CN105608295A - Multi-objective evolutionary algorithm (MOEA) and radial basis function (RBF) neural network optimization modeling method of coking furnace pressure - Google Patents

Abstract

The invention discloses a multi-objective evolutionary algorithm (MOEA) and radial basis function (RBF) neural network optimization modeling method of coking furnace pressure. According to the method, the input/output data of acquisition process objects is combined with an RBF neural network model, and a network layer and parameters of an improved MOEA optimization neural network are used. The method is higher in accuracy and is capable of well describing the dynamic characteristics of the process objects.

Description

The multi-objective genetic algorithm of coking furnace pressure and RBF Neural Network Optimization modeling method

Technical field

The invention belongs to technical field of automation, relate to a kind of multi-objective Genetic of coking furnace pressureAlgorithm and RBF Neural Network Optimization modeling method.

Background technology

In actual industrial process, due to physics or the chemistry of the real process object of many complexityCharacteristic is not known, and making system modelling is in Advanced Control Techniques very important oneLink. For the dynamic characteristic of coking heater furnace pressure, RBF neutral net has wellVelocity of approch, can improve the precision of pressure prediction model simultaneously, again can simplified model knotStructure. Proposing a kind of novel RBF (RBF) neutral net based on real process improvesModel accuracy and its structure of simplification. Multi-objective genetic algorithm (MOEA) is to be based upon nature choosingSelect with natural genetics basis on iteration self-adapting stochastic global optimization searching algorithm, can separateThe indeterminable difficult problem of many traditional optimization of determining. If can be by choosing suitable genetic operator,Multi-objective genetic algorithm and RBF neural network model are combined, can approach rapidly cokingHeating furnace burner hearth actual pressure, has ensured that again model structure is simple.

Summary of the invention

The object of the invention is for the modeling process of coking furnace furnace pressure object more difficultThis problem, by means such as data acquisition, model foundation, optimizations, provides a kind of cokingThe multi-objective genetic algorithm of stove furnace pressure and RBF Parameters of Neural Network Structure Optimization Modeling sideMethod. The method is by the inputoutput data of gatherer process object, in conjunction with RBF neutral netModel, uses Internet and the parameter of improved MOEA optimization neural network.

The step of the inventive method comprises:

The real-time running data of step 1, gatherer process, process of establishing object RBF model, toolBody step is as follows:

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

Wherein, x=(x₁,x₂,…,x_n) representing n input node vector, y represents the output of networkVariable, c_i∈RⁿRepresent the center vector of i hidden layer neuron, RⁿEuclidean space,A Gaussian function, || x-c_i|| represent that x is to c_iRadial distance,σ_iThe sound stage width of Gaussian function, 1≤i≤n_r，n_rThe nodal point number of hidden layer, ω_iRepresent iConnection weight between individual hidden layer and output layer.

Step 2, utilize the parameter of MOEA genetic algorithm optimization RBF neural network model,Concrete steps are:

First 2.1 encode to neural network model parameter, and the l generation that obtains following form dyesColour solid:

Wherein, l=1,2 ..., N, N is population scale size, m, n and n_rPositive integer,1≤m≤5,1≤n≤5,1≤n_r≤60，C_lIn element meet following condition:

$c_{ij}=\left\{\begin{array}{cc}{y}_{\min }+r(y_{\max }-y_{\min })& 1\≤i\≤n_{r}1\≤j\≤n\\ u_{\min }+r(u_{\max }-u_{\min })& 1\≤i\≤n_{r}6\≤j\≤5+m\end{array}\right.$

σ_i＝rw_max1≤i≤n_r

Wherein, r is a random number between-0.5～1.5, u_min,u_maxIt is system inputMinimum of a value and maximum, y_min,y_maxMinimum of a value and the maximum of system output, w_maxBeThe Breadth Maximum of gaussian basis function.

