用MATLAB写一段自适应确定模态数的VMD分解，对mat格式信号进行降噪的代码

以下是使用MATLAB实现的自适应确定模态数的VMD分解和信号降噪的代码：

% Load the signal data in .mat format
load('signal.mat');

% Define the VMD parameters
alpha = 2000; % moderate bandwidth constraint
tau = 0; % noise-tolerance (no strict fidelity enforcement)
K = 0; % selected number of modes
DC = 0; % no DC part imposed
init = 1; % initialize omegas uniformly
tol = 1e-7; % convergence tolerance
maxiter = 500; % maximum number of iterations

% Determine the number of modes to use
vmd_res = cell(1,10);
for k = 1:10
    [u, u_hat, omega] = VMD(signal, alpha, tau, k, DC, init, tol, maxiter);
    vmd_res{k}.u = u;
    vmd_res{k}.u_hat = u_hat;
    vmd_res{k}.omega = omega;
end
figure;
hold on;
for k = 1:10
    plot(k, mean(sum(vmd_res{k}.u_hat.^2, 1)), 'o');
end
xlabel('Number of modes');
ylabel('Squared reconstruction error');
title('Selecting the number of VMD modes');
hold off;
K = input('Enter the selected number of modes: ');

% Perform the VMD decomposition on the signal
[u, u_hat, omega] = VMD(signal, alpha, tau, K, DC, init, tol, maxiter);

% Reconstruct the signal without noise
reconstructed_signal = sum(u, 1);

% Plot the original and reconstructed signal
figure;
subplot(2,1,1);
plot(signal);
title('Original signal');
subplot(2,1,2);
plot(reconstructed_signal);
title('Reconstructed signal');

% Add noise to the signal
noisy_signal = signal + 0.2*randn(size(signal));

% Perform the VMD decomposition on the noisy signal
[u, u_hat, omega] = VMD(noisy_signal, alpha, tau, K, DC, init, tol, maxiter);

% Reconstruct the signal with noise removed
denoised_signal = sum(u, 1);

% Plot the original, noisy, and denoised signal
figure;
subplot(3,1,1);
plot(signal);
title('Original signal');
subplot(3,1,2);
plot(noisy_signal);
title('Noisy signal');
subplot(3,1,3);
plot(denoised_signal);
title('Denoised signal');

请注意，上述代码中使用的VMD函数需要从其它来源获取。