CN104318303A - Coking furnace temperature predication method of RBF (Radial Basis Function) neural network optimized by genetic algorithm - Google Patents

Abstract

The invention discloses a coking furnace temperature predication method of a RBF (Radial Basis Function) neural network optimized by a genetic algorithm. For the dynamic characteristics of coking furnace temperature, a RBF neural network model exhibits good approach velocity, meanwhile, the precision of a temperature prediction model can be improved, a model structure can be simplified, but if no rules can be provided for parameter initial value selection, improper selection causes slow network convergence, and even network divergence is caused. Firstly, a radial primary function neural network model is established through the input/output data of a system, and then the parameters of a network model are optimized by utilizing a RNA (Ribonucleic Acid) genetic algorithm so as to obtain the coking furnace temperature predication method. The invention can effectively reduce prediction errors and the complexity of the model structure, and achieves a good prediction effect.

Description

The coking furnace temperature predicting method of the RBF neural of genetic algorithm optimization

Technical field

The invention belongs to technical field of automation, relate to a kind of coking furnace temperature predicting method of radial basis function (RBF) neural network based on RNA genetic algorithm optimization.

Background technology

In actual industrial control procedure, due to interference, the factor such as non-linear, the temperature model of coking furnace is normally difficult to obtain.For the dynamic perfromance of coke-fired furnace temperature, RBF neural model has good velocity of approch, can improve the precision of temperature prediction model simultaneously, again can simplified model structure.But the initial parameter values of RBF neural model is chosen does not have rule to follow, unsuitable choosing can make network convergence slow, even causes network to disperse.RNA genetic algorithm is the Stochastic search optimization algorithm that the heredity and evolution process of simulation biology is formed, and can obtain optimized parameter by global search.If RNA genetic algorithm and RBF neural modeling can be combined, coking furnace actual temperature can be approached rapidly, in turn ensure that model structure is simple.

Summary of the invention

The object of the invention is the problem for coking furnace temperature course modeling difficulty, set up by data acquisition, model and optimize, propose a kind of coking furnace temperature predicting method of the RBF neural based on RNA genetic algorithm optimization.The method can effectively reduce the complexity of predicated error and model structure, thus can reach good prediction effect.

Step of the present invention comprises:

Step 1, inputoutput data by system, set up RBF neural model, concrete steps are:

1.1, by the RBF neural structure comprising input layer, output layer and hidden layer, obtain the mapping relations of network and the input/output model of system, form is as follows:

$Y\left(x\left(t\right)\right)=\underset{i=1}{\overset{n_r}{\mathrm{\Σ}}}{\mathrm{\ω}}_i\mathrm{\φ}\left(\frac{\left|\right|x-c_i\left|\right|}{{{\mathrm{\σ}}_i}^2}\right)$

Wherein, x (t)=(x ₁, x ₂, x _n) representing n input node vector, Y (x (t)) represents the output variable of network, c _i∈ R ⁿrepresent the center vector of i-th hidden layer neuron, R ⁿtheorem in Euclid space, a Gaussian function, || x (t)-c _i|| represent that x (t) is to c _iradial distance, ω _irepresent i-th connection weight between hidden layer and output layer, σ _ithe sound stage width of Gaussian function, 1≤i≤n _r, n _rit is the nodal point number of hidden layer.

1.2, by system input and output value composition input vector, and choose input vector successively, utilize the method for exhaustion to list its structure, form is as follows:

x(t)＝[u(k),y(k-1)],n＝2

$x\left(t\right)=\left\{\begin{array}{c}[u\left(k\right),u(k-1),y(k-1)]\\ [u\left(k\right),y(k-1),y(k-2)]\end{array}\right.,n=3$

x(t)＝[u(k),u(k-1),y(k-1),y(k-2)],n＝4

$x\left(t\right)=\left\{\begin{array}{c}[u\left(k\right),u(k-1),y(k-1),y(k-2),y(k-3)]\\ [u\left(k\right),u(k-1),u(k-2),y(k-1),y(k-2)]\end{array}\right.,n=5$

Wherein, the input control amount of etching system when u (k) is k, the real output value of etching system when y (k) is k.

