Damage detection based on the analytical signal representation

Analytical signal in complex domain is a signal whose imaginary part is the Hilbert transform of the original one. It has been recognized that the phase and the instantaneous frequency are sensible to small variation of parameters. For civil engineering structures it becomes of primary importance to detect and quantify damage at the early stage and then for very small structural parameter variation, it follows that, using complex representation, the damage detection procedure obtained by using the outlined concept may be reasonable and for single degree of freedom systems the advantages and the effectiveness is apparent. On the other hand for MDOF systems the Hilbert transform technique shows some unsatisfactory behaviors and in literature is referred as “not well behaved Hilbert transform”. In order to overcome such problem the so called empirical mode decomposition proposed by Huang may be used. Since, the empiric mode signals have not an analytic representation, they may be used only in computer routines which often hidden the mathematical and physical significance here it has been proposed the use of Butterworth filters transformed in time domain in order to decompose the signal into a summation of modal responses (and then well behaved Hilbert transform signals). The latter procedure is also effective when one considers noise in the sensors as it happens in the reality.