## 4 GKL Algorithm of Active Suspension
### Data Analysis Based on K-means Clustering Algorithm
#### 4.2.2 Evaluation of Clustering Results
Figure 10: Clustering results of B-20 subsets. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Cluster** & **Number** & \(\mathbf{q_{1}}\) & \(\mathbf{q_{2}}\) & **BA/(\(\mathbf{\mathrm{m}\cdot\mathrm{s}^{-2}}\))** & **SWS/m** & **DTD/m** & **dBA** & **dSWS** & **dDTD** & **L** & **Mode** \\ \hline
5 & 462 & 100,819 & 7448 & 0.6105 & 0.0046 & 0.0021 & \(-\)9.87\% & \(-\)31.06\% & \(-\)10.65\% & 2.4842 & \\
4 & 651 & 83,348 & 5899 & 0.5809 & 0.0048 & 0.0021 & \(-\)13.70\% & \(-\)28.50\% & \(-\)7.92\% & 2.4988 & \\
1 & 497 & 62,033 & 5133 & 0.5474 & 0.0049 & 0.0022 & \(-\)18.60\% & \(-\)25.71\% & \(-\)3.00\% & 2.5219 & \\
7 & 369 & 36,170 & 5662 & 0.5191 & 0.0053 & 0.0022 & \(-\)27.15\% & \(-\)29.69\% & \(-\)3.05\% & 2.5533 & \\
3 & 276 & 19,078 & 5693 & 0.4596 & 0.0053 & 0.0026 & \(-\)31.65\% & \(-\)19.80\% & 15.34\% & 2.6389 & \\
6 & 174 & 10,904 & 4452 & 0.4137 & 0.0057 & 0.0029 & \(-\)38.70\% & \(-\)14.75\% & 27.71\% & 2.7426 & \\
2 & 71 & 6744 & 2112 & 0.3476 & 0.0064 & 0.0034 & \(-\)48.23\% & \(-\)3.30\% & 47.01\% & 2.9548 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Averages of clustering results of B-20 subset. In Tables 6-8, the six different rows represent the changes in driving speed. For each row, we performed 2500 simulations with random weighting coefficients. The listed \(q_{1}\) and \(q_{2}\) are the weight's mean values after mode clustering. Then three performances, BA, SWS, and DTD, are calculated using these \(q_{1}\) and \(q_{2}\). Therefore, the weights would change a lot in different modes, that is to say, the same row's \(q_{1}\) and \(q_{2}\) are much different among the three tables. However, for the same mode (table), each weight matrix at a different speed may have close values. The analysis on the road changing is similar, comparing Table 8 with Table 9.  
Comparing the data in Tables 6-8, different modes have different changing rates of dBA, dSWS, and dDTD. The vehicle speed has less influence on the changing rate. There are diverse control effects of different modes. Comparing the data in Tables 7 and 8, it can be known that the three changing rates change very little with road conditions and driving velocities. It may prove that our classification with the GKL algorithm could guarantee a stable control effect. Therefore, we could assume that the average values of weight \(q_{1}\) and \(q_{2}\) can be used securely. This assumption also shows good adaptability for the new GKL control. The final values of the optimal weighting coefficients for the three performance modes are shown in Table 10. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Road Class** & **Speed** & \(q_{1}\) & \(q_{2}\) & \(\mathbf{BA_{a}/(m\cdot s^{-2})}\) & **SWS\({}_{a}\)/m** & **DTD\({}_{a}\)/m** & **dBA** & **dSWS** & **dDTD** & **L** \\ \hline \multirow{8}{*}{B} & 5 & 56,998 & 5298 & 0.2701 & 0.0025 & 0.0011 & \(-19.71\%\) & \(-25.56\%\) & \(-2.37\%\) & \(2.5236\) \\  & 10 & 63,974 & 5208 & 0.3890 & 0.0035 & 0.0015 & \(-18.27\%\) & \(-26.15\%\) & \(-4.03\%\) & \(2.5155\) \\  & 15 & 59,460 & 5158 & 0.4703 & 0.0043 & 0.0019 & \(-19.31\%\) & \(-25.72\%\) & \(-2.92\%\) & \(2.5206\) \\  & 20 & 62,033 & 5133 & 0.5474 & 0.0049 & 0.0022 & \(-18.60\%\) & \(-25.71\%\) & \(-3.50\%\) & \(2.5219\) \\  & 25 & 55,367 & 5247 & 0.6019 & 0.0056 & 0.0025 & \(-20.10\%\) & \(-25.37\%\) & \(-1.95\%\) & \(2.5258\) \\  & 30 & 59,849 & 5224 & 0.6671 & 0.0061 & 0.0027 & \(-19.17\%\) & \(-25.78\%\) & \(-3.07\%\) & \(2.5198\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Optimal solution and simulation results of comprehensive mode under B-class road.