% 混沌時間序列的 Volterra 自適應預測(一步預測) -- 主函數% 參考文獻：張家樹.混沌時間序列的Volterra自適應預測.物理學報.2000.03%           朱昀.水聲信號非線性分析方法研究.西北工業大學博士學位論文.2002.06.P28-38clcclearclose alldisp('============= volterra  ==============')%--------------------------------------------------% 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)train_num = 500;        % 訓練樣本數test_num = 1500;        % 測試樣本數tau = 1;                % 時延m = 3;                  % 嵌入維數p = 3;                  % Voltera 階數%--------------------------------------------------% 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);%--------------------------------------------------% 前半部分訓練，后半部分測試x_train = x(1:train_num);x_test =  x(train_num+1:train_num+test_num);%--------------------------------------------------% 混沌序列的相空間重構 (phase space reconstruction)% xn為列向量，每一列為一個點　% dn每一點與xn每一列相對應[xn_train,dn_train] = PhaSpaRecon(x_train,tau,m);[xn_test,dn_test] = PhaSpaRecon(x_test,tau,m);%----------------------------------------------------% 訓練與預測tic% 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);err = dn_test - dn_pred;err_mse2 = sum(err.^2)/length(err);err_mse2_std =  err_mse2/var(x)t = toc%----------------------------------------------------% 結果作圖subplot(211);plot(1:length(err),dn_test,'r+:',1:length(err),dn_pred,'bo-');title('真實值(+)與預測值(o)')subplot(212);plot(err,'k');title('預測絕對誤差')