## 2 The Design of the Control System
### Feature Selection  
A feature selection method based on a sigmoid function-based whale optimization algorithm is used according to the requirement for the feature selection of natural driving data. The features most relevant to driving style expression are selected by limiting the range of output values in the location update phase in order to reduce the size of the dataset used for driving style recognition while retaining relevant information. In this paper, the k-means method is used to construct the initial features for driving style feature recognition.  
To complete the feature selection associated with driving style, the continuous WOA must be converted to its corresponding binary space [0, 1]. The use of a sigmoid transfer function can force the search agent to move through the binary space [35; 36], thus improving the whale optimization algorithm for driving style feature selection. The equation is defined as shown in Equation (3).  
\[S(\Delta X_{t})=\frac{1}{1+e^{-\Delta X_{t}}} \tag{3}\]  
where, \(\Delta X_{t}\) denotes the step vector of the search space at. Thereafter the current search agent uses Equation (4) to complete the position update.  
\[X_{t+1}^{d}(t+1)=\begin{cases}1&if\quad rand<S(\Delta X_{t+1})\\ 0&if\quad rand\geq S(\Delta X_{t+1})\end{cases} \tag{4}\]  
where, \(rand\) denotes a random number in (0, 1).  
The objective of feature selection is to find the minimum number of features to select and to obtain the maximum classification accuracy. Based on this objective, both objectives are aggregated and transformed into a single objective problem as in Equation (5), and the minimum fitness value is defined as the sum of the small classification error rate and the minimum number of selected features.  
\[Fitness=\lambda\times E_{r}+\eta\,\frac{|S_{t}|}{|F_{l}|} \tag{5}\]  
where, \(E_{r}\) denotes the classification error rate and \(S_{l}\), \(F_{l}\) are the length of the selected feature subset and the number of all features, respectively. \(\lambda\), \(\eta\) are the degree of importance of classification accuracy and feature subset length, and \(\lambda+\eta=1\). In this paper, we take \(\lambda=0.99\). The fitness value of each solution is continuously calculated during the iterative process and the subset with the smallest fitness value is treated as the optimal solution, based on which the classification accuracy is calculated as in Equation (6).  
\[Accuracy=1-E_{r} \tag{6}\]  
To avoid over-fitting in subsequent calculations, highly correlated features need to be removed. In this paper, the Pearson correlation, a measure of linear correlation between two variables, is used to identify and remove highly correlated features from the  
Figure 1: GPS altitude correction process.  
dataset, allowing the model to focus on the most informative features, thereby improving generalization and performance. It is calculated as in Equation (7).  
\[\rho_{X,Y}=corr(X,Y)=\frac{cov(X,Y)}{\sigma_{X}\sigma_{Y}}=\frac{\sum_{i=1}^{n}( X_{i}-\bar{X})(Y_{i}-\bar{Y})}{\sqrt{\sum_{i=1}^{n}(X_{i}-\bar{X})^{2}}\sqrt{\sum_{i=1}^{ n}(Y_{i}-\bar{Y})^{2}}} \tag{7}\]  
where, \(cov(X,Y)\) are the covariances of the variables \(X\) and \(Y\). \(\sigma_{X}\), \(\sigma_{Y}\) are the standard deviations of the variables \(X\) and \(Y\). \(\bar{X},\bar{Y}\) are the arithmetic mean of the samples \(X_{i}\) and \(Y_{i}\). The value ranges from \([-1,1]\), where the closer it is to \(1\) or \(-1\), the stronger the linear relationship between the features, and the closer it is to \(0\), the weaker or no relationship between the features.