数学建模——LSTM时间序列预测的Matlab实现

data = kw; 
%导入数据，数据必须是一维向量

figure
plot(data)
xlabel("15min Period")
ylabel("Kw")
title("15-minute load")
numTimeStepsTrain = floor(0.9*numel(data));
%划分训练集与测试集，这里选了0.9
%确定训练次数
dataTrain = data(1:numTimeStepsTrain+1);
dataTest = data(numTimeStepsTrain+1:end);
%创建两个数据集 dataTrain和dataTest
mu = mean(dataTrain);
sig = std(dataTrain);
dataTrainStandardized = (dataTrain - mu) / sig;
XTrain = dataTrainStandardized(1:end-1);
YTrain = dataTrainStandardized(2:end);
numFeatures = 1;
numResponses = 1;
numHiddenUnits = 200;
layers = [ ...
    sequenceInputLayer(numFeatures)
    lstmLayer(numHiddenUnits)
    fullyConnectedLayer(numResponses)
    regressionLayer];
%接下来设置求解的各项参数，指定训练选项。将求解器设置为 'adam' 并进行 250 轮训练。要防止梯度爆炸，请将梯度阈值设置为 1。指定初始学习率 0.005，在 125 轮训练后通过乘以因子 0.2 来降低学习率。
options = trainingOptions('adam', ...
    'MaxEpochs',800, ...
    'GradientThreshold',1, ...
    'InitialLearnRate',0.005, ...
    'LearnRateSchedule','piecewise', ...
    'LearnRateDropPeriod',400, ...
    'LearnRateDropFactor',0.2, ...
    'Verbose',0, ...
'Plots','training-progress');
net = trainNetwork(XTrain,YTrain,layers,options);
dataTestStandardized = (dataTest - mu) / sig;
XTest = dataTestStandardized(1:end-1);
net = predictAndUpdateState(net,XTrain);
[net,YPred] = predictAndUpdateState(net,YTrain(end));
numTimeStepsTest = numel(XTest);
for i = 2:numTimeStepsTest
    [net,YPred(:,i)] = predictAndUpdateState(net,YPred(:,i-1),'ExecutionEnvironment','cpu');
end
YPred = sig*YPred + mu;
YTest = dataTest(2:end);
rmse = sqrt(mean((YPred-YTest).^2))
figure
plot(dataTrain(1:end-1))
hold on
idx = numTimeStepsTrain:(numTimeStepsTrain+numTimeStepsTest);
plot(idx,[data(numTimeStepsTrain) YPred],'.-')
hold off
xlabel("Periods of 15-mins")
ylabel("Kw")
title("Forecast")
legend(["Observed" "Forecast"])