Dear Ahmed,

You should clearly distinguish the several issues of your process:

- using a log scale (dB) instead of a linear scale is possible for any quantity - however sound is the only domain where the 0dB reference is unanimous (2E-5Pa). For acceleration, there is no international referential, you must choose it and announce it in the scale (e.g.dB ref 1E-6m*s-2). You can apply this dB scale to any quantity (instant acceleration/time, rms average, FFT spectral density etc etc)

- averaging and filtering a dynamic datum (here acceleration) which must be done in linear scales - dBs cannot be averaged

- converting time-domain data into frequency-domain data in lin or log frequency scales (FFT, third octave...) - you can do this also in data log scales but to keep your dB reference right you must apply the relevant normalization (spectral density...)

From what you describes your data processing seems fine (assuming the original phenomenon is periodic, or better say ergodic, linear and stationary ! Otherwise FFT or any sort of filtering or averaging are illegitimate...)

Dear Bernard Garnier ,

Thank you so much for your valuable suggestions.

Dear Jean Carlos Poletto ,

Thanks a lot for your answer.

I would like to be clear about the method you have mentioned in no.1. Is this direct method suitable for random response like shown in attached figure? Also, if you say something about the calculation procedure, it would be great.

Thank you.

Dear Ahmed,

The first proposal of JC is absolutely valid for all types of signal. The RMS averaging is just what "root mean square" says: average the squared value of each acceleration data over time, then take the square root of the result: it relates to the signal energy density.

Conversely at a glance your signal might not be "random", as it suggests some periodicity at various scales: a global intensity fluctuation every 1.3s ? High frequency oscillations in each burst? Look at it trough different time scales (much longer/much shorter time spans)!

Dear Bernard Garnier ,

Thank you for your concern. I have got your point.

I have determined corresponding vibration value of the referred time domain signal using both methods ( that I followed at the very first and which one is mentioned by Jean Carlos Poletto ). Two methods yield vibration value with difference of 1 to 2 dB. It would be appreciated if you let me know which method seems more appropriate to you.

I am mainly concerned with obtaining RMS value of the time signal to use this value in following formulae. Not much concerned with it's frequency content.

Vibration(dB)= 20*log(a_rms/1E10^-6).

Thank you.