# Vertical Force Monitoring of Racing Tires: A Novel Deep Neural Network-Based Estimation Method
## 3 Random Forest Assisted Deep Neural Network Model
### Implementation Details of the Proposed Method  
Before training the model, all data were normalized to fall within the [0, 1] range, to accelerate the training process. The proposed method was implemented in the Python 3.8, utilizing the TensorFlow 2.4 library. While the training of the model's deep neural network portion took between 50-55 h on a Quadro T2000 GPU, the training of the Random Forest component was completed in just a few minutes. The operational schema of the method, including a workflow diagram, is depicted in Figure 3. In the dual-model structure, the neural network component is trained for feature extraction over the pre-determined maximum number of epochs. If no improvement in loss, as calculated by the loss function described in the previous section, is observed during this specified epoch count, the training is halted. Subsequently, feature extractions are conducted using the most optimally weighted model up to that point, and these features are then forwarded to the Random Forest component, which possesses 10,000 estimator units, for its training phase. If the Random Forest training yields a Mean Absolute Error (MAE) lower than 1.0 kgf, then the training and its estimations are considered valid. Otherwise, the training process restarts from the initial step, specifically from the neural network segment. The details of this flow and the mechanism in Figure 3 are explained below. * The flow starts with training the model, \(\mathcal{N}\), using the training dataset. The training process continues either until the maximum number of epochs is reached or the loss function shows no significant decrease over a certain number of epochs. * After completing one iteration of training, an intermediate model is created by extracting the final layer of the Fully Connected Neural Network, which is the last layer of \(\mathcal{N}\). * Using this intermediate model, features (intermediate vertical force predictions) are collected from the training dataset, which includes acceleration, pressure, and speed data. * These features, along with their corresponding labels, are used to train the Random Forest Regressor. * During inference and testing, the intermediate model is again used to collect features from the test dataset (acceleration, pressure, and speed). The Random Forest Regressor then predicts the final vertical force based solely on these collected features. * If the Mean Absolute Error (MAE) of the predictions on the test dataset exceeds 1.0 kgf, another iteration of training begins for both \(\mathcal{N}\) and the Random Forest Regressor. * The iterative training process continues until the MAE falls below 1. Once this criterion is met, the training process is considered complete, and the final predictions are utilized. In the initial stages of model development, the decision was deliberately made not to incorporate the dropout mechanism. This decision was informed by preliminary observations indicating that the inclusion of dropouts adversely influenced the learning process, hindering the achievement of the desired performance metrics. A particularly concerning issue was the model's tendency to overfit, as evidenced by the Mean Squared Error (MSE) values for the training set approaching near zero while remaining significantly higher for the validation set as the number of training epochs increased. This discrepancy underscored the failure to narrow the gap between the training and validation of MSE values as anticipated. In light of these challenges, the architecture of the model underwent a comprehensive strategic report. The first remedy was the removal of three LSTM (Long Short-Term Memory) layers from the architectural design and their replacement with MGU (Minimal Gated Unit) layers. This change was introduced to reduce the complexity of the model's  
Figure 3: Flowchart of the proposed load estimation mechanism with the RFADNN model. structure, with the assumption that it would help in minimizing overfitting, as outlined in this paper.