基于BP神经网络算法的预测模型研究研究回顾

基本介绍

人工神经网络是一种经典的机器学习模型，随着深度学习的发展神经网络模型日益完善.

神经网络模型实际上是根据训练样本创造出一个多维输入多维输出的函数， 并使用该函数进行预测， 网络的训练过程即为调节该函数参数提高预测精度的过程.神经网络要解决的问题与最小二乘法回归解决的问题并无根本性区别.

回归和分类是常用神经网络处理的两类问题，感知机(Perceptron)是一个简单的线性二分类器， 它保存着输入权重， 根据输入和内置的函数计算输出.人工神经网络中的单个神经元即是感知机.在前馈神经网络的预测过程中，数据流从输入到输出单向流动bp预测风速程序， 不存在循环和返回的通道. 目前大多数神经网络模型都属于前馈神经网络， 在下文中我们将详细讨论前馈过程.所谓全连接是指层A上任一神经元与临近层B上的任意神经元之间都存在连接.反向传播(Back Propagation，BP)是误差反向传播的简称，这是一种用来训练人工神经网络的常见算法， 通常与最优化方法(如梯度下降法)结合使用. 本文介绍的神经网络模型在结构上属于感知机， 因为采用BP算法进行训练， 人们也称其为BP神经网络.研究回顾

BP 神经网络算法已经在预测领域得到了广泛的应用。郝佳莹等根据BP神经网络模型预测，结果表明基于BP 神经网络具有较强的网络泛化能力和预测能力。 基于BP 神经网络算法的预测模型，与传统的多元线性回归模型相比，BP 神经网络模型预测效果要精确得多。 利用基于灰色关联分析的BP 神经网络模型预测bp预测风速程序，取得了良好的预测效果。虽然BP 神经网络已经在多个领域取得了许多成果，BP 神经网络善于处理非线性预测问题，可对任意非线性函数进行逼近，将BP 神经网络算法用于预测将会是一种非常有益的探索。预测效果

程序设计

%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  清空环境变量
warning off             % 关闭报警信息
close all               % 关闭开启的图窗
clear                   % 清空变量
clc                     % 清空命令行
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  导入数据
res = xlsread('data.xlsx');
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  划分训练集和测试集
temp = randperm(103);
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
P_train = res(temp(1: 80), 1: 7)';
T_train = res(temp(1: 80), 8)';
M = size(P_train, 2);
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
P_test = res(temp(81: end), 1: 7)';
T_test = res(temp(81: end), 8)';
N = size(P_test, 2);
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  数据归一化
[p_train, ps_input] = mapminmax(P_train, 0, 1);
p_test = mapminmax('apply', P_test, ps_input);
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
[t_train, ps_output] = mapminmax(T_train, 0, 1);
t_test = mapminmax('apply', T_test, ps_output);
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  创建网络
net = newff(p_train, t_train, 9);
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  设置训练参数
net.trainParam.epochs = 1000;     % 迭代次数 
net.trainParam.goal = 1e-6;       % 误差阈值
net.trainParam.lr = 0.01;         % 学习率
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  训练网络
net = train(net, p_train, t_train);
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  仿真测试
t_sim1 = sim(net, p_train);
t_sim2 = sim(net, p_test);
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  数据反归一化
T_sim1 = mapminmax('reverse', t_sim1, ps_output);
T_sim2 = mapminmax('reverse', t_sim2, ps_output);
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  均方根误差
error1 = sqrt(sum((T_sim1 - T_train).^2) ./ M);
error2 = sqrt(sum((T_sim2 - T_test ).^2) ./ N);
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  绘图
figure
plot(1: M, T_train, 'g-*', 1: M, T_sim1, 'b-o', 'LineWidth', 1)
legend('真实值','预测值')
xlabel('预测样本')
ylabel('预测结果')
string = {'训练集预测结果对比'; ['RMSE=' num2str(error1)]};
title(string)
xlim([1, M])
grid
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
figure
plot(1: N, T_test, 'g-*', 1: N, T_sim2, 'b-o', 'LineWidth', 1)
legend('真实值','预测值')
xlabel('预测样本')
ylabel('预测结果')
string = {'测试集预测结果对比';['RMSE=' num2str(error2)]};
title(string)
xlim([1, N])
grid
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
%%  相关指标计算
% 决定系数 R2
R1 = 1 - norm(T_train - T_sim1)^2 / norm(T_train - mean(T_train))^2;
R2 = 1 - norm(T_test -  T_sim2)^2 / norm(T_test -  mean(T_test ))^2;
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
disp(['训练集数据的R2为：', num2str(R1)])
disp(['测试集数据的R2为：', num2str(R2)])
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
% 平均绝对误差 MAE
mae1 = sum(abs(T_sim1 - T_train)) ./ M ;
mae2 = sum(abs(T_sim2 - T_test )) ./ N ;
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
disp(['训练集数据的MAE为：', num2str(mae1)])
disp(['测试集数据的MAE为：', num2str(mae2)])
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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