Theoretical justification of natural frequency identification in the FDD (Frequency Domain Decomposition) method

This paper is the first to provide a justification for the main criterion of the Frequency Domain Decomposition (FDD) algorithm based on the singular value decomposition of a spectral measured signals’ density. The algorithm is used for monitoring the structures such as buildings, bridges, dams, to determine experimentally their state (under operating conditions) without application of vibroexciters. The criterion is used to search for natural frequencies. The justification included the double-ended estimate for the first singular value of the spectral density matrix, the estimate making it possible to prove strictly the criterion's applicability under some fulfilled conditions.