# Innovative Approach Integrating Machine Learning Models for Coiled Tubing Fatigue Modeling
## 5 Comparison and Performance Criteria  
### Coefficient of Determination (\(R^{2}\))  
\(\mathrm{R^{2}}\) measures how much the variance is explained by the model, where higher \(\mathrm{R^{2}}\) values indicate that the model captures the trend in the data well, but it can be misleading for overfitting (where the model performs well during training but poorly on unseen data).  
\[\mathrm{R^{2}}=\frac{\sum(y_{\mathrm{i}}-\hat{y}_{\mathrm{i}})^{2}}{\sum(y_{ \mathrm{i}}-\overline{y})^{2}} \tag{1}\]  
where \(\mathbf{y_{\mathrm{i}}}\) is the actual target value, \(\hat{y_{\mathrm{i}}}\) is the predicted target value, and \(\overline{y}\) is the mean of the actual values.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Regressor** & **Definition** & **Advantages** & **Objective** \\ \hline Linear Regression & A technique that models the relationship between the input features and the target variable as a straight line. & Easy to interpret and implement - Computationally efficient - Effective for data that have a linear relationship. & To estimate continuous outcomes by fitting a linear equation that minimizes the squared differences between predicted and actual values. \\ \hline Decision Tree & A model that splits the dataset into branches based on feature values to predict the target variable. & Easy to interpret and visualize - Handles both categorical and continuous features - No need for feature scaling. & To make predictions by dividing the data into smaller subsets, forming a tree structure with decision rules at each branch. \\ \hline Random Forest & An ensemble method that constructs multiple decision trees using different data samples and averages the predictions. & More accurate than individual decision trees - Handles non-linear patterns - Less prone to overfitting. & To enhance prediction accuracy by combining the output of multiple decision trees trained on various random samples of the data. \\ \hline XGBoost & A highly optimized version of gradient boosting, designed for fast, scalable, and accurate modeling. & Very efficient with large datasets - Can handle missing data well - Customizable and offers regularization to avoid overfitting. & To deliver fast and accurate predictions using an optimized gradient boosting approach, particularly useful for large and complex datasets. \\ \hline CatBoost & A gradient boosting algorithm specifically designed to handle categorical features directly without needing extensive preprocessing. & Automatically handles categorical data - Less prone to overfitting - Fast and scalable. & To efficiently work with categorical data while delivering high predictive accuracy, reducing the need for feature encoding. \\ \hline Support Vector Regressor (SVR) & A regression model that predicts continuous values by finding a hyperplane in a high-dimensional feature space. & Performs well in high-dimensional spaces - Robust against outliers - Can model non-linear relationships using kernel functions. & To predict continuous values by maximizing the margin of tolerance, especially useful in high-dimensional data with potential outliers. \\ \hline Artificial Neural Networks (ANNs) & A computational model inspired by biological neurons, designed to capture complex patterns through multiple layers of interconnected nodes. & Can model very complex patterns - Can handle non-linear relationships. & To predict continuous values by learning intricate relationships between input features using a multi-layered network structure. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of regression and ANN methods.