## 4 Machine Learning Algorithms and Performance Evaluation Indices  
### Selected Machine Learning Algorithms  
In this study, six machine learning algorithms including DT, RF, SVM, kNN, XGBoost, and NN [8] were employed to develop ML models that predict seismic responses of an NPP structure considering aging deterioration. This section briefly introduces the six selected ML algorithms. Four performance evaluation indices of ML models are also detailed. DT is a widely recognized supervised machine learning algorithm used extensively in classification and regression tasks [33]. It represents decisions and their potential outcomes in a tree-like structure. Each decision node divides the data into subsets based on specific feature values. These partitions aim to maximize the usefulness of each division, often determined by metrics such as Gini impurity, entropy, or variance reduction. The final classifications or outcomes appear as the leaf nodes of the tree. The RF algorithm is a highly effective and versatile ensemble learning technique, valued for its ability to improve prediction accuracy and reduce overfitting [33]. It operates by constructing multiple decision trees, each trained on a unique random subset of the dataset. Furthermore, within the trees, only a randomly selected subset of features is considered at each split--a strategy known as bagging and feature randomization. By introducing variability among the trees, random forests create a robust model that is less sensitive to noise and errors in the data. SVM operates by identifying the optimal hyperplane that separates data points into distinct classes [6]. This hyperplane is carefully selected to maximize the margin--the distance between the hyperplane and the nearest data points from each class, termed support vectors. By maximizing this margin, SVM achieves reliable and robust classification, even in datasets that are complex or noisy. The kNN algorithm is a straightforward yet flexible supervised learning technique widely utilized for both classification and regression tasks [33]. Unlike many machine learning algorithms, kNN operates without a specific training phase. Instead, it predicts outcomes by identifying the k nearest data points, or \"neighbors\", to a given query point in the feature space. For regression tasks, it calculates the average of the neighbors' values to make predictions. The similarity or \"closeness\" between points is typically determined using distance metrics such as Euclidean distance, Manhattan distance, or Minkowski distance, chosen based on the task's specific requirements. XGBoost is an efficient and versatile machine learning algorithm that has become a cornerstone for both classification and regression tasks [7]. Built on the principles of gradient boosting, XGBoost constructs an ensemble of decision trees, where each tree iteratively corrects the residual errors from the previous ones. This stepwise optimization ensures the model achieves highly accurate predictions, even when applied to complex datasets with intricate patterns. Neural networks are a powerful class of machine learning algorithms inspired by the structure and function of the human brain [7]. These models identify patterns within data by passing inputs through layers of interconnected nodes, or \"neurons\", each connection associated with a weight. During training, these weights are updated iteratively using optimization algorithms to minimize the error between the predictions and actual outcomes. A typical neural network consists of three main layers: an input layer that receives raw data, one or more hidden layers that perform intermediate processing, and an output layer that produces the final prediction. In this section, OpenAI's ChatGPT (GPT-4o, accessed in January 2025) was used to help draft brief explanatory descriptions of selected machine learning algorithms by summarizing and clarifying the standard characteristics of algorithms such as randomforest, XGBoost, and neural networks.