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【BP预测】基于鸟群算法优化BP神经网络实现数据预测附Matlab代码

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1 简介

 

热舒适度是室内环境舒适性的评价指标,由于热舒适度的计算是一个复杂的非线性迭代过程,不便应用于空调实时控制系统中,为解决这一问题,可利用BP神经网络算法对热舒适度进行预测.但为了改善传统BP神经网络收敛速度慢的问题,将采用鸟群算法(BSA)来优化BP神经网络初始的权值与阈值.最后,将BSA算法与相近的粒子群算法(PSO)进行对比分析,并利用MATLAB软件进行仿真,使BSA-BP预测模型的仿真结果与基本的BP神经网络预测模型,PSO-BP预测模型的仿真结果进行对比分析.结果表明,BSA-BP预测模型具有较快的收敛速度和较高的预测精度.

 

BSA 算法优化 BP 神经网络的基本思想是: 利 用 BSA 算法的全局搜索能力, 优化 BP 神经网络初始的权值和阈值, 也就是决策变量, 其中每一组决策变量均包含在鸟群个体所处的空间位置中. 然后, 通过适应度函数来衡量个体所处空间位置的优劣度, 并利用鸟群觅食过程中的觅食行为、警戒行为和飞行行为等策略不断更新个体空间位置, 直至获取最佳的个体空间位置, 即获得待优化问题的最佳决策变量

 

 

BSA-BP 算法预测 PMV 指标主要包括以下几个部分: 确定训练样本数据、设计 BP 神经网络结构、利用 BSA 算法优化 BP 神经网络初始的权值和阈值、训练优化后的网络. 具体实现步骤如下:

 

步骤 1. 确定训练样本数据. 确定所需输入变量的取值范围; 然后, 根据 PMV 指标的数学模型, 利用MATLAB 软件编辑 PMV 指标的计算程序, 获取相当数量的样本数据; 最后, 经过预处理, 作为 BP 神经网络的训练样本和测试样本数据.

 

步骤 2. 设计 BP 神经网络结构. 依据标准 BP 神经网络模型以及 PMV 指标的数学模型, 确定 BP 神经网络的层数、每层的神经元数, 以及其他参数.

 

步骤 3. 确定 BSA 算法中各参数. 包括初始化种群规模 N、搜索空间维数 D、最大迭代次数 T、飞行间隔 FQ、觅食概率 P、常量 C、S、a1、a2、FL 以及随机初始化鸟群个体空间位置 xti.

 

步骤 4. 计算 BSA 算法的适应度函数值, 将样本的均方误差作为适应度函数, 找到最小的适应度值, 并保留当前最好个体空间位置. 判断算法终止条件是否满足, 若满足则转至步骤 6, 否则执行步骤

 

5.步骤 5. BSA 算法优化 BP 神经网络初始的权值和阈值. 依据 BSA 算法的步骤, 不断迭代进行寻优, 直到迭代停止, 输出全局最优值, 也就是最优网络初始的权值和阈值, 并将其赋给 BP 神经网络.

 

步骤 6. 训练 BSA 算法优化后的 BP 神经网络. 网络经训练结束后, 将得到最佳的 PMV 指标预测模型.上面所述的实现步骤可见图 3

 

 

2 部分代码

 

