## 4 Conclusions  
In the presence of parameter uncertainty, this study analyzed the ride comfort stochastically through the simulation of a fully coupled human-vehicle model using CarSim software combined with MATLAB/Simulink. Ride comfort was evaluated quantitatively as a ride index using a human-vehicle model according to the BS-6841 standard. In addition, a generalized polynomial chaos extension (gPC) framework was proposed to compute the stochastic response of the human model. Comparing the computational time of gPC with Monte Carlo simulation (MCS), the former proved to be 160 times faster than the latter.  
We also carried out a parametric study of stochastic ride comfort in terms of nonlinearities and uncertain parameters in human models. Two main results were observed. First, the translational parameters of the human model are much more important than the torsional parameters when comparing the standard deviations of the ride index. Second, the use of a nonlinear human model shows that the standard deviation of the ride index is  
Figure 14: Mean and standard deviation of ride index with respect to uncertain damping calculated using the nonlinear and linear human models, where the 1 st column is the mean, the 2 nd column is the standard deviation for \(c_{1}^{*}\), and the 3 rd column is the standard deviation for \(c_{3}^{*}\).  
significantly different from the linear model. Based on the above observations, it can be concluded that the uncertain quantification method and the nonlinear human model are needed for more accurate and precise ride comfort analysis.  
This study also showed the distribution of ride comfort according to the road surface when there is a deviation in the stiffness and damping coefficient for drivers of average body type and weight. In a real driving environment, factors such as posture, road surface, and driving conditions are constantly changing, leading to changes in weight distribution and skin/seat deformation. As a result, even for the same driver or passenger, the response of the human body to vibration becomes unpredictable and uncertain. We expect that the proposed gPC framework can play an important role in automotive engineering as the demand for ride comfort continues to increase. For example, automotive engineers can gain insights from this study to design seats that are robust in terms of ride comfort. In this study, the parameters of \(k_{1}\), \(k_{3}\), \(c_{1}\), and \(c_{3}\) of the human model represent the springs and dampers that connect the human body to the seat cushion. Therefore, based on the results of the study, it is possible to find the optimal seat design parameters that improve ride comfort with a small standard deviation.  
Conceptualization, B.-G.S., J.-J.B. and N.K.; methodology, B.-G.S. and J.-J.B.; software, B.-G.S. and J.-J.B.; validation, B.-G.S. and J.-J.B.; visualization, B.-G.S.; writing--original draft preparation, B.-G.S. and J.-J.B.; supervision, N.K.; funding acquisition, N.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MIST) (No. 2020R1A2C2013256).  
Not applicable.  
The authors declare no conflict of interest.