The data sample of the process object of collection is divided into three parts by 2.2, before 1/3 data sampleFor training data sample Y₁, for calculating output layer weight, middle 1/3 data are second group of numberAccording to sample Y₂, for the neutral net evaluation to every generation, after 1/3 data be optimization dataY₃, for asking for Pareto optimal solution, choose the object function of RBF neutral net, formAs follows:

$Min\left\{\begin{array}{c}{f}_1=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{|Y_1\left(i\right)-{\hat{Y}}_1\left(i\right)|}^2}+\sqrt{\underset{i=1}{\overset{N_2}{\mathrm{\Σ}}}{|Y_2\left(i\right)-{\hat{Y}}_2\left(i\right)|}^2}\\ f_2=(m+n)n_r\end{array}\right.$

Wherein, Min represents to minimize, f₁Represent Y₁And Y₂Mean square deviation, f₂Reflect defeatedEnter the complexity of layer and hidden layer structure,Table respectivelyShow two groups of data sample Y₁And Y₂RBF Neural Network model predictive output, N₁,N₂For choosingThe size of the data sample of getting.

2.3 because the gene in chromosome can morph, p_cFor current individual C_lAnd the next oneIndividual C_l+1Between crossover probability, with crossover probability p_cSelecteed chromosome is intersectedOperation produces daughter chromosome C of future generation_l' and C_l+1'. When mutation operator is carried out, produce at random givenM in scope, n and n_rValue, variation is individual to satisfy condition and carries out according to step 2.1 element individualityVariation obtains new individuality.

2.4 in order to improve the local search ability of MOEA, and Local Operator is designed to following form:

C＝αC_l+(1-α)C_l'

C＝C_l+ΔC_l

Wherein, C_lTo be selected from front λ f₁Individuality, C_l'To be selected from front λ f₂Individuality, λ represents natureNumber, α ∈ (0,1) is random number, works as C_l＝C_l'Δ C_lIn Δ c_ij＝αc_ij,α∈(-1,1)，Local Search probability dynamically changes over following form:

$p_l=0.02+\frac{0.2}{1+\exp \[-0.01(g-G/2)\]}$

Wherein, G represents maximum evolutionary generation, and g represents the algebraically of evolving.

2.5 in the time that individual amount is greater than population scale N, obtains montage operator, and form is as follows

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

Wherein, Af_iI hidden neuron liveness of tabular form, φ_i(x) represent i implicit godThrough first output valve, ρ > 1.

2.6 to set the maximums in excellent genes storehouses be N, by good Gene conservation to gene poolIn, in the time that excellent genes storehouse is greater than N, first quick non-dominated Sorting method is carried out, thenAdministration method is removed from excellent genes storehouse, make all genes meet Pareto optimal solution with dimensionHold diversity and the uniformity of excellent genes.

2.7 are cycled to repeat Optimizing Search according to step 2.2 to the step in step 2.6, reachFinish Optimizing Search to the maximum evolutionary generation formula allowing and calculate, the MOEA after being improvedChromosome after genetic algorithm optimization, the RBF neutral net mould after being optimized after decodingThe parameter of type.

Beneficial effect of the present invention: the present invention passes through the inputoutput data of gatherer process object,In conjunction with RBF neural network model, utilize the MOEA genetic algorithm after improving to optimize RBFThe parameter of neural network model, thus coking furnace furnace pressure Forecasting Methodology obtained. The method is builtVertical model has higher accuracy, can describe well the dynamic characteristic of process object.

Detailed description of the invention

Taking coking furnace furnace pressure as practical object, taking the aperture of damper as input, with JiaoChange stove furnace pressure for output, set up the model of coking furnace furnace pressure.

The step of the inventive method comprises:

The real-time running data of step 1, gatherer process, process of establishing object RBF model, toolBody step is as follows:

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

Wherein, x=(x₁,x₂,…,x_n) representing n input node vector, y represents the output of networkVariable, c_i∈RⁿRepresent the center vector of i hidden layer neuron, RⁿEuclidean space,A Gaussian function, || x-c_i|| represent that x is to c_iRadial distance,σ_iThe sound stage width of Gaussian function, 1≤i≤n_r，n_rThe nodal point number of hidden layer, ω_iRepresent iConnection weight between individual hidden layer and output layer.

Step 2, utilize the parameter of MOEA genetic algorithm optimization RBF neural network model,Concrete steps are:

First 2.1 encode to neural network model parameter, and the l generation that obtains following form dyesColour solid:

Wherein, l=1,2 ..., N, N is population scale size, m, n and n_rPositive integer,1≤m≤5,1≤n≤5,1≤n_r≤60，C_lIn element meet following condition:

$c_{ij}=\left\{\begin{array}{cc}{y}_{\min }+r(y_{\max }-y_{\min })& 1\≤i\≤n_{r}1\≤j\≤n\\ u_{\min }+r(u_{\max }-u_{\min })& 1\≤i\≤n_{r}6\≤j\≤5+m\end{array}\right.$

σ_i＝rw_max1≤i≤nr

Wherein, r is a random number between-0.5～1.5, u_min,u_maxIt is system inputMinimum of a value and maximum, y_min,y_maxMinimum of a value and the maximum of system output, w_maxBeThe Breadth Maximum of gaussian basis function.

