Probability density evolution method for vehicle dynamics analysis under uncertainty

Because of the uncertainties and highly nonlinear characteristics of intelligent vehicles, how to control the motion of intelligent vehicles more accurately and effectively has become the key to the development of intelligent vehicles. In this paper, based on the nonlinearity and parametric uncertainty of the suspension system, the probability density evolution method is used to analyze the variation of the probability density of the suspension dynamic response over time, in order to facilitate more effective motion control. Combining the dynamic random state equation of the suspension and the probability conservation principle in the conservative stochastic system, the generalized probability density evolution equation for vehicle random vibration is established. Considering the nonlinear stiffness of the hydro-pneumatic spring in the suspension system and the uncertainties of the parameters, such as the suspension and the tire, the stochastic vibration response analysis was performed with the sprung-mass acceleration response as an example. The random probability space is discretely selected by the number-theoretic method. Finite-difference method such as Lax-Wendroff scheme and TVD (Total Variation Diminishing) scheme is used to numerically solve the generalized probability density evolution equation, and the variation of the probability density of the response is obtained. The probability density evolution method has good calculation accuracy and can give specific probability distribution information, which lays a foundation for subsequent motion control.