## 4 Results  
### RDE Tests  
The analysis of cycles was performed by looking at the dynamic variables' distribution [32]. In this analysis, the vehicle speed, torque, engine speed, and power were divided into five segments. Figure 5 shows the distribution frequency of these parameters for each RDE cycle. In the case of the vehicle speed, the groups were divided into intervals of 25 km/h till up to 100 km/h, and one more for speeds higher than 100 km/h. The engine torque was also divided into groups of 50 Nm. The engine speed was divided into groups of 50 rpm and, finally, the power in groups of 20 kW. The events in which the power and torque were less than zero corresponded to events when the engine was dragging or the driver was braking. At first sight, the cycles show a great dispersion between each other and consider that all of them are valid, evidencing that a wide variety of cycles fit the regulation. In the case of RDEs 5 and 6, considering that the vehicle speed and power distribution were identical (as defined), the different driver behavior led to different engine operating conditions in terms of torque, engine speed, pedal position, etc. Figure 5c shows that RDE 6 had much fewer points in the strip of greater than 2750 rpm since driver behavior was programmed with the aim that it did before the gearshift, avoiding high engine speed. It could be representative of the down speeding technique [33], which is a current trend where the goal is that the engine works at high performance reducing consumption and, as far as possible, pollutant emissions. The cycles were divided into 13 different bins depending on vehicle speed and power for a deeper analysis. Table 5 shows the conditions of those bins. Figure 5: Distribution of (**a**) vehicle velocity, (**b**) torque, (**c**) engine speed, and (**d**) power. Figure 6 shows the results of the 13 bins applied to the 6 RDE cycles. It can be seen that the dispersion between these cycles increases in the higher power region (bin 8 onwards). As an example, the RDE 2 cycle does not present any values in bins 8, 11, and 12, which denotes that the power was below 40 kW in the urban area. It can also be observed in RDE 2 bin 13, corresponding to the maximum motorway power fraction, the time proportion was the lowest, corresponding to few accelerations and having steadier driving. Another interesting aspect is that RDE 1 was the only one that went into all bins, which implies that this test would make the engine work in more diverse operating conditions than the other ones. Looking at RDEs 3 and 4, and the bins that represent the urban area (3, 6, 9, and 12), the values of bins 3 and 6 are very similar. However, bin 9 of RDE 3 is equal to zero but 0.64% in RDE 4, which involves bigger power that was reached in this cycle in the urban zone due to a higher dynamic solicitation. RPA and VA [95] values also point it out, with RDE 4 above RDE 3, as observed in Figure 3.  
Finally, RDEs 5 and 6 are those that have been generated to avoid aggressive driving. It is especially noticeable in the motorway zone, where the highest values are in bin 7 (low power zone), whilst bins 10 and 13 are less representative. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & \multicolumn{3}{c}{**Power [kW]**} & \\ \hline  & & & - & **>0** & **>20** & **>40** & **>60** \\  & & & \(\leq\)**0** & \(\leq\)**20** & \(\leq\)**40** & \(\leq\)**60** & **-** \\ \hline Dragging & & & Bin 0 & - & - & - & - \\  & \(=\)0(Idle) & & Bin 1 & - & - & - & - \\ Vehicle Speed & \(\geq\)0 & \(<\)60 & - & Bin 2 & Bin 5 & Bin 8 & Bin 11 \\ \([\)km/h\(]\) & \(\geq\)60 & \(<\)90 & - & Bin 3 & Bin 6 & Bin 9 & Bin 12 \\  & \(\geq\)90 & - & - & Bin 4 & Bin 7 & Bin 10 & Bin 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Division of the test into different bins depending on vehicle speed and power. Figure 6: Bin proportions from 2 to 4 (a), 5 to 7 (b), 8 to 10 (c) and 11 to 13 (d) of each cycle.