We are doing some research on the best applications and uses of and for Exponential Averaging. We have not found many good useful technical papers or application notes on Exponential Averaging. We have also found that various vibration analyzers set up Exponential Averaging in different ways causing differing results.

Does anyone know at least one good reference on this topic? We hope these papers will explain how Exponential Averaging works and give examples on how and when it should best be used. We would appreciate your sharing this information with us.

Thank you,
Jim Berry
Technical Associates of Charlotte, PC

Jim,

I guess one has to have a little gray hair to have used this signal analysis function! Try this reference:
"Mechanical Vibration and Shock Measurements" by Jens Trampe Broch published by Bruel & Kjaer April 1984 ISBN 87 87355 36

Its primary application is for non-stationary signals. I have used it for sound measurements and high frequency vibration measurements.

Walt

Mathematically it is well-explained by google search. An exponential-weighted average uses an exponential weighting function so that the most recent values are weighted highest. In contrast a "normal" average or rolling average or "linear average" uses a square-wave weighting function with constant weighting of past values within the window. I see on google a lot of mention of this technique related to stock market stuff.

So we can either average several values of spectra equally (linear) or give higher weight to most recent spectra (exponential).

Walt mentioned that it is useful in non-stationary systems. As far as I recall that means that the frequency content of the signal changes their behavior over time? I guess it makes some sense that in that case you want to pay most attention to the most recent values...I think?

Attached is an excerpt from Mobley's book a reference which supports Walt's statement. After that I will post a few more vibration textbook excerpts in additional posts that mention exponential averaging (I only get one attachment per post).

I think the first two excerpts are talking about exponential averaging in the context of spectrum averaging, which is what I assume the original question was about.

The last two excerpts talk about smoothing/averaging of a time signal. It's a very similar mathematical process which might perhaps be applied to smooth a "live" overall value, but I don't think that's what the original post was talking about.

This message has been edited. Last edited by: electricpete,

MobleyExcerpt.pdf (24 Kb, 30 downloads)

Excerpt from Applied Structural and Mechanical Vibrations

AppliedStructuralAndMechanicalVibrationsExcerpt.pdf (32 Kb, 25 downloads)

Excerpt from Harris' Shock and Vib Handbook Chapter 13

Harris13.pdf (50 Kb, 21 downloads)

Excerpt from Harris' Shock and Vib Handbook chapter 14.

Harris14.pdf (67 Kb, 20 downloads)

One can also view this type of 'average' as a low pass filter, generally calculated recursively. See http://www.prosig.com/signal-processing/DataSmoothing.html

I am trying to copy an exerpt from the Harris re Pete gave but????? Regarding time: stated was (if I got it right) Exp shorter than Lin??? Performing lin avg on machines for maximum repeatability would be 32 avgs (16 = 90+%) for accuracy.?.! However using exp avg on a signal clock or tach for trigger (pre-window or internal trig) a minimum of 128 avgs should be used but 256 or 512 being more desired? And as stated in the first attachment; contineous, stopping at the end of a run.

Anyone have a take or have I lost my mind? That is in contrast to what was in the Harris paragraph or so I took it??????????

Walt,
Thank you for your insight on Exponential Averaging you have shared. This has added to my understanding. I also was around in the 1980’s actively involved with Vibration Analysis.

Electricpete, Thank you for taking the time and effort to locate and send so many good papers on Exponential Averaging. I have gone through these and they have added to my understanding. This helps explain the behavior of several analyzers with which we are applying this averaging technique. We had previously done several Google searches ourselves but had not turned up all the papers you sent. I very much appreciate your valued assistance.
Regards, Jim Berry

Jim - Glad that I could help. I'm a big fan of your training materials. You should stop by here to chat more often.

Sam - I didn't understand those tables discussing number of averages either.

Hi Jim,
Haven't used exponential averaging more than a couple times in 34 years, but do understand it's function. I believe that it falls into the same category as all of the available windows. Someone needed one for a very specific need and created it, for example when was the last time you needed the Blackman-Harris window? You know as well as anyone the trade offs all involve amplitude accuracy vs. frequency accuracy. I have concentrated in mechanical vibration, so unlike the response that referenced sound measurements, the exponential averager doesn't fit my needs. On another subject, I have given up on my own people spreading the word on how to eliminate EDM from VFD's and I am hoping you can spread the word. Drop me a line.
Ron Brook