Estimation of Tire Parameters by a Sensor–Fusion Approach

Abstract The research presents a physical–numerical model of a tire based on the finite element method (FEM). The hyperelastic Mooney–Rivlin solid model represents the behavior of nonlinear materials. To calibrate the uncertain parameters of the FEM model, accelerations obtained from inertial sensors (IMUs) are employed. The calibration process utilizes two complementary approaches: Power Spectrum Density (PSD) analysis and a quantum energy–based method for wavelet bands, referred to as wavelet energy quanta. These techniques enable the optimal estimation of Young’s modulus E opt and the coefficients of the Mooney–Rivlin model, ensuring that the simulated dynamic response a FEM aligns with the measured response a IMU . The calibrated FEM model accurately reproduces the relationship between the friction coefficient µ FEM and the drift angle ⍺, facilitating a direct comparison with Pacejka’s Magic Formula. While Pacejka’s empirical formulation offers a compact and widely accepted parametric representation, the proposed FEM–IMU model provides a more predictive perspective. This model is capable of capturing complex physical phenomena, including load distribution, structural deformation, damping, and material hysteresis. The discrepancies observed in the Pacejka curve depend on the actual viscoelastic and thermodynamic characteristics of the tire, which are not fully captured by the hyperelastic Mooney–Rivlin model or the simplified modeling of the wheel–road contact. However, the FEM–IMU approach demonstrates significant adaptability and predictive capabilities, indicating a promising direction for automatically calibrating constituent parameters and creating physically coherent models of tire dynamic behavior. Additionally, the proposed methodology minimizes parameter uncertainty through robust multi–resolution spectral comparison. This advancement paves the way for a new generation of hybrid physical–data–driven models, enhancing the material and performance characterization of tires.