Damping and frequency from simulation data

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MM 2020-3-31

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https://ww2.mathworks.cn/matlabcentral/answers/514288-damping-and-frequency-from-simulation-data

评论： MD Riaz Pervez 2023-4-28

PositionY_example.mat

I have some simulation data, for example y in the attachment. I can manually calculate the damping and frequency with logarithmic decrement, but can I do this automated? I can't seem to figure out how.

And/or can I fit a nonlinear function through my datapoints? I tried polyfit but that doesn't work with time series.

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Ameer Hamza 2020-4-2

How do you manually calculate the damping and frequency? Is there a mathematical formula? What type of nonlinear fit do you want to fit your data?

MM 2020-4-3

I calculated it like they did here:

https://www.brown.edu/Departments/Engineering/Courses/En4/Notes/vibrations_free_damped/vibrations_free_damped.htm

With damping:

And frequency:

What type of nonlinear fit? I don't know, any that will work. I was hoping a fit would maybe let me help to calculate the frequency and daming ratio

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Answer 1

Ameer Hamza 2020-4-3

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https://ww2.mathworks.cn/matlabcentral/answers/514288-damping-and-frequency-from-simulation-data#answer_423776

在 MATLAB Online 中打开

The following code automatically estimate the parameters from the signal.

load('PositionY_example.mat');
[val, locs] = findpeaks(y.Data);
peak_times = y.Time(locs);
t0 = t(locs(1));
tn = t(locs(2:end));
omega = mean((1:numel(tn))'./(tn-t0));
xt0 = val(1);
xtn = val(2:end);
delta = mean(log(xtn./xt0)./(1:numel(xtn))');
zeta = delta/sqrt(4*pi^2+delta^2);