## 4 Results And Discussions  
The results of the linear regression model, when used to predict the temperature of the robot and when AutoML is used to forecast safety stops during collaborative work are presented in this section. The correlation matrix and studies have shown that the temperature of the each joint and protective stops during collaborative tasks are important factors of the robot manipulator that can influence the reliability of collaborative work. Figure 13 shows the results of a linear regression model used to predict the temperature of a robot while performing human robot collaboration tasks with different loads. The blue data on the graph are the original data and the red data are the predicted variables. Moreover, the graph shows the critical temperature condition when the robot works with maximum loads and normal condition when the robot performs tasks with lighter loads. The Table 4 shows the performance results of the linear regression model. The main evaluation parameters of the model were the Adjusted R squared, multiple R-squared, F-statistics and \(p\)-values. The linear model with all the data resulted in a higher error than for the other experimental setups. The performance of the LM with all the data including the max. medium and min data, resulted in an Adjusted R-squared equal to 0.9346 and a multiple R-squared of 0.9529, which are sufficient to be integrated into the monitoring system as temperature prediction models. Figure 12: Box-plot of the Load with the Speed. H2O AutoML is used to predict safety stops during collaborative tasks. Our dataset is trained in an H2O cluster using R, version 3.6.3. The AutoML function in H2O automates the process of building a large number of models and finds the most suitable model for a given dataset. AutoML includes a \"leaderboard\" of models that are trained in the process. It includes a 5-fold validated model performance, and no hyperparameters were used for the training. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Experimental Setups** & **Res. Std. Err.** & **Multiple R-Squared** & **Adjusted R-Squared** & **F-Statistic** & \(p\)**-Value** \\ \hline UR3 with all the data & 1.865 & 0.9529 & 0.9346 & 52.02 & \textless{1.163}\times 10^{-10}\) \\ UR3 with the Max.Load & 0.1422 & 0.9152 & 0.9151 & \(3.347\times 10^{4}\) & \textless{2.2}\times 10^{-16}\) \\ UR3 with the Medium Load & 0.364 & 0.1571 & 0.1569 & 578.3 & \textless{2.2}\times 10^{-16}\) \\ UR3 with the Min. Load & 0.3832 & 0.3952 & 0.395 & 2027 & \textless{2.2}\times 10^{-16}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performances of the general linear model when predicting the cobot temperature. Figure 13: Temperature prediction results under different conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Input Variables** & **Estimate** & **Std. Error** & **t Value** & **Pr(>|t|)** \\ \hline Intercept & \(1.195\times 10^{+3}\) & \(1.375\times 10^{+3}\) & 0.869 & \textless{0.396248}\) \\ LOAD & \(1.208\times 10^{+1}\) & \(1.041\times 10^{+0}\) & 11.611 & 8.56 \(\times\)\(10^{-10}\) \\ JOINT\_0 & \(1.534\times 10^{+0}\) & \(2.694\times 10^{-1}\) & 5.693 & \(2.13\times 10^{-5}\) \\ SPEED\_ROBOT & \(-6.107\times 10^{-2}\) & \(1.411\times 10^{-2}\) & \(-4.327\) & 0.000406 \\ TIME & \(-7.458\times 10^{-7}\) & \(8.761\times 10^{-7}\) & \(-0.851\) & 0.405837 \\ CURRENT & \(5.800\times 10^{+1}\) & \(2.902\times 10^{+1}\) & 1.999 & 0.060971 \\ VOLTAGE & \(1.048\times 10^{-10}\) & \(2.652\times 10^{-10}\) & 0.395 & 0.697487 \\ POWER & \(-4.051\times 10^{-10}\) & \(2.063\times 10^{-10}\) & \(-1.964\) & 0.065163 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performances of the linear regression model when predicting the robot temperature. for our dataset. Figure 14 shows the performance of AutoML and the importance of the ten models. Users can receive scores of the dataset using the leaderboard frame. Our dataset was trained in a binary classification model, and AUC metrics was used as the main model parameter.