## 2 Materials and Methods
### Data Analysis and Machine Learning Models
#### 2.2.2 Machine Learning Models  
Suitable machine learning models for ABS and aluminum 2024-T3 datasets are Ridge Regression, Lasso Regression, and K-Nearest Neighbors (KNN). Ridge Regression, a linear regression model with L2 regularization, was employed to prevent overfitting and handle multicollinearity in the data. It is computationally efficient and provides interpretable coefficients. Lasso Regression, similar to Ridge Regression, employs L1 regularization, encouraging sparsity in the model coefficients. It automatically performs feature selection, identifying the most relevant features for crack propagation prediction. However, both Ridge Regression and Lasso Regression assume a linear relationship and may struggle to capture complex nonlinear patterns. They can also encounter challenges with multicollinearity when highly correlated features are present.  
KNN algorithm, a non-parametric method, was used as well. It makes predictions based on the proximity of training samples in the feature space, accommodating complex relationships. KNN is relatively easy to understand and implement. However, it can be sensitive to the choice of the number of neighbors (K) and the distance metric. During prediction, it can be computationally expensive, particularly for large datasets. These models are relatively simple, easy to understand, and do not require a lot of computational power, making them a good choice for tasks that need to be run quickly or on resource-constrained systems [1; 2; 13; 24].  
In another experiment using composite data, the crack depth of each concrete type was clustered based on their respective elastic modulus, which varied with changes in temperature. The researcher selected Support Vector Regressor, Random Forest Regressor, and Gradient Boosting Regressor to predict crack depth for composite data based on their ability to handle complex datasets with non-linear relationships between the features and the target variable and many hyperparameters that can be fine-tuned to improve performance. The Random Forest Regressor, an ensemble learning method that combines multiple decision trees, was utilized. It handles high-dimensional data effectively, mitigates overfitting, and captures complex relationships between input features and crack propagation. However, Random Forest Regressor can be computationally expensive, especially for large datasets. It may struggle to identify subtle patterns and can be challenging to interpret due to its ensemble nature.  
Support Vector Regression (SVR) was also utilized, as it is effective in handling both linear and nonlinear relationships. It can manage high-dimensional data and, by selecting appropriate kernel functions, capture complex patterns. However, SVR can be sensitive to the choice of hyperparameters and kernel functions. It may also face limitations in dealing with very large datasets due to computational requirements.  
Gradient Boosting Regressor, which constructs an ensemble of weak prediction models to sequentially correct errors, was another model used. It handles complex relationships well, performs admirably with high-dimensional data, and typically exhibits high prediction accuracy. However, Gradient Boosting Regressors can be computationally intensive and may require careful hyperparameter tuning. Without proper regularization, it is also prone to overfitting [11; 15].  
It is important to note that the benefits and drawbacks mentioned above are general considerations for the respective machine learning models. The specific performance of these models in predicting crack propagation would depend on factors, such as the quality and size of the dataset, appropriate feature selection, and careful hyperparameter tuning [1; 2].