基于经验模态分解 时序分析 核主成分分析 长短期记忆网络 多维时间序列预测 LSTM多维时间序列预测模型 LSTM和 MD-LSTM进行对比

EMD-KPCA-LSTM 基于经验模态分解和核主成分分析的长短期记忆网络多维时间序列预测MATLAB代码含LSTM、EMD-LSTM、EMD-KPCA-LSTM三个模型的对比matlab参考文档基于EMD-PCA-LSTM的光伏功率预测模型研究内容本案例使用数据集是北半球光伏功率共四个输入特征太阳辐射度 气温 气压 大气湿度一个输出预测光伏功率; 预测对象可以是电力负荷、风速、光伏等等时间序列数据集;代码注释清楚可以读取本地EXCEL数据**以下代码仅供参考**实现基于EMD-KPCA-LSTM的多维时间序列预测模型并与LSTM和EMD-LSTM进行对比。以下是详细的步骤和代码。环境准备确保您已经安装了MATLAB并且具有以下工具箱Statistics and Machine Learning ToolboxSignal Processing ToolboxNeural Network Toolbox数据加载与预处理我需要加载和预处理数据。假设的数据存储在一个Excel文件中包含四个输入特征太阳辐射度、气温、气压、大气湿度和一个输出特征光伏功率。以下是数据加载和预处理的脚本data_preprocessing.m:[titleData Preprocessing ScriptforSolar Power Prediction]% Define pathsexcelFilePathdatasets/solar_power_data.xlsx;% Load data from ExcelrawDatareadtable(excelFilePath);% Convert table to matrixdataMatrixtable2array(rawData);% Normalize the features[numRows,numCols]size(dataMatrix);XdataMatrix(:,1:numCols-1);% Input featuresydataMatrix(:,numCols);% Output feature (Solar Power)% Min-Max normalizationminValsmin(X);maxValsmax(X);X_normalized(X-minVals)./(maxVals-minVals);% Split data into training, validation, and test setstrainRatio0.7;valRatio0.15;testRatio0.15;numTrainSamplesfloor(trainRatio*numRows);numValSamplesfloor(valRatio*numRows);numTestSamplesnumRows-numTrainSamples-numValSamples;X_trainX_normalized(1:numTrainSamples,:);y_trainy(1:numTrainSamples);X_valX_normalized(numTrainSamples1:numTrainSamplesnumValSamples,:);y_valy(numTrainSamples1:numTrainSamplesnumValSamples);X_testX_normalized(numTrainSamplesnumValSamples1:end,:);y_testy(numTrainSamplesnumValSamples1:end);% Save preprocessed datasave(preprocessed_datasets/preprocessed_data.mat,X_train,y_train,X_val,y_val,X_test,y_test);disp(Preprocessed data saved to: preprocessed_datasets/preprocessed_data.mat);EMD分解接下来我们使用经验模态分解EMD来分解输入信号。以下是EMD分解的脚本emd_decomposition.m:[titleEMD Decomposition Script]% Load preprocessed dataload(preprocessed_datasets/preprocessed_data.mat);% Apply EMD to each input feature[X_emd_train,imfsTrain]emd_decompose_features(X_train);[X_emd_val,imfsVal]emd_decompose_features(X_val);[X_emd_test,imfsTest]emd_decompose_features(X_test);% Save decomposed datasave(preprocessed_datasets/emd_decomposed_data.mat,X_emd_train,imfsTrain,X_emd_val,imfsVal,X_emd_test,imfsTest);disp(EMD decomposed data saved to: preprocessed_datasets/emd_decomposed_data.mat);function[X_emd,imfs]emd_decompose_features(X)[~,numFeatures]size(X);X_emdzeros(size(X));imfscell(numFeatures,1);fori1:numFeatures imfComponentsemd(X(:,i));imfs{i}imfComponents;X_emd(:,i)sum(imfComponents);endendKPCA降维接下来我们使用核主成分分析KPCA对EMD分解后的数据进行降维。以下是KPCA降维的脚本kpca_reduction.m:[titleKPCA Reduction Script]% Load EMF decomposed dataload(preprocessed_datasets/emd_decomposed_data.mat);% Apply KPCA to each input feature[X_kpca_train,kpcaModels]kpca_reduce_features(X_emd_train);[X_kpca_val,~]kpca_reduce_features(X_emd_val,kpcaModels);[X_kpca_test,~]kpca_reduce_features(X_emd_test,kpcaModels);% Save reduced datasave(preprocessed_datasets/kpca_reduced_data.mat,X_kpca_train,X_kpca_val,X_kpca_test);disp(KPCA reduced data saved to: preprocessed_datasets/kpca_reduced_data.mat);function[X_kpca,models]kpca_reduce_features(X,existingModels)[~,numFeatures]size(X);X_kpcazeros(size(X));modelscell(numFeatures,1);fori1:numFeaturesifnargin1||isempty(existingModels{i})kpcaModelkpca(X(:,i), KernelFunction,rbf,NumComponents,2);models{i}kpcaModel;elsekpcaModelexistingModels{i};endX_kpca(:,i)predict(kpcaModel,X(:,i));endendLSTM模型训练我们将分别训练三种模型LSTM、EMD-LSTM和EMD-KPCA-LSTM。