A new uncertain analysis method and its application in vehicle dynamics

• A new uncertain analysis method for systems with hybrid uncertain parameters.
• The proposal of a Polynomial-Chaos-Chebyshev-Interval (PCCI) method.
• The proposal of two types of uncertainty evaluation indexes.
• The application in vehicle dynamics, such as a 4-DOF vehicle roll plan mode.

This paper proposes a new uncertain analysis method for vehicle dynamics involving hybrid uncertainty parameters. The Polynomial Chaos (PC) theory that accounts for the random uncertainty is systematically integrated with the Chebyshev inclusion function theory that describes the interval uncertainty, to deliver a Polynomial-Chaos-Chebyshev-Interval (PCCI) method. The PCCI method is non-intrusive, because it does not require the amendment of the original solver for different and complicated dynamics problems. Two types of evaluation indexes are established: the first includes interval mean (IM) and interval variance (IV), and the second are the mean of lower bound (MLB), the variance of lower bound (VLB), the mean of upper bound (MUB) and the variance of upper bound (VUB). The Monte Carlo method is combined with the scanning method to produce the reference results, and then a 4-DOF vehicle roll plan model is employed to demonstrate the effectiveness of the proposed method for vehicle dynamics.