% ------------------------------------------------------------------------
% Bird Swarm Algorithm (BSA) (demo)
% This is a simple demo version only implemented the basic idea of BSA for
% solving the unconstrained problem, namely Sphere function.
%
%
% The parameters in BSA are presented as follows.
% FitFunc    % The objective function
% M          % Maxmimal generations (iterations)
% pop        % Population size
% dim        % Dimension
% FQ         % The frequency of birds' flight behaviours
% c1         % Cognitive accelerated coefficient
% c2         % Social accelerated coefficient
% a1, a2     % Two paramters which are related to the indirect and direct
%              effect on the birds' vigilance bahaviors.
%
% Using the default value, BSA can be executed using the following code.
% [ bestX, fMin ] = BSA
% ------------------------------------------------------------------------
% Main programs
function [ bestX, fMin ,yy] = BSA( FitFunc, M, pop, dim, FQ, c1, c2, a1, a2 )
% Display help
help BSA.m
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% set the default parameters
% set the parameters
lb= -100*ones( 1,dim );   % Lower bounds
ub= 100*ones( 1,dim );    % Upper bounds
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Initialization
for i = 1 : pop
    x( i, : ) = lb + (ub - lb) .* rand( 1, dim );
    fit( i ) = FitFunc( x( i, : ) );
end
pFit = fit; % The individual's best fitness value
pX = x;     % The individual's best position corresponding to the pFit
[ fMin, bestIndex ] = min( fit );  % fMin denotes the global optimum
% bestX denotes the position corresponding to fMin
bestX = x( bestIndex, : );
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Start the iteration.
for iteration = 1 : M
    prob = rand( pop, 1 ) .* 0.2 + 0.8;%The probability of foraging for food
    if( mod( iteration, FQ ) ~= 0 )
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        % Birds forage for food or keep vigilance
        sumPfit = sum( pFit );
        meanP = mean( pX );
        for i = 1 : pop
            if rand < prob(i)
                x( i, : ) = x( i, : ) + c1 * rand.*(bestX - x( i, : ))+ ...
                    c2 * rand.*( pX(i,:) - x( i, : ) );
            else
                person = randiTabu( 1, pop, i, 1 );
                x( i, : ) = x( i, : ) + rand.*(meanP - x( i, : )) * a1 * ...
                    exp( -pFit(i)/( sumPfit + realmin) * pop ) + a2 * ...
                    ( rand*2 - 1) .* ( pX(person,:) - x( i, : ) ) * exp( ...
                    -(pFit(person) - pFit(i))/(abs( pFit(person)-pFit(i) )...
                    + realmin) * pFit(person)/(sumPfit + realmin) * pop );
            end
            x( i, : ) = Bounds( x( i, : ), lb, ub );
            fit( i ) = FitFunc( x( i, : ) );
        end
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    else
        FL = rand( pop, 1 ) .* 0.4 + 0.5;    %The followed coefficient
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        % Divide the bird swarm into two parts: producers and scroungers.
        [ans, minIndex ] = min( pFit );
        [ans, maxIndex ] = max( pFit );
        choose = 0;
        if ( minIndex < 0.5*pop && maxIndex < 0.5*pop )
            choose = 1;
        end
        if ( minIndex > 0.5*pop && maxIndex < 0.5*pop )
            choose = 2;
        end
        if ( minIndex < 0.5*pop && maxIndex > 0.5*pop )
            choose = 3;
        end
        if ( minIndex > 0.5*pop && maxIndex > 0.5*pop )
            choose = 4;
        end
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        if choose < 3
            for i = (pop/2+1) : pop
                x( i, : ) = x( i, : ) * ( 1 + randn );
                x( i, : ) = Bounds( x( i, : ), lb, ub );
                fit( i ) = FitFunc( x( i, : ) );
            end
            if choose == 1
                x( minIndex,: ) = x( minIndex,: ) * ( 1 + randn );
                x( minIndex, : ) = Bounds( x( minIndex, : ), lb, ub );
                fit( minIndex ) = FitFunc( x( minIndex, : ) );
            end
            for i = 1 : 0.5*pop
                if choose == 2 || minIndex ~= i
                    person = randi( [(0.5*pop+1), pop ], 1 );
                    x( i, : ) = x( i, : ) + (pX(person, :) - x( i, : )) * FL( i );
                    x( i, : ) = Bounds( x( i, : ), lb, ub );
                    fit( i ) = FitFunc( x( i, : ) );
                end
            end
        else
            for i = 1 : 0.5*pop
                x( i, : ) = x( i, : ) * ( 1 + randn );
                x( i, : ) = Bounds( x( i, : ), lb, ub );
                fit( i ) = FitFunc( x( i, : ) );
            end
            if choose == 4
                x( minIndex,: ) = x( minIndex,: ) * ( 1 + randn );
                x( minIndex, : ) = Bounds( x( minIndex, : ), lb, ub );
                fit( minIndex ) = FitFunc( x( minIndex, : ) );
            end
            for i = (0.5*pop+1) : pop
                if choose == 3 || minIndex ~= i
                    person = randi( [1, 0.5*pop], 1 );
                    x( i, : ) = x( i, : ) + (pX(person, :) - x( i, : )) * FL( i );
                    x( i, : ) = Bounds( x( i, : ), lb, ub );
                    fit( i ) = FitFunc( x( i, : ) );
                end
            end
        end
    end
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % Update the individual's best fitness vlaue and the global best one
    for i = 1 : pop
        if ( fit( i ) < pFit( i ) )
yy(iteration)=fit( i );
            pFit( i ) = fit( i );
            pX( i, : ) = x( i, : );
        end
        if( pFit( i ) < fMin )
            fMin = pFit( i );
            yy(iteration)= fMin ;
            bestX = pX( i, : );
        else
%             yy(iteration)=yy(iteration-1);
        end
    end
end
% End of the main program
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The following functions are associated with the main program
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This function is the objective function

 

3 仿真结果

 

 

 

 

4 参考文献

 

[1]郭彤颖, 陈露. 基于鸟群算法优化BP神经网络的热舒适度预测[J]. 计算机系统应用, 2018, 27(4):5.

 

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部分理论引用网络文献,若有侵权联系博主删除。

 

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