# Vertical Force Monitoring of Racing Tires: A Novel Deep Neural Network-Based Estimation Method
## 2 Related Works
### Hybrid and Pure Neural Network Approaches in Vertical Tire Force Estimation  
The studies in this category use the robustness and sensitivity of the extended Kalman filter (EKF) as well as the adaptability and learning capabilities of neural networks in handling nonlinear systems. By integrating these two approaches, the aim is to alleviate the limitations of each method and provide a more accurate and comprehensive solution for estimating tire forces. The reviewed literature ranges from early applications of EKF in tire force estimation to more recent developments involving neural network architectures. This section will focus on how these hybrid methods improve estimation accuracy and provide a detailed discussion of their role in advancing tire force estimation technologies. [PERSON] et al. [1] use the Genetic Algorithm to optimize a Backpropagation (BP) neural network to predict vertical tire forces. This method takes advantage of the robust global search capability of the Genetic Algorithm to address the tendency of the BP neural network to get stuck in local minima. The input parameters for their algorithm include inflation pressure, speed, longitudinal data, contact patch length, radial displacement peak, and wear amount.The calculation of radial displacement relies on double integration of acceleration signals obtained from a accelerometer embedded in the tire. While this approach effectively derives displacement from acceleration, it is inherently sensitive to noise and drift in the raw acceleration data, which can significantly impact the accuracy of the displacement estimation. Moreover, the double integration process amplifies low-frequency noise, necessitating the application of filtering techniques that may inadvertently remove critical signal components. In [18], a comparative analysis is performed on neural networks using the Resilient Backpropagation (Rprop) algorithm, Recurrent Neural Networks (RNN), and Random Forests (RFs) [19]. The method relies on indirectly identifying the tire contact patch using acceleration signals, which introduces potential limitations in accuracy. Variations in tire types and hardness may impact the reliability of the contact patch estimation. Ref. [20] propose a method to describe radial loads on tire-tired vehicles using a one-dimensional Convolutional Neural Network (1D CNN) and a Bidirectional Gated Recurrent Unit (BiGRU). However, the method relies on onboard sensors mounted on the vehicle body and axles to measure physical quantities such as vertical and angular acceleration. While these sensors provide valuable data for estimating vertical force, their placement on the vehicle rather than directly within the tire structure introduces limitations. Onboard sensors are susceptible to noise, vibrations, and interference from the vehicle chassis and suspension system, which can degrade the accuracy of the force estimation. The vertical acceleration of the vehicle body, the vertical acceleration of the axles, pitch angular acceleration, rolling angular acceleration, and rolling angular acceleration are used as input variables. Then, the vertical forces at each wheel are used as outputs. [PERSON] et al. [21] conducted a study on the normal forces exerted by tires on automotive vehicles using an LSTM model. The input data for LSTM models include pitch ratio, vertical velocity of the sprung mass, acceleration, rolling acceleration, and pitch acceleration.The vertical force estimation method proposed in the study, which employs an LSTM model, has limitations related to its data-driven structure and training process. The model is trained using simulation data generated using CarSim, which may not fully represent the variability in operational environments. Robustness analysis, as conducted within the study, indicates that the model is sensitive to parametric uncertainties, such as changes in vehicle mass and tire stiffness, and to sensor noise.