基于分位数回归的双向长短期记忆网络QRBiLSTM的数据回归区间预测,多输入单输出模型（Matlab完整源码和数据）

%% 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','sheet1','A2:H104'); %% 数据分析 num_size = 0.7; % 训练集占数据集比例 outdim = 1; % 最后一列为输出 num_samples = size(res, 1); % 样本个数 res = res(randperm(num_samples), :); % 打乱数据集（不希望打乱时，注释该行） 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); %% 数据平铺 P_train = double(reshape(P_train, f_, 1, 1, M)); P_test = double(reshape(P_test , f_, 1, 1, N)); t_train = t_train'; t_test = t_test' ; %% 数据格式转换 for i = 1 : M p_train{i, 1} = P_train(:, :, 1, i); end for i = 1 : N p_test{i, 1} = P_test( :, :, 1, i); end %% 创建模型BiLSTM for i = 0.1:0.1:0.9 layers = [ ... sequenceInputLayer(f_,'name','input') %输入层设置 bilstmLayer(10,'Outputmode','sequence','name','hidden1') reluLayer % Relu激活层 dropoutLayer(0.3,'name','dropout_1') bilstmLayer(10,'Outputmode','last','name','hidden2') dropoutLayer(0.3,'name','drdiopout_2') fullyConnectedLayer(outdim,'name','fullconnect') % 全连接层设置（影响输出维度）（cell层出来的输出层） quanRegressionLayer('out',i)]; % 参数设置 options = trainingOptions('adam', ... % Adam 梯度下降算法 'MiniBatchSize', 30, ... % 批大小 'MaxEpochs', 100, ... % 最大迭代次数 'InitialLearnRate', 1e-2, ... % 初始学习率为 'LearnRateSchedule', 'piecewise', ... % 学习率下降 'LearnRateDropFactor', 0.5, ... % 学习率下降因子 'LearnRateDropPeriod', 50, ... % 经过训练后 学习率为 0.01 * 0.5 'Shuffle', 'every-epoch', ... % 每次训练打乱数据集 'Plots', 'none', ... % 不画出曲线 'Verbose', 1); % % 网络训练 net1 = trainNetwork(p_train, t_train, layers, options); net2(floor(i*10)) = trainNetwork(p_train, t_train, layers, options); end %% 仿真测试 t_sim1 = predict(net1, p_train); t_sim2 = predict(net1, p_test ); % 区间预测 for i = 1:length(net2) l_sim1(:, i) = predict(net2(i), p_train); l_sim2(:, i) = predict(net2(i), p_test ); end %% 查看网络结构 analyzeNetwork(net1) %% 数据反归一化 L_sim1 = mapminmax('reverse', l_sim1, ps_output); L_sim2 = mapminmax('reverse', l_sim2, ps_output); 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 fill([1 : M, M : -1 : 1], [L_sim1(:, 1); flipud(L_sim1(:, 9))], ... 'r', 'FaceColor', [1, 0.8, 0.8], 'EdgeColor', 'none') hold on plot(1 : M, T_train, 'r-', 1 : M, T_sim1, 'b-', 'LineWidth', 1) legend('90%的置信区间', '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 fill([1 : N, N : -1 : 1], [L_sim2(:, 1); flipud(L_sim2(:, 9))], ... 'r', 'FaceColor', [1, 0.8, 0.8], 'EdgeColor', 'none') hold on plot(1 : N, T_test, 'r-', 1 : N, T_sim2, 'b-', 'LineWidth', 1) legend('90%的置信区间', '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 % 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)]) %% 指标计算(区间覆盖率和区间平均宽度百分比) L_sim1 = L_sim1'; T_train = T_train'; L_sim2 = L_sim2'; T_test = T_test' ; picp1 = PICP (L_sim1, T_train); pimw1 = PIMWP(L_sim1, T_train); disp(['训练集的区间覆盖率为:', num2str(picp1), '。区间平均宽度百分比为:', num2str(pimw1)]) picp2 = PICP (L_sim2, T_test); pimw2 = PIMWP(L_sim2, T_test); disp(['测试集的区间覆盖率为:', num2str(picp2), '。区间平均宽度百分比为:', num2str(pimw2)])