## 4 Results and Discussion
Among those cycles, dual-mode combustion can bring the largest benefit in the MANHATTAN cycle and the NYCC cycle, and the MPG improvement is around 9-10 percent compared with single SI mode combustion. The main reason is that for cycles with traffic, the engine's output power is limited by NVH constraints and the engine's operation is not in the efficient range, while HCCI combustion could have high efficiency under those conditions. Furthermore, Strategy 3 has minimal SOC fluctuations and relatively lower engine start times. Strategy 1 has the most frequent engine on/off switches due to the deficiency of hysteresis. From the aspect of the optimal EF parameters \(\alpha\) and \(\beta\), it is obvious that they are driving-cycle-dependent for all strategies. In other words, they are sensitive to the driving \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Cycle** & **Strategy** & \(\alpha\) & \(\beta\) & **MPG** & **Improvement (\%)** & **max \(\Delta\)SOC** & **Engine On/Off** \\ \hline \multirow{4}{*}{UDDS} & SI w/o NVH & 3.26 & 0.05 & 48.63 & & 0.86 & 179 \\  & SI w/NVH & 3.52 & 0.156 & 45.9 & & 4.05 & 26 \\  & SI/HCCI & 3.2 & 0.022 & 48.84 & 5.0 & 0.64 & 59 \\ \hline \multirow{4}{*}{HWFET} & SI w/o NVH & 3.2 & 0.026 & 43.7 & & 1.38 & 142 \\  & SI w/NVH & 3.27 & 0.023 & 42.43 & & 1.37 & 43 \\  & SI/HCCI & 3.19 & 0.024 & 44.28 & 3.1 & 0.9 & 27 \\ \hline \multirow{4}{*}{MANHATTAN} & SI w/o NVH & 3.27 & 0.025 & 36.95 & & 0.45 & 18 \\  & SI w/NVH & 3.68 & 0.021 & 33.31 & & 0.25 & 14 \\  & SI/HCCI & 3.22 & 0.02 & 37.04 & 9.9 & 0.24 & 25 \\ \hline \multirow{4}{*}{NYCC} & SI w/o NVH & 3.26 & 0.026 & 37.14 & & 0.54 & 14 \\  & SI w/NVH & 3.56 & 0.022 & 33.96 & & 0.35 & 11 \\  & SI/HCCI & 3.21 & 0.02 & 37.23 & 8.8 & 0.18 & 16 \\ \hline \multirow{4}{*}{US06} & SI w/o NVH & 3.12 & 0.035 & 37.29 & & 2.1 & 77 \\  & SI w/NVH & 3.16 & 0.027 & 36.44 & & 1.48 & 42 \\ \cline{1-1}  & SI/HCCI & 3.14 & 0.042 & 37.06 & 1.3 & 1.64 & 33 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of fuel economy and optimal EF between different strategies. conditions, and in Strategy 2, they have the highest sensitivity. In detail, \(\alpha\) is relatively larger in higher speed cycles, and \(\beta\) could vary significantly since it is required to reduce SOC fluctuations. However, in Strategy 3, both \(\alpha\) and \(\beta\) do not vary too much between different driving cycles, which can guarantee better robustness in real-time applications, since the load condition is usually unknown during real-world driving. To further investigate the improvement in fuel economy achieved by the dual-mode combustion engine, more data reflecting the engine and battery performance, such as the average BSFC and battery loss, were recorded as shown in Table 3.  
It can be seen that, under Strategy 1, the average BSFC of the engine is a constant for all the driving cycles, which is the global optimal value that the engine can achieve within the whole BSFC map. This is similar to the \"thermostat\" strategy, which also operates the engine at a fixed optimal point; however, the engine on/off algorithm is different between thermostat and Strategy 1, which results in a better fuel economy by applying ECMS, and the comparison is omitted here. With Strategy 2, the engine's output power is limited by the NVH constraint; thus, the achieved average BSFC was higher than the global optimum. Furthermore, in the MANHATTAN and NYCC cycles, the average BSFC is significantly higher than in the other strategies; this can explain the much lower MPG for these cycles under Strategy 2 in Table 2.  
With SI/HCCI dual-mode combustion, the engine will not always operate at the global optimal point which is in the SI combustion region. Therefore, the average BSFC of a cycle under Strategy 3 is lower than it is under Strategy 1. However, from Table 2, it can be seen that, in most of the cycles, Strategy 3 can achieve an even higher MPG than Strategy 1.