【信号去噪】基于融合正余弦和柯西变异麻雀算法优化变分模态分解SCSSA-VMD实现信号去噪附Matlab代码...

融合正余弦与柯西变异算法提升SCSSA-VMD信号去噪效率

原创已于 2024-12-23 22:29:29 修改 · 119 阅读

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于 2023-11-05 23:16:28 首次发布

本文介绍了一种结合正余弦约束和柯西变异麻雀算法的优化策略，用于改进变分模态分解SCSSA-VMD在信号去噪中的性能，强调了这种方法在提高信号质量和可靠性方面的有效性。

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🔥 内容介绍

信号去噪一直是数字信号处理领域的一个重要研究方向。在实际应用中，由于信号受到各种干扰和噪声的影响，需要对信号进行去噪处理，以提高信号的质量和可靠性。本文将介绍一种基于融合正余弦和柯西变异麻雀算法优化变分模态分解SCSSA-VMD实现信号去噪的算法流程。

首先，介绍一下SCSSA-VMD算法。SCSSA-VMD是一种基于变分模态分解(VMD)的信号去噪算法，它可以将信号分解成一系列固有模态函数(IMF)。这些IMF是不同频率的信号成分，可以通过对这些IMF进行加权和来重建原始信号。SCSSA-VMD算法在VMD分解过程中加入了正余弦函数的约束，以增强分解的稳定性和准确性。

然后，介绍一下柯西变异麻雀算法。柯西变异麻雀算法是一种优化算法，它基于柯西分布和变异策略，通过对候选解进行随机变异和选择，来搜索最优解。柯西分布具有长尾特性，可以避免算法陷入局部最优解。变异策略可以保证算法的全局搜索能力。

接下来，介绍一下融合正余弦和柯西变异麻雀算法优化SCSSA-VMD的算法流程。首先，将待处理的信号进行SCSSA-VMD分解，得到一系列IMF。然后，将正余弦函数加入到VMD分解过程中，得到正余弦约束下的IMF。接着，将柯西变异麻雀算法应用于IMF的加权和，以优化重建信号的质量和可靠性。最后，通过对优化后的IMF进行加权和，得到去噪后的信号。

总的来说，融合正余弦和柯西变异麻雀算法优化SCSSA-VMD是一种有效的信号去噪算法。它不仅可以提高信号的质量和可靠性，还可以保证算法的全局搜索能力和稳定性。在实际应用中，可以根据具体情况选择不同的参数和算法流程，以达到最佳效果。

📣 部分代码

function [u, u_hat, omega] = VMD(signal, alpha, tau, K, DC, init, tol)
%
%
% Input and Parameters:
% ---------------------
% signal  - the time domain signal (1D) to be decomposed
% alpha   - the balancing parameter of the data-fidelity constraint
% tau     - time-step of the dual ascent ( pick 0 for noise-slack )
% K       - the number of modes to be recovered
% DC      - true if the first mode is put and kept at DC (0-freq)
% init    - 0 = all omegas start at 0
%                    1 = all omegas start uniformly distributed
%                    2 = all omegas initialized randomly
% tol     - tolerance of convergence criterion; typically around 1e-6
%
% Output:
% -------
% u       - the collection of decomposed modes
% u_hat   - spectra of the modes
% omega   - estimated mode center-frequencies
%---------- Preparations

% Period and sampling frequency of input signal
save_T = length(signal);
fs = 1/save_T;

% extend the signal by mirroring
T = save_T;
f_mirror(1:T/2) = signal(T/2:-1:1);
f_mirror(T/2+1:3*T/2) = signal;
f_mirror(3*T/2+1:2*T) = signal(T:-1:T/2+1);
f = f_mirror;

% Time Domain 0 to T (of mirrored signal)
T = length(f);
t = (1:T)/T;

% Spectral Domain discretization
freqs = t-0.5-1/T;

% Maximum number of iterations (if not converged yet, then it won't anyway)
N = 500;

