Numerical Solution of Stochastic Differential Equations with Application to Vehicle Handling

To solve the dynamic response problem that contains uncertain parameters needs, the stochastic differential equations needs to be calculated. Interval analysis has been widely used to solve engineering problems which contain many uncertain parameters usually. But the numerical solution method for stochastic differential equations based on the interval analysis method was seldom investigated. In this study a new numerical interval method for the stochastic differential equations based on the Euler's method is presented, which can be used to solve the linear system effectively and efficiently. The probabilistic and interval dynamics analysis of a two-degree-of-freedom bike car model with uncertain parameters are presented. Considering the automotive parameters which include the length from the front and rear axles to center of gravity of vehicle, front and rear tire cornering stiffness as interval variables, the lower and upper bound of the vehicle handling random responses are obtained by the proposed numerical interval method. The probabilistic dynamic responses of the vehicle handling are also obtained by using the Monte Carlo simulation method. The comparison between the numerical interval method and the Monte Carlo simulation method indicates the proposed numerical interval method is effective.