Correlation of measurements in the frequency domain
Correlation of measurements in the frequency domain
(OP)
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?
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?





RE: Correlation of measurements in the frequency domain
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Correlation of measurements in the frequency domain
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
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Correlation of measurements in the frequency domain
Thanks again for your help.
RE: Correlation of measurements in the frequency domain
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
RE: Correlation of measurements in the frequency domain
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?