From acceleration to FFT and to displacement - how to?

[RPJ]

Hello!

I am acquiring acceleration from two sensors. It is relatively easy to apply the FFT (using an advanced vi) and see it in a chart. However, I am not sure what should I do to see the displacement or, better said, how should I integrate (two times) to get the displacement?
There are two things I would like to do:
1) Take the original acceleration signal and integrate it two times to get the displacement; then apply the FFT to this displacement.
2) Take the original acceleration, apply the FFT, and then integrate two times (the FFT output); compare the result with the displacement FFT obtained at point 1.

From some previous discussions I understood that the problem with integration is that apparently it introduces some kind of offset and I will have to get rid of it.
Unfortunately I am not very familiar with vibrations and this adds up to my LabView burden...

Does anybody have some example or suggestions?

RPJ.

[Ronman]

---

@RPJ wrote:
Hello!

I am acquiring acceleration from two sensors. It is relatively easy to apply the FFT (using an advanced vi) and see it in a chart. However, I am not sure what should I do to see the displacement or, better said, how should I integrate (two times) to get the displacement?
There are two things I would like to do:
1) Take the original acceleration signal and integrate it two times to get the displacement; then apply the FFT to this displacement.
2) Take the original acceleration, apply the FFT, and then integrate two times (the FFT output); compare the result with the displacement FFT obtained at point 1.

From some previous discussions I understood that the problem with integration is that apparently it introduces some kind of offset and I will have to get rid of it.
Unfortunately I am not very familiar with vibrations and this adds up to my LabView burden...

Does anybody have some example or suggestions?

RPJ.

---

I have built a vi that does single integration (from acceleration to velocity) I plan to continue with a second integration to displacement.

First, I took the time signal and performed a highpass filter (5hz high pass). This is to remove the integration ramp down near 0.

Then, I integrated the signal. Finally, since the accel signal is g's and velocity (for us Americans) is in inches/second, I inserted a math block and multiplied the array by 384 (the number of inches in 32 feet).

Works great!

[ElSmitho]

http://zone.ni.com/devzone/conceptd.nsf/webmain/BFC420D779576B0A06256A03000B2C63#1

Applicable picture caption "Some LabVIEW code that converts an acceleration signal to velocity and then to displacement appears below."


This website will also offer a sidebar with information on signal processing etc... I think you'll find it rather useful, or so I hope.
They've even got an example that comes from an older version of LabView.

Best of wishes, and remember, vibration is your friend.

Sincerely,
ElSmitho

[RPJ]

Thank you ElSmitho.

I looked at that example before but I did not understand how it works (each step, and why).
I am trying to find out something easier to digest...

RPJ

[RPJ]

Ronman:

Your solution sounds good. Are you confident it is?
Could you actually show what you just explained?
I do not understand what you are trying to say with "This is to remove the integration ramp down near 0."

Thanks.

[ElSmitho]

Salutations,

First of all, when performing an FFT you take something from the Time Domain into the Frequency Domain. Which, by all means isn't a problem. However, associated with any signal there is some DC amount, which is why you normally have a filter to help remove this. The integration issue will cause a shift, due to this value (i believe...)

As far as integration goes, you're sampling something so you can generate a table of information. Look into common integration techniques, such as Simpson's 1/3'd rule or the Trapezoidal Rule.

Either of those should be able to resolve your issue for integration. They also have associated error's with them, which there is a formula for that as well. Please excuse me, i don't remember all those formulae.

Once you do the double integral, you should be able to FFT whatever you want.

If this isn't getting anywhere near to helping you, inform me and maybe i'll be quiet 😉

Sincerely,
E. Smith

[Ron@ld]

"RPJ" <x@no.email> schreef in bericht news:200672@exchange.ni.com...
> Hello!<br><br>I am acquiring acceleration from two sensors. It is
relatively easy to apply the FFT (using an advanced vi) and see it in a
chart. However, I am not sure what should I do to see the displacement or,
better said, how should I integrate (two times) to get the
displacement?<br>There are two things I would like to do:<br>1) Take the
original acceleration signal and integrate it two times to get the
displacement; then apply the FFT to this displacement.<br>2) Take the
original acceleration, apply the FFT, and then integrate two times (the FFT
output); compare the result with the displacement FFT obtained at point
1.<br><br>From some previous discussions I understood that the problem with
integration is that apparently it introduces some kind of offset and I will
have to get rid of it.<br>Unfortunately I am not very familiar with
vibrations and this adds up to my LabView burden...<br><br>Does anybody have
some example or suggestions?<br><br>RPJ.

RPJ.

I did a lot of vibration measurements using a DC-accelerometer (this is used
e.q. in elevators etc.)
Think of:
1. Aliasing (can cause serious problems, so understand why to do filtering
front end)
2. Removing DC before integrating
3. Removing DC before integrating again!!

Then do the FFT's

I can see the true displacement when using this technique!

Ron@ld

[RPJ]

OK - what is a DC-accelerometer (do you have a good link)?
Does this have to do with Removing DC before integrating and Removing DC before integrating again? DC is direct current? I suppose not... I have ICP accelerometers - do I still have to do a DC removal before integration?
Do you have an example or you are referring to the same example from NI site previously recommended?

Thank you for your time and explanations.

Radu

[Ron@ld]

Good link might be found at Monitran.

DC accelerometer is actually going down to zero. Normally a accelerometer in
combination with some kind of instrument uses a high-pass filter and works
from app. 10 [Hz].
The DC one goes down to 0 [Hz] (which is actually stand still....)

I would remove DC component yes.

Kind regards

Ron@ld



"RPJ" <x@no.email> schreef in bericht news:203477@exchange.ni.com...
> OK - what is a DC-accelerometer (do you have a good link)?<br>Does this
have to do with Removing DC before integrating and Removing DC before
integrating again? DC is direct current? I suppose not... I have ICP
accelerometers - do I still have to do a DC removal before
integration?<br>Do you have an example or you are referring to the same
example from NI site previously recommended?<br><br>Thank you for your time
and explanations.<br><br>Radu

[rwbrook@integratedps.com]

You talk about removing the DC component, but don't elaborate on how you accomplish this.
Ron