【信號(hào)去噪】基于融合正余弦和柯西變異麻雀算法優(yōu)化變分模態(tài)分解SCSSA-VMD實(shí)現(xiàn)信號(hào)去
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智能優(yōu)化算法?? ? ??神經(jīng)網(wǎng)絡(luò)預(yù)測?? ? ??雷達(dá)通信?? ? ?無線傳感器?? ? ? ?電力系統(tǒng)
信號(hào)處理?? ? ? ? ? ? ?圖像處理?? ? ? ? ? ? ??路徑規(guī)劃?? ? ??元胞自動(dòng)機(jī)?? ? ? ?無人機(jī)
?? 內(nèi)容介紹
信號(hào)去噪一直是數(shù)字信號(hào)處理領(lǐng)域的一個(gè)重要研究方向。在實(shí)際應(yīng)用中，由于信號(hào)受到各種干擾和噪聲的影響，需要對信號(hào)進(jìn)行去噪處理，以提高信號(hào)的質(zhì)量和可靠性。本文將介紹一種基于融合正余弦和柯西變異麻雀算法優(yōu)化變分模態(tài)分解SCSSA-VMD實(shí)現(xiàn)信號(hào)去噪的算法流程。
首先，介紹一下SCSSA-VMD算法。SCSSA-VMD是一種基于變分模態(tài)分解(VMD)的信號(hào)去噪算法，它可以將信號(hào)分解成一系列固有模態(tài)函數(shù)(IMF)。這些IMF是不同頻率的信號(hào)成分，可以通過對這些IMF進(jìn)行加權(quán)和來重建原始信號(hào)。SCSSA-VMD算法在VMD分解過程中加入了正余弦函數(shù)的約束，以增強(qiáng)分解的穩(wěn)定性和準(zhǔn)確性。
然后，介紹一下柯西變異麻雀算法?？挛髯儺惵槿杆惴ㄊ且环N優(yōu)化算法，它基于柯西分布和變異策略，通過對候選解進(jìn)行隨機(jī)變異和選擇，來搜索最優(yōu)解?？挛鞣植季哂虚L尾特性，可以避免算法陷入局部最優(yōu)解。變異策略可以保證算法的全局搜索能力。
接下來，介紹一下融合正余弦和柯西變異麻雀算法優(yōu)化SCSSA-VMD的算法流程。首先，將待處理的信號(hào)進(jìn)行SCSSA-VMD分解，得到一系列IMF。然后，將正余弦函數(shù)加入到VMD分解過程中，得到正余弦約束下的IMF。接著，將柯西變異麻雀算法應(yīng)用于IMF的加權(quán)和，以優(yōu)化重建信號(hào)的質(zhì)量和可靠性。最后，通過對優(yōu)化后的IMF進(jìn)行加權(quán)和，得到去噪后的信號(hào)。
總的來說，融合正余弦和柯西變異麻雀算法優(yōu)化SCSSA-VMD是一種有效的信號(hào)去噪算法。它不僅可以提高信號(hào)的質(zhì)量和可靠性，還可以保證算法的全局搜索能力和穩(wěn)定性。在實(shí)際應(yīng)用中，可以根據(jù)具體情況選擇不同的參數(shù)和算法流程，以達(dá)到最佳效果。
?? 部分代碼
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 signalsave_T = length(signal);fs = 1/save_T;% extend the signal by mirroringT = 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 discretizationfreqs = 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 modeAlpha = alpha*ones(1,K);% Construct and center f_hatf_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 memu_hat_plus = zeros(N, length(freqs), K);% Initialization of omega_komega_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 0if DC ? ?omega_plus(1,1) = 0;end% start with empty dual variableslambda_hat = zeros(N, length(freqs));% other initsuDiff = tol+eps; % update stepn = 1; % loop countersum_uk = 0; % accumulator% ----------- Main loop for iterative updateswhile ( 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 earlyN = min(N,n);omega = omega_plus(1:N,:);% Signal reconstructionu_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 partu = u(:,T/4+1:3*T/4);% recompute spectrumclear u_hat;for k = 1:K ? ?u_hat(:,k)=fftshift(fft(u(k,:)))';endend
?? 運(yùn)行結(jié)果
?? 參考文獻(xiàn)
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