_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_实现基于EMD-KPCA-LSTM多维时间序列预测模型，与LSTM和EMD-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，
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以下代码仅供参考

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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 Toolbox
• Signal Processing Toolbox
• Neural 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:

[<title="Data Preprocessing ScriptforSolar Power Prediction">]% Define pathsexcelFilePath='datasets/solar_power_data.xlsx';% Load data from ExcelrawData=readtable(excelFilePath);% Convert table to matrixdataMatrix=table2array(rawData);% Normalize the features[numRows,numCols]=size(dataMatrix);X=dataMatrix(:,1:numCols-1);% Input featuresy=dataMatrix(:,numCols);% Output feature (Solar Power)% Min-Max normalizationminVals=min(X);maxVals=max(X);X_normalized=(X-minVals)./(maxVals-minVals);% Split data into training, validation, and test setstrainRatio=0.7;valRatio=0.15;testRatio=0.15;numTrainSamples=floor(trainRatio*numRows);numValSamples=floor(valRatio*numRows);numTestSamples=numRows-numTrainSamples-numValSamples;X_train=X_normalized(1:numTrainSamples,:);y_train=y(1:numTrainSamples);X_val=X_normalized(numTrainSamples+1:numTrainSamples+numValSamples,:);y_val=y(numTrainSamples+1:numTrainSamples+numValSamples);X_test=X_normalized(numTrainSamples+numValSamples+1:end,:);y_test=y(numTrainSamples+numValSamples+1: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:

[<title="EMD 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_emd=zeros(size(X));imfs=cell(numFeatures,1);fori=1:numFeatures imfComponents=emd(X(:,i)');imfs{i}=imfComponents';X_emd(:,i)=sum(imfComponents)';endend

KPCA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:

[<title="KPCA 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_kpca=zeros(size(X));models=cell(numFeatures,1);fori=1:numFeaturesifnargin==1||isempty(existingModels{i})kpcaModel=kpca(X(:,i)', 'KernelFunction','rbf','NumComponents',2);models{i}=kpcaModel;elsekpcaModel=existingModels{i};endX_kpca(:,i)=predict(kpcaModel,X(:,i)');endend

LSTM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:

[<title="LSTM Training Script">]% Load preprocessed dataload('preprocessed_datasets/preprocessed_data.mat');% Prepare sequences for LSTMsequenceLength=24;% 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,NumFeatures=numel(X_train,2))lstmLayer(100)fullyConnectedLayer(1)regressionLayer];options=trainingOptions('adam',...'MaxEpochs',50,...'GradientThreshold',1,...'InitialLearnRate',0.005,...'LearnRateSchedule','piecewise',...'LearnRateDropFactor',0.2,...'LearnRateDropPeriod',50,...'Verbose',0,...'Plots','training-progress');net=trainNetwork(X_seq_train,y_seq_train,layers,options);% Evaluate LSTM modely_pred_lstm=net.predict(X_seq_test);mse_lstm=mean((y_pred_lstm-y_seq_test).^2);rmse_lstm=sqrt(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)numSamples=numel(y)-seqLen+1;X_seq=cell(numSamples,1);y_seq=zeros(numSamples,1);fori=1:numSamples X_seq{i}=X(i:i+seqLen-1,:);y_seq(i)=y(i+seqLen-1);endend

EMD-LSTM模型训练

以下是EMD-LSTM模型训练的脚本emd_lstm_training.m:

