Low frequency (1hz) displacement from acceleration

[StephenArcher]

I'm new to vibration analysis and I'm interested in measuring the dynamics of a rail vehicle.
I'm proposing to use a fibre optic gyroscope to measure roll acceleration (of approx 1 hz), but I need to be able to calculate roll displacement. I understand the usual method is to integrate acceleration using fft, however the time resolution of the fft will be poor because of the large window needed for low frequencies. This will cause problems as the roll acceleration may change significantly over the fft window.

Can anyone suggest other methods to do this kind of analysis. I'm looking into Charge Amplifiers with built in integrators such as the Bruel & Kjaer 2635.

Any help is appreciated.

 

[GregLocock]

The 2635 is a wonderful charge amp but its real time integration feature is not trustworthy in all circumstances, and since you will be doing a double integration at very low frequency I think you'll be lucky to get good results. If you can get hold of the manual it explains the problem in some detail.

Double integration is incredibly error prone anyway - can't you get an inclinometer?


Cheers

Greg Locock

 

[MikeyP]

A note about the fft issue you raised:

The resolution will not be poor at low frequencies if you use a low sampling frequency.

delta_f = 1/(N*delta_t)

where delta_f is the frequency resolution in Hz, N is the number of sample points in the window, and delta_t is the sampling interval (1/sample frequency).

A sampling frequency of 10 Hz and window length of 512 points will give you a frequency resolution of about 50 spectral lines per Hz.

M

 

[StephenArcher]

Looking at the data sheets for the Bruel & Kjaer 2635 it seems that as you say, it wouldn't be adequate. The displacement gain has already rolled off significantly at 1 hz.

I should explain that I've also been asked to measure lateral movement (~2 Hz) and vertical bounce (~1 hz) of the wagon and the most difficult part of the problem is that it has to be quick to set up on a wagon because the experiment has to be repeated around 40 times. This rules out using displacement pots as they take too long to set up.
So it looks as though I'll have to use accelerometers and find a way to accurately calculate displacement.

Can anyone shed any light on integration in the time domain? I assume it is necessary to keeping setting boundary conditions to account for drift and errors. Is it possible to high pass filter an acceleration signal to remove drift and then integrate with a quadrature function or are there other problems associated with this method?

 

[NicolasJobert]

Stephen

as Greg said, double integration is hardly an option. I have tried it myself a few times (also with a BK 2635 charge amp vs non contact optical devices) and the results kept being very poor, although I used many analog/signal processing tricks in order to improve the whole process.

If you are stuck with your accelerometer measurements, I suggest that you :
- do not use 2635 charge amp, because of the distortion below 1 Hz (or 0.2 Hz), and because of the low frequency noise content (1/f spectral density). Use rather 'absolute' accelerometers (induction), the ones that see +/-1g when you hold them head up / head down....
- in any case, use mechanical filters to protect your accelerometers from the high frequency content of the vibrations in which you are NOT interested. Those high frequency are highly likely to contaminate your measurements. Also use analog low pass analog filters, if you can.
- once this is done, use time domain integration instead of frequency domain integration. If you can, use forward backward numerical low pass filters (see the filtfilt function in MATLAB).

Good luck

Nicolas

 

[StephenArcher]

Thanks Nicolas, your info is helpful.

I'll have a look into those methods.