ABSTRACT
Let Zk k k nR∈= [Re ;Im ]F 2 be an augmented vector of the real and imaginary part of Fk , where in operational modal analysis, only the FFT data confined to a selected frequency band dominated by the target modes are used. Based on Bayes’ Theorem, the posterior Probability Density Function (PDF) of θ given the data is expressed by:
p( | p) ( ) (p | )θ{ }k { }k (3) where p( ) is the prior PDF. Assuming no prior information, the posterior PDF p( | ){ }kZ is proportional to the ‘likelihood function’ p( | ).{ }k θ The MPV of the modal parameters θ can be determined by maximizing p( | ){ }kZ and hence p( | ).{ }k θ It is usually working with the Nega-
tive Log-Likelihood Function (NLLF) L( ), which satisfies
p( | ) [ ( )]θL{ }k (4) By this way, minimizing L( ) with respect to
θ will be equivalent to maximizing p( | ).{ }kZ By directly performing the optimization, there
will be some computational problems, i.e., the illcondition problem and the computational difficulties caused by the large number of measured dofs. Fast algorithms have been developed to solve these problems, making this method identify modal parameters efficiently (Au 2011, Au 2012a, b).
