Damper-B-PINN: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Vehicle State Estimation

TL;DR

This work tackles dynamic wheel-load estimation in noisy vehicle environments by combining a refined suspension linkage-level model with a Bayesian physics-informed neural network. The Damper-B-PINN framework integrates a damper-characteristic physics conditioning module (DPC) and a normal-sigmoid dropout-based variational inference to fuse physics priors with data while quantifying uncertainty. Key contributions include a 2-DOF suspension model, a physics-conditioned Bayesian learning scheme, and extensive validation on CarSim simulations and a Formula Student race car, demonstrating improved accuracy and robustness over state-of-the-art PINN baselines under diverse and extreme conditions. The approach has practical implications for ADAS and high-performance vehicle control, with future work aimed at enabling real-time onboard implementation and broader chassis validation.

Abstract

Accurate state estimation is fundamental to intelligent vehicles. Wheel load, one of the most important chassis states, serves as an essential input for advanced driver assistance systems (ADAS) and exerts a direct influence on vehicle stability and safety. However, wheel load estimation remains challenging due to the complexity of chassis modeling and the susceptibility of nonlinear systems to noise. To address these issues, this paper first introduces a refined suspension linkage-level modeling approach that constructs a nonlinear instantaneous dynamic model by explicitly considering the complex geometric structure of the suspension. Building upon this, we propose a damper characteristics-based Bayesian physics-informed neural network (Damper-B-PINN) framework to estimate dynamic wheel load, which leverages the suspension dynamics as physical guidance of PINN while employing Bayesian inference to mitigate the effects of system noise and uncertainty. Moreover, a damper-characteristic physics conditioning (DPC) module is designed for embedding physical prior. The proposed Damper-B-PINN is evaluated using both high-fidelity simulation datasets generated by CarSim software and real-world datasets collected from a Formula Student race car. Experimental results demonstrate that our Damper-B-PINN consistently outperforms existing methods across various test conditions, particularly extreme ones. These findings highlight the potential of the proposed Damper-B-PINN framework to enhance the accuracy and robustness of dynamic wheel load estimation, thereby improving the reliability and safety of ADAS applications.

Figures (8)

• Figure 1: Testing platform (A Formula Student racing car) and standard testing circuits.
• Figure 2: Overview of the proposed damper characteristics-based Bayesian physics-informed neural network (Damper-B-PINN) framework: (1) Bayesian Estimation: We employ a novel variational inference method with normal-sigmoid dropout to estimate the posterior distribution of the network parameters. (2) Physics Conditioning Embedding: A damper characteristic feature-wise conditioning module deeply embeds physical information to guide the model.
• Figure 3: Front suspension model for wheel load estimation: Two-degree-of-freedom (2 DOF) with bumping and steering.
• Figure 4: Structure of the proposed DPC module.
• Figure 5: Overview of the experiments: The input data are directly obtained by software in the simulation, while in the real-world experiments, they are collected by the corresponding sensors on the chassis. In the simulation, 14 types of vehicle models and 10 types of scenarios are selected for data collection. The real-world experiments are conducted on a Formula Student race car and completed in a standard test site. The collected data undergo offline calculation to obtain the output.