## 2 Materials and Methods
### CRISP-DM Methodology  
In this study, the CRISP-DM model, which was developed in response to the needs and common problems in data mining projects in the mid-1990s, was used. The most important factors in the success of the methodology are its independence from industry, tools and applications [49]. The CRISP-DM methodology consists of six main steps: business understanding, data understanding, data preprocessing, modelling, evaluation, and deployment [48; 50]. The general workflow of the CRISP-DM methodology and the illustration of the operations executed in the study were given in Figure 7.  
Figure 6: Typical force–deformation graph. The aim of the business understanding step of the study is to predict the briquette deformation energy using different ensemble learning methods. The data understanding step includes the discovery of the data to be used in the analysis and the recognition of the data and its accuracy. At this stage, basic statistical analyses were performed. The data pre-processing step includes the discovery of the data to be used in the analysis and the recognition of the data and its accuracy. At this stage, basic statistical analyses were performed. In the data pre-processing step, missing data in the dataset were removed. Additionally, outlier and noisy data were discovered via local outlier factor analysis [51]. In the modeling step, to predict briquette deformation energy, various ensemble learning algorithms were performed. Extreme Gradient Boosting, CatBoost, and Random Forest ensemble learning algorithms were applied. While 70% of the dataset was used for training the models, the remaining 30% was used for testing the trained models. The evaluation phase is an extremely important stage. It is highly important to determine the metrics to be used in interpreting the model results and the visualization tools to be used to show the results. Selection of appropriate metrics and visualization tools is important for accurate interpretation. Line plots were used to visualize model results. The predicted value in the established models is the deformation energy of the briquette. Since this variable takes continuous values, the problem is a regression problem. In line with the information obtained from the literature, coefficient of determination (R\({}^{2}\)), mean absolute percentage error (MAPE), root mean square error (RMSE), and mean absolute error (MAE) metrics are frequently used in evaluating regression problems [2; 52]. Mathematical representations of the metrics used in the evaluation of established ensemble learning models are given in Equations (1)-(4). R\({}^{2}\), known as a measure of the success of independent variables in predicting the dependent variable, is defined as the rate at which the independent variables explain the variance in the dependent variable [53]. In the R\({}^{2}\) metric, which has a value between 0 and 1, an R\({}^{2}\) value approaching 1 indicates that the success of the established regression model is high. More clearly, the whole variance in the dependent variable is explained by the independent variables [52]. \[R^{2}=1-\frac{\sum_{i=1}^{m}(X_{i}-Y_{i})^{2}}{\sum_{i=1}^{m}(\overline{Y}-Y_{ i})^{2}} \tag{1}\]  
Figure 7: Illustration of the general workflow of the study with CRISP-DM methodology [50]. \[RMSE=\sqrt{\frac{1}{m}\sum_{i=1}^{m}(X_{i}-Y_{i})^{2}} \tag{2}\]  
\[MAE=\frac{1}{m}\sum_{i=1}^{m}\left|X_{i}-Y_{i}\right| \tag{3}\]  
\[MAPE=\frac{1}{m}\sum_{i=1}^{m}\left|\frac{Y_{i}-X_{i}}{Y_{i}}\right| \tag{4}\]  
The RMSE is the square root of the mean of the squares of all the errors. In the RMSE metric, which takes values between [0, \(\infty\)), values close to 0 indicate that the model is successful [46; 54]. For regression models, the MAPE is another performance metric that has a very intuitive interpretation in terms of relative error.