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# How to derive displacements from measured accelerations

Valued Contributor

Hello,

currently I try to calculate deflections from measured accelerations. Ideally a simple double integration should get me there. However as I understand because of measurement errors etc. some preconditioning of the data needs to be done. Now I am trying to figure out what would be an appropriate way. I'm using the "Time Signal Calculator" in "Time Data Selection".

So far I have established:

- DOUBLEINTEGRATE does basically what I want. However there seem to be some caveats.

- Frequencies above 1/4 of the sample frequency should not be used to avoid over- or under-estimation. Use the RESAMPLING function to double the sample frequency for example. -> Maybe I can apply a low-pass filter to cut off any amplitudes above the 1/4th threshold of the sample frequency

- DC and very low frequencies should have been removed, as they would otherwise cause drifts. Use the DETREND_AC function to remove trenfs of up to degree 6 for example. -> Maybe I can apply a high-pass filter to cut off all frequencies below the interested frequency range. What is the difference between a high-pass filter and the detrend_ac function?

Given that the acceleration data has a sample frequency of 6000 Hz (hence 1/4th being 1500 Hz) and is stored in CH1, does the following formula yield good results?

`DOUBLEINTEGRATE(FILTER_LP(FILTER_HP(CH1;5;2;IIR(2;10));1500;2;IIR(1));1)`

The lower cut-off frequency of 5 Hz I selected arbitriarily. What would be a good criteria for that? I know that my acceleration sensor anyway doesn't work below 1 Hz or so.

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# Re: How to derive displacements from measured accelerations

Siemens Phenom

hello,

Rather than recreate the answer here, have you searched the FAQ's installed with Simcenter Testlab rev 17 or 18 or searched through them on the GTAC Solution Center?

If so, you will find FAQ 630 which is "How to 'correctly' integrate time data within Time Domain Integration?"

Here is the link to the one on the support site:  https://solutions.industrysoftware.automation.siemens.com/view.php?sort=desc&q=INTEGRATE&dt=faq&pd=l...

I normally use something like this:   Detrend, upsample by 4, integrate or double integrate, resample back down and then a HP filter.  I usually HP filter between 1-2.5 Hz.  5 Hz would be OK if you don't care about the motion below 5 Hz.

Example if my original signal was Fs=2048 Hz:

FILTER_HP(RESAMPLING(DOUBLEINTEGRATE(RESAMPLING(DETREND_AC(CH1;2);8192;80;0.01;50;15);2);2048;80;0.01;50;15);2.5;2;IIR(1))

If you replace  CH1 with CHx and then use Repeat for to list the channel numbers (1:10 for example), you can do allyour channels at once.

# Re: How to derive displacements from measured accelerations

Valued Contributor
Hello Kevin_Grenier,

thank you very much, for you fast and super helpful answer. I had looked a bit in the documentation, but obviously not good enough.
Thanks also for the trick with the CHx repeat for. Just for others as I was searching a bit: There is a "Repeat for..." Column where you can specify the channels of interest.

# Re: How to derive displacements from measured accelerations

Valued Contributor

With using resample I get an error in "Time Data Processing" stating that there are different sampling frequencies within the same channel group. But that is actually not true. I specified resampling that way that the frequencies should match the ones I used with the other channels.

Am I doing something wrong, or is this a bug in the software? I am using Simcenter Testlab Version 18.2

That is the Formula I used to generate the last channel:

FILTER_HP(RESAMPLING(DOUBLEINTEGRATE(RESAMPLING(DETREND_AC(CH3;2);24000;80;0.01;50;15);2);6000;80;0.01;50;15);2.5;2;IIR(1))

# Re: How to derive displacements from measured accelerations

Siemens Phenom

If you press OK, you can then look at the new runs to identify which channel is throwing the error and then investigate.

Or reach out to your local support team and they can Skype with you to take a look.

# Re: How to derive displacements from measured accelerations

Valued Contributor

I checked already all channels and all Acoustic Channels have Fs=48000Hz, all Vibration Channels have Fs=6000Hz and all Tacho Channels have Fs=6000Hz. So it should be fine. However I still get that error. If I click "OK" and ignore it, calculating something in "Time Data Processing" will result in a severe error:

I thought maybe there are happening rounding errors with the sample frequency so that it doesn't fit 100% of what it was.

I'll try to connect with my local support team.

# Re: How to derive displacements from measured accelerations

Siemens Phenom

You could always move the results of your formula to the Other group and see if that works.  If not, the support group can assist.