Identification of non-linear systems using multi-scale ridges and skeletons of the wavelet transform

A new procedure of non-linear system identification is presented. The procedure employs the slowly-varying, time-dependent amplitude and phase functions of the impulse response of the system. These instantaneous characteristics are obtained from the ridges and skeletons of the wavelet transform. The ridge extraction procedure uses the modulus of the transform and involves a combinatorial optimization algorithm based on simulated annealing. The method is illustrated using two simple simulated examples. It is shown that the procedure can be used for multi-degree-of-freedom systems due to the frequency localization property of the continuous Grossman-Morlet wavelets. (C) 1998 Academic Press.