Nonlinear car following behavior detection method integrating Gaussian process regression and stochastic differential equation modeling

Abnormal car-following behavior detection is critical for intelligent transportation and autonomous driving. Traditional deterministic models struggle with nonlinearity and stochasticity in real driving. This paper proposes a hybrid approach integrating Gaussian process regression (GPR) with stochastic differential equations (SDEs). First, inspired by molecular dynamics, we model car-following via three stimuli—distance difference, velocity difference, and a prediction term—to build a linearly weighted acceleration model. A molecular force field potential function uniformly describes repulsive and attractive effects, yielding a physically interpretable baseline. Then, GPR learns nonlinear residuals unexplained by this baseline, while SDEs capture inherent random fluctuations. Finally, a standardized anomaly score and adaptive threshold enable real-time detection and classification of abnormal behaviors. Experiments demonstrate that our fusion model effectively captures complex nonlinearities and randomness without sacrificing physical interpretability, offering a new pathway for safety warning and behavior analysis in connected and autonomous vehicle environments.