algorithm provided by the present invention is simple in structure, make full use of search procedure particle neighborhood information guiding search direction, and adjust the particle neighborhood according to the time period and form, take all factors into consideration computation complexity, fast convergence, effective search ability, aspect such as of overall importance.

Chaos system parameter estimation techniques of the present invention is shared neighborhood information with thought and is incorporated in the particle cluster algorithm, made full use of the interparticle evolution-information of search procedure, increased the diversity of particle, avoided the precocious convergence of algorithm, thereby optimization searching efficient and performance have been improved greatly, make the search particle can jump out local optimum, the ability of searching optimum of enhancement algorithms easily.Since the information sharing of the interparticle neighborhood extreme value of search, energy interactive information between the particle in the search procedure, thus can realize collaborative and intelligently explore area of space.

The present invention also can be applicable to the fields such as node covering of Image Edge-Detection, neural metwork training, sensing net except being applied to the chaos system parameter estimation.

Description of drawings

Fig. 1 is a process flow diagram of the present invention.

Fig. 2 is

The estimation curve figure of chaos system parameter a.

Fig. 3 is

The estimation curve figure of chaos system parameter b.

Fig. 4 is

The estimation curve figure of chaos system parameter c.

Embodiment

Have neighborhood information particle cluster algorithm (NPSO) and be and be subjected to the occurring in nature collective behaviour and often depend on the inspiration of social recognition structure and produce, different cognitive structures can have influence on the cluster effect of total system.Corresponding to particle cluster algorithm,, can give full play to its whole optimizing ability and convergence if can use the neighborhood information of particle rightly.The main thought of this algorithm is that the global extremum by individual extreme value, neighborhood extreme value and the population of following the tracks of particle upgrades particle's velocity and position, when reaching end condition, determines that current globally optimal solution is the optimum solution of this problem.

In order to understand technical scheme of the present invention better, below embodiment is described in further detail, and embodiment is described, but be not limited thereto in conjunction with an application example.

Embodiment: consider as follows

Chaos system

$\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=-y\left(t\right)-z\left(t\right)\\ \stackrel{\·}{y}\left(t\right)=x\left(t\right)+\mathrm{ay}\left(t\right)\\ \stackrel{\·}{z}\left(t\right)=b+(x\left(t\right)-c)z\left(t\right)\end{array}\right.$

In the formula, parameter a, b, c the unknown.Work as a=0.432, b=2, during c=4, system presents chaos phenomenon.The objective of the invention is and to go out unknown parameter according to the chaos state sequence estimation of said system.

The workflow of the inventive method as shown in Figure 1, embodiment can be divided into following a few step:

(1) produce T=300 chaos discrete-time series (x (t), y (t), z (t)) by chaos system, wherein t is the series of discrete time series from 1 to T.

(2) initialization.Determine the population scale M=20 of population, dimension size D=3, picked at random s _I1∈ [01], s _I2∈ [05], s _I3The initial position vector of ∈ [010] constituent particle is s _i=(s _I1, s _I2, s _I3), the velocity vector of picked at random particle correspondence is v _i=(v _I1, v _I2, v _I3), i=1,2 ..., M, study factor c ₁=c ₂=c ₃=1.4962, maximal rate V _Max=10, each neighborhood particle is counted N=5(and is made MmodN=0), iterations k=1, maximum iteration time K _Max=60.

(3) calculate the fitness function of each particle.At first according to the discrete-time series of chaos system variable, determine the fitness function of estimated parameter correspondence, its formula is:

$e_i^k=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}\{{(x\left(t\right)-x_i^k\left(t\right))}^2+{(y\left(t\right)-y_i^k\left(t\right))}^2+{(z\left(t\right)-z_i^k\left(t\right))}^2\}$

Wherein, Be to obtain the pairing system state variables sequence of parameter behind the k time iteration particle group optimizing, (x (t), y (t), z (t)) is the real system state variable sequence that records in (1) step.

(4) determine the neighborhood scheme.If k＜K _Max, adopt

Construct q=M/N neighborhood; Otherwise, adopt

Construct q=M/N neighborhood, j=1,2 ..., q.First particle of each neighborhood can be accepted global information, and other particles are only accepted neighborhood information.

