## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Motor Type** & \begin{tabular}{c} **Motor Power** \\ **(kW)** \\ \end{tabular} & \begin{tabular}{c} **Minimum Overall** \\ **Specific Energy** \\ **Consumption** \\ **(kJ/kg)** \\ \end{tabular} & \begin{tabular}{c} **Overall Specific Energy** \\ **Consumption Percent** \\ **Saving Related to the** \\ **Reference M4 DOL** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Optimum** \\ **Gearbox Ratio** \\ **Percent Variation** \\ **Efficacy** \\ \end{tabular} & \
\begin{tabular}{c} **Overall** \\ **Speed** \\ **(RPM)** \\ \end{tabular} &
\begin{tabular}{c} **Decanter** \\ **(A rms)** \\ \end{tabular} \\ \hline M2 & 3 & 30.136 & 1.56 & \(-\)39 & 0.8172 & 4915.7 & 5.6 \\ M3 & 4 & 29.981 & 2.06 & \(-\)37 & 0.8214 & 4916.1 & 6.5 \\ M4 & 5.5 & 29.850 & 2.49 & \(-\)34 & 0.8249 & 4916.1 & 6.6 \\ M5 & 7.5 & 29.660 & 3.11 & \(-\)28 & 0.8302 & 4915.9 & 6.9 \\ M6 & 11 & 29.401 & 3.96 & \(-\)10 & 0.8375 & 4916.1 & 7.1 \\ M7 & 15 & 29.386 & 4.01 & +7 & 0.8380 & 4916.1 & 9.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulink simulation results of the optimum overall specific energy consumption (OSEC) and the related overall process efficiency (OPE) at the optimum gearbox ratio percent variation that guarantees the minimum OSEC, for each motor from M2 to M7. The interactions among the variables have been considered up to a degree of five: i.e., the considered multilinear model, when expressed in Wilkinson notation, was  
\(\mathrm{y}\sim 1+\mathrm{x1^{\prime}2}+\mathrm{x1}\times\mathrm{x2^{\prime}2}+ \mathrm{x1^{\prime}3}+(\mathrm{x1^{\prime}2})\mathrm{x2}+\mathrm{x1}\mathrm{:} (\mathrm{x2^{\prime}2})+\mathrm{x2^{\prime}3}+\mathrm{x1^{\prime}4}+(\mathrm{x1^ {\prime}3})\mathrm{:}\mathrm{x2}+(\mathrm{x1^{\prime}2})\mathrm{:}(\mathrm{x2^ {\prime}2})+\mathrm{x1}\mathrm{:}(\mathrm{x2^{\prime}3})+\mathrm{x2^{\prime}4}\)  
\(+\mathrm{x1^{\prime}5}+(\mathrm{x1^{\prime}4})\mathrm{:}\mathrm{x2}+(\mathrm{x 1^{\prime}3})\mathrm{:}(\mathrm{x2^{\prime}2})+(\mathrm{x1^{\prime}2})\mathrm{ :}(\mathrm{x2^{\prime}3})+\mathrm{x1}\mathrm{:}(\mathrm{x2^{\prime}4})+\mathrm{ x2^{\prime}5}\)  
The model consists of 21 terms comprising the intercept term. The normal algorithms used for the prediction assessment of multilinear models have been applied to this analysis. In particular, a 10-fold cross-validation using 500 Montecarlo runs was performed to assess the predictive performance of the model. The regression method used was principal component regression (PCR). The multiple linear regression technique is used to statistically assess any existing relationship and to establish to what extent the model performs in the prediction of the property value; in our case, this corresponds to the confidence of the prediction of the OSEC value; the predicting capability must be quantified by a statistical point of view using techniques such as cross-validation (CV), involving the random partitioning of samples into complementary subsets such as the k-fold CV, or leave-one-out CV; these methods allow one to estimate the prediction capability of the model measured by the widespread ratio of the standard deviation of calibration data to the standard error of prediction data (RPD), as extensively described in the literature [24; 25; 26; 27; 28]. An RPD value greater than or equal to 5.0 indicates that the model is adequate for quality control, and a value greater than or equal to 8.1 indicates that the model is suitable to quantitatively measure the property of interest [25; 29]. Subsequently, the ratio of the standard deviation of calibration data to the standard error of prediction data (RPD) was used to assess the prediction suitability; the RPD value was 37.21 \(\pm\) 0.03 (that can be considered excellent), with a relative percent error in predicting the OSEC less than \(\pm\)0.98% at 95% confidence bounds. These results guarantee the greater predictive confidence of the calculated model.