% 混沌時間序列的 volterra 預測(一步預測) -- 主函數% 使用平臺 - Matlab6.5 / Matlab7.0% 作者：陸振波，海軍工程大學% 歡迎同行來信交流與合作，更多文章與程序下載請訪問我的個人主頁% 電子郵件：luzhenbo@yahoo.com.cn% 個人主頁：http://luzhenbo.88uu.com.cnclcclearclose all%--------------------------------------------------% 公共參數k1 = 6000;              % 前面的迭代點數k2 = 2000;              % 后面的迭代點數 (總樣本數)%--------------------------------------------------% 產生混沌序列        sigma = 10;        % Lorenz 方程參數 ab = 8/3;           %                 br = 34;            %                 c            y = [-1,0,1];      % 起始點 (1 x 3 的行向量)h = 0.01;          % 積分時間步長z = LorenzData(y,h,k1+k2,sigma,r,b);X = z(k1+1:end,1);        %--------------------------------------------------X = normalize_a(X,1);   % 信號歸一化到均值為0,振幅為1tau = 10;               % 時延m = 3;                  % 嵌入維數p = 3;                  % Volterra階數%--------------------------------------------------train_num = 500        % 訓練樣本數test_num = 1500         % 測試樣本數%--------------------------------------------------% 混沌序列的相空間重構 (phase space reconstruction)x_train = X(1:train_num);x_test =  X(train_num+1:train_num+test_num);[xn_train,dn_train] = PhaSpaRecon(x_train,tau,m);[xn_test,dn_test] = PhaSpaRecon(x_test,tau,m);%------------------------------------------------------% 訓練與預測% 訓練算法求權矢量[Wn,err_mse1] = volterra_train_lu(xn_train,dn_train,p);err_mse1_std = err_mse1/var(X)% 測試樣本的一步預測dn_pred = volterra_test(xn_test,p,Wn);err2 = dn_test - dn_pred;err_mse2 = sum(err2.^2)/length(err2);err_mse2_std =  err_mse2/var(X)%----------------------------------------------------% 結果作圖figure;subplot(211);plot(1:length(err2),dn_test,'r+:',1:length(err2),dn_pred,'bo-');title('真實值(+)與預測值(o)')subplot(212);plot(err2,'k');title('預測絕對誤差')