[<title="EMD-LSTM Training Script">]% Load EMD decomposed dataload('preprocessed_datasets/emd_decomposed_data.mat');% Prepare sequences for EMD-LSTMsequenceLength=24;% 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,NumFeatures=numel(X_emd_train,2))lstmLayer(100)fullyConnectedLayer(1)regressionLayer];options=trainingOptions('adam',...'MaxEpochs',50,...'GradientThreshold',1,...'InitialLearnRate',0.005,...'LearnRateSchedule','piecewise',...'LearnRateDropFactor',0.2,...'LearnRateDropPeriod',50,...'Verbose',0,...'Plots','training-progress');net_emd=trainNetwork(X_seq_train,y_seq_train,layers,options);% Evaluate EMD-LSTM modely_pred_emd_lstm=net_emd.predict(X_seq_test);mse_emd_lstm=mean((y_pred_emd_lstm-y_seq_test).^2);rmse_emd_lstm=sqrt(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)numSamples=numel(y)-seqLen+1;X_seq=cell(numSamples,1);y_seq=zeros(numSamples,1);fori=1:numSamples X_seq{i}=X(i:i+seqLen-1,:);y_seq(i)=y(i+seqLen-1);endend

EMD-KPCA-LSTM模型训练

以下是EMD-KPCA-LSTM模型训练的脚本emd_kpca_lstm_training.m:

[<title="EMD-KPCA-LSTM Training Script">]% Load KPCA reduced dataload('preprocessed_datasets/kpca_reduced_data.mat');% Prepare sequences for EMD-KPCA-LSTMsequenceLength=24;% 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,NumFeatures=numel(X_kpca_train,2))lstmLayer(100)fullyConnectedLayer(1)regressionLayer];options=trainingOptions('adam',...'MaxEpochs',50,...'GradientThreshold',1,...'InitialLearnRate',0.005,...'LearnRateSchedule','piecewise',...'LearnRateDropFactor',0.2,...'LearnRateDropPeriod',50,...'Verbose',0,...'Plots','training-progress');net_emd_kpca=trainNetwork(X_seq_train,y_seq_train,layers,options);% Evaluate EMD-KPCA-LSTM modely_pred_emd_kpca_lstm=net_emd_kpca.predict(X_seq_test);mse_emd_kpca_lstm=mean((y_pred_emd_kpca_lstm-y_seq_test).^2);rmse_emd_kpca_lstm=sqrt(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)numSamples=numel(y)-seqLen+1;X_seq=cell(numSamples,1);y_seq=zeros(numSamples,1);fori=1:numSamples X_seq{i}=X(i:i+seqLen-1,:);y_seq(i)=y(i+seqLen-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:

[<title="Result 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 testingsequenceLength=24;% 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_lstm=net.predict(X_seq_test);% Predict using EMD-LSTM modely_pred_emd_lstm=net_emd.predict(X_seq_test);% Predict using EMD-KPCA-LSTM modely_pred_emd_kpca_lstm=net_emd_kpca.predict(X_seq_test);% Calculate RMSE for each modelmse_lstm=mean((y_pred_lstm-y_seq_test).^2);rmse_lstm=sqrt(mse_lstm);mse_emd_lstm=mean((y_pred_emd_lstm-y_seq_test).^2);rmse_emd_lstm=sqrt(mse_emd_lstm);mse_emd_kpca_lstm=mean((y_pred_emd_kpca_lstm-y_seq_test).^2);rmse_emd_kpca_lstm=sqrt(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)numSamples=numel(y)-seqLen+1;X_seq=cell(numSamples,1);y_seq=zeros(numSamples,1);fori=1:numSamples X_seq{i}=X(i:i+seqLen-1,:);y_seq(i)=y(i+seqLen-1);endend

使用说明

1. 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。

2. 运行脚本：

   • 在MATLAB命令窗口中依次运行以下脚本：
     • data_preprocessing.m
     • emd_decomposition.m
     • kpca_reduction.m
     • lstm_training.m
     • emd_lstm_training.m
     • emd_kpca_lstm_training.m
     • result_comparison.m

3. 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：

1. 数据预处理脚本(data_preprocessing.m)
2. EMD分解脚本(emd_decomposition.m)
3. KPCA降维脚本(kpca_reduction.m)
4. LSTM训练脚本(lstm_training.m)
5. EMD-LSTM训练脚本(emd_lstm_training.m)
6. EMD-KPCA-LSTM训练脚本(emd_kpca_lstm_training.m)
7. 结果比较脚本(result_comparison.m)