以下是LSTM模型训练的脚本lstm_training.m:[titleLSTM Training Script]% Load preprocessed dataload(preprocessed_datasets/preprocessed_data.mat);% Prepare sequences for LSTMsequenceLength24;% Example sequence length of 24 time steps[X_seq_train,y_seq_train]prepare_sequences(X_train,y_train,sequenceLength);[X_seq_val,y_seq_val]prepare_sequences(X_val,y_val,sequenceLength);[X_seq_test,y_seq_test]prepare_sequences(X_test,y_test,sequenceLength);% Train LSTM modellayers[sequenceInputLayer(sequenceLength,NumFeaturesnumel(X_train,2))lstmLayer(100)fullyConnectedLayer(1)regressionLayer];optionstrainingOptions(adam,...MaxEpochs,50,...GradientThreshold,1,...InitialLearnRate,0.005,...LearnRateSchedule,piecewise,...LearnRateDropFactor,0.2,...LearnRateDropPeriod,50,...Verbose,0,...Plots,training-progress);nettrainNetwork(X_seq_train,y_seq_train,layers,options);% Evaluate LSTM modely_pred_lstmnet.predict(X_seq_test);mse_lstmmean((y_pred_lstm-y_seq_test).^2);rmse_lstmsqrt(mse_lstm);fprintf(LSTM Model RMSE: %.4f\n,rmse_lstm);% Save trained modelsave(trained_models/lstm_model.mat,net);disp(LSTM model saved to: trained_models/lstm_model.mat);function[X_seq,y_seq]prepare_sequences(X,y,seqLen)numSamplesnumel(y)-seqLen1;X_seqcell(numSamples,1);y_seqzeros(numSamples,1);fori1:numSamples X_seq{i}X(i:iseqLen-1,:);y_seq(i)y(iseqLen-1);endendEMD-LSTM模型训练以下是EMD-LSTM模型训练的脚本emd_lstm_training.m:[titleEMD-LSTM Training Script]% Load EMD decomposed dataload(preprocessed_datasets/emd_decomposed_data.mat);% Prepare sequences for EMD-LSTMsequenceLength24;% Example sequence length of 24 time steps[X_seq_train,y_seq_train]prepare_sequences(X_emd_train,y_train,sequenceLength);[X_seq_val,y_seq_val]prepare_sequences(X_emd_val,y_val,sequenceLength);[X_seq_test,y_seq_test]prepare_sequences(X_emd_test,y_test,sequenceLength);% Train EMD-LSTM modellayers[sequenceInputLayer(sequenceLength,NumFeaturesnumel(X_emd_train,2))lstmLayer(100)fullyConnectedLayer(1)regressionLayer];optionstrainingOptions(adam,...MaxEpochs,50,...GradientThreshold,1,...InitialLearnRate,0.005,...LearnRateSchedule,piecewise,...LearnRateDropFactor,0.2,...LearnRateDropPeriod,50,...Verbose,0,...Plots,training-progress);net_emdtrainNetwork(X_seq_train,y_seq_train,layers,options);% Evaluate EMD-LSTM modely_pred_emd_lstmnet_emd.predict(X_seq_test);mse_emd_lstmmean((y_pred_emd_lstm-y_seq_test).^2);rmse_emd_lstmsqrt(mse_emd_lstm);fprintf(EMD-LSTM Model RMSE: %.4f\n,rmse_emd_lstm);% Save trained modelsave(trained_models/emd_lstm_model.mat,net_emd);disp(EMD-LSTM model saved to: trained_models/emd_lstm_model.mat);function[X_seq,y_seq]prepare_sequences(X,y,seqLen)numSamplesnumel(y)-seqLen1;X_seqcell(numSamples,1);y_seqzeros(numSamples,1);fori1:numSamples X_seq{i}X(i:iseqLen-1,:);y_seq(i)y(iseqLen-1);endendEMD-KPCA-LSTM模型训练以下是EMD-KPCA-LSTM模型训练的脚本emd_kpca_lstm_training.m:[titleEMD-KPCA-LSTM Training Script]% Load KPCA reduced dataload(preprocessed_datasets/kpca_reduced_data.mat);% Prepare sequences for EMD-KPCA-LSTMsequenceLength24;% Example sequence length of 24 time steps[X_seq_train,y_seq_train]prepare_sequences(X_kpca_train,y_train,sequenceLength);[X_seq_val,y_seq_val]prepare_sequences(X_kpca_val,y_val,sequenceLength);[X_seq_test,y_seq_test]prepare_sequences(X_kpca_test,y_test,sequenceLength);% Train EMD-KPCA-LSTM modellayers[sequenceInputLayer(sequenceLength,NumFeaturesnumel(X_kpca_train,2))lstmLayer(100)fullyConnectedLayer(1)regressionLayer];optionstrainingOptions(adam,...MaxEpochs,50,...GradientThreshold,1,...InitialLearnRate,0.005,...LearnRateSchedule,piecewise,...LearnRateDropFactor,0.2,...LearnRateDropPeriod,50,...Verbose,0,...Plots,training-progress);net_emd_kpcatrainNetwork(X_seq_train,y_seq_train,layers,options);% Evaluate EMD-KPCA-LSTM modely_pred_emd_kpca_lstmnet_emd_kpca.predict(X_seq_test);mse_emd_kpca_lstmmean((y_pred_emd_kpca_lstm-y_seq_test).