# Vertical Force Monitoring of Racing Tires: A Novel Deep Neural Network-Based Estimation Method
## 3 Random Forest Assisted Deep Neural Network Model
### Conventional Random Forest Approach  
The aim of this study is to estimate vertical tire force, which can indeed be approached using the Random Forest (RF) method. However, it is crucial to acknowledge the specific limitations associated with RF in this context. Random inputs and features yield effective results in classification tasks, yet exhibit less efficacy in regression scenarios [19]. As a result, one of the main challenges in overcoming this performance limitation is the reliance on manual feature engineering. This means that the success of the model depends heavily on how well the features are selected and designed from the dataset. This is especially important for time series data such as acceleration signals, where recognizing time-dependent features such as sequential signal patterns and moving averages is crucial [26]. Another limitation of Random Forest (RF) is its tendency toward static modeling. It struggles to effectively capture the dynamics of systems that evolve over time. In such a case, it becomes problematic when dealing with systems that exhibit temporal changes and long-term dependencies, such as forces derived from acceleration data. Moreover, RF can encounter serious performance issues when handling high-dimensional data. The training and estimation processes can become resource-intensive and time-consuming, especially with larger datasets. This challenge is further compounded by the need for a more comprehensive feature space and the complexity of feature engineering. In the context of this study, Random Forest encounters several notable challenges:  
* _Sequential dependencies:_ RF treats each data point independently, failing to capture the sequential dependencies inherent in the 251-point voltage signal. These dependencies, both short term and long term, are crucial for accurately estimating the target force value. * _Aggregate effects of sequential data:_ The target force value reflects the cumulative effect of all 251 voltage points. RF processes each point in isolation and cannot account for this aggregate relationship. * _Low variance in the target variable:_ All 251 points are labeled with the same force value, which reduces the variance in the target variable. This hinders RF's ability to optimize its decision trees effectively and limits its generalization capability. * _Complex nonlinear relationships:_ The voltage signal exhibits nonlinear patterns and trends that RF struggles to model with its decision tree structure, leading to suboptimal regression performance. * _Identifying critical patterns:_ Some regions within the sequential data are more influential on the target force value. However, RF fails to prioritize these critical patterns, treating all data points equally. * _Lack of contextual information:_ Constant parameters such as pressure and rotational speed significantly influence the voltage signal. RF cannot directly incorporate these contextual factors without explicit feature engineering, which may introduce errors or biases. * _Time series challenges in RF:_ While RF can be effective in time series tasks using lag features or sliding windows, such techniques are limited to capturing short-term dependencies. In our problem, the voltage signal requires modeling long-term dependencies and cumulative effects across the entire sequence, which RF is unable to achieve effectively. Therefore, when considering the estimation of vertical tire force, where the data are characterized by time-sensitive dynamics and the relationships within them are complex, the limitations of RF become apparent. These challenges highlight the need for methodologies that can better manage dynamic systems, temporal changes, and complex dependencies found in time series data. To address the limitations of Random Forest (RF) in vertical force estimation using sequential data, the proposed methodology integrates advanced techniques to enhance RF's ability to handle sequential data and complex relationships effectively.