近年来，随着房屋建筑、水利、交通等土木工程的大力发展，我国的混凝土年用量逐年攀升。相关统计数据表明，目前我国的混凝土年用量约为24～30亿立方米，混凝土结构约占全部工程结构的90%上，可以预见，混凝土将是现阶段及未来一段时间内我国主导的工程结构材料。

2.2 解题思路及步骤

%% 清空环境变量
clear all
clc

%% 导入数据
load concrete_data.mat
% 随机产生训练集和测试集
n = randperm(size(attributes,2));
% 训练集——80个样本
p_train = attributes(:,n(1:80))';
t_train = strength(:,n(1:80))';
% 测试集——23个样本
p_test = attributes(:,n(81:end))';
t_test = strength(:,n(81:end))';

%% 数据归一化

% 训练集
[pn_train,inputps] = mapminmax(p_train');
pn_train = pn_train';
pn_test = mapminmax('apply',p_test',inputps);
pn_test = pn_test';
% 测试集
[tn_train,outputps] = mapminmax(t_train');
tn_train = tn_train';
tn_test = mapminmax('apply',t_test',outputps);
tn_test = tn_test';

%% SVM模型创建/训练

% 寻找最佳c参数/g参数
[c,g] = meshgrid(-10:0.5:10,-10:0.5:10);
[m,n] = size(c);
cg = zeros(m,n);
eps = 10^(-4);
v = 5;
bestc = 0;
bestg = 0;
error = Inf;
for i = 1:m
    for j = 1:n
        cmd = ['-v ',num2str(v),' -t 2',' -c ',num2str(2^c(i,j)),' -g ',num2str(2^g(i,j) ),' -s 3 -p 0.1'];
        cg(i,j) = svmtrain(tn_train,pn_train,cmd);
        if cg(i,j) < error
            error = cg(i,j);
            bestc = 2^c(i,j);
            bestg = 2^g(i,j);
        end
        if abs(cg(i,j) - error) <= eps && bestc > 2^c(i,j)
            error = cg(i,j);
            bestc = 2^c(i,j);
            bestg = 2^g(i,j);
        end
    end
end
% 创建/训练SVM  
cmd = [' -t 2',' -c ',num2str(bestc),' -g ',num2str(bestg),' -s 3 -p 0.01'];
model = svmtrain(tn_train,pn_train,cmd);

%% SVM仿真预测
[Predict_1,error_1] = svmpredict(tn_train,pn_train,model);
[Predict_2,error_2] = svmpredict(tn_test,pn_test,model);
% 反归一化
predict_1 = mapminmax('reverse',Predict_1,outputps);
predict_2 = mapminmax('reverse',Predict_2,outputps);
% 结果对比
result_1 = [t_train predict_1];
result_2 = [t_test predict_2];

%% 绘图
figure(1)
plot(1:length(t_train),t_train,'r-*',1:length(t_train),predict_1,'b:o')
grid on
legend('真实值','预测值')
xlabel('样本编号')
ylabel('耐压强度')
string_1 = {'训练集预测结果对比';
           ['mse = ' num2str(error_1(2)) ' R^2 = ' num2str(error_1(3))]};
title(string_1)
figure(2)
plot(1:length(t_test),t_test,'r-*',1:length(t_test),predict_2,'b:o')
grid on
legend('真实值','预测值')
xlabel('样本编号')
ylabel('耐压强度')
string_2 = {'测试集预测结果对比';
           ['mse = ' num2str(error_2(2)) ' R^2 = ' num2str(error_2(3))]};
title(string_2)

%% BP 神经网络

% 数据转置
pn_train = pn_train';
tn_train = tn_train';
pn_test = pn_test';
tn_test = tn_test';
% 创建BP神经网络
net = newff(pn_train,tn_train,10);
% 设置训练参数
net.trainParam.epcohs = 1000;
net.trainParam.goal = 1e-3;
net.trainParam.show = 10;
net.trainParam.lr = 0.1;
% 训练网络
net = train(net,pn_train,tn_train);
% 仿真测试
tn_sim = sim(net,pn_test);
% 均方误差
E = mse(tn_sim - tn_test);
% 决定系数
N = size(t_test,1);
R2=(N*sum(tn_sim.*tn_test)-sum(tn_sim)*sum(tn_test))^2/((N*sum((tn_sim).^2)-(sum(tn_sim))^2)*(N*sum((tn_test).^2)-(sum(tn_test))^2)); 
% 反归一化
t_sim = mapminmax('reverse',tn_sim,outputps);
% 绘图
figure(3)
plot(1:length(t_test),t_test,'r-*',1:length(t_test),t_sim,'b:o')
grid on
legend('真实值','预测值')
xlabel('样本编号')
ylabel('耐压强度')
string_3 = {'测试集预测结果对比(BP神经网络)';
           ['mse = ' num2str(E) ' R^2 = ' num2str(R2)]};
title(string_3)

4 延伸阅读

4.1 核函数对模型性能的影响