Physics-constrained multi-output cGAN for efficient prediction of triaxial tyre-road contact stresses

Abstract

Accurate characterization of the triaxial contact stress field at the tyre-road interface is crucial for tyre design and pavement analysis; however, classic measurements and finite-element (FE) simulations are both costly and time-consuming. This paper presents a physically constrained multi-output conditional generative adversarial network (PMOC-GAN), which can rapidly predict the triaxial stress distribution at the contact interface between the tyre and the road. Once trained on FE-generated stress fields, the PMOC-GAN requires only tyre pressure, load, rolling speed, and slip ratio to generate full-field maps of vertical, longitudinal, and transverse stress across the entire contact patch. The network uses a three-branch generator and axis-specific discriminators to model directional stress features, with mechanical and friction constraints ensuring physical consistency. Evaluated on a 235/65R18 Standard tyre dataset, the PMOC-GAN achieves kilopascal-level mean absolute errors, and reduces MSE by approximately 27–34% compared with the cGAN baseline. Through transfer learning, the model adapts to a structurally similar 235/65R18 Low-cost tyre using only 225 target samples, reducing the prediction error by approximately 65% relative to training from scratch and markedly decreasing data requirements. These results demonstrate an efficient and transferable deep learning tool for modeling tyre-road interaction.