Predictive Vehicle Stability Assessment Using Lyapunov Exponent Under Extreme Conditions

Under extreme conditions, vehicles may encounter critical instability and cause traffic accidents due to the tire force saturation. In such cases, accurately predicting the vehicle instability is conducive to vehicle safety because drivers or vehicle controllers can be alerted and take early interventions to ensure driving safety. However, the existing stability assessment methods tend to be conservative, hard to quantify, and often ignore the coupled longitudinal and lateral dynamics, as well as the nonlinear characteristics of tires. Simultaneously, under extreme operating conditions, the assessment of vehicle potential risk imposes higher demands on the prediction accuracy of vehicle motion states. To address these 2 issues, this paper proposes a predictive vehicle stability assessment method using 3-dimensional Lyapunov exponents (3D-LEs) for a nonlinear vehicle system. Firstly, a nonlinear 8-degree-of-freedom vehicle dynamics model is constructed for an electric vehicle, aiming to capture the coupling dynamic characteristics and the tire force saturation under extreme conditions. To minimize the simulation-reality disparities, the vehicle parameters are automatically calibrated through Bayesian optimization using field test data. Secondly, to predict the potential risk of vehicle instability precisely, a physics-informed neural network based state prediction module is established for the vehicle stability assessment system. The ordinary differential equations of the vehicle system are integrated into neural networks to obtain physically consistent predictions of vehicle dynamic motion. Finally, the 3D-LEs, encompassing lateral motion, yaw motion, and roll motion, are employed to concurrently evaluate vehicle stability. Experimental results demonstrate that the predictive vehicle stability assessment method accurately evaluates the stability of predicted state sequences, enabling safer and more stable control under extreme conditions.