(5) the k+1 time iteration, particle are according to following formula renewal speed and position:

$v_i^{k+1}={\mathrm{wv}}_i^k+c_1{r}_1(p_i^k-s_i^k)+c_2{r}_2(p_g^k-s_i^k)Y_i+c_3{r}_2({\mathrm{pl}}_i^k-s_i^k)(1-Y_i)$

$s_i^{k+1}=s_i^k+v_i^{k+1}$

Wherein: i=1,2 ..., M, inertia weight

w _Max=0.9, w _Min=0.4(adopts the linear decrease weight here); r ₁, r ₂Get equally distributed random number between [0,1],

Be the desired positions (individual extreme value) of i particle experience,

Be the desired positions (global extremum) of all particle population experience, Be the desired positions (neighborhood extreme value) of all particle experience in the corresponding neighborhood of i particle, Y _iFor neighborhood learning ability function, get the random number between [0,1], obtain the ability of the overall situation or neighborhood knowledge with the difference particle.

(6) if reach maximum iteration time (k=K _Max), then optimizing finishes resulting global optimum

Be the optimized parameter value (a of chaos system parameter estimation ^*, b ^*, c ^*); Otherwise k:=k+1 forwards (3) to.

Fig. 2, Fig. 3 and Fig. 4 have shown a respectively, the parameter estimation result of b and c.As seen from the figure, three parameters all reach global optimum after about 45 iteration.As seen, the present invention program's effect in the chaos system parameter estimation is better, and has good robustness.

Above the chaos system parameter estimation techniques based on the neighborhood information optimized Algorithm of the present invention is had been described in detail, but specific implementation form of the present invention is not limited thereto.Concerning the those skilled in the art in present technique field, the various conspicuous change of under the situation of spirit that does not deviate from the method for the invention and claim scope it being carried out is all within protection scope of the present invention.

Claims (1)

1. the chaos system method for parameter estimation based on the neighborhood information optimized Algorithm is characterized in that, comprises the steps:

(1) produce T chaos discrete-time series (x (t), y (t), z (t)) by chaos system, wherein (x (t), y (t), z (t)) is the state variable of chaos system, and t is the series of discrete time series from 1 to T;

(2) initialization; Determine the population scale M of population, dimension size D, the particle position vector is s _i=(s _I1, s _I2..., s _ID), the velocity vector of particle correspondence is v _i=(v _I1, v _I2..., v _ID), i=1,2 ..., M, study factor c ₁=c ₂=c ₃=1.4962, maximal rate V _Max, each neighborhood particle is counted N, makes MmodN=0, iterations k=1, maximum iteration time K _Max

(3) calculate the fitness function of each particle; According to the discrete-time series of chaos system variable, determine the fitness function of estimated parameter correspondence, its formula is:

$e_i^k=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}\{{(x\left(t\right)-x_i^k\left(t\right))}^2+{(y\left(t\right)-y_i^k\left(t\right))}^2+{(z\left(t\right)-z_i^k\left(t\right))}^2\}$

Wherein, t is the series of discrete time series from 1 to T,

Be to obtain the pairing system state variables sequence of parameter behind the k time iteration particle group optimizing, (x (t), y (t), z (t)) real system state variable sequence for recording;

(4) determine the neighborhood scheme; If k＜K _Max, adopt

Construct q=M/N neighborhood; Otherwise, adopt

Construct q=M/N neighborhood, j=1,2 ..., q; First particle of each neighborhood can be accepted global information, and other particles are only accepted neighborhood information;

(5) the k+1 time iteration, particle are according to following formula renewal speed and position:

$v_i^{k+1}={\mathrm{wv}}_i^k+c_1{r}_1(p_i^k-s_i^k)+c_2{r}_2(p_g^k-s_i^k)Y_i+c_3{r}_2({\mathrm{pl}}_i^k-s_i^k)(1-Y_i)$

$s_i^{k+1}=s_i^k+v_i^{k+1}$

Wherein: i=1,2 ..., M, M are population size, w is an inertia weight; c ₁, c ₂, c ₃Be the study factor, r ₁, r ₂Get equally distributed random number between [0,1],

Be the desired positions of i particle experience,

Be the desired positions of all particle population experience,

Be the desired positions of all particle experience in the corresponding neighborhood of i particle, Y _iBe neighborhood learning ability function, get constant or random number between [0,1], obtain the ability of the overall situation or neighborhood knowledge with the difference particle;

(6) if reach maximum iteration time k=K _Max, then optimizing finishes resulting global optimum

Be the optimized parameter value of chaos system parameter estimation, stop; Otherwise k:=k+1 turns to step (3).

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