^2);rmse_emd_kpca_lstmsqrt(mse_emd_kpca_lstm);fprintf(EMD-KPCA-LSTM Model RMSE: %.4f\n,rmse_emd_kpca_lstm);% Save trained modelsave(trained_models/emd_kpca_lstm_model.mat,net_emd_kpca);disp(EMD-KPCA-LSTM model saved to: trained_models/emd_kpca_lstm_model.mat);function[X_seq,y_seq]prepare_sequences(X,y,seqLen)numSamplesnumel(y)-seqLen1;X_seqcell(numSamples,1);y_seqzeros(numSamples,1);fori1:numSamples X_seq{i}X(i:iseqLen-1,:);y_seq(i)y(iseqLen-1);endend结果比较最后我们将比较三种模型的预测结果。以下是结果比较的脚本result_comparison.m:[titleResult Comparison Script]% Load preprocessed dataload(preprocessed_datasets/preprocessed_data.mat);% Load trained modelsload(trained_models/lstm_model.mat);load(trained_models/emd_lstm_model.mat);load(trained_models/emd_kpca_lstm_model.mat);% Prepare sequences for testingsequenceLength24;% Example sequence length of 24 time steps[X_seq_test,y_seq_test]prepare_sequences(X_test,y_test,sequenceLength);% Predict using LSTM modely_pred_lstmnet.predict(X_seq_test);% Predict using EMD-LSTM modely_pred_emd_lstmnet_emd.predict(X_seq_test);% Predict using EMD-KPCA-LSTM modely_pred_emd_kpca_lstmnet_emd_kpca.predict(X_seq_test);% Calculate RMSE for each modelmse_lstmmean((y_pred_lstm-y_seq_test).^2);rmse_lstmsqrt(mse_lstm);mse_emd_lstmmean((y_pred_emd_lstm-y_seq_test).^2);rmse_emd_lstmsqrt(mse_emd_lstm);mse_emd_kpca_lstmmean((y_pred_emd_kpca_lstm-y_seq_test).^2);rmse_emd_kpca_lstmsqrt(mse_emd_kpca_lstm);fprintf(LSTM Model RMSE: %.4f\n,rmse_lstm);fprintf(EMD-LSTM Model RMSE: %.4f\n,rmse_emd_lstm);fprintf(EMD-KPCA-LSTM Model RMSE: %.4f\n,rmse_emd_kpca_lstm);% Plot predictions vs actual valuesfigure;plot(y_seq_test,b,DisplayName,Actual);hold on;plot(y_pred_lstm,r--,DisplayName,LSTM);plot(y_pred_emd_lstm,g-.,DisplayName,EMD-LSTM);plot(y_pred_emd_kpca_lstm,m:,DisplayName,EMD-KPCA-LSTM);xlabel(Time Steps);ylabel(Solar Power);title(Comparison of Models);legend show;grid on;function[X_seq,y_seq]prepare_sequences(X,y,seqLen)numSamplesnumel(y)-seqLen1;X_seqcell(numSamples,1);y_seqzeros(numSamples,1);fori1:numSamples X_seq{i}X(i:iseqLen-1,:);y_seq(i)y(iseqLen-1);endend使用说明配置路径确保datasets/solar_power_data.xlsx文件存在并且包含所需的列。确保所有文件名和路径与脚本中的路径一致。运行脚本在MATLAB命令窗口中依次运行以下脚本data_preprocessing.memd_decomposition.mkpca_reduction.mlstm_training.memd_lstm_training.memd_kpca_lstm_training.mresult_comparison.m注意事项确保所有必要的工具箱已安装特别是Statistics and Machine Learning Toolbox,Signal Processing Toolbox, 和Neural Network Toolbox。根据需要调整参数如sequenceLength,MaxEpochs,InitialLearnRate等。示例假设您的数据文件夹结构如下datasets/ └── solar_power_data.xlsx并且solar_power_data.xlsx包含五个列太阳辐射度、气温、气压、大气湿度、光伏功率。运行上述脚本后您可以查看各种图表和预测结果。总结我们可以构建一个全面的时间序列预测系统包括数据加载、预处理、EMD分解、KPCA降维以及LSTM、EMD-LSTM和EMD-KPCA-LSTM模型的训练和评估。以下是所有相关的代码文件数据预处理脚本(data_preprocessing.m)EMD分解脚本(emd_decomposition.m)KPCA降维脚本(kpca_reduction.m)LSTM训练脚本(lstm_training.m)EMD-LSTM训练脚本(emd_lstm_training.m)EMD-KPCA-LSTM训练脚本(emd_kpca_lstm_training.m)结果比较脚本(result_comparison.m)