Desenvolvimento de Soft-Sensors utilizando MGGP e aprendizado de máquinas para estimação de forças de veículos com pneu inteligente

Abstract

With technological advancement, vehicles have evolved from purely mechanical systems to intelligent platforms equipped with embedded sensing. Although this instrumentation increases vehicle intelligence and safety, it also raises costs, limiting the dissemination of advanced technologies. In this context, Soft Sensors become an alternative by inferring quantities of interest from correlated variables measured by low-cost sensors, as is the case with Intelligent Tires. In this work, we develop Soft Sensors based on NARX (Nonlinear AutoRegressive with eXogenous inputs)/FIR (Finite Impulse Response) models identified by the evolutionary algorithm MGGP (Multigene Genetic Programming) to estimate the forces Fx, Fy and Fz on the wheels of a passenger vehicle, using exclusively acceleration data from intelligent tires. The problem was formulated as MIMO, since the inputs correspond to the accelerations in the three axes along the tire rotation angle and the outputs are the three forces. The input features were extracted in the contact patch region, organized by rotation angle with a resolution of 2.5 ◦ , evaluating three intervals (±10◦ , ±20◦ and ±35◦ ), different delay configurations and two training strategies, with tire-specific models and models trained with all four tires simultaneously (generalization). The validation included maneuvers with different predominant forces (straight line, Slalom, Double Lane Change, constant cornering, cornering with braking and random steering), in addition to a comparison with machine learning models (LSTM, GRU and MLP) using the MAPE and R 2 metrics. The results indicated that the ±10◦ interval tends to produce less accurate models with higher variance, while ±20◦ and ±35◦ showed paired performance, suggesting that ±20◦ is already sufficient for force prediction. It was also observed that models with only one delay can reduce variance and outperform configurations with multiple delays. In the best case, considering the critical forces associated with each operating condition, the NARX/FIR models identified via MGGP achieved MAPE ≤ 12% and R 2 ≥ 0.80 for these predominant forces, maintaining superior performance compared to LSTM, GRU and MLP under the evaluated conditions. Regarding generalization, models trained with data from all four tires simultaneously showed competitive performance compared to specific ones, reinforcing the practical relevance of the MIMO/generalist approach. Structural analysis revealed relevant couplings between forces, with recurrence of autoregressive terms between Fy and Fz . Finally, the NARX/FIR models via MGGP outperformed LSTM, GRU and MLP under the evaluated conditions, maintaining low complexity by using only 63 parameters. Thus, the results confirm the potential of intelligent tires and MGGP for estimating dynamic quantities, with implications for more accessible, redundant and safe vehicle systems.