Curve fitting noisy experimental FFT response (transfer function) data of resonace

[eatfood]

Say you get FFT of some response (be it vibration or noise spectra). If the Q-factor is low and the system is noisy, its possible you can have some frequencies having higher or equal amplitude than at other frequencies which are not the actual resonance peak. In other words, the signal to noise ratio is too high and the accuracy of the frequency determination is lowered.

Simply taking the maximum amplitude as the resonance will not do in a noisy system because the error may be too large. Curve fitting may be needed.

What method do you use or algorithm to fit experimental frequency response data of say measured vibration or sound data?

In some situations, the transfer function follows the Lorentzian distribution. If that were the case for your system, what method do you use to curve fit your experimental data in order to extract resonance for the system? What about curve fitting all other higher frequency peaks (say other noise peaks or modes)?

What if your mechanical system is not lorentzian in nature? For example if you have anti-resonance somewhere, or if you have mode-coupled response. How do you curve fit for these situations?

 

[GregLocock]

Frankly what I do is tidy up my test technique and reacquire the data.

Curve fitting noisy FRFs is a huge field. Exactly what sort of S/N ratio are you talking about? Can you post some examples in csv format? Do you have several FRFs from the same structure or just one?



Cheers

Greg Locock


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[eatfood]

Correcting my typo: I meant to say in the OP that the signal to noise ratio is too low in the first paragraph.

I dont have any data with me at the moment on hand, but just imagine the worst kind. Very noisy. Highly damped. Very low Q-factor. Very broad frequency bandwidth at -3db. The kind you can barely make out the resonance. S/N maybe barely above 1. Low resolution FFT data. So curve fitting is in order.

One could redo the test or make a better setup, but if the system is naturally like this then there is little that can be done (e.g. resonance of a structural element in water, such as vibration of a rudder of a boat while fully immersed in a body of water.

So how does one go about curve fitting the data? Especially for complex systems that dont follow generic SDOF transfer functions (often fitted to a Lorentzian)?

 

[hacksaw]

fitting only works with low noise, unless you are characterizing noise, as in the previous post, clean up the data collection

 

[eatfood]

Yes, but sometimes you cannot eliminate noise or the system is inherently noisy or low Q-factor, like the water-immersed rudder example I was mentioning. Surely there has to be a method?

Ok, but lets forget about the issue of a noisy system. What are the methods used for curve fitting in general (for even high Q systems)?

 

[IRstuff]

"Yes, but sometimes you cannot eliminate noise or the system is inherently noisy or low Q-factor, like the water-immersed rudder example I was mentioning. Surely there has to be a method"

Sine sweeps should have no noise. Where is this "noise" coming from?

TTFN
faq731-376

 

[Vibac]

... but if the system is naturally like this then there is little that can be done (e.g. resonance of a structural element in water, such as vibration of a rudder of a boat while fully immersed in a body of water.

Eatfood, are you familiar with Operational Modal Analysis (OMA), aka Ambient Modal Analysis, aka Output-only Modal Analysis? These techniques are specifically intended for random, uncontrolled excitation such as wind, waves, traffic, etc. There is a variety of algoritms available, and the most advanced ones called Stochastic Subspace Identification (SSI) are really powerful in situations with highly dampened structures and weak excitation.
Commercial tools for OMA have been around since roughly year 2000, and a few examples of providers are SVIBS, LMS, and Bruel & Kjaer.

In OMA you don't measure the excitation force, only the responses. For this reason you won't get FRFs as in traditional modal analysis. Instead the natural frequencies, mode shapes and damping ratios are extracted using other specialized algorithms.

 

[Vibac]

... Also: The way I see it traditional modal analysis works best with "deterministic", controlable measureable excitation. On the contrary, OMA methods work best in situations with stochastic excitation, random in both time and space. Hence the alternative name Ambient Modal Analysis. So, what is unwanted noise for trad. methods is fully useful excitation for OMA methods!
Here is a great ressource on theory and applications:

http://svibs.com/solutions/papers.aspx

 

[GregLocock]

"What are the methods used for curve fitting in general (for even high Q systems)? "

In general you can either build a database of frequencies, dampings and amplitude and phase for each response point and do some sort of fit back to the original data, or you can do circle fits, or you can do time based elimination. I'm sure there are other methods, but I suspect these days the first is most often used, at least for large surveys.

Cheers

Greg Locock


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[eatfood]

I have the data for the non-FRF FFT. The FRF is just the processed raw FFT data where amplitude is Aresponse/Aexcitation both of which are measured. But the noise issue is still there though, if the system being measured is inherently noisy or very low in quality factor. Perhaps the displacement itself is also quite low intrinsically and the amplitude sensitivity of the transducer is certainly one that is limited also, thus signal to noise is low.

 

[GregLocock]

Ab./Fc is not a common way of establishing Hbc, have a look at any basic text on signal analysis for the common formulations. Now, I don't know why exactly the usual formulation is used (I do know roughly), but I bet those texts explain it in sufficient and boring detail. Frankly you seem to be wandering around a large and well explored field with a blindfold on.



Cheers

Greg Locock


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