## 4 SMC Parameters Tuning Based on PACSA
### Design of Objective Function based on AHP
#### 4.1.2 Weighting Coefficient Optimization of the Objective Function based on AHP  
The weighting coefficients have a great influence on the value of the objective function; therefore, it is essential to reasonably select the weighting coefficients of the objective function. In this study, the weighting coefficients are determined by AHP to avoid multifarious trial and error. AHP is used for multi-criteria decision making in which the factors are arranged in a hierarchical structure [33]. The weight coefficients evaluation process of the objective function based on AHP is shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**RMS**} & \(\sigma_{\tilde{z}_{s}}\) & \(\sigma_{\tilde{\varphi}}\) & \(\sigma_{z_{sl}-z_{sl}}\) & \(\sigma_{z_{ur}-z_{ur}}\) & \(\sigma_{z_{ul}-z_{ql}}\) & \(\sigma_{z_{ur}-z_{qr}}\) \\  & 0.92 & 1.18 & 0.032 & 0.0008 & 0.00214 & 0.0096 \\ \hline \multirow{2}{*}{**Quantized ScaleFactor**} & \(\gamma_{1}\) & \(\gamma_{2}\) & \(\gamma_{3}\) & \(\gamma_{4}\) & \(\gamma_{5}\) & \(\gamma_{6}\) \\  & 1 & 0.6 & 826.56 & 13,225 & 184,819.64 & 9184.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quantized scale factor values table. 1. Set up hierarchical analysis model  
The hierarchical analysis model is displayed in Figure 8, where the first level evaluation feature is composed of ride comfort and handling stability during the vehicle driving. The second level evaluation feature includes vehicle vertical acceleration, dynamic deflection of left and right tire, left- and right-side suspension dynamic deflection, and roll angle acceleration of the vehicle. Therefore, the structure of the hierarchical analysis model is derived from the objective function to acquire the priority of the evaluation feature on each level. 2. Construct judgment matrix \(T\)  
The judgment matrix \(T\) is applied to distinguish the relative emphasis of evaluation features per hierarchical layer. T is constructed by using a nominal scale from 0 to 9 with the value \(a_{ij}\), which is assigned to express the relative importance of evaluation element \(a_{i}\) over \(a_{j}\). The matrix \(T=\left\{a_{ij}\right\}\) is established by the importance comparison between evaluation features. 3. Calculate weight vector corresponding to \(T\)  
The weight vector can be written as \(\Lambda=\left(\tau_{1},\tau_{2},\ldots,\tau_{r}\right)^{T}\), where \(r\) denotes numbers of evaluation features per level. \(\Lambda\) is gained through the normalization process for judgment matrix T.  
Figure 8: Hierarchical analysis model of AHP. Figure 7: Weight coefficients evaluation process based on analytic hierarchy process (AHP). 4. Consistency check of judgment matrix  
Generally, CI (consistency index) is used to check the consistency deviation of the judgment matrix, whose expression is shown as follows. \[CI=\frac{\eta_{\max}-m}{m-1} \tag{26}\]  
where \(m\) represents the order of judgment matrix \(T\). \(\eta_{\max}\) indicates the root of maximum eigenvector value. At the same time, the formula of \(\eta_{\max}\) is displayed as follows. \[\eta_{\max}=\sum_{i=1}^{r}\frac{\left(T\tau\right)_{i}}{r\tau_{i}} \tag{27}\]  
In addition, in order to check the consistency more effectively, CR (ratio of consistency check) is introduced as shown in the following equation. \[CR=\frac{CI}{RI} \tag{28}\]  
where RI is the reference criterion, and Table 3 shows the value of RI. If the value of CR is less than 0.10, it means that the consistency check is qualified. 5. Calculate the weight of evaluation features per level  
If the judgment matrix satisfies the consistency, then the weight of the evaluated feature on each level is the eigenvector obtained; otherwise, the eigenvector needs to be calculated. The weights of evaluation features on two levels can be calculated by means of the four steps mentioned above. If \(\tau_{first}=\left\{\rho_{i}\right\}\), \(\tau_{\sec{ond}}=\left\{q_{j}\right\}\), then the weight of the lowest level feature is described as follows.