I don't think this is the right board for this topic ... but here's something that might get you started.
If you can adjust the input signal - which might be possible if you are dealing with a nonlinear simulation or experiment you can change to get different results, just do a step change and there are equations that relate the damping to amount of overshoot in the output response. There are equations that will also give the natural frequency.
If you can't and you have to use system identification, there are many things you need to check with your data to make sure it is suitable before using (e.g. that it has correct sampling/duration for dynamics, sufficient input signal variation, etc.). Then identify a second order model to the data, and convert the resulting discrete model into continuous transfer function, and the damping ratio and natural frequency will come out of the coefficients (look for standard 2nd order transfer function to see which are which).
As for validating - simply apply the input signal to the identified model (discrete and continuous) and its output should match the actual system output reasonably well. Useful to do a few other sanity checks (steps, bode plots) as well, if your original input signal is not so good.
Consultant Control Engineer
www-isc-ltd.com
