## 6 Prediction Performance Evaluation by Reducing the Input Dimension of ML Model  
As previously mentioned, time history analyses for 500 earthquake loads were conducted to create a database for a machine learning model aimed at predicting the seismic response of NPP structures. Due to the size and complexity of the finite element analysis model used, each time history analysis took approximately 3 to 4 h to complete. Despite this effort, the number of training datasets, i.e., 400 (80% of the total 500 datasets), is relatively small compared to the number of input features utilized. Nevertheless, it remains inefficient to expand the dataset by conducting additional time history analyses, which require substantial computational resources. To address this issue, this study introduces an input dimensionality reduction technique to efficiently train and predict using the machine learning model. Reducing the input dimensions of a machine learning model presents several advantages, including the prevention of overfitting and improvement of the model's generalization ability by eliminating unnecessary features and conserving only the most significant ones. Moreover, input dimension reduction minimizes the required size of the training dataset, thus reducing the computational time needed to develop the database, as well as the training time and memory usage. Generally, input dimensionality reduction techniques are divided into feature selection and feature extraction methods, where feature selection involves identifying and preserving the most critical features from an array of available options, and feature extraction entails combining existing features to generate new, more informative ones. To select a feature, it is crucial to evaluate how significantly it influences the prediction performance of the machine learning model among various input features. The RF algorithm calculates feature importance, which offers an overall assessment of the contribution of each feature to the model's predictions during the output computation process. The calculated feature importance values are presented in Figure 14, and based on these values, this study selected the following features. As demonstrated in Figure 14, the features with the most significant influence on the output of the machine learning model, ranked by importance, were PGA, SMA, and ARMS. These features predominantly pertain to acceleration response. On the other hand, features  
Figure 14: Analysis of feature importance using the Random Forest algorithm. like SMV and PGV, associated with velocity response, were of the lowest importance. The results in Figure 14 differ from those in Figure 10 because the two analyses are based on fundamentally different principles. Figure 10 presents Pearson correlation coefficients, which reflect only the linear relationships between individual input variables and the output. In contrast, Figure 14 shows feature importance values derived from the Random Forest model, which account for both nonlinear effects and interactions among variables during model training. Therefore, an input feature may exhibit low correlation but still have high importance in the prediction model, or vice versa. These analyses confirmed that acceleration-based intensity measures and aging-sensitive material properties (damping ratio and elastic modulus) have a significant influence on seismic response predictions. The feature selection was performed by sequentially adding them from the most to the least significant. The variation in the prediction performance (R\({}^{2}\)) of the RF machine learning model, as influenced by the number of features included, is depicted in Figure 15. As illustrated in Figure 15, models incorporating more than eight input features ranked by importance display comparable seismic response prediction performance, with a coefficient of determination (R\({}^{2}\)) approximately 0.9. The two graphs atop Figure 15 juxtapose the predicted and target values generated by the machine learning model.