# Vertical Force Monitoring of Racing Tires: A Novel Deep Neural Network-Based Estimation Method
## 1 Introduction  
The estimation of vertical tire forces exerted on racing tires is an important cornerstone in vehicle dynamics and motorsport engineering. This aspect is fundamental, as the enhanced grip significantly influences a racing vehicle's speed, safety, and cornering abilities, which are essential under the high-speed and often variable conditions encountered in competitive racing. Real-time monitoring of vertical tire forces is fundamental for ensuring driving safety and handling stability. Several studies propose algorithms to combine intelligent tire technology with neural network theory to estimate vertical forces effectively, such as [PERSON] et al. [1]. The importance of accurately predicting vertical forces for advanced vehicle control systems is a popular technology. Engineers tailor suspension configurations by accurately assessing vertical loads that offer the optimum balance between responsiveness and stability. This balance is crucial to maintaining high speeds while driving on the complex dynamics of a racetrack. The research by [PERSON] et al. [2] underscores the importance of accurately estimating verticalforces as part of a broader vehicle stability framework. Furthermore, [PERSON] et al. [3] explore various vertical load estimation methods. Their findings reveal that accurate vertical load estimation is critical for optimizing tire utilization and enhancing vehicle handling and stability. According to the internal reports of the Cyber Tire Team of Pirelli Factory, who are the official tire manufacturer for the Formula 1 competition, analyzing vertical forces that act on racing tires allows for teams to better understand and predict tire wear and suspension component durability, aiding in strategic decisions about pit stops and car setups, and ensuring that the vehicle maintains peak performance throughout the race. The road-holding and braking performance of road vehicles is largely determined by the forces and moments acting on them. Accurately measuring or estimating these tire forces and moments is crucial for analyzing and controlling vehicle behavior [4]. Typically, traditional vehicle control systems estimate vertical tire forces using observer-based methods based on data from onboard sensors. However, these methods often rely on simplified vehicle models to estimate tire-related variables, especially in longitudinal and lateral dynamics. This reliance can lead to unreliable estimates under challenging conditions, such as sudden wheel load fluctuations, and can cause significant uncertainties primarily due to the use of these simplified models. Secondly, certain parameters within these tire models vary as the tire wears, leading to inaccuracies in the tire model. This requires periodic calibration of tire characteristic tests [1]. Despite the importance of vertical force estimation, there are significant problems in the literature. In the literature, parameters that are irrelevant, excessive, or insufficient in relation to those directly affecting vertical force have often been used. This has negatively impacted the accuracy of analyses. Most studies have relied on measurements taken from outside the tire. However, this approach has allowed for external vehicle data to interfere, leading to distorted estimations. Additionally, the datasets commonly used in the literature often fail to include the correct parameters, and the absence of sensors capable of measuring from within the tire has further hindered the ability to achieve accurate results. In this study, acceleration, speed, and internal pressure were used to achieve better MAE values, which directly affect the vertical force. This study focuses on the parameters that directly affect the vertical force and aimed to address a significant gap in the literature by avoiding common problems such as using the wrong parameters. In this study, a novel hybrid approach called Random Forest-Assisted Deep Neural Network (RFADNN) is proposed to estimate vertical force, and this approach combines the strengths of other models.