多序列：http://t.csdn.cn/yfjoh

数据在评论区，导入自己的数据即可预测并画图

<code>%% 1.环境清理

clear, clc, close all;

%% 2.导入数据,单序列

D=readmatrix('B.xlsx');

data=D(:,2);%要求行向量

data1=data;

% 原始数据绘图

figure

plot(data,'-s','Color',[0 0 255]./255,'linewidth',1,'Markersize',5,'MarkerFaceColor',[0 0 255]./255)

legend('原始数据','Location','NorthWest','FontName','华文宋体');

xlabel('样本','fontsize',12,'FontName','华文宋体');

ylabel('数值','fontsize',12,'FontName','华文宋体');

%% 3.数据处理

nn=1500;%训练数据集大小

numTimeStepsTrain = floor(nn);%nn数据训练 ，N-nn个用来验证

[XTrain,YTrain,XTest,YTest,mu,sig] = shujuchuli(data,numTimeStepsTrain);

%% 4.定义LSTM结构参数

numFeatures= 1;%输入节点

numResponses = 1;%输出节点

numHiddenUnits = 500;%隐含层神经元节点数

%构建 LSTM网络

layers = [sequenceInputLayer(numFeatures)

lstmLayer(numHiddenUnits) %lstm函数

dropoutLayer(0.2)%丢弃层概率

reluLayer('name','relu')% 激励函数 RELU

fullyConnectedLayer(numResponses)

regressionLayer];

XTrain=XTrain';

YTrain=YTrain';

%% 5.定义LSTM函数参数

def_options();

%% 6.训练LSTM网络

net = trainNetwork(XTrain,YTrain,layers,options);

%% 7.建立训练模型

net = predictAndUpdateState(net,XTrain);

%% 8.仿真预测(训练集)

M = numel(XTrain);

for i = 1:M

[net,YPred_1(:,i)] = predictAndUpdateState(net,XTrain(:,i),'ExecutionEnvironment','cpu');%

end

T_sim1 = sig*YPred_1 + mu;%预测结果去标准化 ，恢复原来的数量级

%% 9.仿真预测(验证集)

N = numel(XTest);

for i = 1:N

[net,YPred_2(:,i)] = predictAndUpdateState(net,XTest(:,i),'ExecutionEnvironment','cpu');%

end

T_sim2 = sig*YPred_2 + mu;%预测结果去标准化 ，恢复原来的数量级

%% 10.评价指标

% 均方根误差

T_train=data1(1:M)';

T_test=data1(M+1:end)';

error1 = sqrt(sum((T_sim1 - T_train).^2) ./ M);

error2 = sqrt(sum((T_sim2 - T_test ).^2) ./ N);

% 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(['验证集数据的MAE为：', num2str(mae2)])

% MAPE

maep1 = sum(abs(T_sim1 - T_train)./T_train) ./ M ;

maep2 = sum(abs(T_sim2 - T_test )./T_test) ./ N ;

disp(['训练集数据的MAPE为：', num2str(maep1)])

disp(['验证集数据的MAPE为：', num2str(maep2)])

% RMSE

RMSE1 = sqrt(sumsqr(T_sim1 - T_train)/M);

RMSE2 = sqrt(sumsqr(T_sim2 - T_test)/N);

disp(['训练集数据的RMSE为：', num2str(RMSE1)])

disp(['验证集数据的RMSE为：', num2str(RMSE2)])

%% 11. 绘图

figure

subplot(2,1,1)

plot(T_sim1,'-s','Color',[255 0 0]./255,'linewidth',1,'Markersize',5,'MarkerFaceColor',[250 0 0]./255)

hold on

plot(T_train,'-o','Color',[150 150 150]./255,'linewidth',0.8,'Markersize',4,'MarkerFaceColor',[150 150 150]./255)

legend( 'LSTM拟合训练数据','实际分析数据','Location','best');

title('LSTM模型预测结果及真实值','fontsize',12)

xlabel('样本','fontsize',12);

ylabel('数值','fontsize',12);

xlim([1 M])

