## 4 Results and Discussions
### System Identification Analysis
#### 4.2.1 Training Setting Evaluation
The numbers of MF are evaluated with sigmoid function of MF type, and the MF types are evaluated with two MF. Furthermore, all evaluations use the MISO model with two time-delays input, while model 3 is the best. The number of iterations is evaluated and 10 iterations is used; the RMSE for 10 and 50 are 7.78 \(\times\) 10\({}^{-3}\) and 8.17 \(\times\) 10\({}^{-3}\) g, respectively. The \(R^{2}\), MAE and RMSE show better performance of model 3 with two MF (Table 3). When increasing the MFs to more than two, the performance parameters become worse. Thus, two MFs are used in our case. In addition, four common MF types are evaluated in Table 3, and it can be seen that the sigmoid function has a good performance. The sigmoid function is presented in Equation (12). \[u_{P_{k,j}}\left(u^{i}\right)=\frac{1}{1+\mathrm{e}^{-\mathrm{a}\left(u^{i}- \mathrm{c}\right)}} \tag{12}\]  
where a and c parameters denote the shape and behavior of the MF, respectively [24]. These parameters are called the premise parameters as they are adjustable parameters in the premise part. Figure 8 shows the initial and final MF before and after training for the selected model (model 3). It shows that significant modifications have been done to the shapes of initial MFs through the learning process. After determining the initial value of the premise parameter and the architecture of the predictive model, the network was trained by the hybrid technique. Therefore, the number and type of MF are an important parameter in identifying the model selected. The evaluation of SISO (model 1) and MISO (models 2 and 3) are presented in Table 4 with sigmoid function and two MFs. Herein, the ANFIS models are multi inputs models and do not support single input [3; 23]. Therefore, to design the SISO model in this case, it is assumed that seismic signal and \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**MF No.** & \(\mathbf{R^{2}}\) & **MAE (g)** & **RMSE (g)** & **MF types** & \(\mathbf{R^{2}}\) & **MAE (g)** & **RMSE (g)** \\ \hline
2 & 0.97 & \(5.58\times 10^{-3}\) & \(7.78\times 10^{-3}\) & Gaussian & 0.93 & \(8.51\times 10^{-3}\) & 0.012 \\
3 & \(-0.59\) & 0.045 & 0.118 & trapezoidal & 0.79 & \(7.74\times 10^{-3}\) & 0.016 \\
4 & \(-0.54\) & 0.071 & 0.359 & triangle & 0.84 & 0.014 & 0.030 \\
6 & \(-0.63\) & 0.049 & 0.109 & sigmoid & 0.97 & \(5.58\times 10^{-3}\) & \(7.78\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Membership function (MF) numbers and type’s performance evaluation. Figure 7: Nonlinear AutoRegresive with eXogenous inputs (NARX) identification model 8 for the acceleration response. one time-delayed for the seismic signal are used in the input parameters as a single input. Therefore, the two inputs for one parameter (seismic signal) are assumed as a one input model, which is in the model 1. Models 2 and 3 are designed based on the seismic signals and time-delayed output of the structure behavior measurements as input and the predictive structure behavior as output. Table 4 reports that the highest value of \(R^{2}\) and the lowest values of MAE and RMSE for the training case were peculiar to the ANFIS model 3, hence, it could be concluded that model 3-ANFIS is the most suitable one to be used for this study. Figure 9 illustrates the response of the controlled structure and predictions of model 3-ANFIS, with high correlation between the observed and predicted signals. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & \(R^{2}\) & **MAE (g)** & **RMSE (g)** \\ \hline Model 1 & 0.38 & 0.016 & 0.023 \\ Model 2 & 0.13 & 0.018 & 0.032 \\ Model 3 & 0.97 & \(5.58\times 10^{-3}\) & \(7.78\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Adaptive neuro-fuzzy inference system (ANFIS) models performance evaluation. Figure 8: Initial (**a**) and final (**b**) membership functions of model 3. Figure 9: Model 3-ANFIS model identification for the acceleration behavior.