The data sample of the process object of collection is divided into three parts by 2.2, before 1/3 data sampleFor training data sample Y₁, for calculating output layer weight, middle 1/3 data are second group of numberAccording to sample Y₂, for the neutral net evaluation to every generation, after 1/3 data be optimization dataY₃, for asking for Pareto optimal solution, choose the object function of RBF neutral net, formAs follows:

$Min\left\{\begin{array}{c}{f}_1=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{|Y_1\left(i\right)-{\hat{Y}}_1\left(i\right)|}^2}+\sqrt{\underset{i=1}{\overset{N_2}{\mathrm{\Σ}}}{|Y_2\left(i\right)-{\hat{Y}}_2\left(i\right)|}^2}\\ f_2=(m+n)n_r\end{array}\right.$

Wherein, Min represents to minimize, f₁Represent Y₁And Y₂Mean square deviation, f₂Reflect defeatedEnter the complexity of layer and hidden layer structure,Table respectivelyShow two groups of data sample Y₁And Y₂RBF Neural Network model predictive output, N₁,N₂For choosingThe size of the data sample of getting.

2.3 because the gene in chromosome can morph, p_cFor current individual C_lAnd the next oneIndividual C_l+1Between crossover probability, with crossover probability p_cSelecteed chromosome is intersectedOperation produces daughter chromosome C of future generation_l' and C_l+1'. When mutation operator is carried out, produce at random givenM in scope, n and n_rValue, variation is individual to satisfy condition and carries out according to step 2.1 element individualityVariation obtains new individuality.

2.4 in order to improve the local search ability of MOEA, and Local Operator is designed to following form:

C＝αC_l+(1-α)C_l'

C＝C_l+ΔC_l

Wherein, C_lTo be selected from front λ f₁Individuality, C_l'To be selected from front λ f₂Individuality, λ represents natureNumber, α ∈ (0,1) is random number, works as C_l＝C_l'Δ C_lIn Δ c_ij＝βc_ij,α∈(-1,1)，Local Search probability dynamically changes over following form:

$p_l=0.02+\frac{0.2}{1+\exp \[-0.01(g-G/2)\]}$

Wherein, G represents maximum evolutionary generation, and g represents the algebraically of evolving.

2.5 in the time that individual amount is greater than population scale N, obtains montage operator, and form is as follows

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

Wherein, Af_iI hidden neuron liveness of tabular form, φ_i(x) represent i implicit godThrough first output valve, ρ > 1.

2.6 to set the maximums in excellent genes storehouses be N, by good Gene conservation to gene poolIn, in the time that excellent genes storehouse is greater than N, first quick non-dominated Sorting method is carried out, thenAdministration method is removed from excellent genes storehouse, make all genes meet Pareto optimal solution with dimensionHold diversity and the uniformity of excellent genes.

2.7 are cycled to repeat Optimizing Search according to step 2.2 to the step in step 2.6, reachFinish Optimizing Search to the maximum evolutionary generation formula allowing and calculate, the MOEA after being improvedChromosome after genetic algorithm optimization, the RBF neutral net mould after being optimized after decodingThe parameter of type.

Claims (1)

1. the multi-objective genetic algorithm of coking furnace pressure and RBF Neural Network Optimization modeling method, itsThe concrete steps that are characterised in that the method are:

The real-time running data of step 1, gatherer process, process of establishing object RBF model, concreteStep is as follows:

1.1 by the RBF neural network structure that comprises input layer, output layer and hidden layer, obtains networkMapping relations be the input/output model of system, form is as follows:

Wherein, x=(x₁,x₂,…,x_n) representing n input node vector, y represents that the output of network becomesAmount, c_i∈RⁿRepresent the center vector of i hidden layer neuron, RⁿEuclidean space,A Gaussian function, || x-c_i|| represent that x is to c_iRadial distance, σ_iThe sound stage width of Gaussian function, 1≤i≤n_r，n_rThe nodal point number of hidden layer, ω_iRepresent that i impliesConnection weight between layer and output layer;

