Claudio is right...

If hopefully you have acquired the PSD of the acceleration, then by integrating over the whole frequency range you get the square of the acceleration module (the phase is lost) assuming all units and calibrations are right, the FFT frequency window, sampling duration and anti-aliasing filters setting is appropriate, and the signal is stationary during the whole acquisition window. (that's quite a number of assumptions on your capability to use professionally a FFT analyser...)

If you miss this signal processing background knowledge, you better go back to a vibration analysis expert to guide you!

You need to make a time domain simulation. Yes, Mr. Padrazzi is right; if your psd is that of horisontal ground acceleration, it will have the unit (m/s^2)^2/(1/s). You will find routines for time domain simulations from spectra in E. Strømmen: «Structural dynamics» or «Theory of bridge aerodynamics», both published at Springer Verlag. Matlab has routines for converting from time domain into frequency domain, but not the other way around. Good luck.

If you know the theory, it takes less than 10 Matlab programming lines to perform a random simulation from a psd.

Relationships between various frequency domain and the time domain representation of vibration signals are explained in

Book Vibration Control for Optomechanical Systems

Hi

By 'acceleration', I am guessing that you ask for the RMS value? It is a common output from PSDs.

I am guessing that you measure acceleration and thus, have acceleration as acc2/Hz, which is PSD. You might have acc/sqrt(Hz), if so, you simply square data to get PSD.

The RMS value can be derived from the PSD by numerical integration, ie

RMS = sqrt(sum(PSD*df)), which can be made crude as a sum or more elaborate using, say Simpson integration.

Assuming the crest factor, you can estimate Peak as Sqrt(2)*RMS and Peak-to-Peak as 2*sqrt(2)*RMS. This should be a reasonable guess as your data is from a test bench at which noise probably was used as excitation source signal.

Hope this helps

Claes