## 4 Model for Prediction of Dynamic Characteristics  
The r-SVM model is a regression analysis model that extends the SVM theory; it has been considered an effective prediction method [14; 31; 32; 33; 34]. The existing neural network follows the empirical risk minimization (ERM) principle, whereas the SVM model follows the structural risk minimization (SRM) principle. The ERM principle minimizes errors in training data, whereas the SRM principle maintains a balance between the training data and test data errors. Therefore, the SVM principle has a better generalization performance in prediction problems [35]. Figure 8: Variation in compressor discharge temperature over time with refrigerant charge amount. Figure 7: Variation in evaporation temperature over time with refrigerant charge amount. In this study, a dynamic model was developed based on the r-SVM machine learning model. When the experimental data are {(x\({}_{1}\), y\({}_{1}\)),..., (x\({}_{m}\), y\({}_{m}\))}, x consists of a multivariate set of predictors with the response variable y. The r-SVM model has the maximal deviation \(\epsilon\) from the response variable y and tries to find the function f(x) as flat as if possible. In the SVM principle, which is a nonparametric model, f(x) is defined as in Equation (1); \(<\) w,x \(>\) is the dot product of w and x similar to Equation (2). w is the flatness, and b is the bias. To allow an error higher than \(\epsilon\), f(x) can be obtained by introducing the slack variable \(\xi_{i}\), \(\xi_{i}\)* and the penalty constant C, thereby transforming it into a convex optimization problem, as shown in Equation (3):  
\[\text{f(x)}=\text{$<$ w,x}>+\text{b}, \tag{1}\]  
\[\parallel w\parallel^{2}=<\ w,w\ >, \tag{2}\]  
\[\text{Minimize }\frac{1}{2}\parallel w\parallel^{2}+C\sum_{i=1}^{  
In the training phase, the average RMSEs of the prediction models for the condensation temperature and degree of subcooling were 0.51 and 0.83 \({}^{\circ}\)C, and the respective average RMSEs of the test data were 0.53 and 0.84 \({}^{\circ}\)C, respectively. The trained models for the prediction of the condensation temperature and degree of subcooling effectively predicted new untrained data. However, the compressor discharge temperature had a relatively large error, and the model prediction accuracy decreased owing to the increasing prediction error. The accuracies of the power consumption prediction model for the training and test data were 5.54% and 5.6%, respectively.  
\[\text{RMSE}=\sqrt{\sum_{i=1}^{n}\frac{\left(y_{pred}-y_{meas}\right)^{2}}{n}}. \tag{4}\]  
The prediction results of the dynamic models of the condensation temperature, degree of subcooling, compressor discharge temperature, and power consumption developed in this study are compared with the test data in Figure 9. The results correspond to outdoor and initial indoor temperatures of 35 \({}^{\circ}\)C and 600, 700, 800, and 900 g refrigerant charge amounts; the curves represent the predicted values of the developed model, while the symbols represent the experimental test data. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Kernel**} & \multirow{2}{*}{**K-Fold**} & \multirow{2}{*}{**Response Variable**} & \multirow{2}{*}{**C**} & \multirow{2}{*}{**\(\epsilon\)**} & \multicolumn{2}{c}{**RMSE**} \\ \cline{5-8}  & & & & & **Training Data** & **Test Data** \\ \hline \multirow{3}{*}{Linear} & \multirow{3}{*}{5} & T\({}_{\text{c,sat}}\) & 0.509 & 0.101 & 0.51 \({}^{\circ}\)C & 0.53 \({}^{\circ}\)C \\  & & \(\Delta\)T\({}_{\text{sc}}\) & 0.414 & 0.076 & 0.83 \({}^{\circ}\)C & 0.84 \({}^{\circ}\)C \\  & & T\({}_{\text{dis}}\) & 0.461 & 0.301 & 3.76 \({}^{\circ}\)C & 5.12 \({}^{\circ}\)C \\  & & W & 20.3 & 29.8 & 5.54\% & 5.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimized parameters of support vector machine (SVM) in grid search. Figure 9: _Cont_. The predicted condensation temperature was lower than the experimental result under undercharged conditions and higher under overcharged conditions.