## 4 GKL Algorithm of Active Suspension
### Active Suspension Machine Learning Dataset  
The performance of vehicle suspension is affected by many factors, which can be divided into internal and external factors. In terms of the internal factors, according to the LQR control principle, the selection of weighting coefficients has a great influence on the control effect. In terms of the external factors, the performance of suspension is affected by road roughness and vehicle motion state. Therefore, we take these two kinds of factors into account together. We selected five factors, including road class, vehicle speed \(u\), DTD weighting coefficient \(q_{1}\), SWS weighting coefficient \(q_{2}\), and BA weighting coefficient \(q_{3}\) as independent variables to carry out simulations and build the machine learning dataset of LQR control active suspension. In the sample simulation, the BA weighting coefficient \(q_{3}\) is set as 1 for simplification, and the other four factors are selected as independent variables. The construction process of the machine learning dataset is shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Road Class**} & \multirow{2}{*}{**Suspension Type**} & \multicolumn{4}{c}{**RMS Values**} \\ \cline{3-5}  & & **BA** & **SWS** & **DTD** \\ \hline \multirow{3}{*}{A} & Passive & 0.3377 & 0.0034 & 0.0011 \\  & GA-LQR & 0.2900 & 0.0023 & 0.0010 \\  & Improvement/\% & \(-14.14\%\)1  & \(-32.94\%\) & \(-7.30\%\) \\ \hline \multirow{3}{*}{B} & Passive & 0.6755 & 0.0068 & 0.0023 \\  & GA-LQR & 0.5780 & 0.0043 & 0.0021 \\  & Improvement/\% & \(-14.44\%\) & \(-36.62\%\) & \(-7.32\%\) \\ \hline \multirow{3}{*}{C} & Passive & 1.3526 & 0.0135 & 0.0045 \\  & GA-LQR & 1.1616 & 0.0091 & 0.0041 \\  & Improvement/\% & \(-14.12\%\) & \(-32.94\%\) & \(-7.19\%\) \\ \hline \multirow{3}{*}{D} & Passive & 2.7168 & 0.0271 & 0.0093 \\  & GA-LQR & 2.3298 & 0.0182 & 0.0086 \\ \cline{1-1}  & Improvement/\% & \(-14.25\%\) & \(-32.87\%\) & \(-7.58\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RMS values and improvement rate of suspension performance indexes. 1. Generate random numbers A possible weighting space is constructed based on the optimal solution optimized by GA. Two scaling factors, 1.75 and 1.1 in this case, are used to limit the range of weighting coefficients \(q_{1}\) and \(q_{2}\), that is \(q_{1}\in[0,120000]\), \(q_{2}\in[0,10000]\). Then, 50 random numbers are generated in their respective intervals to form 2500 combinations of the weights. The random numbers are generated with the Linear congruential method as follows. Generate random seeds: \[S_{0}=seed;\] (15) Generate random numbers: \[S_{i+1}=aS_{n}+b[MOD(M)]\] (16) where \(A\), \(B\), and \(M\) are integer constants, \(MOD\) is the remainder operation. The generated Two-dimensional random data points, \((q_{1i},q_{2j})\) in this case, are listed in Table 4;  
Figure 7: Process of constructing the machine learning dataset of LQR control active suspension. 2. Select road class According to the ride comfort test standards of passenger cars (ISO2631-1), the road roughness coefficient \(G_{0}\) of four road classes (A, B, C, and D) is selected in turn;
3. Select driving speed Select six driving speeds (5, 10, 15, 20, 25, and 30 m/s) in turn;
4. Select the weighting coefficients of performance indexes Select the weights \(q_{1}\) and \(q_{2}\) of DTD and SWS in turn;
5. Model simulation After all independent variables have been selected, the \(1/4\) vehicle model is run for simulation;
6. Construct the machine learning dataset of LQR active suspension The results of each simulation are output and saved in the form of a matrix to construct the machine learning dataset of LQR active suspension (\(4\times 6\times 50\times 50=60\),000 samples in total).