Step 2, utilize RNA genetic algorithm to optimize the parameter of RBF neural model, concrete steps are:

2.1, first quaternary coding is carried out to neural network model parameter, obtains the l of following form for chromosome:

Wherein, l=1,2 ..., N, N are population scale sizes, 1≤n _r≤ D, D are the maximal values of hidden layer node, C _ld × (n+1) matrix, representing matrix C _lin be positioned at n-th of the n-th row _rthe center vector of individual hidden layer neuron.

2.2, choose the objective function of RBF neural, form is as follows:

$J(C_l,{\mathrm{\ω}}_l)=\underset{t=1}{\overset{N_1}{\mathrm{\Σ}}}{|Y_1\left(t\right)-{\hat{Y}}_1\left(t\right)|}^2+\underset{t=1}{\overset{N_2}{\mathrm{\Σ}}}{|Y_2\left(t\right)-{\hat{Y}}_2\left(t\right)|}^2+\mathrm{\λ}(n_r+n)$

Wherein, λ is the coefficient between 0 to 1, Y ₁(t), Y ₂t () is the prediction output valve of neuron in the k moment to the k+t moment of RBF neural respectively, be and prediction output valve Y ₁(t), Y ₂the desired output of t neural network that () is corresponding, N ₁, N ₂two the population samples chosen from N respectively.

2.3, choose the fitness function of RNA genetic algorithm, and calculate individual fitness value, form is as follows:

f＝1/J(C _l,ω _l)

Wherein, f is individual fitness function.When fitness function value is greater than fitness preset value f _ztime, genetic algorithm stops.

2.4, utilize wheel robin to determine selection opertor, form is as follows:

$P\left(C_l\right)=\frac{f\left(C_l\right)}{\underset{l=1}{\overset{N}{\mathrm{\Σ}}}f\left(C_l\right)}$

Wherein, P (C _l) be individual C _lselect probability, f (C _l) be individual C _ladaptive value.

2.5, the selection opertor in step 2.4 is utilized by individual choice higher for chromosome fitness out with crossover probability p _ccarry out interlace operation, produce of future generation individual.

2.6, choose suitable mutation operator, form is as follows:

$p_m=a_0+\frac{b_0}{1+e^{a(g-g_0)}}$

Wherein, a ₀represent mutation probability p _minitial value, b ₀be the degree of mutation probability, g is the algebraically of evolving, g ₀be that mutation probability changes very large evolutionary generation, a is variation rate.

2.7, when individual amount is greater than population scale N, obtain montage operator, form is as follows:

${\mathrm{Af}}_i={\mathrm{\ρe}}^{-\left|\right|x-c_i\left|\right|}\frac{{\mathrm{\φ}}_i\left(x\right)}{\underset{i=1}{\overset{n_r}{\mathrm{\Σ}}}{\mathrm{\φ}}_i\left(x\right)},(i=\mathrm{1,2},...,n_r)$

Wherein, ρ gets positive number.

2.8, calculating the fitness value of each individuality according to step 2.3, and judge whether to meet end condition, if met, is then the optimum solution of parameter, carries out next step operation.If do not met, then perform step 2.3 to 2.7, meet end condition until find.

2.9, decode to chromosome, form is as follows:

$c_{\mathrm{ij}}=x_{j,\min }+\frac{Q}{4^L-1}\·(x_{j,\max }-x_{j,\min })1\≤i\≤n_r,1\≤j\≤n$

${\mathrm{\σ}}_j=\frac{Q}{4^L-1}{w}_{\max }$

Wherein, the integer that the quaternary decoding of Q to be length be L produces, x _{j, min}and x _{j, max}be respectively minimum value and the maximal value of input variable, w _maxit is the maximal value of the sound stage width of Gaussian function.

2.10, choose n=2 successively according to the step 1.2 in step 1, input node vector x (t) when 3,4 and 5, and repeat the step in step 2.1 to 2.9, the parameter of optimization neural network.

Step 3, the neural network parameter after being optimized brought in step 1 solve forecast model by step 2, and utilize this forecast model to predict the output of process.At subsequent time, continue to predict real process according to the step in step 1 to step 2, circulate successively.

Beneficial effect:

First the method sets up RBF neural model by the inputoutput data of system, then utilizes RNA genetic algorithm to carry out the parameter of optimized network model, thus obtains the temperature predicting method of coking furnace.The method can effectively reduce the complexity of predicated error and model structure, can reach good prediction effect.

