【lssvm回归预测】基于变模态结合秃鹰算法优化最小二乘支持向量机VMD-BES-LSSVM实现数据预测模型（多输入单输出）含Matlab代码

% test-script for VMD% authors: Dominique Zosso and Konstantin Dragomiretskiy% zosso@math.ucla.edu --- http://www.math.ucla.edu/~zosso% Initial release 2013-12-12 (c) 2013%% When using this code, please do cite our paper:% -----------------------------------------------% K. Dragomiretskiy, D. Zosso, Variational Mode Decomposition, IEEE Trans.% on Signal Processing (in press)% please check here for update reference: %          http://dx.doi.org/10.1109/TSP.2013.2288675%--------------- Preparationclear all;close all;clc;% Time Domain 0 to Tfs=400;T=60;nn=fs*T;t=1/fs:1/fs:T;freqs = ((1/T:1/T:fs)-fs/2-1/T);% nn = 1000;% T=1;% fs = nn/T;% t = (1:nn)/fs;% freqs = ((1/T:1/T:fs)-fs/2-1/T);% freqs = 2*pi*(t-0.5-1/nn)*T*nn;% center frequencies of componentsf_1 = 20;f_2 = 60;f_3 = 100;f_4 = 50;% modesv_1 = (cos(2*pi*f_1*t));v_2 = 1/4*(cos(2*pi*f_2*t));v_3 = 1/16*(cos(2*pi*f_3*t));v_4=1/3*(cos(2*pi*f_4*t));% % for visualization purposes% fsub = {};% wsub = {};% fsub{1} = v_1;% fsub{2} = v_2;% fsub{3} = v_3;% wsub{1} = 2*pi*f_1;% wsub{2} = 2*pi*f_2;% wsub{3} = 2*pi*f_3;% composite signal, including noise% f=csvread('17.txt',0,0,[0 0 nn-1 0]);f = v_1 + v_2 + v_3 + v_4+0.1*randn(size(v_1));f_hat = fftshift((fft(f)));% some sample parameters for VMDalpha = 2000;        % moderate bandwidth constrainttau = 0.001;            % noise-tolerance (no strict fidelity enforcement)K = 4;              % 3 modesDC = 0;             % no DC part imposedinit = 1;           % initialize omegas uniformlytol = 1e-7;%--------------- Run actual VMD code[u, u_hat, omega] = VMD(f, alpha, tau, K, DC, init, tol);omega=omega*fs;%--------------- Visualization% For convenience here: Order omegas increasingly and reindex u/u_hat[~, sortIndex] = sort(omega(end,:));omega = omega(:,sortIndex);u_hat = u_hat(:,sortIndex);u = u(sortIndex,:);linestyles = {'b', 'g', 'm', 'c', 'c', 'r', 'k'};figure('Name', 'Composite input signal' );plot(t,f, 'k');set(gca, 'XLim', [0 1]);% for sub = 1:length(fsub)%     figure('Name', ['Input signal component ' num2str(sub)] );%     plot(t,fsub{sub}, 'k');%     set(gca, 'XLim', [0 1]);% endfigure('Name', 'Input signal spectrum' );plot(freqs(nn/2+1:end), abs(f_hat(nn/2+1:end)), 'k');% loglog(freqs(nn/2+1:end), abs(f_hat(nn/2+1:end)), 'k');% set(gca, 'XLim', [1 nn/2]*pi*2, 'XGrid', 'on', 'YGrid', 'on', 'XMinorGrid', 'off', 'YMinorGrid', 'off');% ylims = get(gca, 'YLim');% hold on;% for sub = 1:length(wsub)%     plot([wsub{sub} wsub{sub}], 'k--');% %     loglog([wsub{sub} wsub{sub}], ylims, 'k--');% end% set(gca, 'YLim', ylims);figure('Name', 'Evolution of center frequencies omega');for k=1:K    plot(omega(:,k), 1:size(omega,1), linestyles{k});%      semilogx(2*pi/fs*omega(:,k), 1:size(omega,1), linestyles{k});    hold on;end% set(gca, 'YLim', [1,size(omega,1)]);% set(gca, 'XLim', [2*pi,0.5*2*pi/fs], 'XGrid', 'on', 'XMinorGrid', 'on');figure('Name', 'Spectral decomposition');plot(freqs(nn/2+1:end), abs(f_hat(nn/2+1:end)), 'k:');% loglog(freqs(nn/2+1:end), abs(f_hat(nn/2+1:end)), 'k:');% set(gca, 'XLim', [1 nn/2]*pi*2, 'XGrid', 'on', 'YGrid', 'on', 'XMinorGrid', 'off', 'YMinorGrid', 'off');hold on;for k = 1:K    plot(freqs(nn/2+1:end), abs(u_hat(nn/2+1:end,k)), linestyles{k});%     loglog(freqs(nn/2+1:end), abs(u_hat(nn/2+1:end,k)), linestyles{k});end% set(gca, 'YLim', ylims);for k = 1:K    figure('Name', ['Reconstructed mode ' num2str(k)]);    plot(t,u(k,:), linestyles{k});   hold on;%     if ~isempty(fsub)%         plot(t, fsub{min(k,length(fsub))}, 'k:');%     end    set(gca, 'XLim', [0 1]);end