% For future generalizations: individual alpha for each mode
Alpha = alpha*ones(1,K);

% Construct and center f_hat
f_hat = fftshift((fft(f)));
f_hat_plus = f_hat;
f_hat_plus(1:T/2) = 0;

% matrix keeping track of every iterant // could be discarded for mem
u_hat_plus = zeros(N, length(freqs), K);

% Initialization of omega_k
omega_plus = zeros(N, K);
switch init
    case 1
        for i = 1:K
            omega_plus(1,i) = (0.5/K)*(i-1);
        end
    case 2
        omega_plus(1,:) = sort(exp(log(fs) + (log(0.5)-log(fs))*rand(1,K)));
    otherwise
        omega_plus(1,:) = 0;
end

% if DC mode imposed, set its omega to 0
if DC
    omega_plus(1,1) = 0;
end

% start with empty dual variables
lambda_hat = zeros(N, length(freqs));

% other inits
uDiff = tol+eps; % update step
n = 1; % loop counter
sum_uk = 0; % accumulator



% ----------- Main loop for iterative updates




while ( uDiff > tol &&  n < N ) % not converged and below iterations limit
    
    % update first mode accumulator
    k = 1;
    sum_uk = u_hat_plus(n,:,K) + sum_uk - u_hat_plus(n,:,1);
    
    % update spectrum of first mode through Wiener filter of residuals
    u_hat_plus(n+1,:,k) = (f_hat_plus - sum_uk - lambda_hat(n,:)/2)./(1+Alpha(1,k)*(freqs - omega_plus(n,k)).^2);
    
    % update first omega if not held at 0
    if ~DC
        omega_plus(n+1,k) = (freqs(T/2+1:T)*(abs(u_hat_plus(n+1, T/2+1:T, k)).^2)')/sum(abs(u_hat_plus(n+1,T/2+1:T,k)).^2);
    end
    
    % update of any other mode
    for k=2:K
        
        % accumulator
        sum_uk = u_hat_plus(n+1,:,k-1) + sum_uk - u_hat_plus(n,:,k);
        
        % mode spectrum
        u_hat_plus(n+1,:,k) = (f_hat_plus - sum_uk - lambda_hat(n,:)/2)./(1+Alpha(1,k)*(freqs - omega_plus(n,k)).^2);
        
        % center frequencies
        omega_plus(n+1,k) = (freqs(T/2+1:T)*(abs(u_hat_plus(n+1, T/2+1:T, k)).^2)')/sum(abs(u_hat_plus(n+1,T/2+1:T,k)).^2);
        
    end
    
    % Dual ascent
    lambda_hat(n+1,:) = lambda_hat(n,:) + tau*(sum(u_hat_plus(n+1,:,:),3) - f_hat_plus);
    
    % loop counter
    n = n+1;
    
    % converged yet?
    uDiff = eps;
    for i=1:K
        uDiff = uDiff + 1/T*(u_hat_plus(n,:,i)-u_hat_plus(n-1,:,i))*conj((u_hat_plus(n,:,i)-u_hat_plus(n-1,:,i)))';
    end
    uDiff = abs(uDiff);
    
end


%------ Postprocessing and cleanup


% discard empty space if converged early
N = min(N,n);
omega = omega_plus(1:N,:);

% Signal reconstruction
u_hat = zeros(T, K);
u_hat((T/2+1):T,:) = squeeze(u_hat_plus(N,(T/2+1):T,:));
u_hat((T/2+1):-1:2,:) = squeeze(conj(u_hat_plus(N,(T/2+1):T,:)));
u_hat(1,:) = conj(u_hat(end,:));

u = zeros(K,length(t));

for k = 1:K
    u(k,:)=real(ifft(ifftshift(u_hat(:,k))));
end

% remove mirror part
u = u(:,T/4+1:3*T/4);

% recompute spectrum
clear u_hat;
for k = 1:K
    u_hat(:,k)=fftshift(fft(u(k,:)))';
end

end