Model order in curve fitting

[GMarsh]

Hi,

Can someone suggest how to decide the model order (or size) while curve fitting in modal analysis? As the curve fitting model order is increased, number of stable poles are increasing. But as some of these are computational modes, I want to know if there are any thumb rules or guidelines in selecting model order for a given type of structure - say lightly damped, heavily damped, etc. What is the minimum order one usually starts with ?

Thank you.

Kind regards
Geoff

 

[GregLocock]

Depends on the software you are using and the fitting method.

A typical approach 20 years ago would have been to calculate the mode indicator function, and use roughly twice the number of modes it suggested.

LMS has a nice plot of modal frequencies vs number of modes which is handy.

Way back when I would page through every response, identify the frequency of every peak, and use that table.





Cheers

Greg Locock


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[GMarsh]

Hi Greg,

I am using LMS only. Can you please be a bit more descriptive about the twice the number of modes concept?

I am attaching here a file with two stabilisation diagrams with 3 zones marked. As you can see in zone 1 it shows stable mode (from lower order of modes) though there is no visible droop in mode indicator function curves (top two curves). So should I select it or not?

And in zone 2 mode gets stabilised only after model size of 72.

In zone 3, even though there is a clear peak, the mode gets stabilised only after 80 modes.

This makes me think if there is an optimum or rule of thumb on number of modes (model size in curve fitting) which we should restrict ourselves.

Thank you.

Geoff

 

[GregLocock]

I'd say you are going for far too many frequencies in those plots. The high frequency one is so messy that it is just chucking in local modes to account for every blip (I haven't the faintest how LMS does all this by the way).

can you do a plot of the whole frequency range, and 0-50 modes, and MI2 and MI3 (imganariness and gross amplitude respectively) all overlaid.

Cheers

Greg Locock


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[GMarsh]

Hi Greg,

Thank you. I think I didn't understand exactly what you asked for. However I am attaching a picture with frequency range up to 6000Hz and model size 50 modes. And Imaginary MIFs overlaid. And bottom curve is the amplitude of one of the drive point FRF. Please note that I acquired FRFs up to 16kHz to find certain very high frequency modes of interest. But at the moment I am concentrating only up to 6 kHz.

Is this what you asked ? If not, please tell me what you meant.

As you can see, with model size 50 only a few are picked as stable modes though visible you can see many peaks in FRF.

Kind regards
Geoff

 

[GregLocock]

Yes that plot was what I wanted. It is rather messy. I'd try extracting 90 and 120 modes for that set of data and comparing the resynthesised FRFs.



Cheers

Greg Locock


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[GMarsh]

Hi Greg,

Thank you for this. Any hint how you estimated that 90-120 ?

Kind regards
Geoff

 

[amanuensis]

Hello,
It's not very clear what is the benefit to use an algorithm to detect the modes, because you see them!
Why don't you use a pick peak method to find the modal parameters, then as Greg said, you can tune this parameters by matching the experimental curve with the resynthetised one.

I use two very powerful Excel files to do this :
Pick peak method
Fitting method

You can try them if you want, they are free.

Regards
Amanuensis

 

[GMarsh]

Amanuensis,

As I understand, peak picking is a SDOF (Single Degree of Freedom) method. You can do that if you have few response curves with few modes and that to widely separated. In addition, you will not be able to capture all modes of a structure in every FRF. Reasons are many - the accelerometer might be situated at a nodal point for a particular mode, participation factor may be very weak for some modes, etc.

MDOF (Multi DOF) methods are powerful in the sense that they fit many FRFs at a time. Even with MDOF methods, you need assistance of tools such as MIF (Mode Indicator Function) to be certainly able to tell if there is a genuine mode or it is a computational mode. Or repeated roots (symmetric modes), etc.

Peak picking is ok for initial checks during running the test for having a quick look at the mode shapes which makes you ascertain if your set up is right or not like your accelerometer direction is ok,etc.

Geoff

 

[amanuensis]

Thanks Geoff for this answer. I'm quite impressed by your knowledge in modal analysis.
Actually, till today, I had never heard about the MIF. Yet, it seems necessary to know linear algebra to understand the meaning of this indicator...

 

[GregLocock]

I agree that 50 isn't enough so I doubled it!

How many points are in your survey? It might be worth putting together a subset of the interesting and important ones, and just using those to identify frequencies.

Cheers

Greg Locock


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[GMarsh]

Hi Greg, Thank you.

There are total 144 points! How to identify subset of important ones ?

For e.g. please find attached picture of casing which you might have seen earlier in two previous posts. Now looking at the picture, which points do you want me to create subset? I want to capture axially 2nd order modes and circumferentially up to 16th order modes (due to some interest in frequency). That is circumferential profile with 16 petals. On safer side I made it 18. Hence total 36 points. So highest frequency worst case would be like \/\/\/ shape along the circumference with one point at each extreme.

Kind regards
Geoff

 

[GregLocock]

I don't know if I've said this before but chasing modes on very symmetrical structures such as thin walled tubes is always going to be tricky.

In this case I'd just take 10 points randomly scattered over the body, prepare modal indicator functions from them, and then choose another 10 and repeat.

If they throw up common frequencies, great, if not then you just have to start overlaying each response and seeing what is going on (which is the best way anyway)

The way I'd prefer to examine the high frequency modes of that thing is with a remote sensing technique such as laser doppler, and a sine sweep.


Cheers

Greg Locock


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[amanuensis]

The modes depend on the boundary conditions. What is the interest to seek precisely the modes under these circumstances? At high frequencies, are you certain not measuring the modes of the mounting?
In my opinion, a test with the structure with free-free boundary conditions would be more appropriaite. Indeed,the structure is so simple that it's easy to calculate its modes by finite elements method. Then you can compare the both.

 

[GregLocock]

Well, testing with the realistic bcs gives you the best shot at getting damping, which your FEA won't.



Cheers

Greg Locock


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[amanuensis]

Correct. But the material seems to be steel or aluminum. So it can be supposed that damping is around 0.01. The error on this value should not be too important.
I'm french, so please forgive the English mistakes I can make.

 

[amanuensis]

Otherwise, the Greg's method for finding out the resonance frequencies is very interesting! This approach reminds me genetic algorithm. Do you use this kind of algorithm along with modal indicator functions?

 

[GregLocock]

I haven't tried GA on modal fitting, that's an interesting idea.

To be honest I haven't run a large scale modal in 9 years or more, so I'm certainly not up on current techniques.

Cheers

Greg Locock


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[GMarsh]

Hi Greg, amanuensis,

Thank you for your inputs. I did FE modelling as well simulating the boundary condition with some approximation which would affect damping mostly like bolted joints replaced by rigid node connections. But the thing is FE predicts 106 modes within the frequency range of interest and I am curve fitting clear stable modes more than 400 within the same range. I am really wondering where from these many modes are coming, all seems to be genuinely stable.

I don't know that GA on MIFs as well. I will look at it sometime. Sounds interesting.

Kind regards
Geoff

 

[GregLocock]

OK, can you plot the modal density vs frequency (ie number of modes per bandwidth), for the FEA and the real system.

I notice you haven't mentioned much what is happening below 800 hz, if you don't get good correlation at low frequencies then it is unlikely you'll get good correlation at high frequency.



Cheers

Greg Locock


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