Frequency domain decomposition


The frequency domain decomposition 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 output data.

Algorithm

  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 vectors, 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. These peaks correspond to the mode shapes.
  4. # Using the mode shapes, an input-output system realization can be written.