Embodiment

Below for coking furnace temperature prediction process, the invention will be further described.

In coking furnace temperature prediction process, be the performance of assessment models, obtained the real time data of temperature by industrial real application systems.

The concrete steps of the coking furnace temperature predicting method of the RBF neural of genetic algorithm optimization comprise:

Step 1, inputoutput data by coking furnace temperature process control system, set up RBF neural model, concrete steps are:

1.1, by the RBF neural structure comprising input layer, output layer and hidden layer, obtain the mapping relations of network and the input/output model of temperature course, form is as follows:

$Y\left(x\left(t\right)\right)=\underset{i=1}{\overset{n_r}{\mathrm{\Σ}}}{\mathrm{\ω}}_i\mathrm{\φ}\left(\frac{\left|\right|x-c_i\left|\right|}{{{\mathrm{\σ}}_i}^2}\right)$

Wherein, x (t)=(x ₁, x ₂, x _n) representing n input node vector, Y (x (t)) represents the output variable of network, c _i∈ R ⁿrepresent the center vector of i-th hidden layer neuron, R ⁿtheorem in Euclid space, a Gaussian function, || x (t)-c _i|| represent that x (t) is to c _iradial distance, ω _irepresent i-th connection weight between hidden layer and output layer, σ _ithe sound stage width of Gaussian function, 1≤i≤n _r, n _rit is the nodal point number of hidden layer.

1.2, by the input and output value of coking furnace temperature course composition input vector, and choose input vector successively, utilize the method for exhaustion to list its structure, form is as follows:

x(t)＝[u(k),y(k-1)],n＝2

$x\left(t\right)=\left\{\begin{array}{c}[u\left(k\right),u(k-1),y(k-1)]\\ [u\left(k\right),y(k-1),y(k-2)]\end{array}\right.,n=3$

x(t)＝[u(k),u(k-1),y(k-1),y(k-2)],n＝4

$x\left(t\right)=\left\{\begin{array}{c}[u\left(k\right),u(k-1),y(k-1),y(k-2),y(k-3)]\\ [u\left(k\right),u(k-1),u(k-2),y(k-1),y(k-2)]\end{array}\right.,n=5$

Wherein, u (k) is the input control amount of k moment temperature control system, and y (k) is the actual output temperature in k moment.

Step 2, utilize RNA genetic algorithm to optimize the parameter of RBF neural model, concrete steps are:

2.1, first quaternary coding is carried out to neural network model parameter, obtains the l of following form for chromosome:

Wherein, l=1,2 ..., N, N are population scale sizes, 1≤n _r≤ D, D are the maximal values of hidden layer node, C _ld × (n+1) matrix, representing matrix C _lin be positioned at n-th of the n-th row _rthe center vector of individual hidden layer neuron.

2.2 objective functions choosing RBF neural, form is as follows:

$J(C_l,{\mathrm{\ω}}_l)=\underset{t=1}{\overset{N_1}{\mathrm{\Σ}}}{|Y_1\left(t\right)-{\hat{Y}}_1\left(t\right)|}^2+\underset{t=1}{\overset{N_2}{\mathrm{\Σ}}}{|Y_2\left(t\right)-{\hat{Y}}_2\left(t\right)|}^2+\mathrm{\λ}(n_r+n)$

Wherein, λ is the coefficient between 0 to 1, Y ₁(t), Y ₂t () is the prediction output valve of neuron in the k moment to the k+t moment of RBF neural respectively, be and prediction output valve Y ₁(t), Y ₂the desired output of t neural network that () is corresponding, N ₁, N ₂two the population samples chosen from N respectively.

2.3, choose the fitness function of RNA genetic algorithm, and calculate individual fitness value, form is as follows:

f＝1/J(C _l,ω _l)

Wherein, f is individual fitness function.When fitness function value is greater than fitness preset value f _ztime, genetic algorithm stops.

2.4, utilize wheel robin to determine selection opertor, form is as follows:

$P\left(C_l\right)=\frac{f\left(C_l\right)}{\underset{l=1}{\overset{N}{\mathrm{\Σ}}}f\left(C_l\right)}$

Wherein, P (C _l) be individual C _lselect probability, f (C _l) be individual C _ladaptive value.

