## 4 Result
### Comparison of Result of ML Techniques  
To compare the created models, we simulated 10 different measurements with different input parameters. Table 6 displays the predicted values of the impact force depending on the model used. Summary results of the accuracy of the models for predicting the impact force of all models considered are presented in Table 7. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{5}{c}{**Input Variable**} & \multicolumn{5}{c}{**Prediction—Impact Force (kN)**} \\ \hline
**H (m)** & **W (kg)** & **I** & **S (N-mm\({}^{-1}\))** & **Regression Model** & \
\begin{tabular}{c} **Decision Tree** \\ **Regression Model** \\ \end{tabular} &
\begin{tabular}{c} **Random** \\ **Forest Model** \\ \end{tabular} & **ANN Model** \\ \hline
0.5 & 95 & Sphere & 1000 & 14.462 & 15.780 & 10.429 & 12.706 \\
1.1 & 70 & Sphere & 1000 & 13.828 & 19.575 & 15.645 & 16.020 \\
1.5 & 65 & Sphere & 2000 & 18.133 & 19.575 & 15.844 & 18.219 \\
1.8 & 85 & Sphere & 630 & 23.662 & 25.950 & 22.279 & 24.034 \\
2.1 & 55 & Sphere & 630 & 18.897 & 19.918 & 14.721 & 16.405 \\
0.5 & 95 & Pyramid & 1000 & 15.357 & 15.780 & 10.637 & 13.934 \\
1.1 & 70 & Pyramid & 1000 & 14.736 & 19.575 & 15.796 & 16.826 \\
1.5 & 65 & Pyramid & 2000 & 19.041 & 19.575 & 15.939 & 19.049 \\
1.8 & 85 & Pyramid & 630 & 24.570 & 25.950 & 22.189 & 24.314 \\
2.1 & 55 & Pyramid & 630 & 19.805 & 19.918 & 14.646 & 16.566 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Prediction of impact force (\(n=10\) measurements). Figure 15: Prediction vs. reality (ANN model). * The ANN model is the most powerful model, it has the lowest MSE, MAE and RMSE values and at the same time the highest R\({}^{2}\) values, explaining almost the entire variability of the data. * The second-best model is the random forest model. Although its error metrics are higher than those of ANN, they are still significantly lower than those of linear regression and the regression tree. The value of R\({}^{2}\) = 0.963 confirms that the Random Forest model explains much of the variability of the data. Random Forest is a very strong model that has shown excellent predictive ability, much better than a single regression tree. Due to its structure (many trees, random selection of variables for division), it was able to better identify and evaluate the contribution of variable S. It can be a good substitute for the ANN model. * In the case of the regression model, the results are not bad. The value of R\({}^{2}\) is close to 0.95, indicating that there is a fairly strong linear relationship between the predictors and the target variable. Linear regression is a good baseline model, and its performance here shows that the data also has a linear component. It is suitable for a simpler and more illustrative interpretation of the model. * The regression tree has the worst results. It was found that the regression tree is the least suitable choice for prediction in this case, although it also serves as the basis for the Random Forest method. Table 8 provides a final summary and comparison of individual models based on the selected desired characteristics. In the case where we require the most accurate model regardless of complexity, the ANN model is the best. With a model that gives good results and is a little simpler, the random forest model is advantageous. The linear regression model gives slightly worse results, but due to its simplicity and practicality it is sufficient in many cases. With linear regression, the model equation is easy to interpret, and the regression tree also shows branching and decision-making. The random forest model and the ANN model are more difficult to interpret. In the next step, residual analysis was performed for all the models obtained. Residuals were defined as the difference between the experimental (actual) F\({}_{\text{E}}\) and theoretical (predicted) values of the impact force for each model case (F\({}_{\text{R}}\), F\({}_{\text{T}}\), F\({}_{\text{RF}}\), F\({}_{\text{ANN}}\)).