Matlab PSO-BP 基于粒子群算法优化BP神经网络的数据时序预测 含测试数据集 预测图像和评价指标详细

%% 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（时间序列的单列数据） result = xlsread('数据集.xlsx'); %% 数据分析 num_samples = length(result); % 样本个数 kim = 15; % 延时步长（kim个历史数据作为自变量） zim = 1; % 跨zim个时间点进行预测 %% 构造数据集 for i = 1: num_samples - kim - zim + 1 res(i, :) = [reshape(result(i: i + kim - 1), 1, kim), result(i + kim + zim - 1)]; end %% 数据集分析 outdim = 1; % 最后一列为输出 num_size = 0.7; % 训练集占数据集比例 num_train_s = round(num_size * num_samples); % 训练集样本个数 f_ = size(res, 2) - outdim; % 输入特征维度 %% 划分训练集和测试集 P_train = res(1: num_train_s, 1: f_)'; T_train = res(1: num_train_s, f_ + 1: end)'; M = size(P_train, 2); P_test = res(num_train_s + 1: end, 1: f_)'; T_test = res(num_train_s + 1: end, f_ + 1: end)'; 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); %% 节点个数 inputnum = size(p_train, 1); % 输入层节点数 hiddennum = 5; % 隐藏层节点数 outputnum = size(t_train, 1); % 输出层节点数 %% 建立网络 net = newff(p_train, t_train, hiddennum); %% 设置训练参数 net.trainParam.epochs = 1000; % 训练次数 net.trainParam.goal = 1e-6; % 目标误差 net.trainParam.lr = 0.01; % 学习率 net.trainParam.showWindow = 0; % 关闭窗口 %% 参数初始化 c1 = 4.494; % 学习因子 c2 = 4.494; % 学习因子 maxgen = 30; % 种群更新次数 sizepop = 5; % 种群规模 Vmax = 1.0; % 最大速度 Vmin = -1.0; % 最小速度 popmax = 2.0; % 最大边界 popmin = -2.0; % 最小边界 %% 节点总数 numsum = inputnum * hiddennum + hiddennum + hiddennum * outputnum + outputnum; for i = 1 : sizepop pop(i, :) = rands(1, numsum); % 初始化种群 V(i, :) = rands(1, numsum); % 初始化速度 fitness(i) = fun(pop(i, :), hiddennum, net, p_train, t_train); end %% 个体极值和群体极值 [fitnesszbest, bestindex] = min(fitness); zbest = pop(bestindex, :); % 全局最佳 gbest = pop; % 个体最佳 fitnessgbest = fitness; % 个体最佳适应度值 BestFit = fitnesszbest; % 全局最佳适应度值 %% 迭代寻优 for i = 1 : maxgen for j = 1 : sizepop % 速度更新 V(j, :) = V(j, :) + c1 * rand * (gbest(j, :) - pop(j, :)) + c2 * rand * (zbest - pop(j, :)); V(j, (V(j, :) > Vmax)) = Vmax; V(j, (V(j, :) < Vmin)) = Vmin; % 种群更新 pop(j, :) = pop(j, :) + 0.2 * V(j, :); pop(j, (pop(j, :) > popmax)) = popmax; pop(j, (pop(j, :) < popmin)) = popmin; % 自适应变异 pos = unidrnd(numsum); if rand > 0.95 pop(j, pos) = rands(1, 1); end % 适应度值 fitness(j) = fun(pop(j, :), hiddennum, net, p_train, t_train); end for j = 1 : sizepop % 个体最优更新 if fitness(j) < fitnessgbest(j) gbest(j, :) = pop(j, :); fitnessgbest(j) = fitness(j); end % 群体最优更新 if fitness(j) < fitnesszbest zbest = pop(j, :); fitnesszbest = fitness(j); end end BestFit = [BestFit, fitnesszbest]; end %% 提取最优初始权值和阈值 w1 = zbest(1 : inputnum * hiddennum); B1 = zbest(inputnum * hiddennum + 1 : inputnum * hiddennum + hiddennum); w2 = zbest(inputnum * hiddennum + hiddennum + 1 : inputnum * hiddennum ... + hiddennum + hiddennum * outputnum); B2 = zbest(inputnum * hiddennum + hiddennum + hiddennum * outputnum + 1 : ... inputnum * hiddennum + hiddennum + hiddennum * outputnum + outputnum); %% 最优值赋值 net.Iw{1, 1} = reshape(w1, hiddennum, inputnum); net.Lw{2, 1} = reshape(w2, outputnum, hiddennum); net.b{1} = reshape(B1, hiddennum, 1); net.b{2} = B2'; %% 打开训练窗口 net.trainParam.showWindow = 1; % 打开窗口 %% 网络训练 net = train(net, p_train, t_train); %% 仿真预测 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, 'r-', 1: M, T_sim1, 'b-', '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, 'r-', 1: N, T_sim2, 'b-', '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 %% 误差曲线迭代图 figure plot(1: length(BestFit), BestFit, 'LineWidth', 1.5); xlabel('粒子群迭代次数'); ylabel('适应度值'); xlim([1, length(BestFit)]) string = {'模型迭代误差变化'}; title(string) grid on %% 相关指标计算 % 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)]) % 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)]) % MBE mbe1 = sum(T_sim1 - T_train) ./ M ; mbe2 = sum(T_sim2 - T_test ) ./ N ; disp(['训练集数据的MBE为：', num2str(mbe1)]) disp(['测试集数据的MBE为：', num2str(mbe2)]) % MAPE mape1 = sum(abs((T_sim1 - T_train)./T_train)) ./ M ; mape2 = sum(abs((T_sim2 - T_test )./T_test )) ./ N ; disp(['训练集数据的MAPE为：', num2str(mape1)]) disp(['测试集数据的MAPE为：', num2str(mape2)]) %% 绘制散点图 sz = 25; c = 'b'; figure scatter(T_train, T_sim1, sz, c) hold on plot(xlim, ylim, '--k') xlabel('训练集真实值'); ylabel('训练集预测值'); xlim([min(T_train) max(T_train)]) ylim([min(T_sim1) max(T_sim1)]) title('训练集预测值 vs. 训练集真实值') figure scatter(T_test, T_sim2, sz, c) hold on plot(xlim, ylim, '--k') xlabel('测试集真实值'); ylabel('测试集预测值'); xlim([min(T_test) max(T_test)]) ylim([min(T_sim2) max(T_sim2)]) title('测试集预测值 vs. 测试集真实值')