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时序分解 | Matlab基于WOA-MVMD鲸鱼算法优化多元变分模态分解

news 来源：原创 2025/5/5 7:20:41

时序分解 | Matlab基于WOA-MVMD鲸鱼算法优化多元变分模态分解

效果一览

在这里插入图片描述

基本介绍

WOA-MVMD鲸鱼算法优化多元变分模态分解时间序列信号分解可直接运行分解效果好适合作为创新点（Matlab完整源码和数据)，以包络熵为适应度函数。

1.利用鲸鱼优化算法优化参数k、alpha，分解效果好，包含边际谱、频率图、收敛曲线等图，满足您的需求，使用者较少，适合作为创新点。

2.采用西储大学数据集，运行主程序main即可。

3.包含WOA-MVMD迭代曲线图、MVMD分解图、IMF频域图、包含Hilbert(2D）边际谱图、包含Hilbert(3D）边际谱图。

程序设计

完整源码私信回复Matlab基于WOA-MVMD鲸鱼算法优化多元变分模态分解


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%% 适应度函数
function [ff, min_entropy] = CostMVMD(c, X)alpha = c(1);   % 平滑参数K = round(c(2));% 模态数tau = 0;        % 拉格朗日乘子法步长DC = 0;         % 是否提取直流分量init = 1;       % 初始中心频率选择方法tol = 1e-7;     % 收敛阈值% 调用MVMD函数[u, ~, ~] = MVMD(X, alpha, tau, K, DC, init, tol);% 计算每个模态的包络熵fitness = zeros(1, K);for i = 1:Kxx = abs(hilbert(u(i, :))); % 对IMF分量进行希尔伯特变换并求幅值xxx = xx / sum(xx); % 归一化ssum = 0;for ii = 1:size(xxx, 2)bb = xxx(1, ii) * log(xxx(1, ii)); % 计算包络熵ssum = ssum + bb;  % 求和endfitness(i) = -ssum;   % 加负号以使得最小化包络熵endff = min(fitness); % 返回最小适应度值min_entropy = ff;  % 输出最终的最小包络熵值
end
%% MVMD函数
function [u, u_hat, omega] = MVMD(signal, alpha, tau, K, DC, init, tol)
[x, y] = size(signal);
if x > yC = y;% number of channelsT = x;% length of the Signalsignal = signal';
elseC = x;% number of channelsT = y;% length of the Signal
end
%---------- Preparations
% Sampling Frequency
fs = 1/T;
% Mirroring
f(:,1:T/2) = signal(:,T/2:-1:1);
f(:,T/2+1:3*T/2) = signal;
f(:,3*T/2+1:2*T) = signal(:,T:-1:T/2+1);
% Time Domain 0 to T (of mirrored signal)
T = size(f,2);
t = (1:T)/T;
% frequencies
freqs = t-0.5-1/T;
% Construct and center f_hat
f_hat = fftshift(fft(f,[],2),2);
f_hat_plus = f_hat;
f_hat_plus(:,1:T/2) = 0;
%------------ Initialization
% Maximum number of iterations 
N = 500;
% For future generalizations: individual alpha for each mode
Alpha = alpha*ones(1,K);
% matrix keeping track of every iterant 
u_hat_plus_00 = zeros(length(freqs), C, K);
u_hat_plus = zeros(length(freqs), C, K);
omega_plus = zeros(N, K);
% initialize omegas uniformly
switch initcase 1omega_plus(1,:) = (0.5/K)*((1:K)-1);case 2omega_plus(1,:) = sort(exp(log(fs) + (log(0.5)-log(fs))*rand(1,K)));otherwiseomega_plus(1,:) = 0;
end
% if DC mode imposed, set its omega to 0
if DComega_plus(1,1) = 0;
end
% start with empty dual variables
lambda_hat = zeros(length(freqs), C, N); 
% other inits
uDiff = tol+eps; % update step
n = 1; % loop counter
sum_uk = zeros(length(freqs), C); % accumulator
%--------------- Algorithm of MVMD
while ( uDiff > tol &&  n < N ) % not converged and below iterations limit	% update modesfor k = 1:K% update mode accumulatorif k > 1sum_uk = u_hat_plus(:,:,k-1) + sum_uk - u_hat_plus_00(:,:,k);elsesum_uk = u_hat_plus_00(:,:,K) + sum_uk - u_hat_plus_00(:,:,k);end% update spectrum of mode through Wiener filter of residualsfor c = 1:Cu_hat_plus(:,c,k) = (f_hat_plus(c,:).' - sum_uk(:,c) - lambda_hat(:,c,n)/2)./(1+Alpha(1,k)*(freqs.' - omega_plus(n,k)).^2);end% update first omega if not held at 0if DC || (k > 1)% center frequenciesnumerator = freqs(T/2+1:T)*(abs(u_hat_plus(T/2+1:T,:, k)).^2);denominator = sum(abs(u_hat_plus(T/2+1:T,:,k)).^2);temp1 = sum(numerator);temp2 = sum(denominator);omega_plus(n+1,k) = temp1/temp2;endend% Dual ascentlambda_hat(:,:,n+1) = lambda_hat(:,:,n) + tau*(sum(u_hat_plus,3) - f_hat_plus.');% loop countern = n+1;u_hat_plus_m1 = u_hat_plus_00;u_hat_plus_00 = u_hat_plus;% converged yet?uDiff = u_hat_plus_00 - u_hat_plus_m1;uDiff = 1/T*(uDiff).*conj(uDiff);uDiff = eps+abs(sum(uDiff(:)));
end
%------ Post-processing and cleanup
% discard empty space if converged early
N = min(N,n);
omega = omega_plus(1:N,:);
% Signal reconstruction
u_hat = zeros(T, K, C);
for c = 1:Cu_hat((T/2+1):T,:,c) = squeeze(u_hat_plus((T/2+1):T,c,:));u_hat((T/2+1):-1:2,:,c) = squeeze(conj(u_hat_plus((T/2+1):T,c,:)));u_hat(1,:,c) = conj(u_hat(end,:,c));
end
u = zeros(K,length(t),C);
for k = 1:Kfor c = 1:Cu(k,:,c)=real(ifft(ifftshift(u_hat(:,k,c))));end
end
% remove mirror part
u = u(:,T/4+1:3*T/4,:);
% recompute spectrum
clear u_hat;
for k = 1:Kfor c = 1:Cu_hat(:,k,c)=fftshift(fft(u(k,:,c)))';end
end
u_hat = permute(u_hat, [2 1 3]);
end