How can I obtain accurate and high-quality FRF results?

I have followed Mathieu NOE's approach from this post to calculate the FRF.

Are there any ways to improve my FRF, such as using filters or averaging techniques?

Please find the attached code and data for reference.

Thank you for your assistance!

[Ali]

time_data file

[Mathieu NOE]

hello Ali

can you confirm that the data contains 5 hits of the same systems ? seems to me you have concatenated 5 hits with different hammer force ?

Name Size Bytes Class Attributes

accel_signal_raw 65536x5 2621440 double

force_signal_raw 65536x5 2621440 double

time_data 65536x1 524288 double

Answer 1

[Mathieu NOE]

hello again

I made very few changes to the code - I think that you cannot get any better results if you use only one hit data. To get bettet results you need to have multiple hits so you increase the signal to noise ratio and remove (average) tiny artefacts you randomly generate at each hit.

attached is the code for 5th hit only and this is the result I have obtained

NB that if your purpose is to get the FRF only up to 1 kHz, then there is no need to use a sampling rate as high as yours (100 kHz). Fs = 4 kHz would suffice and that would make your data size smaller and speed up the fft computation (also use power of 2 for nfft).

also the coherence plot for a single hit is always zero - so in this case you cannot really assess the "quality" of your FRF estimation , as coherence is meaningfull only for multiple hits.

my result so far :

[Mathieu NOE]

hello again

with a tiny code modification, now you can use all 5 hits in your FRF computation

the only code modification is :

% force_signal_raw = force_signal_raw(:, 5); % Raw force signal in mV
force_signal_raw = force_signal_raw(:); % ENTIRE Raw force signal in mV

% accel_signal_raw = accel_signal_raw (:, 5); % Raw accel signal in mV
accel_signal_raw = accel_signal_raw (:); % ENTIRE Raw accel signal in mV

new result :

now you see a coherence plot that shows in which frequency range the FRF estimation is correct . When either the input or output signals are too weak and burried in the background noise , you get low valued coherence (results are not robust). When coherence approaches 1 then you have good quality estimation.

[Mathieu NOE]

I changed a bit the last code so you can easily see the effect of windowing - see attachment

• on the force sensor I use a force window that put a big portion of the force signal to zero after the hit
• on the accel signal I use a exp decaying window to reduce the effect of noise of the trailing portion of the signal

this is now appearing in figure(2) : you can see when I force the force signal to zero and also the accel signal go down toward zero a bit faster as before (without window)

be aware that using a lot of exponential decay by windowing appears as more damping in the FRF so use it wisely. If you want to mesure FRFs with very low damping (and capture accurately this damping without using exp window be sure to have records that last enough - without truncating the signal)

Microsoft Word - Windows and Leakage_Overview.doc

resulting FRF with force / exp windows : (looks smoother with a bit more apparent damping)

[Ali]

Hi engineer Mathieu,

Thanks for the updated code and suggestions! I appreciate your effort!

[Mathieu NOE]

as always, my pleasure !