The use of smart control devices such as magnetorheological (MR), electrorheological (ER) damper, variable friction devices, and etc. promises a high potential of increase in the reliability of buildings under destructive environmental forces ranging from strong winds to earthquakes. These benefits come with the challenge of modeling the structure integrated with the nonlinear smart dampers. The integration of the building with smart dampers may introduce nonlinearities despite the building behaving linearly. (Kim et al. 2009). Thus, it is critically important to develop an effective model such that the nonlinear behavior of a smart building is captured. In this chapter, a method is studied that efficiently (in terms of computational load) identifies nonlinear behavior of seismically excited buildings equipped with smart dampers.
An essential part of modeling smart structures is system identification (SI) that develops a numerical model based on experimental data collected from the smart structure. The SI models are used to reliably estimate the complex behavior of the smart structure subject to a variety of dynamic loading scenarios using the inputs (in this case earthquake and control force) and outputs (in this case, displacements on the particular stories). There are two different SI approaches: parametric and nonparametric approaches (Bani-Hani et al., 1999). The parametric SI approach identifies certain properties of the dynamic system to be modeled, e.g. stiffness and damping parameters of a building (Jalili-Kharaajoo, 2004). The nonparametric SI approach uses a black box model that is trained using the input-output relationship of the structural system (Filev, 1991). The nonparametric SI generally does not require accurate physical representation of the structure. Therefore, it is easily applicable to nonlinear modeling of the structural system, which has previously been successfully performed with neural networks and fuzzy logic systems.
One of the most commonly used nonparametric approaches of SI is fuzzy inference system which uses fuzzy set theory to build a set of rules. This can be effective in dealing with nonlinearities and uncertainties of dynamic systems (Gu & Oyadiji, 2008). Fuzzy logic has been used for many SI problems (Takagi & Sugeno, 1985; Yan & Langari, 1998; Kim et al. 2011) since the pioneering work of Zadeh (1965). Studies on Takagi-Sugeno (TS) fuzzy models conducted in recent years mostly deal with effective representation of nonlinear systems using fuzzy sets, fuzzy rules and a set of local liner models (Filev, 1991; Golparakrishnan et al. 2010; Johansen & Babuska, 2003). One of the main applications of fuzzy logic theory has been nonlinear fuzzy control system design in the field of large-scale infrastructure (Guo et al. 2011; Kim et al. 2009; Mitchell et al. 2012). Estimation of the parameters of a fuzzy inference system requires many trials and errors. Hence, neural networks have been used to determine these parameters.