Harmonic wavelet-based statistical linearization of the Bouc-Wen hysteretic model

Abstract

A harmonic wavelet-based statistical linearization method is developed for determining the Evolutionary Power Spectrum (EPS) of the response of a single-degree-of-freedom Bouc-Wen hysteretic oscillator subject to random excitation. Specifically, relying on a rigorous locally stationary wavelet-based representation of random processes, a representation of the process corresponding to a specific scale and translation level is utilized to obtain excitation-response EPS relationships. To this aim, optimal and response dependent equivalent linear elements corresponding to the specific frequency and time band are introduced. This leads to an iterative determination of the response EPS. Thus, a joint time-frequency response analysis is achieved, readily applicable even for cases of physically realistic non-separable excitation EPS. Pertinent Monte Carlo simulations demonstrate the reliability and accuracy of the method. studies (e.g. Lin et al. 1989) and for the response analysis of soil deposits (e.g. Pires, 1996). One of the reasons for the popularity of the model, besides its versatility in efficiently capturing a wide range of hysteretic behaviors, is the option of explicitly computing equivalent linear elements. Specifically, a statistical linearization method (e.g. Roberts and Spanos, 2003) was proposed by Wen (1980) where closed form expressions were derived for the equivalent linear elements of the Bouc-Wen model. The method exhibited improved accuracy in comparison to earlier attempts which involved the assumption of a narrow-band response (e.g. Wen, 1976). Further, the model was extended to account for structural degradation (Baber and Wen, 1981), pinching effects (Foliente et al. 1996), and asymmetric hysteresis (Dobson et al. 1997; Song and Der Kiureghian, 2006). A detailed presentation of the applications and the extensions of the Bouc-Wen model can be found in review papers and books, such as the ones by Wen (1986, 1989), by Ikhouane and Rodellar (2007) and by Ismail et al. (2009). Further, statistical linearization based algorithms for the analysis of the Bouc-Wen model were discussed in Faravelli et al. (1998) from a mathematically rigorous point of view. Ma et al. (2004) suggested that certain parameters of the model are insensitive, and thus a significant simplification of the model is possible. In Yang et al. (1991) the