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.[1][2]

## Algorithm

1. Estimate the power spectral density matrix G^yy(jω) at discrete frequencies ω=ωi.
2. Do a singular value decomposition of the power spectral density, i.e. G^yy(jωi)=UiSiUiH where Ui=[ui1,ui2,...,uim] is a unitary matrix holding the singular vectors uij, Si is the diagonal matrix holding the singular values sij.
3. 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.[1]
1. Using the mode shapes, an input-output system realization can be written.

## See also

* Eigensystem realization algorithm \- an input/output identification technique

## References

1. ↑ 1.0 1.1 Brincker, R.; Zhang, L.; Andersen, P. (2001). "Modal identification of output-only systems using frequency domain decomposition". Smart Materials and Structures 10 (3): 441. doi:10.1088/0964-1726/10/3/303. Bibcode: 2001SMaS...10..441B. http://vbn.aau.dk/ws/files/203990023/Modal_Identification_of_Output_Only_Systems_using_Frequency_Domain_Decomposition.pdf.
2. ↑ Brincker, R.; Zhang, L.; Andersen, P. (February 7–10, 2000). "Modal Identification from Ambient Response Using Frequency Domain Decomposition". San Antonio, TX. http://www.svibs.com/solutions/literature/2000_2.pdf. Retrieved March 11, 2012.

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