# Assessment of Earthquake Destructive Power to Structures Based on Machine Learning Methods
## 3 Sample Preparation  
In this study, a relatively simple structural model named elasto-plastic single degree-of-freedom (SDOF) model is adopted, as shown in Figure 2a. The model can capture the elasto-plastic mechanical properties of multi-story buildings and simple girder bridges [31; 32]. The elastic parameters of the SDOF model include the natural vibration period and the elastic damping ratio. A tri-linear backbone curve is adopted for the interstory performance of the SDOF model, as shown in Figure 2b [4]. The parameters of the backbone curve parameter include yield strength to weight ratio, peak to yield strength ratio, and the secondary stiffness ratio. The secondary stiffness ratio is defined by the ratio of post-yield stiffness to the elastic stiffness. A single-parameter hysteretic model is adopted for the SDOF system (Figure 2c). The hysteretic parameters reflect the ratio of the hysteretic area of the pinching model to that of the full bi-linear model (Figure 2c). The parameters of the elasto-plastic SDOF model adopted in this paper are shown in Table 2.  
Considering that the characteristics of different ground motions vary significantly, to cover different types of ground motions as much as possible, 5057 ground motion records were collected from the pacific earthquake engineering research (PEER) center ground motion database [33]. The obtained ground motions were recorded from 1935 to 2003, of which earthquake magnitude ranges from 4.2 to 7.9. Most of the ground motions were recorded in the US and Japan. Some typical earthquakes are Chi-Chi, El Centro, Northridge, Landers, and Kobe earthquakes. The acceleration response spectra of some selected ground motions are shown in Figure 3. As evident in Figure 3, the randomness of different ground motions is significant. To expand the training data for better generalization of the machine learning model, the ground motion records are normalized and rescaled to ten different peak ground accelerations (PGA) (i.e., PGA = 1 - 10 m/s\({}^{2}\)), respectively. As a result, 50,570 ground motion acceleration sequences are obtained. Subsequently, THAs are performed to obtain the maximum response displacements of the SDOF model subjected to 50,570 ground motions. Finally, 50,570 ground motion acceleration sequences, together with the corresponding maximum response displacements, are taken as the dataset for model training.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Natural Period (s)** & \begin{tabular}{c} **Damping** \\ **Ratio** \\ \end{tabular} & \begin{tabular}{c} **Yield Strength to** \\ **Weight Ratio** \\ \end{tabular} & \begin{tabular}{c} **Peak to Yield** \\ **Strength Ratio** \\ \end{tabular} & \
\begin{tabular}{c} **Secondary** \\ **Stiffness Ratio** \\ \end{tabular} &
\begin{tabular}{c} **Hysteretic** \\ **Parameter** \\ \end{tabular} \\ \hline \hline
0.5 & 0.05 & 0.097 & 2.61 & 0.25 & 0.4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Structural parameters of the elasto-plastic SDOF model.  
Figure 2: Single degree-of-freedom (SDOF) shear model: (**a**) SDOF shear model; (**b**) tri-linear backbone curve; (**c**) single-parameter hysteretic model.  
The dataset is divided into a training set, a validation set, and a test set. According to the research of [PERSON] [34], the test set should be large enough to give high confidence in the overall performance of the model. In this study, sample split experiments show that a test set size of 1000 can reasonably reflect the performance of the prediction model. Therefore, the original sample set is divided into 48,570, 1000, and 1000 samples for the training, validation, and test sets, respectively. It is worth noting that the original 50,570 sample set is generated using 5057 ground motion records in ten different PGAs. To makes sure that the ground motions in the test and validation sets are completely different from those in the training set, 4857, 100, and 100 ground motion records are randomly selected to generate the training, validation, and test sets, respectively.