I have results for repeated vibration test (excitation and response) in time domain. I need to calculate average frf (using cpsd 'Sxy/Sxx') of these test results.
- when i use [abs{(sum(Sxy) / number of test) / (sum(Sxx) / number of test)}] i got something different than what i have for the single test, also it looks much noise.
- but when i use [{(sum(abs(Sxy)) / number of test) / (sum(abs(Sxx)) / number of test)}] i got better smooth results.
which one of these two methods is true and is there a nice reference to read in deep ?
thank you
Hi Ahmed,
I think you're interested to find the average and the general trend of your plot. One of the ways that can be helpful to do that is the Moving Average method. You can do that using Matlab (https://www.mathworks.com/help/econ/moving-average-trend-estimation.html?searchHighlight=moving%20average). Or, you can fit your data using moving average in excel Curve Fitting Toolbox.
I hope that was helpful.
Ibrahim
Dear Ahmed,
Actually there are three often considered approaches for averaging the frequency response functions. The so-called H1, H2 and Hv estimator, all three are techniques to average out the spectrum all three have their underlying assumption to avoid a bias (No noise on input / No noise on output / noise on both input and output).
An interesting read might be the second chapter, especially section 2.5, of the PhD of Peter Verboven (See link).
I hope this helped to answer your question. Feel free to contact me if you have further questions.
Kind regards,
Wout
http://mech.vub.ac.be/avrg/PhD/thesis_PV_web.pdf
Sorry Ahmed for this maybe stupid check ...
In the first case, when you do sum(Sxy), Sxy is a complex number, real and imaginary part, or you are using amplitude and phase description?
It's important that you use real and imaginary description and not the other one.
Mauro Terraneo
thank you all, now I changed the method. Instead of repeating the test several times, I'm using single test for longer time . then I divided the time history to small windows.
results look better but I still want to know how to average the results of the different test (repeated tests).
I'm going to add some more comments and images later.
Dear Ibrahim Awad, thank you for replay , I'm looking for averaging frf results, which is help in reducing noise rather than filtering noise.
Dear Wout Weijtjens, thank you very much for the good reference I'm going to check it soon.
Dear Mauro Terraneo, thank you for replying, Sxy is complex number I think the main question is when exactly I need to take the absolute of the Sxy . is it before summation and dividing to Sxx or after summation and dividing ?
thanks
ahmed
Dear Ahmed Yashar,
As suggestion, I suggest you to also analize the use a proper block size and be careful with the aplication of widow function. As stated by Avitabile is a evil necessary, but if is possible you can employ a periodic excitation and avoid the needed of widow function.
At first you sum, then you apply the abs.
In fact you at first calculate the averaged Sxy like a complex number and then you transform it in magnitude and phase to better understand the frequency content.
Mauro Terraneo
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