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frequency domain decomposition : ウィキペディア英語版
frequency domain decomposition

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 \hat_(j\omega) at discrete frequencies \omega = \omega_i.
# Do a singular value decomposition of the power spectral density, i.e. \hat_(j \omega_i) = U_i S_i U_i^H where U_i = () is a unitary matrix holding the singular values u_, S_i is the diagonal matrix holding the singular values s_.
# For an n degree of freedom system, then pick the n 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.

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