Data-Driven Modeling of Tire–Soil Interaction With Proper Orthogonal Decomposition-Based Model Order Reduction

A data-driven model capable of predicting time-domain solutions of a high-fidelity tire–soil interaction model is developed to enable quick prediction of mobility capabilities on deformable terrain. The adaptive model order reduction based on the proper orthogonal decomposition (POD), for which the high-dimensional equations are projected onto the reduced subspace, is utilized as the basis for predicting the time-domain tire–soil interaction behavior. The projection-based model order reduction, however, requires many online matrix operations due to the successive updates of the nonlinear functions and Jacobians at every time-step, thereby hindering the computational improvement. Therefore, a data-driven approach using a long short-term memory (LSTM) neural network is introduced to predict the reduced order coordinates without the projection and time integration processes for computational speedup. With this model, a hybrid data-driven/physics-based off-road mobility model is proposed, where four separate LSTM-POD data-driven tire–soil interaction models are integrated into the physics-based multibody dynamics (MBD) vehicle model through a force–displacement coupling algorithm. By doing so, the individual data-driven tire–soil interaction model can be constructed efficiently, and the MBD and LSTM models are assembled as a single off-road mobility model and analyzed with existing off-road mobility solvers. The predictive ability and computational benefit of the proposed data-driven tire–soil interaction model with the POD-based model order reduction are examined with several numerical examples.