The frequency domain decomposition (FDD) is an output-only system identification technique popular in civil engineering, in particular in structural health monitoring. As an output-only algorithm, it is useful when the input data is unknown. FDD is a modal analysis technique which generates a system realization using the frequency response given (multi-)output data.
Algorithm
- Estimate the power spectral density matrix
G ^ y y ( j ω ) at discrete frequenciesω = ω i - Do a singular value decomposition of the power spectral density, i.e.
G ^ y y ( j ω i ) = U i S i U i H U i = [ u i 1 , u i 2 , . . . , u i m ] is a unitary matrix holding the singular valuesu i j S i s i j - For an
n degree of freedom system, then pick then dominating peaks in the power spectral density using whichever technique you wish (or manually). These peaks correspond to the mode shapes.- Using the mode shapes, an input-output system realization can be written.
References
Frequency domain decomposition Wikipedia(Text) CC BY-SA