Step 2, utilize the parameter of MOEA genetic algorithm optimization RBF neural network model, concreteStep is:

First 2.1 encode to neural network model parameter, obtains the l of following form for dyeingBody:

Wherein, l=1,2 ..., N, N is population scale size, m, n and n_rPositive integer,1≤m≤5,1≤n≤5,1≤n_r≤60，C_lIn element meet following condition:

$c_{ij}=\left\{\begin{array}{cc}{y}_{\min }+r(y_{\max }-y_{\min })& 1\≤i\≤n_{r}1\≤j\≤n\\ u_{\min }+r(u_{\max }-u_{\min })& 1\≤i\≤n_{r}6\≤j\≤5+m\end{array}\right.$

σ_i＝rw_max1≤i≤n_r

Wherein, r is a random number between-0.5～1.5, u_min,u_maxThat system is inputtedLittle value and maximum, y_min,y_maxMinimum of a value and the maximum of system output, w_maxIt is gaussian basisThe Breadth Maximum of function;

The data sample of the process object of collection is divided into three parts by 2.2, before 1/3 data sample beTraining data sample Y₁, for calculating output layer weight, middle 1/3 data are second group of data sample Y₂, for the neutral net evaluation to every generation, after 1/3 data be optimization data Y₃, for askingGet Pareto optimal solution, choose the object function of RBF neutral net, form is as follows:

$Min\left\{\begin{array}{c}{f}_1=\sqrt{\underset{i=1}{\overset{N}{\Σ}}{|Y_1\left(i\right)-{\hat{Y}}_1\left(i\right)|}^2}+\sqrt{\underset{i=1}{\overset{N_2}{\Σ}}{|Y_2\left(i\right)-{\hat{Y}}_2\left(i\right)|}^2}\\ f_2=(m+n)n_r\end{array}\right.$

Wherein, Min represents to minimize, f₁Represent Y₁And Y₂Mean square deviation, f₂Reflect input layerWith the complexity of hidden layer structure,Represent respectively two groups of data sample Y₁And Y₂'sThe output of RBF Neural Network model predictive, N₁,N₂For the size of the data sample chosen;

2.3 because the gene in chromosome can morph, p_cFor current individual C_lWith next individualC_l+1Between crossover probability, with crossover probability p_cSelecteed chromosome is carried out to interlace operation generationDaughter chromosome C ' of future generation_lAnd C '_l+1; When mutation operator is carried out, produce at random the m in given range, nAnd n_rValue, variation individual according to step 2.1 element individuality satisfy condition make a variation obtain new individualBody;

2.4 in order to improve the local search ability of MOEA, and Local Operator is designed to following form:

C＝αC_l+(1-α)C_l'

C＝C_l+ΔC_l

Wherein, C_lTo be selected from front λ f₁Individuality, C_l'To be selected from front λ f₂Individuality, λ represents natural number,α ∈ (0,1) is random number, works as C_l＝C_l'Δ C_lIn Δ c_ij＝αc_ij, α ∈ (1,1), Local SearchProbability dynamically changes over following form:

$p_l=0.02+\frac{0.2}{1+\exp \[-0.01(g-G/2)\]}$

Wherein, G represents maximum evolutionary generation, and g represents the algebraically of evolving;

2.5 in the time that individual amount is greater than population scale N, obtains montage operator, and form is as follows

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

Wherein, Af_iI hidden neuron liveness of tabular form, φ_i(x) represent i hidden neuronOutput valve, ρ > 1;

2.6 to set the maximums in excellent genes storehouses be N, by good Gene conservation in gene pool,In the time that excellent genes storehouse is greater than N, first quick non-dominated Sorting method is carried out, then by Zhi PeifangMethod removes from excellent genes storehouse, makes all genes meet Pareto optimal solution to maintain excellent genesDiversity and uniformity;

2.7 are cycled to repeat Optimizing Search according to step 2.2 to the step in step 2.6, reach fairThe maximum evolutionary generation formula of being permitted finishes Optimizing Search to be calculated, the MOEA genetic algorithm after being improvedChromosome after optimization, the parameter of the RBF neural network model after being optimized after decoding.