# Vertical Force Monitoring of Racing Tires: A Novel Deep Neural Network-Based Estimation Method
## 2 Related Works
### Analysis of Methodological Constraints in Related Works
#### 2.3.5 Data Driven Estimation Approaches  
Data-driven approaches are independent of parameters such as variable vehicle mass, center of gravity, center of gravity height, contact patch length, or wear, eliminating the need for measuring or estimating these factors. This independence allows for greater prediction generalizability across varying conditions compared to vehicle and tire model-based approaches. Furthermore, they can effectively model the unmodeled or partially modeled nonlinear dynamics of the system.  
In [18], noise filtering and the limitations of the Random Forest technique present significant constraints in vertical force estimation. Relying primarily on the deformation frequency for noise filtering assumes static operating conditions and fails to account for variations in speed and tire pressure, which directly impact deformation characteristics. Lower speeds reduce the deformation frequency [25], altering the dynamic behavior of the tire and potentially leading to inaccurate noise filtering. If noise filtering is inaccurate, the boundaries of the contact patch may also be incorrectly identified. Even if the contact patch boundaries are correctly determined, the performance of data-driven models in force estimation may still degrade due to the loss of critical information during the filtering process. On the other hand, the RF technique, while effective for feature-based regression, struggles with time series data due to its inability to capture temporal dependencies inherent in sequential signals like those generated during tire deformation. The lack of a mechanism to model dynamic relationships limits its performance in such contexts, further highlighting the constraints of addressing both noise and temporal complexity within a single framework.  
In the research by [20], the method for vertical force estimation considers the use of indirect measurements and noise filtering techniques. The approach relies on onboard sensors to record vertical accelerations and angular dynamics of the vehicle's body and axles, rather than directly obtaining signals from the tire. Indirect measurements may include signals influenced by noise or external factors, which could contribute to variability in the estimation process. When applied to racing tires, where forces can change rapidly under dynamic conditions, the ability to accurately capture these variations using indirect measurements may be influenced by the resolution and responsiveness of the sensors. The noise filtering technique utilizes the five-point cubic smoothing method, which aims to reduce high-frequency random noise. It can also smooth over localized variations and abrupt changes in the signal that could carry relevant information. The fixed window size used in this method presents a trade-off: smaller windows might leave some noise unfiltered, whereas larger windows could overly smooth the signal, potentially obscuring important trends.  
Additionally, low-frequency noise might remain present in the filtered signal, as this type of noise is less likely to be removed by the smoothing process. Max pooling, employed in feature extraction, further shapes the data by selecting the maximum value within a defined window. While this approach simplifies the data, it might exclude other potentially relevant values within the same region, which could affect the level of detail available for further learning process.  
In the studies [21, 22], the vertical force estimation method utilizes onboard sensors to capture signals such as vertical accelerations and angular dynamics of the vehicle body and axles. Similar to the approach described in [20], this reliance on onboard sensors introduces a dependency on indirect measurements, which do not directly capture the vertical forces at the tire. As a result, the estimation process must infer tire forces from data that may be influenced by external disturbances, noise, and the inherent limitations of the sensors themselves.