## 3 Results and Discussion
### Model Development
#### 3.1.2 Machine Learning Models
**(a)** Machine learning models for data provided by [PERSON] _et al._[1]; **(b)** machine learning models for data provided by [PERSON] _et al._[24]; **(c)** machine learning models for data provided by [PERSON] _et al._[25]; and **(d)** machine learning models for data provided by all the three experimental reports [1,24,25]. Table 1 and Figure 4a show that the prediction results of machine learning models are generally acceptable, with lower RMSEs than that of linear regression. The SVM and MLFN with 31 nodes (MLFN-31) have the lowest RMSEs (0.11 and 0.10 respectively) and both having the prediction accuracy of 100% (under the tolerance of 30%). However, in our machines, the MLFN-31 requires 2 h for model training, while the SVM only needs about one second, which is also the shortest training time among the results in Table 1. Therefore, the SVM can be defined as the most suitable model for the prediction using the data provided by [PERSON] _et al._[1]. The RMSEs shown in Table 2 and Figure 4b are comparatively higher than those in Table 1. Additionally, in Table 2, the RMSEs and training times of ANNs are comparatively higher than those of the SVM (RMSE: 6.09; training time: 0:00:01). The linear regression has the highest RMSE when testing (86.33). It can be apparently seen that the SVM is the most suitable model for the prediction using the data provided by [PERSON] _et al._[24]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Type** & **RMSE (for Testing)** & **Training Time** & **Prediction Accuracy** \\ \hline Linear Regression & 86.33 & 0:00:01 & 63.4\% \\ SVM & 6.09 & 0:00:01 & 100\% \\ GRNN & 14.77 & 0:00:02 & 96.2\% \\ MLFN 2 Nodes & 35.41 & 0:02:18 & 82.7\% \\ MLFN 3 Nodes & 16.84 & 0:02:55 & 96.2\% \\ MLFN 4 Nodes & 12.14 & 0:03:38 & 96.2\% \\ MLFN 5 Nodes & 10.67 & 0:04:33 & 96.2\% \\ MLFN 6 Nodes & 8.35 & 0:04:54 & 98.1\% \\ MLFN 7 Nodes & 14.77 & 0:06:06 & 96.2\% \\ MLFN 8 Nodes & 13.06 & 3:19:52 & 96.2\% \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ MLFN 29 Nodes & 25.46 & 0:31:00 & 90.4\% \\ MLFN 30 Nodes & 24.25 & 0:34:31 & 90.4\% \\ MLFN 31 Nodes & 21.23 & 0:42:16 & 90.4\% \\ MLFN 32 Nodes & 13.40 & 3:38:17 & 96.2\% \\ MLFN 33 Nodes & 24.84 & 0:47:06 & 90.4\% \\ MLFN 34 Nodes & 20.65 & 0:53:14 & 90.4\% \\ MLFN 35 Nodes & 22.46 & 0:58:16 & 90.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Prediction models using experimental data by [PERSON] _et al._[24]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Type** & **RMSE (for Testing)** & **Training Time** & **Prediction Accuracy** \\ \hline Linear Regression & 15.87 & 0:00:01 & 94.1\% \\ SVM & 13.93 & 0:00:01 & 94.1\% \\ GRNN & 9.53 & 0:00:01 & 100\% \\ MLFN 2 Nodes & 2.72 & 0:01:13 & 100\% \\ MLFN 3 Nodes & 5.10 & 0:01:19 & 100\% \\ MLFN 4 Nodes & 14.05 & 0:01:36 & 94.1\% \\ MLFN 5 Nodes & 2.77 & 0:02:25 & 100\% \\ MLFN 6 Nodes & 2.85 & 0:02:31 & 100\% \\ MLFN 7 Nodes & 15.72 & 0:03:15 & 94.1\% \\ MLFN 8 Nodes & 3.46 & 0:03:40 & 100\% \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ MLFN 29 Nodes & 68.34 & 0:15:03 & 82.4\% \\ MLFN 30 Nodes & 47.09 & 0:17:58 & 82.4\% \\ MLFN 31 Nodes & 52.60 & 0:22:01 & 82.4\% \\ MLFN 32 Nodes & 40.03 & 0:27:46 & 82.4\% \\ MLFN 33 Nodes & 20.69 & 0:39:27 & 94.1\% \\ MLFN 34 Nodes & 352.01 & 0:56:26 & 11.8\% \\ MLFN 35 Nodes & 145.61 & 5:01:57 & 11.8\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Prediction models using experimental data by [PERSON] _et al._[25]. In Table 3 and Figure 4c, the RMSE of the SVM is relatively higher than those of GRNN and MLFNs with low numbers of nodes. The MLFN with two nodes (MLFN-2) has the lowest RMSE (2.72) and a comparatively good prediction accuracy (100%, under the tolerance of 30%) among all models in Table 3 and, also, the training time of the MLFN-2 is comparatively short (0:01:13). Interestingly, when the numbers of nodes increase to 34 and 35, their corresponding prediction accuracies decrease to only 11.8%.