## 3 Proposed Credibility Evaluation Methodology
### Dynamics-Based Fidelity Evaluation
Here, \(a_{x},a_{y}\), and \(a_{z}\) represent the vehicle's acceleration along the X-, Y-, and \(Z\)-axes, respectively [52]. \[F_{x} =m\cdot a_{x},\] \[F_{y} =m\cdot a_{y}, \tag{17}\] \[F_{z} =m\cdot(a_{z}-g).\]  
The equation of a vehicle's rotational motion explains the relationship between torque (moment) and angular acceleration when the vehicle rotates around each axis. Rotational motion is defined by the relationship \(M=I\cdot\alpha\), which corresponds to [PERSON]'s second law. Here, the moment of inertia (\(I\)) along each axis quantifies an object's resistance to rotational motion. The rotational motions of a vehicle can be represented by Equation (18), which can be utilized to predict and control the vehicle's attitude changes. Here, \(M_{x}\), \(M_{y}\), and \(M_{z}\) denote the roll moments generated around the X-, Y-, and Z-axes of the vehicle; \(I_{x}\), \(I_{y}\), and \(I_{z}\) represent the vehicle's moments of inertia in the roll, pitch, and yaw directions; and \(\bar{\phi}\), \(\bar{\theta}\), and \(\bar{\psi}\) represent the corresponding angular accelerations, respectively [53]. \[M_{x} =I_{x}\cdot\bar{\phi},\] \[M_{y} =I_{y}\cdot\bar{\theta}, \tag{18}\] \[M_{z} =I_{z}\cdot\bar{\psi}.\]  
To quantitatively assess the dynamic consistency between simulation tests and real-vehicle tests, the normalized root-mean-square error (NRMSE) was adopted as the primary evaluation metric. NRMSE expresses the deviation between two datasets in a standardized form, enabling objective comparison between variables of different scales [54]. In this study, the credibility of the simulation model was evaluated by systematically quantifying the differences between the simulation results and experimental data based on NRMSE. This evaluation methodology is defined by Equations (19) and (20):  
\[f_{4}(y_{1},\,y_{2})=\sqrt{\frac{1}{N}\Sigma_{i=1}^{N}(y_{2,i}-y_{1,i})^{2}}, \tag{19}\]  
\[f_{5}(y_{1},y_{2})=\frac{f_{4}(y_{1},\,y_{2})}{y_{2,max}-y_{2,min}}\times 100, \tag{20}\]  
where \(y_{1,i}\) and \(y_{2,i}\) denote the experimental and simulation data, respectively; \(N\) is the total number of data samples; and \(y_{2,max}\) and \(y_{2,min}\) refer to the maximum and minimum values of the experimental or simulation dataset, respectively. The dynamic consistency index, derived from the test parameters in the 6 DOF motion equations, is computed by cross-comparing the \(i\)-th and \(j\)-th repetitions of the XILS and real-vehicle tests. When the \(k\)-th scenario is repeated \(N\) times in both the XILS and real tests, the results for the \(q\)-th DOF in the \(i\)-th XILS repetition and the \(j\)-th real-test repetition are denoted by \(D_{q}\big{(}v_{k|i}\big{)}\) and \(D_{g}\big{(}r_{k|j}\big{)}\), respectively. Based on the comparison metric \(f_{5}\), the dynamic similarity indices for the three types of comparisons between the \(i\)-th and \(j\)-th repetitions can be expressed by Equations (21)-(23):  
\[D_{q}(v_{k})_{ij}=f_{5}\big{(}D_{q}(v_{k}|i),D_{q}(v_{k}|j)\big{)}  
Equation (23) constitutes a multi-valued dynamic similarity index considering the cross-comparison between repeated tests. To represent these values as a single value for each scenario, Equations (24)-(26) are utilized:  
\[D_{q}\;(v_{k})=\frac{2}{N(N-1)}{\sum_{i=1}^{N-1}}{\sum_{j=2}^{N}}D_{q}(v_{k})_{ ij}, \tag{24}\]  
\[D_{q}\;(r_{k})=\frac{2}{N(N-1)}{\sum_{i=1}^{N-1}}{\sum_{j=2}^{N}}D_{q}(r_{k})_{ ij}, \tag{25}\]  
\[F_{y} =m\cdot a_{y}, \tag{17}\]0  
The values computed through the three types of comparisons based on Equation (26) represent the dynamic consistency index of the \(q\)-th DOF parameter for the \(k\)-th scenario.