基于时空RBF-NN的混沌时间序列预测（Matlab代码实现）

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目录

💥1 概述

📚2 运行结果

🎉3 参考文献

🌈4 Matlab代码实现

💥1 概述

本文中用于混沌时间序列预测任务的径向基函数神经网络（RBF-NN）的两种变体。特别是，用传统实现了RBF，并将性能与时空RBF-NN进行了Mackey-Glass时间序列预测。

📚2 运行结果

Mackey_Glass_Time_Series_Prediction_ST_RBF ：

Mackey_Glass_Time_Series_Prediction_RBF ：

部分代码：

clc
clear all
close all

ST_RBF = load('ST_RBF.mat');
RBF = load('RBF.mat');

%%  Results
% Input and output signals (training phase)
figure
plot(ST_RBF.indt,ST_RBF.f_train,'k','linewidth',ST_RBF.lw);
hold on;
% plot(RBF.indt,RBF.f_train,'r','linewidth',RBF.lw);
plot(RBF.indt,RBF.y_train,'.:b','linewidth',RBF.lw);
plot(ST_RBF.indt,ST_RBF.y_train,'--r','linewidth',ST_RBF.lw);
xlim([ST_RBF.start_of_series_tr+ST_RBF.time_steps ST_RBF.end_of_series_tr]);
h=legend('Actual Value (Training)','RBF Predicted (Training)','ST-RBF Predicted (Training)','Location','Best');
grid minor
xlabel('Sample #','FontSize',ST_RBF.fsize);
ylabel('Magnitude','FontSize',ST_RBF.fsize);
set(h,'FontSize',12)
set(gca,'FontSize',13)
saveas(gcf,strcat('Time_SeriesTraining.png'),'png')

% Input and output signals (test phase)
figure
plot(ST_RBF.indts,ST_RBF.f_test,'k','linewidth',ST_RBF.lw);
hold on;
plot(RBF.indts,RBF.y_test,'.:b','linewidth',RBF.lw);
plot(ST_RBF.indts,ST_RBF.y_test,'--r','linewidth',ST_RBF.lw);
xlim([ST_RBF.start_of_series_ts+ST_RBF.time_steps ST_RBF.end_of_series_ts]);
h=legend('Actual Value (Testing)','RBF Predicted (Testing)','ST-RBF Predicted (Testing)','Location','Best');
grid minor
xlabel('Sample #','FontSize',ST_RBF.fsize);
ylabel('Magnitude','FontSize',ST_RBF.fsize);
set(h,'FontSize',12)
set(gca,'FontSize',13)
saveas(gcf,strcat('Time_SeriesTesting.png'),'png')

% Objective function (MSE) (training phase)
figure
plot(RBF.start_of_series_tr:RBF.end_of_series_tr-1,10*log10(RBF.I(1:RBF.end_of_series_tr-RBF.start_of_series_tr)),'+-b','linewidth',RBF.lw)
hold on
plot(ST_RBF.start_of_series_tr:ST_RBF.end_of_series_tr-1,10*log10(ST_RBF.I(1:ST_RBF.end_of_series_tr-ST_RBF.start_of_series_tr)),'+-r','linewidth',ST_RBF.lw)
h=legend('RBF (Training)','ST-RBF (Training)','Location','North');
grid minor
xlabel('Sample #','FontSize',ST_RBF.fsize);
ylabel('MSE (dB)','FontSize',ST_RBF.fsize);
set(h,'FontSize',12)
set(gca,'FontSize',13)
saveas(gcf,strcat('Time_SeriesTrainingMSE.png'),'png')

% Objective function (MSE) (test phase)
figure
plot(RBF.start_of_series_ts+RBF.time_steps:RBF.end_of_series_ts,10*log10(RBF.I(RBF.end_of_series_tr-RBF.start_of_series_tr+1:end)),'.:b','linewidth',RBF.lw+1)
hold on
plot(ST_RBF.start_of_series_ts+ST_RBF.time_steps:ST_RBF.end_of_series_ts,10*log10(ST_RBF.I(ST_RBF.end_of_series_tr-ST_RBF.start_of_series_tr+1:end)),'.:r','linewidth',ST_RBF.lw+1)
h=legend('RBF (Testing)','ST-RBF (Testing)','Location','South');
grid minor
xlabel('Sample #','FontSize',ST_RBF.fsize);
ylabel('MSE (dB)','FontSize',ST_RBF.fsize);
set(h,'FontSize',12)
set(gca,'FontSize',13)
saveas(gcf,strcat('Time_SeriesTestingMSE.png'),'png')

% Mean square error
[[10*log10(((RBF.f_train'-RBF.y_train)*(RBF.f_train'-RBF.y_train)')/length(RBF.y_train)) ...
10*log10(((RBF.f_test'-RBF.y_test)*(RBF.f_test'-RBF.y_test)')/length(RBF.y_test))];
[10*log10(((ST_RBF.f_train'-ST_RBF.y_train)*(ST_RBF.f_train'-ST_RBF.y_train)')/length(ST_RBF.y_train)) ...
10*log10(((ST_RBF.f_test'-ST_RBF.y_test)*(ST_RBF.f_test'-ST_RBF.y_test)')/length(ST_RBF.y_test))]]

🎉3 参考文献

[1]Sadiq, Alishba, et al. “Chaotic Time Series Prediction using Spatio-Temporal RBF Neural Networks.” 2018 3rd {IEEE} International Conference on Emerging Trends in Engineering, Sciences and Technology ({ICEEST}), {IEEE}, 2018

🌈4 Matlab代码实现