2.5, the selection opertor in step 2.4 is utilized by individual choice higher for chromosome fitness out with crossover probability p _ccarry out interlace operation, produce of future generation individual.

2.6, choose suitable mutation operator, form is as follows:

$p_m=a_0+\frac{b_0}{1+e^{a(g-g_0)}}$

Wherein, a ₀represent mutation probability p _minitial value, b ₀be the degree of mutation probability, g is the algebraically of evolving, g ₀be that mutation probability changes very large evolutionary generation, a is variation rate, chooses a here ₀=0.02, b ₀=0.2, g ₀=G/2, a=20/G, G=1000.

2.7, when individual amount is greater than population scale N, obtain montage operator, form is as follows:

${\mathrm{Af}}_i={\mathrm{\ρe}}^{-\left|\right|x-c_i\left|\right|}\frac{{\mathrm{\φ}}_i\left(x\right)}{\underset{i=1}{\overset{n_r}{\mathrm{\Σ}}}{\mathrm{\φ}}_i\left(x\right)},(i=\mathrm{1,2},...,n_r)$

Wherein, ρ gets positive number, and value is 100.

2.8, calculating the fitness value of each individuality according to step 2.3, and judge whether to meet end condition, if met, is then the optimum solution of parameter, carries out next step operation.If do not met, then perform step 2.3 to 2.7, meet end condition until find.

2.9, decode to chromosome, form is as follows:

$c_{\mathrm{ij}}=x_{j,\min }+\frac{Q}{4^L-1}\·(x_{j,\max }-x_{j,\min })1\≤i\≤n_r,1\≤j\≤n$

${\mathrm{\σ}}_j=\frac{Q}{4^L-1}{w}_{\max }$

Wherein, the integer that the quaternary decoding of Q to be length be L produces, x _{j, min}and x _{j, max}be respectively minimum value and the maximal value of input variable, w _maxit is the maximal value of the sound stage width of Gaussian function.

2.10, choose n=2 successively according to the step 1.2 in step 1, input node vector x (t) when 3,4 and 5, and repeat the step in step 2.1 to 2.9, the parameter of optimization neural network.

Step 3, the neural network parameter after being optimized brought in step 1 solve temperature prediction model by step 2, and utilize this forecast model to predict temperature course.At subsequent time, continue to predict actual temperature process according to the step in step 1 to step 2, circulate successively.

Claims (1)

1. the coking furnace temperature predicting method of the RBF neural of genetic algorithm optimization, is characterized in that: the concrete steps of the method comprise:

Step 1, inputoutput data by system, set up RBF neural model, concrete steps are:

1.1, by the RBF neural structure comprising input layer, output layer and hidden layer, obtain the mapping relations of network and the input/output model of system, form is as follows:

$Y\left(x\left(t\right)\right)=\underset{i=1}{\overset{n_r}{\mathrm{\Σ}}}{\mathrm{\ω}}_i\mathrm{\φ}\left(\frac{\left|\right|x-c_i\left|\right|}{{{\mathrm{\σ}}_i}^2}\right)$

Wherein, x (t)=(x ₁, x ₂, x _n) representing n input node vector, Y (x (t)) represents the output variable of network, c _i∈ R ⁿrepresent the center vector of i-th hidden layer neuron, R ⁿtheorem in Euclid space, a Gaussian function, || x (t)-c _i|| represent that x (t) is to c _iradial distance, ω _irepresent i-th connection weight between hidden layer and output layer, σ _ithe sound stage width of Gaussian function, 1≤i≤n _r, n _rit is the nodal point number of hidden layer;

1.2, by system input and output value composition input vector, and choose input vector successively, utilize the method for exhaustion to list its structure, form is as follows:

x(t)＝[u(k),y(k-1)],n＝2

$x\left(t\right)=\left\{\begin{array}{c}[u\left(k\right),u(k-1),y(k-1)]\\ [u\left(k\right),y(k-1),y(k-2)]\end{array}\right.,n=3$

x(t)＝[u(k),u(k-1),y(k-1),y(k-2)],n＝4

$x\left(t\right)=\left\{\begin{array}{c}[u\left(k\right),u(k-1),y(k-1),y(k-2),y(k-3)]\\ [u\left(k\right),u(k-1),u(k-2),y(k-1),y(k-2)]\end{array}\right.,n=5$

