## 4 ML-Based Classification Model for the Determination of Column Failure Modes  
In this study, the most suitable model was selected using classification model performance indicators to evaluate the performance of the RC column failure-mode-prediction models. The performance indicators used to evaluate the classification models include \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Parameter** & **Value** \\ \hline \multirow{2}{*}{ANN} & Number of Layers & 2 \\ \cline{2-3}  & Activations & tanh \\ \hline \multirow{2}{*}{KNN} & Number of Neighbors & 3 \\ \cline{2-3}  & Distance & cityblock \\ \hline \multirow{2}{*}{DT} & Minimum of Leaf Size & 1 \\ \cline{2-3}  & Maximum Depth of the Tree & 177 \\ \hline \multirow{4}{*}{RF} & Method & AdaBoostM2 \\ \cline{2-3}  & Maximum Depth of the Tree & 5 \\ \cline{2-3}  & Number of Learning Cycles & 488 \\ \cline{2-3}  & Learning Rate & 0.9274 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of hyperparameters. the accuracy, precision, recall, F1-score, and area under the curve (AUC), which can be determined using a confusion matrix. Table 4 illustrates the basic concept of a confusion matrix. When classifying flexure failure (positive) and shear failure (negative), a true negative (TN) value is identified when the actual shear failure is correctly predicted as shear failure and a true positive (TP) value is determined when the actual flexure failure is predicted as flexure failure. A false negative (FN) occurs when the actual flexure failure is incorrectly predicted as shear failure, and a false positive (FP) occurs when the actual shear failure is incorrectly predicted as flexure failure. These prediction outcomes are used to determine the accuracy (ratio of correctly predicted cases to the total predictions), precision (ratio of actual flexure failures among those predicted as flexure failures), recall (ratio of actual flexure failures predicted as such), and F1-score (harmonic mean of recall and precision), which are calculated using Equations (2)-(5), respectively. Increasing precision tends to decrease recall and vice versa, creating a trade-off relationship. The receiver operating characteristic (ROC) curve is a graph plotted with sensitivity and 1-specificity. Here, sensitivity is the same as recall and specificity is calculated using Equation (6). AUC refers to the area under the ROC curve. A superior classification model is characterized by an AUC value close to 1, and its graph tends to approach the top left corner. \[Accuracy=\frac{(TP+TN)}{(TP+TN+FP+FN)} \tag{2}\]  
\[Precision=\frac{TP}{(TP+FP)} \tag{3}\]  
\[Recall=\frac{TP}{(TP+FN)} \tag{4}\]  
\[F1-score=\frac{2\times Precision\times Recall}{(Precision+Recall)} \tag{5}\]  
\[Specificity=\frac{TN}{(TN+FP)} \tag{6}\]  
Figure 3 shows the confusion matrices for each machine learning model used in this study. A confusion matrix allows us to compare the actual classes for given input variables with the predicted classes from the machine learning model for the same input variables. In the confusion matrix of this study, the labels 1 to 3 indicate the flexural failure, shear failure, and flexural-shear failure types, respectively. The columns of the matrix represent the predicted classes, and the rows indicate actual classes. The cells along the diagonal indicate correctly classified observations. For example, in the case of the ANN model, it can be observed that out of 59 datapoints known to be of the flexural failure type, 59 were correctly classified as a flexural failure type. Out of four datapoints known to be of the shear failure type, two were correctly classified as a shear failure type; one was misclassified as a flexural failure type and one as a flexural-shear failure type. Among the 12 datapoints known to be of the flexural-shear failure type, 5 were correctly classified as being of the flexural-shear failure type, 3 were misclassified as a flexural failure type, and 4 were misclassified as a shear failure type. For the ANN and KNN models, the overall precision, recall, and F1