利用Matlab中的粒子群优化改进VMD方法选优组件，实现数字信号去噪 - 包含Matlab源代码及1979期刊内容

%% 基于粒子群算法（Particle Swarm Optimization Algorithm)
%% 的经验模态分解的信号去燥算法研究
clc
clear all
close all

n=1024;
fs=1024;
t=(0:1:n-1)/fs;
s=sin(2*pi*16*t);
% some sample parameters for VMD
alpha = 2000; % moderate bandwidth constraint
tau = 0; % noise-tolerance (no strict fidelity enforcement)
K = 4; % 4 modes
DC = 0; % no DC part imposed
init = 1; % initialize omegas uniformly
tol = 1e-7;


%计算信号强度，信号强度就是信号能量，等于信号取值的平方/信号长度
% sigpower=sum(abs(s(:).^2))/length(s(:));
%设置信噪比（linear）
% snr=100;
%产生噪声
% noise=sqrt(sigpower/snr)*3*randn(1,n);%randn产生均值为零，标准差为前面系数的高斯白噪声
% y=s+noise;
y=awgn(s,10,'measured','db');
%% 噪声信号EMD分解
imf=emd(y);
%--------------- Run actual VMD code
[u, u_hat, omega] = VMD(y, alpha, tau, K, DC, init, tol);

[m,n]=size(u);
nVar=m-1;%变量维数

% % CPSO 参数
c1 =1.4495;
c2 =1.4495;
%w=1;
Vmin = -1;
Vmax = 1;
maxiter = 100; % 迭代次数
sizepop = 10; % 种群数量
popmin = zeros(1,nVar); % 参数取值下界
popmax = ones(1,nVar); % 参数取值上界
% % 初始化种群
for i=1:sizepop
%pop(i,:) = init_individual(popmin,popmax,nVar,1); % 随机初始化个体
pop(i,:)=popmin + (popmax-popmin).*round(rand(1,nVar));
fitness(i) = EMD_fun(pop(i,:),s,imf,nVar);
V(i,:)=Vmin+(Vmax-Vmin)*round(rand(1,nVar));
end
% 记录一组最优值
[bestfitness,bestindex]=min(fitness);
zbest=pop(bestindex,:); % 全局最佳
gbest=pop; % 个体最佳
fitnessgbest=fitness; % 个体最佳适应度值
fitnesszbest=bestfitness; % 全局最佳适应度值
% 迭代寻优
for i=1:maxiter

% 云理论优化的PSO的权值
%fbest = fitnesszbest;
% favg = mean( fitness );
% index=[];index = find(fitness>favg);
% favg1 = mean( fitness(index) );
% index=[];index = find(fitness<=favg);
% favg2 = mean( fitness(index) );

for j=1:sizepop

% if fitness(j)>favg1
% w=0.2;
% elseif fitness(j)>favg2 && fitness(j)<=favg1
% Ex = fbest;
% En = (favg-fbest)/c1;
% He = En/c2;
% En1 = normrnd( En,He );
% w = 0.9-0.5*exp( -(fitness(j)-Ex).^2/2/En1/En1 );
% else
% w = 0.9;
%