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Topic: random time-series displacement data from PSD and back again
Replies: 5   Last Post: Jun 24, 2013 9:01 PM

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Jim Schwendeman

Posts: 7
Registered: 6/21/13
random time-series displacement data from PSD and back again
Posted: Jun 21, 2013 4:10 PM
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Howdy Forum,

I have a project where I have a vibration PSD profile (G^2/Hz). I'd like to use this to create random time-series displacement data to feed into a dynamic model to evaluate performance in the presence of vibe.

The problem occurs when I convert from G^2/Hz to displacement/time, and then back to the identical (or very near it) G^2/Hz profile. I create random time-series data, but when I convert back to the frequency domain, it doesn't match up. The re-created PSD has content up to twice the frequency domain I'm initially putting in, and the RMS values don't match up. This sanity check needs to work before I can confidently put the time-series data into the model, so I'm a bit hung up...

Code below:
% Create noise (centered 1), pump it through PSD, and then calc gRMS
noise_range = 0.02
noise = noise_range*randn(1,N)+(1-noise_range/2);
PSD_noise = PSD.*noise;

%Calculate gRMS for original PSD and noise-injected PSD
gRMS = sqrt(max(cumtrapz(PSD0(:,1),PSD0(:,2))));
gRMS_noise = sqrt(max(cumtrapz(f,PSD_noise)));
%These match up, the gRMS of my noisy PSD is nearly identical to my input PSD

% Create time and displacement
t = linspace(0, N*dt, N);
x = (1/sqrt(N))*real(ifft(sqrt(PSD_noise)));
x = (x*9.81)./sqrt(std(x));
disp('Parceval"s Theorem says this result should = gRMS')
sum(abs(x).^2)
%This answer is similar to the gRMS of my noisy/input PSD, but now off by ~10%

%Now I convert time-series displacement back to frequency domain and should get the same PSD back out:
N = length(x);
xdft = fft(x);
xdft = xdft(1:N/2+1);
psdx = (1/(Fs*N)).*abs(xdft).^2;
psdx(2:end-1) = 2*psdx(2:end-1);
psdx = psdx*sqrt(N)*9.81;
freq = 0:Fs/length(x):Fs/2;

When I end up plotting freq vs psdx, I get frequency content over double of what was put in, and my gRMS is orders of magnitude below what was expected.

Any thoughts?
Jim



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