Correlation of measurements in the frequency domain

[BatmobilePilot]

I've got a few data sets with about 10 measurements each, and in some of the data sets one or two parameters went bad. Of course it was expensive to gather this data (helicopter flight testing) so going back and re-doing the test is not an option. Typical. So I'd like to replace the bad data with generated data, based on relationships derived when all parameters were healthy.

I can plainly see in the data that there are some consistent correlations between all parameters in the frequency domain, but often with a non-zero phase relationship, so a multiple-input linear regression method in the time domain using Minitab software or similar is out. Is there an analogous multiple-input frequency domain method I could use to get what I'm after? I'm familiar with FRF or Crosspower methods to calculate transmissibility, but those are single-input single output as far as I know. Anybody have any ideas for how I should tackle this problem?

 

[GregLocock]

Check out partial coherence methods. This is the basis of multiple input multi output (MIMO) modal analysis, which sounds like a similar problem.



Cheers

Greg Locock


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[GregLocock]

I've had a rethink. Helicopter vibration is largely periodic and phase locked, hence a partial coherence method, while useful as understanding, won't actually work.

So, we have to build a model. This needs to be broadcast loud and clear to the eventual users of the data, you are no longer wearing a white tunic, you have gone to the Dark side and need to wear a bucket on your head.

The model is pretty straightforward, if rather large

response for channel a for test 1 is R1a+i.I1a

real part of the transfer function between channels a and b is RTFab, and RTFab=RTFba, for all tests. That is we are assuming reciprocity and linearity.

Similarly ITFab=ITFba

So for a given frequency bin, for the real part only, for channel a for test 1

R1a=(RTFab.R1b+RTfac.R1c+....+RTFaz.R1z)+RN1a-(ITFab.I1b+ITFac.I1c+....+ITFaz.I1z)

and for channel b and test 2

R2b=(RTFab.R2a+RTfbc.R2c+....+RTFbz.R2z)+RN2b-(ITFab.I2a+ITFbc.I2c+....+ITFbz.I2z)

and so on for the other 24 channels in this case and however many tests

Similarly for the imaginary part

RN is the real part of the noise, which is unique for each channel and test.

Then sum the squares of the noises, and use that as the error in whatever optimising routine comes to hand, the objective being to reduce sigma N^2 to zero.

Then repeat all that for the imaginary part.

Then repeat all that for all the frequencies of interest.

If that sounds too hard then companies that can do it for you include Vipac in Australia, Prosig in the UK, LMS in Belgium and doubtless many others.

It is likely that it will cost you more than retesting the helicopter, in my directly relevant experience, especially as the number of unknowns (ie bad channels per event) rises.





Cheers

Greg Locock


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[BatmobilePilot]

Thanks Greg. You would crap your pants at our cost per flight hour. Definitely cheaper to pay someone to work on this for months than to re-fly. We actually already have a contract with LMS (FYI they just recently switched from waffles to sausage having been taken over by Siemens). They've been very helpful to me in the past so I'll check with them to see if they have an off-the-shelf solution before I dive in with matlab. I would love to come up with an easy to use method since this situation comes up all the time.

Thanks again for your help.

 

[SomptingGuy]

You may want to do some

http://WWW (or

DSP sources) research with the term "virtual coherence". This is essentially an attempt to dig out the truly incoherent sources from a set of highly coherent/correlated measured signals. I recall people like LMS were publishing articles about this in the 90s. I think LMS were even selling it as an optional extra for their previous generation NVH kit (CADA-X Fourier Monitor).

My recollection was that when the measurements are vibration signals on a running vehicle, you normally ended up with one huge source and a few minor ones. The huge one being the engine. All very interesting though. Was based heavily on principal component analysis. Quite easy to implement/experiment in Matlab, given the basic maths and an appreciation of matrix algebra.

- Steve

 

[GregLocock]

Sounds like LMS is the way to go. I was sort of keen to automate it a bit, but the unknowns are scattered throughout the matrix, depending on which channels were working at the time. It'd be interesting to see what LMS come up with, I have been out of NVH (and hence LMS) for 12 years now, and never really got into the crunching side of CADA X.



Cheers

Greg Locock


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