## 4 Results and Discussion
### Comparison of Overall Accuracy of Model Predictions and Variance in Prediction Error  
Multiple k-fold cross validation tests (k = 5 and number of repeats = 3) are carried out considering the entire dataset to evaluate the overall performance (average testing MAPE and MAE, and the variance in testing MAPE and MAE) of all ML models. Note that for hyperparameter training, the k-fold cross validation tests are performed using the training dataset only, while this final k-fold cross validation test uses the entire dataset. Figure 13 presents the results of the MAPE of predictions of AAR obtained using six nonlinear machine learning and deep learning models (KNN, SVR, RFR, ABR, GBR, and ANN) along with the baseline MLR model. The hyperparameters of all models are kept constant as obtained from the hyperparameter tuning phase of each model. For each model, the testing MAPE results are plotted in the form of boxplots, showing the average MAPE, median MAPE, and the 10 th, 25 th, 75 th and 90 th percentile values of MAPE (obtained from 15 values of MAPE for each model). The first observation from Figure 13 is that the average testing MAPE of all six nonlinear models are better (smaller) than that of the baseline MLR model. Among the six nonlinear models, except for the SVR model, the average testing MAPE of the models are smaller than 0.15, and the results for the average MAPE are remarkably consistent across different ML models. The ANN model has the smallest average MAPE value (0.128) and relatively lower variance in MAPE (0.05), indicating that the ANN model outperforms all other models developed in this study for the problem considered. Based on the overall average MAPE in predictions, the ANN model improves the prediction accuracy by 43% compared to the MLR model (MAPE of 0.128 versus 0.225). As the difference in overall model performance in terms of average accuracy among five nonlinear models is relatively small (average MAPE varies from 0.13 to 0.15), and if one prefers simpler ML models, KNN and all three DTR-based ensemble models are almost equally effective for the prediction of AAR. Figure 14 presents the results obtained from the same k-fold cross validation tests (same as the one presented in Figure 13), in the form of MAE in predictions of AAR. As can be observed from Figure 14, the results for testing MAE show a very similar trend that is observed for testing MAPE (Figure 13). Except for the SVR model, the overall average MAE of the other five nonlinear ML models varies between 0.083 and 0.092, once again indicating a remarkable consistency across different ML models. The overall average MAE in predictions of all six nonlinear ML models varies between 0.08 and 0.1, indicating that the maximum acceleration transmitted to structures supported by rocking foundations can be predicted within an average error limit of 8% to 10% of peak ground acceleration of the earthquake. Figure 13: Boxplots of MAPE in the predictions of AAR of machine leaning models during final five-fold cross validation tests of models. Table 3 summarizes the average MAPE and MAE of predictions of all seven ML models in repeated five-fold cross validation tests. Also included in Table 3 is the MAPE and MAE of the statistics-based simple linear regression (SLR) best fit model presented in Figure 3 (using the relationship between log (\(C_{r}/a_{max}\)) and log (AAR)). As can be seen from Table 3, from the statistics based SLR model to MLR machine learning model, the results do not seem to vary much. However, the six nonlinear ML models developed in this study for the prediction of AAR show a significant difference in accuracy. In order to compare the performance of the models using a different error criterion, which is not used in the training phase of models nor in the hyperparameter tuning, a third error measure is also considered. For this purpose, root mean squared error (RMSE), a commonly used error measure in machine learning, is selected.