## 3 Results
### Energy Boxplot  
As mentioned in Section 1, the patent described in [30] proposes a methodology where the electrical energy is measured during the lifting operation of a pallet truck to estimate the weight of the lifted load based on a linear function of the energy consumed in the process. Considering this approach, in this section the first step is to visualize the relation between the demanded energy and the lifted weight for the electric forklift used in this study. It is important to note that, compared with the electric forklift, a pallet truck has a lower lifting capacity and is limited to lifting the load just enough to clear the floor, without the ability to stack or operate at height. Thus, electric forklifts are used in more demanding applications requiring vertical load movement and greater capacity, whereas pallet trucks are ideal for short-range, low-height material transport. Figure 6 presents a boxplot showing the energy demanded by the LM (in kWs or equivalently kJ) during the load lifting process performed by the electric forklift, as a function of the lifted weight (in kg). Each box illustrates the variability in energy demand for a specific weight, highlighting the median (red line), interquartile range (box limits), and extreme values (whiskers). Although there is a general trend of increasing energy consumption with increasing weight, the relationship is not linear. There are weight ranges where energy demanded shows high dispersion or even decreases compared to the previous weight level. Specifically, for weights above  
Figure 5: Extended view of original and filtered signals during 500.5 kg lifting operation: (**a**) voltage, (**b**) current, (**c**) and power.  
800 kg, energy consumption does not follow a clear increasing pattern. Overall, the figure indicates that there is no direct linear relationship between the lifted weight and the energy demanded, highlighting the need for a more detailed analysis.  
To clarify this behavior, Figure 7 shows LM power demand plots during vertical lifting of 800.5 kg, 1002.5 kg, and 1202.0 kg loads, each raised to a height of 2 m. This figure provides deeper insight into the power demand dynamics during lifting operations at higher load levels. By examining the instantaneous power profiles, it is possible to identify fluctuations, peak values, and the overall energy demanded by the LM, that may explain the non-linear relationship observed between energy consumption and lifted weight in Figure 6. Figure 7 displays the instantaneous demanded power in kW as a function of time in s, along with the total energy consumed (E) during the lifting process. This figure shows that the energy required to lift the load depends not only on the weight but also on the lifting time (or lifting speed). In subplot (b), the 1002.5 kg load is lifted more quickly, resulting in a peak power around \(\sim\)10 kW and lower total energy consumption of 93.1 kJ. In contrast, subplot (a) shows a lower peak power (\(\sim\)8.3 kW) but with a higher energy demand of 107.1 kJ due to a higher lifting time commanded by the operator. Figure 7c shows the highest peak power (up to 12 kW) but with the longer lifting time, indicating that the higher demanded energy (140.0 kJ) is mainly due to the higher load weight lifted (1202.0 kg). These plots support the conclusion that lifting speed commanded by the operator greatly influences the efficiency of the electro-hydraulic lifting system governed by the LM. A faster lifting speed may reduce the energy required even for higher load weights (as shown in Figure 7b), which explains the non-linear relationship between load weight and energy consumption observed in Figure 6. Therefore, lifting speed significantly influences the overall energy performance (i.e., energy efficiency) and should be considered in any load weight estimation strategy.  
Figure 6: Boxplot of the electric energy demanded by LM, as function of load weight during the lifting process.