## 3 Results and Discussion
### Models Based on Decision Trees XGBoOST, LightGbmRegression, and FastTreeRegression  
The best XGBoost model for the problem discussed in this paper was built with use of the hyperparameters [30] listed below:  
* max_depth = 8;
* learning_rate = 0.1;
* n_estimators = 1000; \begin{table}
\begin{tabular}{c c c} \hline \hline
**Network Structure** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline MLP 5-9-1 & 1.266 & 0.298 \\ MLP 5-9-1 & 1.074 & 0.312 \\ MLP 5-6-1 & 0.411 & 0.265 \\ MLP 5-9-1 & 0.953 & 0.298 \\
**MLP 5-8-1** & **0.176** & **0.302** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: RMSE and R\({}^{2}\) values for the best MLP neural networks considered in this study. The best solution is bolded. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Network Structure** & **Correlation** & **Correlation** & **Correlation** \\
**\begin{tabular}{c} **Coefficient** \(r\) \\ **(Learning)** \\ \end{tabular} & \
\begin{tabular}{c} **Coefficient** \(r\) \\ **(Testing)** \\ \end{tabular} &
\begin{tabular}{c} **Coefficient** \(r\) \\ **(Validation)** \\ \end{tabular} \\ \hline MLP 5-9-1 & 0.537 & 0.532 & 0.570 \\ MLP 5-9-1 & 0.569 & 0.542 & 0.567 \\ MLP 5-6-1 & 0.522 & 0.505 & 0.519 \\ MLP 5-9-1 & 0.528 & 0.544 & 0.568 \\
**MLP 5-8-1** & **0.545** & **0.550** & **0.555** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The MLP network correlation coefficient \(r\) for different network structures. The network with the best performance is shown in bold. * objective = \"reg:squarederror\";
* booster = \"gbtree\". The values of the metrics assessing the quality of the model obtained in this way are presented in Table 5.  
A key advantage of decision trees is their ability to quickly determine the importance of a given feature for the developed model. XGBoost identified the features' importance (Figure 7), indicating that the factor with the greatest influence on the conicity prediction (and, indeed, on the value of this quantity describing the uniformity of tires) was the width of TP1. The impact of the other independent variables is approximately 30-45% lower. Moreover, its advantage over the ML_NET library is its ability to precisely analyze the course of calculations in a\"step-by-step\" manner (similar to MLP) due to the environment it uses. This translates into a better understanding of the principle of operation of the built model. Based on 132 conducted trials, ML_NET identified the two best models for the problem, which are shown in Table 6.  
Whenselecting the best possible model to solve a given production problem, the possibility of implementing it into the existing IT infrastructure should be considered. It is important to match the required computing power to the hardware used in the enterprise \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Trial** & **Trainer** & **R2** & **RMSE** \\ \hline
26 & FastTreeRegression & 0.7163 & 0.085 \\
24 & LightGbmRegression & 0.7070 & 0.086 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results for the best models explored by ML_NET. \begin{table}
\begin{tabular}{c c} \hline \hline
**RMSE** & **R2** \\ \hline
0.1156 & 0.5182 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results for the best XGBoost model. Figure 7: Feature importance of the XGBoost model. in question. The expected implementation costsare also important. It is crucial to define the term \"accuracy\" for each individual case in order to determine the algorithm that will be most suitable for the nature of the problem. Moreover, the response time of the model based on the data received online should guarantee a smooth production process. In order to effectively predict the length of gas turbine fatigue cracks, the authors of [31] compared multiple linear and polynomial regression, random forest, kernel-based methods, AdaBoost, XGBoost, and artificial neural networks in the context of a small dataset (approximately 30 observations).