RT Journal Article ID 5f6644fd14055d02 A1 Kong, Fan A1 Kougioumtzoglou, Ioannis A. A1 Spanos, Pol A1 Li, Shujin T1 NONLINEAR SYSTEM RESPONSE EVOLUTIONARY POWER SPECTRAL DENSITY DETERMINATION VIA A HARMONIC WAVELETS BASED GALERKIN TECHNIQUE JF International Journal for Multiscale Computational Engineering JO JMC YR 2016 FD 2016-09-23 VO 14 IS 3 SP 255 OP 272 K1 stochastic processes K1 power spectral density K1 statistical linearization K1 harmonic wavelet K1 Galerkin technique AB A generalized harmonic wavelets (GHWs-) based statistical linearization technique is developed for determining the response evolutionary power spectral density (PSD) of nonlinear time-varying oscillators. Specifically, a recently derived GHWs-based input-output relationship for linear systems is utilized that circumvents the assumption/restriction of local stationarity inherent in earlier treatments of the problem. Next, this excitation-response relationship is extended via statistical linearization to account for nonlinear systems as well. This involves the concept of determining optimal equivalent linear elements corresponding to specific time and frequency bands, whereas the response evolutionary PSD is determined via an iterative scheme. Pertinent numerical examples and Monte Carlo simulation data are included as well for demonstrating the reliability of the technique. PB Begell House LK https://www.dl.begellhouse.com/journals/61fd1b191cf7e96f,35d6eeb80bd15206,5f6644fd14055d02.html