Frequency domain decomposition

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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]


  1. Estimate the power spectral density matrix at discrete frequencies .
  2. Do a singular value decomposition of the power spectral density, i.e. where is a unitary matrix holding the singular values , is the diagonal matrix holding the singular values .
  3. For an degree of freedom system, then pick the 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[edit]


  1. ^ a b 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. 
  2. ^ Brincker, R.; Zhang, L.; Andersen, P. (February 7–10, 2000). "Modal Identification from Ambient Response Using Frequency Domain Decomposition" (PDF). Proc. of the 18th International Modal Analysis Conference. San Antonio, TX. Retrieved March 11, 2012.