## 5 Discussion and Sensitivity Analysis of RRBCS Based on the Optimization Results  
From the above discussion, it could be seen clearly that on the three different tire-road adhesion condition, the influence of control parameters on the performance of RRBCS was different. Therefore, simulation tests were designed to analyze the sensitivity of the different tire-road condition to optimization objective functions. The simulation results of three driving cycles were statistically analyzed, as shown in Figures 14-16.  
As depicted in Figure 14, when the PTAC was in the range of 0-0.35 and 0.55-1.0, \(I_{bp\_cyc}\) were similar and close before and after parameters optimization. There was a significant difference before and after optimization when the PTAC was in the range of 0.35-0.55. Compared with the braking process controlled by RRBCS before parameters optimization, \(I_{bp\_cyc}\) decreased significantly and \(\Delta I_{bp\_cyc}\) was up to about 7% when \(\mu_{max}\) = 0.38. In addition, the performance result of recovery energy was similar to BP. As depicted in Figure 15, when the adhesion coefficient was in the range of 0.35-0.5, the recovery braking energy controlled by the proposed control strategy after parameters optimization was about 26.71%. Compared with the braking process controlled by RRBCS before parameters optimization, the recovery braking energy could improve 19.3% after parameters optimization, which denotes that the RRBCS was effective to improve the regenerative energy after parameters optimization.  
As depicted in Figure 16, when the tire-road adhesion coefficient was in the range of 0.2-0.5, after parameters optimization, \(I_{bclr\_cyc}\) reduced slightly and \(\Delta I_{bclr\_cyc}\) was up to about 1.2% when \(\mu_{max}\) = 0.52. When the adhesion coefficient was in the range of 0.55-0.75, \(\Delta I_{bclr\_cyc}\) decreased significantly and \(\Delta I_{bclr\_cyc}\) was up to about 5.3% when \(\mu_{max}\) = 0.63, which denotes that the RRBCS was effective to reduce the battery capacity loss rate after parameters optimization.  
The optimization calculation results are shown in Table 5.  
As shown in Table 5, after parameters optimization, \(I_{bp\_cyc}\) reduced about 4.7%-7.1% when \(\mu_{max}\) = 0.38, \(I_{rble\_cyc}\) reduced about 16.1%-19.3% when \(\mu_{max}\) = 0.42, and \(I_{bclr\_cyc}\) reduced about 4.8% when \(\mu_{max}\) = 0.62. As a comparison, the results of this optimal response to different tire-road conditions reflected different performances, which means that the sensitivity of optimization parameters to different road conditions was different. This is due to three main reasons: first, the vehicle's safety is the main factor in the emergency situation, and the optimization direction is more focused on ensuring braking safety, especially on low and medium tire-road adhesion conditions; second, the regenerative braking torque will \"enter ahead\" to increase the regenerative braking energy while ensuring braking safety; and third, regenerative braking torque participates in energy recovery in advance, which causes increased recovery current from zero. Overall RRBCS was robust to change on the road conditions and the effectiveness of the proposed strategy could be verified by tests.  
Figure 16: Optimization results in three driving cycles before and after optimization: (a) \(I_{bclr\_cyc}\) and (b) \(\Delta I_{bclr\_cyc}\).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{3}{c}{\(I_{bp\_cyc}\)} & \multicolumn{3}{c}{\(I_{rble\_cyc}\)} & \multicolumn{3}{c}{\(I_{bclr\_cyc}\)} & \multicolumn{3}{c}{\(I_{bclr\_cyc}\)} \\ \cline{2-10}  & **WLTP** & **NEDC** & **CLTC** & **WLTP** & **NEDC** & **CLTC** & **WLTP** & **NEDC** & **CLTC** \\ \hline \(\mu_{max}\) & 0.38 & 0.38 & 0.38 & 0.42 & 0.42 & 0.42 & 0.64 & 0.62 & 0.62 \\ \(\Delta I_{max}\) (\%) & \(-\)4.7 & \(-\)7.1 & \(-\)5.9 & \(-\)16.1 & \(-\)19.3 & \(-\)18.4 & \(-\)4.9 & \(-\)4.8 & \(-\)4.8 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results of optimization.