## 3 Results
By analyzing the coefficient of variation of the model coefficients, it is possible to eliminate some interaction terms that decrease the model performance. In fact, because the 10-fold CV gives ten estimates of the regression coefficient of each term, the identification of the problematic term could be performed considering the absolute value of the reciprocal of the coefficient of variation of the ten estimates of each  
Figure 3: The minimum overall specific energy consumption (OSEC) versus the electric motor nominal mechanical power is related to a high degree of correlation (R\({}^{2}\) = 0.99427) to a Gompertz sigmoid function. coefficient (INVCV) arising from the CV phase (i.e., the mean absolute value of the estimates of the regression coefficient divided by its standard deviation). The minimum value of INVCV identifies the coefficient having the maximum estimated relative error (i.e., its coefficient of variation), and, therefore, it allows the identification of the interfering term that should be discarded on the next algorithm loop. This method of \"coefficient of variation algorithm\" (CVA) has been successfully used in other research, showing excellent results [28; 30]. The method allowed a reduction of the terms considered in the model. The model was reduced to 16 terms, comprising the intercept term. Its expression, in Wilkinson notation, is  
\[\text{y}\sim 1+\text{x1}+\text{x2}+\text{x1}\text{'2}+\text{x1}\text{:}\text{x2 }+\text{x2}\text{'2}+\text{x1}\text{'3}+(\text{x1}\text{'2})\text{:}\text{x2}+ \text{x1}\text{:}(\text{x2}\text{'2})+\text{x1}\text{'4}+(\text{x1}\text{'3}) \text{:}\text{x2}+(\text{x1}\text{'2})\text{:}(\text{x2}\text{'2})+\text{x2} \text{'4}+\text{x1}\text{'5}+(\text{x1}\text{'4})\text{:}\text{x2}+\text{x2} \text{'5}\]  
In Figure 4, the contour plots of the found model calculated over the span of motor powers and GRPV values are reported. Figure 4 shows the existence of a minimum OSEC of 28.41 kJ/kg, located at GRPV\(=-6.8\%\), and a motor power of 13.6 kW. It has to be highlighted that Figure 3 does not show the existence of this minimum. Figures 5 and 6 show the further steps taken into account to successfully close the minimization step. From a survey market of the currently available IMs and VFDs, the trend of their cost has been calculated, as depicted in Figure 5. The trend line is hypothesized to be a power law equation. Moreover, hypothesizing that the cost of the IM + VFD is spread over ten campaigns, and that the overall processed product is 226,685 kg for each campaign (627 overall working hours), then the related incidence of machines cost per kg of processed product can be calculated. Figure 4: OSEC values (kJ/kg) contour plots of the found multilinear model calculated over the span of motor powers and GRPV values. The cross marker indicates the minimum value of OSEC. The cost related to the OSEC is obtained considering an energy cost of 0.20 EUR/kWh (the average price for medium-sized consumers in the EU in the second half of 2023, according to Eurostat). Thus, the data of Table 5 can be transformed into the specific cost due to the process per kg of processed product (SCOPP). The sum of these two costs brings the data shown in Figure 6 representing the classical curve that allows the minimization of costs. Figure 6 shows the sum between the machines' cost (IM + VFD on ten campaigns) and the specific cost due to the process per kg of processed product versus the size of the IM and VFD used. The interpolating curve is hypothesized to be a parabolic law; this hypothesis allows us to straightforwardly obtain the minimum of the curve. The predicted optimum size of the IM + VFD (the minimum of the curve) to be used results in 3.0 kW (the minimum tested motor), this being far from the size of the motor currently used on the real machine (5.5 kW). This is mainly due to the low cost of electric energy when compared with the purchase of the machines. However, the time required to bring the decanter up to the rated speed must also be taken into account.