Observing Liquid Sloshing Based on a Multi-Degree-of-Freedom Pendulum Model and Free Surface Fluctuation Sensor

Rollover prevention of partially filled tank trucks is an ongoing challenge in the road transportation industry, with the core challenge being real-time perception and observation of the liquid state inside the tank. In order to realize reliable observation of a sloshing liquid, this article first proposes a sloshing modeling method based on a multi-degree-of-freedom pendulum model and derives the double mass trammel pendulum model (DMTP, 2DOF) accordingly, which accurately reflects the sloshing dynamics under wider operating conditions. Second, a free surface fluctuation sensor is designed based on magnetostriction, capable of measuring the inclination and height of the liquid level inside tanks filled with hazardous chemicals. Finally, the unscented Kalman filter (UKF) is utilized to synthesize the information of the two, establishing a credible real-time observation of the sloshing liquid. Verified using a vehicle–fluid coupled co-simulation, under the condition of a consecutive double lane change, the observation error of the proposed method is only 25.9% of that of the open-loop calculation, providing a secure guarantee for the observation of the state variables of the single pendulum model (SP) used for most kinds of anti-rollover control.