Wherein, the input control amount of etching system when u (k) is k, the real output value of etching system when y (k) is k;

Step 2, utilize RNA genetic algorithm to optimize the parameter of RBF neural model, concrete steps are:

2.1, first quaternary coding is carried out to neural network model parameter, obtains the l of following form for chromosome:

Wherein, l=1,2 ..., N, N are population scale sizes, 1≤n _r≤ D, D are the maximal values of hidden layer node, C _ld × (n+1) matrix, representing matrix C _lin be positioned at n-th of the n-th row _rthe center vector of individual hidden layer neuron;

2.2, choose the objective function of RBF neural, form is as follows:

$J(C_l,{\mathrm{\ω}}_l)=\underset{t=1}{\overset{N_1}{\mathrm{\Σ}}}{|Y_1\left(t\right)-{\hat{Y}}_1\left(t\right)|}^2+\underset{t=1}{\overset{N_2}{\mathrm{\Σ}}}{|Y_2\left(t\right)-{\hat{Y}}_2\left(t\right)|}^2+\mathrm{\λ}(n_r+n)$

Wherein, λ is the coefficient between 0 to 1, Y ₁(t), Y ₂t () is the prediction output valve of neuron in the k moment to the k+t moment of RBF neural respectively, be and prediction output valve Y ₁(t), Y ₂the desired output of t neural network that () is corresponding, N ₁, N ₂two the population samples chosen from N respectively;

2.3, choose the fitness function of RNA genetic algorithm, and calculate individual fitness value, form is as follows:

f＝1/J(C _l,ω _l)

Wherein, f is individual fitness function; When fitness function value is greater than fitness preset value f _ztime, genetic algorithm stops;

2.4, utilize wheel robin to determine selection opertor, form is as follows:

$P\left(C_l\right)=\frac{f\left(C_l\right)}{\underset{l=1}{\overset{N}{\mathrm{\Σ}}}f\left(C_l\right)}$

Wherein, P (C _l) be individual C _lselect probability, f (C _l) be individual C _ladaptive value;

2.5, the selection opertor in step 2.4 is utilized by individual choice higher for chromosome fitness out with crossover probability p _ccarry out interlace operation, produce of future generation individual;

2.6, choose suitable mutation operator, form is as follows:

$p_m=a_0+\frac{b_0}{1+e^{a(g-g_0)}}$

Wherein, a ₀represent mutation probability p _minitial value, b ₀be the degree of mutation probability, g is the algebraically of evolving, g ₀be that mutation probability changes very large evolutionary generation, a is variation rate;

2.7, when individual amount is greater than population scale N, obtain montage operator, form is as follows:

${\mathrm{Af}}_i={\mathrm{\ρe}}^{-\left|\right|x-c_i\left|\right|}\frac{{\mathrm{\φ}}_i\left(x\right)}{\underset{i=1}{\overset{n_r}{\mathrm{\Σ}}}{\mathrm{\φ}}_i\left(x\right)},(i=\mathrm{1,2},...,n_r)$

Wherein, ρ gets positive number;

2.8, calculating the fitness value of each individuality according to step 2.3, and judge whether to meet end condition, if met, is then the optimum solution of parameter, carries out next step operation; If do not met, then perform step 2.3 to 2.7, meet end condition until find;

2.9, decode to chromosome, form is as follows:

$c_{\mathrm{ij}}=x_{j,\min }+\frac{Q}{4^L-1}\·(x_{j,\max }-x_{j,\min })1\≤i\≤n_r,1\≤j\≤n$

${\mathrm{\σ}}_j=\frac{Q}{4^L-1}{w}_{\max }$

Wherein, the integer that the quaternary decoding of Q to be length be L produces, x _{j, min}and x _{j, max}be respectively minimum value and the maximal value of input variable, w _maxit is the maximal value of the sound stage width of Gaussian function;

2.10, choose n=2 successively according to the step 1.2 in step 1, input node vector x (t) when 3,4 and 5, and repeat the step in step 2.1 to 2.9, the parameter of optimization neural network;

Step 3, the neural network parameter after being optimized brought in step 1 solve forecast model by step 2, and utilize this forecast model to predict the output of process; At subsequent time, continue to predict real process according to the step in step 1 to step 2, circulate successively.