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MAXIMUM LIKELIHOOD ESTIMATION OF DAMPING IN THE FREQUENCY DOMAIN DECOMPOSITION METHOD

. The Frequency Domain Decomposition (FDD) method consists on identifying natural frequencies and mode shapes of structural and mechanical system as the peaks of a frequency plot. However, the damping ratio is not an output of FDD, but it is calculated in secondary step. In this work a new method is proposed to estimate the damping ratios. The idea is to use maximum likelihood estimation, where the likelihood function is deﬁned in terms of the innovations of the state space model. This is a highly nonlinear and complicated function of the unknown parameters, so a numerical method must be used to ﬁnd the maximum. In this work, the BFGS algorithm has been chosen. This method also allows quantifying the uncertainty of the parameters using the Hessian matrix. Due to the nature of the method, there are not problems with closely spaced or repeated modes.