## 5 Hybrid Seismic Analyses of Studied Building Models
### Computation Time of the Proposed Hybrid Seismic Analysis  
After validating the accuracy of the hybrid analysis, its applicability is investigated hereafter. Developed MLM is incorporated into the numerical integration method (here, OpS method) to predict the shear force at the target component or group of components (here, isolation layer) and at each time step. The resulting hybrid integration module, written in a Python script herein, is to be implemented within a structural analysis software for the common use of practitioners. The optimization of the network architecture might be time-consuming, but once the MLM is trained, it can be saved and reused in any new structural model containing the same target component or group of components. For similar nonlinear structural RPPs, it is recommended to adopt the same RNN architecture determined in this paper for a straightforward application. Therefore, the key factor in evaluating the applicability of the hybrid analysis is its computation time.  
Table 6 presents the computation times of the twelve hybrid seismic analyses performed in this study: Buildings 1, 2, and 3 subjected to GMs 2, 3, 4, and 5. A Python script is written to perform the structural analysis of corresponding MDOFs and to load previously developed MLMs. All computations are performed on the same CPU (16 Intel(r) Xeon(r) W-2245 CPUs) and using the TensorFlow [36] machine learning library. When assuming a specific computer's performance, the consumed time depends mainly on the number of integration time-steps since the MLM would make predictions at each step. This number is a function of the duration of the GM, the original time step of the record (here, 0.02 s), and its subdivision (here, by 5) commonly chosen for accurate NTHA. The minimum computation time corresponds to GM2 (the shortest duration) and has an average of 12.80 min. The most time-consuming case happens obviously for the GM5 of longest duration, with an average value of 38.12 min. Furthermore, computation times of hybrid analyses of different buildings under the same GM are almost the same since analytical models describing the behavior of the respective superstructures are processed in a very short time (here, less than 1 s). It will only increase if more MLMs are used to simulate other components in the same building. Since the structural design is performed once in a lifetime of a building, the additional computation time is supposedly negligible. Considering the accuracy advantage and the reasonable computation time, the efficiency of the proposed hybrid seismic analysis is proven in this study.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **GM2** & **GM3** & **GM4** & **GM5** \\  & **(Kobe 1995 NS)** & **(Taft 1960 EW)** & **(Tohoku 1978 NS)** & **(El Centro 1940 NS)** \\ \hline GM duration (s) & 15 & 19 & 23 & 27 \\ \hline Integration time steps & 3750 & 4750 & 5750 & 6750 \\ \hline \multirow{3}{*}{Time (min)} & B01\_05F\_LMM\_SI & 12.71 & 19.18 & 29.93 & 39.30 \\  & B02\_10F\_LMM\_SI & 12.66 & 20.25 & 29.53 & 38.76 \\ \cline{1-1}  & B03\_15F\_LMM\_SI & 12.93 & 19.08 & 26.75 & 36.31 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Computation time of performed hybrid seismic analyses.  
Figure 15: Nonlinear cyclic hystreses of isolation level of Building 3.