# Enhancing Safety in Automatic Electric Vehicle Charging: A Novel Collision Classification Approach
## 4 Experimental Results and Discussion  
### Feature Selection Results  
This section emphasizes effective feature selection using the predefined feature representation outlined in Table 2, which is an extension of the work presented in [8]. The identifiers 'T' and 'F' are used to denote time domain features and frequency domain features, respectively. To ensure optimal model performance during feature selection, the initial step involved the critical task of hyperparameter optimization for various models utilizing predefined features. In this context, we set the effective period length to 800 sample points, and the chosen optimization method was the Grid Search approach [35]. A Grid Search systematically explores a predefined hyperparameter space through exhaustive attempts of  
Figure 4: Waveform of a typical collision vibration signal. (**a**) Raw acceleration. (**b**) Normalized acceleration. (**c**) Raw angular velocity. (**d**) Normalized angular velocity. Figure 3: Workflow of the proposed collision classification method. different parameter combinations to identify the optimal combination on the validation set. To capture comprehensive feature information, the incorporation of a sliding window is imperative. However, the selection of an appropriate sliding window size is pivotal. A window that is too small may risk losing medium-scale features, influenced by transient information, leading to an increased number of extracted features and, subsequently, elevated data feature redundancy, thereby reducing computational efficiency. Conversely, an excessively large window size induces significant overlap, resulting in information redundancy and a reduction in independence between features. Moreover, an overly large size may average or blur specific feature variations, causing distortion. We determined the sliding window length to be 20% of the effective period's length, with a 50% overlap between adjacent sliding windows. Additionally, to avoid the leakage of testing information during the feature selection process, we solely utilized the C1 dataset to optimize model parameters. The optimization results for the hyperparameters of different models are presented in Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature Type** & **Name of Feature** & **Feature Definition** \\ \hline T1 & Mean & \(M=\dfrac{1}{n}\sum_{i=1}^{u}\tau_{i}\) \\ \hline T2 & Median & \(M_{d}=\left\{\dfrac{\tau_{n/2}+\tau_{(n/2)+1}}{2},\ n\text{ \ is\ even}\right.\) \\ \hline T3 & Root mean square & \(RMS=\sqrt{\dfrac{1}{n}\sum_{i=1}^{u}\tau_{i}^{2}}\) \\ \hline T4 & Variance & \(V=\dfrac{1}{n}\sum_{i=1}^{u}\left(\tau_{i}-M\right)^{2}\) \\ \hline T5 & Standard deviation & \(SD=\sqrt{V}\) \\ \hline T6 & Skewness & \(SK=\dfrac{1}{n}V^{-(3/2)}\sum_{i=1}^{u}\left(\tau_{i}-M\right)^{3}\) \\ \hline T7 & Kurtosis & \(K=\dfrac{1}{n}V^{-2}\sum_{i=1}^{u}\left(\tau_{i}-M\right)^{4}-3\) \\ \hline T8 & Coefficient of variation & \(CV=\dfrac{SD}{M}\) \\ \hline T9 & Extreme range & \(ER=\max(\left|\tau_{i}\right|)-\min(\left|\tau_{i}\right|)\) \\ \hline T10 & Extreme deviation & \(ED=\max(\left|\tau_{i}\right|)-M\) \\ \hline T11 & Energy increasing rate & \(EIR=\dfrac{1}{2}\text{lg}(\dfrac{\sum_{i=i/2}^{u}\tau_{i}^{2}}{\sum_{i=1}^{u/2 }\tau_{i}^{2}})\) \\ \hline F1 & Mean frequency & \(\overline{f}\) \\ \hline F2 & Fundamental frequency & \(f^{*}\) \\ \hline F3 & Spectral amplitude corresponding to mean frequency & \(S\Big{(}\overline{f}\Big{)}\) \\ \hline F4 & Spectral amplitude corresponding to fundamental frequency & \(S(f^{*})\) \\ \hline F5 & Phase angle corresponding to mean frequency & \(\phi\Big{(}\overline{f}\Big{)}\) \\ \hline F6 & Phase angle corresponding to fundamental frequency & \(\phi(f^{*})\) \\ \hline F7 & Average signal energy & \(E_{a}=\sqrt{\dfrac{1}{n}\sum_{i=1}^{u}\left|S(f_{i})\right|^{2}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Predefined feature representations. On the basis of parameter optimization, further steps of feature selection were carried out.