# Vertical Force Monitoring of Racing Tires: A Novel Deep Neural Network-Based Estimation Method
## 6 Conclusions  
In this paper, a novel hybrid methodology is proposed to address serious problems in vertical tire force estimation, particularly in cases involving dynamic and noisy conditions. The proposed approach improves the resilience and adaptability of tire force estimation tasks by combining advanced deep learning architectures with classic machine learning methods. The proposed method significantly enhanced Random Forest's performance by integrating deep learning-derived features. The proposed method was specifically designed to address the methodological constraints identified in the literature while leveraging existing network structures. These constraints include deformation frequency filtering limitations, reliance on tire geometric  
Figure 33: Performance of the proposed technique (RFADNN) at different speeds and under different pressure values: **(top)**: 30 km/h and 200 kPa, **(second)**: 50 km/h and 200 kPa, **(middle)**: 70 km/h and 200 kPa, **(fourth)**: 50 km/h and 220 kPa, **(bottom)**: 70 km/h and 220 kPa. parameters, computational challenges in vehicle model-based methods, and the inability to model sequential dependencies in Random Forest approaches. Our study successfully overcomes these challenges, achieving notable improvements in performance and robustness. Conventional filters that handle deformation frequency signals using cutoff frequencies frequently malfunction in a variety of pressure and speed scenarios. This problem was immediately solved by the Multihead Attention mechanism, which dynamically recognized and prioritized important patterns in the sequential data while adding pressure and speed as inputs to provide robustness against variation. Approaches reliant on geometric parameters such as tire radius or contact patch dimensions often encounter issues due to wear and pressure fluctuations. Our method addresses this limitation by utilizing raw sensor data and extracting features through deep learning layers, which enhances adaptability to dynamic conditions without the reliance on predefined geometric parameters. Some traditional methods rely on the double integration of acceleration signals to calculate peak radial displacement and relate it to vertical force, which can result in misleading estimations due to accumulated noise and drift. Instead of focusing solely on area- or volume-based calculations, the proposed method emphasizes sequential dependencies and the intrinsic shape of the signal. The model captures temporal patterns and prioritizes critical features in the acceleration signal, enabling more accurate and reliable vertical force estimations with the help of speed and pressure measurement data. For real-time applications, such as motorsport races, traditional models often require substantial computational resources and rely on indirect measurements. While the variable height of the center of gravity is typically assumed to be constant, the mass of the vehicle is required to be calculated in real-time to accurately estimate the vertical force on the tires. The proposed method is applicable for real-time estimations, as it directly utilizes acceleration measurements from the tire and eliminates the need for vehicle parameter assumptions or calculations. Additionally, the incorporation of the Minimal Gated Unit reduced the number of LSTM units, thereby decreasing the computational load without compromising the model's ability to capture sequential dependencies. Because Random Forest methods are static, they have historically struggled to handle sequential data. The proposed method enhanced the feature space with sequential and contextual information by extracting learned features of acceleration data from the last layer of the model's Fully Connected Layer and training the Regressive Random Forest with these features, combined with speed and pressure data. This approach enabled the Random Forest component to efficiently manage intricate temporal interactions with the support of the front deep neural network elements.