## 4 Simulation Results  
In order to verify the effectiveness of the proposed method, simulation tests were conducted under a test driving cycle, which was a random combination of six standard driving cycles: NurembergR36, HL05, SC03, REP05, HWFET, and FTP. The velocity profile of the cycle and the result of the on-line DPR are shown in Figure 9. The sampling time for the simulation was 0.1 s. Both the initial and the reference SOCs were set to 0.7. For simplicity, the proposed adaptive-ECMS based on DPR is hereinafter referred to as the \"proposed method\". In this part, simulation results are demonstrated to verify the drivability improvements. Comparison of the torque split factor is shown in Figure 10. When the weighting factor \(\alpha=0\), the engine on/off events took place as much as 828 times for the test cycle. After the constraint was imposed, the frequency of changing of the torque split factor decreased to a large extent, which means that less driving mode switching occurred, better drivability could be expected, and engine on/off events dropped by 62.6%. Improvement of the CVT speed ratio signal is shown in Figure 11. When the weighting factor \(\beta=0\), the fluctuation of the speed ratio was rather frequent and drastic. After the constraint was imposed, the speed ratio signal was smoothed and more representative of real-world driving behavior. Although the introduction of penalty terms inherently leads to extra fuel consumption, for the test cycle, the equivalent fuel consumption only increased by 1.1%, which is fairly acceptable. Figure 8: Schematic diagram of the adaptive equivalent consumption minimization strategy (A-ECMS). Figure 9: Velocity profile and the DPR result. To examine the fuel economy improvement of the proposed method, an adaptive-ECMS with a PI controller and a DPR-algorithm-based A-ECMS as reported in [17] were calculated under test cycles for comparison. For simplicity, the former is referred to as the \"A-ECMS\", and the mean equivalent factor of four driving patterns for an initial SOC of 0.7 was selected as the nominal equivalent factor. The latter is referred to as the \"DPR A-ECMS\", in which the nominal equivalent factor was periodically updated only by the selected driving pattern. The off-line ECMS with an optimal equivalent factor served as the benchmark for the on-line strategies. In Figure 12, the optimal equivalent factor for the corresponding test cycle was 2.987, and the equivalent factors for on-line strategies varied continuously with time and fluctuated around the optimal equivalent factor. As can be seen from Figure 13, for the proposed method, the battery SOC decreased at the beginning of the driving cycle, since the nominal equivalent factor was relatively smaller, and the penalty for the use of battery power was smaller as a result. At about 1200 s, when the HEV was in engine recharge mode, the vehicle speed suddenly decreased, and the battery SOC increased to 0.9 due to the braking energy regeneration. At this time, the equivalent factor decreased rapidly to penalize the output of the engine power, and the SOC was quickly controlled within the target range. At the end of the test cycle, compared with the off-line ECMS, the SOC for on-line strategies did not perfectly converge with the initial SOC; however, the proposed method showed better robustness. Note that for A-ECMS, better fuel economy and SOC management can be expected for a smaller nominal equivalent factor. Figure 11: Comparison of the CVT speed ratio. Figure 10: Comparison of the torque split factor. The comparison of the cumulated fuel consumption and the final SOC is shown in Table 4. The fuel consumption for the DPR A-ECMS was very close to that of the proposed method and off-line ECMS; however, the constraint effect on the final state was relatively poor. Considering the correction of the total fuel consumption at the end of the driving cycle, the actual fuel consumption will be even higher.