## 1 Introduction  
Recently, application of control systems on smart structures in many fields of engineering has been greatly increased. These control systems are used to control the dynamic behavior of complex structural systems of structures located at high risks areas [1; 2; 3]. Passive and active control systems are used to control the vibration of structures subjected to wind, seismic loads, etc. More information regarding the control state gets can be found in [1; 4; 5]. Passive control systems are commonly used for building structures. Vibration control and damage detection of regular and irregular buildings are summarized in [5; 6; 7]. [PERSON] et al. [8] studied an experimental regular frame steel building with passive and semi-active control system under seismic loads. In their study, they reported the effectiveness of the used control system in reducing the seismic effects. Moreover, [PERSON] [9] and [PERSON] et al. [10] presented a controlled irregular building performance under seismic effects, and observed that the controlled system can reduce the nonlinear performance of structures. In addition, [PERSON] and [PERSON] [5] performed a complete experimental study on three passive control systems including tuned liquid column damper (TLCD), tuned liquid damper (TLD) and tuned mass damper (TMD) to identify the damping and mass contributions of each system in the building vibration reduction. They found that the TMD control system has the highest damping contribution by 49.1% vibration mitigation. Furthermore, many advantages of the TMD over liquid passive controller system are reported in [10]. Therefore, this study focuses on the performance of the TMD controlled structures (as experimental study). Smart structures performance is controlled in time and frequency domains. In time domain, the magnitude and time period affects decrease, as well as the power spectrum density decreases with the increase of the TMD mass [5]. Moreover, the response of controlled structures decrease more than uncontrolled ones [4]. The nonlinearity performance of controlled structures occurs due to the nonlinearity damping devices of structures [1; 3; 10]. As such, nonlinear mathematical models are needed to study the relation between input loads and output performance of smart structures to develop predicting models for the performance of controlled structures. Some researchers designed identifications models for smart structures equipped with magnetorheological (MR) damper systems [1; 3; 11]. This study aims at developing a new application for nonlinear system identification (SI) for describing the behavior of seismically excited building attached with TMD control system. Commonly, the parametric and non-parametric models are the categories of system identification (SI) [1; 12]. The models that are dependent on the physical quantities are considered as parametric models, while the models used to train the input-output map of structural system are non-parametric [1]. Two non-parametric models are defined: input-output and output-only models. More details on structures identification models can be found in [13; 14]. The output-only SI is commonly used for structures long monitoring systems [12]. In this paper, an input-output SI model is used and the data is collected from an experimental study. Adaptive neuro-fuzzy interference system (ANFIS) is the widely SI method applied for the response of controlled structures [1; 3]. Two systems are developed by [PERSON] et al. [1] and [PERSON] et al. [3] including the wavelet and one time-delayed ANFIS models, and they were effective in identifying structural behaviors. In their studies, the wavelet analysis is used to de-noise the input signal(s) of the identification models. Therefore, with the filtered data this model is insignificant, as some information on the structural performance can be lost. The one time-delayed ANFIS model is applied; however, in this study, we have used one and two time-delays for the output of the ANFIS model.