The findpeaks function has a number of name-value pair arguments that you can use. The two I use most often are 'MinPeakProminence' and 'MinPeakDistance'. The first selects the peaks based on their relation to the signal levels around them, and the second does not return peaks within a specified distance of identified peaks. One or botth of those (and possibly others) should do what you want.
load('data.mat')
% whos
v_data = data;
v_mean = mean(v_data,2)'; %getting mean
v_std = std(v_data, 0, 2)'; %getting standard deviation
v_smooth = smooth(v_mean); %smoothing out noisy data
t = v_data(:,1); %picking off a time vector
ind_1 = 1:length(t);
t = t(ind_1);
v = v_smooth(ind_1);
ind_2 = 1:length(t);
[ pks, locs] = findpeaks(v(ind_2), 'MinPeakProminence',7.5, 'MinPeakDistance',280);
n_peaks = numel(locs);
%---Calculate Logarithmic Decrement and damping ratio
log_dec = zeros(length(n_peaks));
for nn = 1:n_peaks-1
log_dec(nn)= log(pks(nn)/pks(nn+1)); % computed with n = 1 periods apart
end
mean_dec = mean(log_dec); %average decrement
%---damping ratio---
damp_ratio = 1/sqrt(1+((2*pi/(mean_dec))^2))
pf = polyfit(t(locs), log(pks), 3);
curve_fit = exp(polyval(pf,t));
figure()
axes
plot(t, v_data(:,2), 'Displayname', 'Data 1'); hold on;
plot(t, v_data(:,3), 'Displayname', 'Data 2');
plot(t, v_data(:,4), 'Displayname', 'Data 3');
plot(t, v_data(:,5), 'Displayname', 'Data 4');
plot(t, v_data(:,6), 'Displayname', 'Data 5');
plot(t(locs), pks, 'rd', 'markersize', 10, 'displayname', 'Peaks'); hold on;
plot(t, v_smooth, 'k', 'linewidth', 1.5, 'Displayname', 'Smoothed Average Data');
plot( t, curve_fit,'g-.','LineWidth', 1.5, 'Displayname', 'Peak Envelope');
grid minor
title('Data: 1 - 5');
legend('location', 'ne');
xlabel('Time (s)'); ylabel('Velocity (m/s)');
I do not understand your data, and apparently the smoothing steps interact with the returned peaks. This is an improvement, however you will need to continue experimenting yourself to get the results you want.
Meanwhile see: How to filter noise from time-frequency data and find natural frequency of a cantilever? for one approach to fitting this sort of problem.
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