%-------------------------------------------------------------------------------------

subplot(2,1,2)

bar((T_sim1 - T_train)./T_train)

legend('LSTM模型训练集相对误差','Location','best')

title('LSTM模型训练集相对误差','fontsize',12)

ylabel('误差','fontsize',12)

xlabel('样本','fontsize',12)

xlim([1 M]);

%-------------------------------------------------------------------------------------

figure

subplot(2,1,1)

plot(T_sim2,'-s','Color',[0 0 255]./255,'linewidth',1,'Markersize',5,'MarkerFaceColor',[0 0 255]./255)

hold on

plot(T_test,'-o','Color',[0 0 0]./255,'linewidth',0.8,'Markersize',4,'MarkerFaceColor',[0 0 0]./255)

legend('LSTM预测测试数据','实际分析数据','Location','best');

title('LSTM模型预测结果及真实值','fontsize',12)

xlabel('样本','fontsize',12);

ylabel('数值','fontsize',12);

xlim([1 N])

%-------------------------------------------------------------------------------------

subplot(2,1,2)

bar((T_sim2 - T_test )./T_test)

legend('LSTM模型测试集相对误差','Location','NorthEast')

title('LSTM模型测试集相对误差','fontsize',12)

ylabel('误差','fontsize',12)

xlabel('样本','fontsize',12)

xlim([1 N]);

%% 12.预测未来

P = N-nn;% 预测未来数量

YPred_3 = [];%预测结果清零

[T_sim3] = yuceweilai(net,XTrain,data,P,YPred_3,sig,mu)

%% 13.绘图

figure

plot(1:size(data,1),data,'-s','Color',[255 0 0]./255,'linewidth',1,'Markersize',5,'MarkerFaceColor',[250 0 0]./255)

hold on

%plot(size(data,1)+1:size(data,1)+P,T_sim3,'-o','Color',[150 150 150]./255,'linewidth',0.8,'Markersize',4,'MarkerFaceColor',[150 150 150]./255)

legend( 'LSTM预测结果','Location','NorthWest');

title('LSTM模型预测结果','fontsize',12)

xlabel('样本','fontsize',12);

ylabel('数值','fontsize',12);

上面代码中对应的function函数：

shujuchuli.m

function [XTrain,YTrain,XTest,YTest,mu,sig] = shujuchuli(data,numTimeStepsTrain)

dataTrain = data(1:numTimeStepsTrain+1,:);% 训练样本

dataTest = data(numTimeStepsTrain:end,:); %验证样本

%训练数据标准化处理

mu = mean(dataTrain,'ALL');

sig = std(dataTrain,0,'ALL');

dataTrainStandardized = (dataTrain - mu) / sig;

XTrain = dataTrainStandardized(1:end-1,:);% 训练输入

YTrain = dataTrainStandardized(2:end,:);% 训练输出

%测试样本标准化处理

dataTestStandardized = (dataTest - mu) / sig;

XTest = dataTestStandardized(1:end-1,:)%测试输入

YTest = dataTest(2:end,:);%测试输出

XTest=XTest';

YTest=YTest';

end

yuceweilai.m

function [T_sim3] = yuceweilai(net,XTrain,data,P,YPred_3,sig,mu)

net1 = resetState(net);

net1 = predictAndUpdateState(net1,XTrain);

[net1,YPred_3] = predictAndUpdateState(net1,data(end));

for i = 2:P

[net1,YPred_3(:,i)] = predictAndUpdateState(net1,YPred_3(:,i-1),'ExecutionEnvironment','cpu');

end

T_sim3 = sig*YPred_3 + mu;

end

def_options.m

options = trainingOptions('adam', ... % adam优化算法 自适应学习率

'MaxEpochs',500,...% 最大迭代次数

'MiniBatchSize',10, ...%最小批处理数量

'GradientThreshold',1, ...%防止梯度爆炸

'InitialLearnRate',0.005, ...% 初始学习率

'LearnRateSchedule','piecewise', ...

'LearnRateDropPeriod',125, ...%125次后 ，学习率下降

'LearnRateDropFactor',0.2, ...%下降因子 0.2

'ValidationData',{XTrain,YTrain}, ...

'ValidationFrequency',5, ...%每五步验证一次

'Verbose',1, ...

'Plots','training-progress');

运行结果：