The OMA or output-only method is basically used to identify the modal characteristics of structure during operation without the need to measure the input excitation or in cased where the input excitation is not deterministic. The main concern is that the excitation must be approximately stochastic with as many excitation sources as possible, preferably more the number of degrees of freedom. The resulting Operational Deflection Shapes (ODS) contain the overall dynamic response of a structure due to forced and resonant vibration.

As for your question, the FDD is an output-only modal identification algorithm and doesn’t directly produce the forced vibration response. As the input excitation is not measured, the collected data cannot be directly interpreted as the excitation. In fact, the excitation needs to be backtracked form the data collecting process, in which both the structure and the measurements systems add and remove components from the excitations. That is the structure will add modal characteristics, while the measurements add noise, aliasing and other phenomena; all such contributions are to be taken into consideration in the analysis of data.

Finally, in your proposed system of an eccentric mass excitation (deterministic input), you can easily measure the forced response at any point on the structure.

I hope this answer would shed some light on your question.

I think, Yes it works.

for any type of excitation we can determine the vibration characteristics by OMA

But the problem may be appear is poor response in some points and dominance of noises.

The white noise is the best input excitation for OMA