Integrating accleration signal

[suviuuno]

Hi,

We are testing effect of accumulator in rock drill concept. We have mounted two tri-accelerometers in hydraulic hoses that feed the drill to capture the difference in acceleration/frequency, if any.
To my surprise, results were fairly same.

Now, I would be interested in position difference. Integrating signal directly gives garbage. I have tried spline interpolation with still garbage results. Signal appears to shoot way off the course. I do not have much experience in signal processing.

I have 5sec sample with 5kHz. Does someone have insight into this?

Thanks,

suviuuno

 

[SomptingGuy]

You need to low-pass filter your signal below anything of any interest. Even then the phase response of your filter may scupper you. I've seen this sort of (apparently good) idea end in tears many times before.

 

[GregLocock]

double integration in the time domain is rarely succesful, in my experience. Even singe integration raises more problems than it solves, often. When we are interested in acceleration and displacement, we measure acceleration and displacement.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[SomptingGuy]

Sorry. I meant high-pass. But my other comments still hold and I agree with Greg - use a displacement transducer if that's what you really want.

 

[suviuuno]

Thanks for helpful information SomptingGuy and Greg. I will set up a small experiment, where I will measure displacement as well just to see the difference.
I filtered signal and got what might be in the right area. Quite hard to say, I think. I'll keep you posted.

 

[Rob45]

I have heard, from an application engineer at Head Acoustics, that you should obtain at least 100 cycles of your lowest frequency of interest. That would suggest that 20 Hz is the lowest frequency your 5-sec sample could tell you anything meaningful about.
But why not just try manually calculating the displacement at a couple of points, based on your acceleration data, and compare that to your integration results?

I've done double-integration on acceleration data a number of times using Head Acoustics' Artemis software, and have always had good agreement with calculated results for individual frequencies, and have only gotten "nonsense" results for very low frequencies.

Regards,
- R

 

[dolsoi]

It is not possible to obtain a DC displacement (at 0Hz) from an accerlation measurement, but AC displacement. (suppose that an apple drops at the accerlation of gravity, where is the position now?) In the frequency domain, it can be rather easily done by dividing the accerlation by -w^2, where w is the angular frequency. There are some commercial signal conditioner that have integrators inside, for example, Nexus (a B&K subcidiary). What it does for a single integration is, as someone said above, (a pure integrator) times (a second order high pass filter of cutoff frequency of either 0.1 Hz or 1 Hz and damping rator of about 0.7). A double integration can be done in a similar way. Hope this textbook style information helps.
Cheers, dolsoi

 

[GregLocock]

...and if you try to do it in the conditioning amp, read the manual carefully. The B&K 2635 charge amps, for example, claimed to be able to integrate accelerometers, but only within strict limits.


Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MikeyP]

You can do this with a reasonable amount of success in the frequency domain provided you carry out your measurement carefully.

To avoid leakage problems in the freq domain integration, you have to have a signal that begins and ends at zero. The usual approach is to apply a window (e.g. flat-top for a long data record like yours) but windowing is a non-linear process and would screw up your results big-style. The trick is to ensure that your measurement does not require windowing.

Start the da6a acquisition with the drill at rest. Start up the drill. Run it for your 5 seconds. Turn it off. Give it some time for all the vibrations to die away. Then stop the acquisition.

You can then easily fft and integrate and hp filter in the frequency domain without any phase issues and transform back to the time domain.

I have done this, even when the dominant frequency of interest was as low as 10 Hz.

M

--
Dr Michael F Platten

 

[electricpete]

I have done this a few times in excel.

One rule I have is to apply the high-pass filter as mentioned by Sompting guy (to remove dc component) at each stage. Before the first integration, after the first integration, and after the second integration. There should be no dc in acceleration, velocity or displacement of a stationary vibrating component anyway, so you're not losing any info. With reasonably high sample rate in relation to sampled signal and the understanding that the low freq components have been removed, I believe you can expect good result.s

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[electricpete]

my discussion applies purely to integration in the time domain. I didn't see any mention of frequency domain or FFT in the original post. But of course integration in the frequency magnitude domain is fairly trivial.

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[SomptingGuy]

electricpete,

How do you high pass filter in Excel?

 

[electricpete]

Lots of ways. Low pass filters are easier than high but you can often use a low-pass filter to build a high pass filter.

What's the simplest low-pass filter? Moving average. The more points you include in the average, the lower the cutoff.

How to turn into a high-pass filter? Just subtract the moving average from the point. The formula for B101 might be +A101 - sum(A2:A200)/199.

Copy to B102 as +A102 - sum(A3:A201)/199
etc

You end up with the output of the filter having 100 less points on the beginning and the end than the input of the filter... not a big problem if you have a lot of data.

That's just a start. Of course digital diltering is a well-studied field. You can define your filter parameters and determine required FIR filter coefficients using Matlab (and then implement the filter in excel).

Of course google is your friend. Here is a spreadsheet already built:

http://www.univie.ac.at/cga/tools/http://www.univie.ac.at/cga/tools/

Also check out dspguide.com or google for "numerical recipes"

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[SomptingGuy]

Digital filtering is nothing new to me. I'm just amazed that people bother doing it in Excel. Then again when all you have is a hammer, everything starts to look like a nail.

 

[SomptingGuy]

Sorry, last post sounded somewhat snotty. Thank you for the links (I already have dspguide bookmarked and my NR is getting really shabby these days). However, I still HATE Excel.

 

[electricpete]

You ask a question: "How do you high pass filter in Excel?"

I answered it.

Then you tell me that digital filtering is nothing new to you. Jeesh.

Next time you want to make an editorial comment, please have the courtesy not to pose it in the form of a question so people won't waste time answering it.

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[suviuuno]

All,

Thanks for helpful comments. I am getting reasonable results now, however, I have not verified it by displacement transducer yet.
Thanks again.

suviuuno