Calculating absolute DISplacement from measured ACCelereation?

[golubovski]

Hello,

I get accurate VEL and DIS from measured ACC taken off vibrations. I need to know if accurate DIS movement in one direction can be calculated from measured ACC. I get different results when experimenting and I expect that the LowStop filtering before the integration kills somehow important info in the DC-to-LowCutOff part of the spectrum.

I ask this because to use DIS sensors (LVDT, LP, ...) is impossible since they all need to be "anchored" to be able to sense the relative displacement, and the use of DIS sensors is therefore impossible for my application.

So basically I need to know if accurate incidental DIS can be calculated with the use of IEPE ACC (not a DC capable MEMS).

Thanks in advance,

[DFGray]

Short answer - no.  Acceleration is the second derivative of displacement.  Every time you take a derivative, you leave a constant behind (derivative of a constant is zero).  So when you reverse the process and take a double integral of an acceleration, you have to deal with two constants.  If you have two boundary conditions (e.g. starting velocity was v₀, starting postion was x₀), then you can calculate what these two constants are.  However, with just the acceleration data, you cannot.

[golubovski]

Hello DFGray,

Thanks for the prompt response! Yes, starting conditions are always NULL - movement begins suddenly from steady state (V0=X0=0). Can I calculate the DIS and how Low-CutOff limit of the DSA (NI-9234 is 0.5Hz) reflects on the calculation? If IEPE (AC coupled) ACC is a problem, would a MEMS (DC) ACC do the job?

R

[DFGray]

The frequency filtering will effect your final result, but how much depends upon how your acceleration changes with time.  If you have significant components below 0.5Hz, you will want to DC couple your 9234 and use a DC coupled accelerometer.  Be very careful, however.  This sort of measurement is very easy to get wrong, since a small offset in your sensor signal could result in a large change in displacement if you run your calculation for very long.  Your results will also vary depending on the length of time you run the data (offset translates into an error which increases linearly with time).  You may want to take some data before your actual data run to empirically determine your offset on a per run basis.

If you have both sensors available, it would be worth doing a quick run with both and running a power spectrum on the resultant signal to determine how much of your signal lies below 0.5Hz.  You will need several seconds worth of data to do a good estimation.  If you can't do several seconds worth of data, you may not have an issue since it will only show up with longer integrations.