## 3 Methodology
### BFRS Detection Algorithm from Multi-Sensor Stream Data
In Figure 16b,c, the detected BFRS are 11 by the CWT method and 9 by the original CNN method, and both of them perform similarly with 4 wrong BFRS; however, there are more correct BFRS in Figure 16b than that of Figure 16c. Compared with other results, there are 22 BFRS detected by the proposed method, and 17 BFRS are correctly detected, which is the highest value among all results. The detailed statistics of the experiment results for Area C are depicted in Table 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Detected BFRS** & **Correct BFRS** & **Wrong BFRS** & _Precision_ & _Recall_ & _F-Score_ \\ \hline Adaptive threshold value & 41 & 18 & 23 & 43.90\% & 75.00\% & 0.5538 \\ CWT & 14 & 9 & 5 & 64.29\% & 37.50\% & 0.4737 \\ Original CNN & 14 & 8 & 6 & 57.14\% & 33.33\% & 0.4210 \\ The proposed method & 20 & 14 & 6 & 70.00\% & 58.33\% & 0.6363 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistics of the comparison results in Area B. In Table 5, the _precision_, _recall_, and _F-score_ are computed according to the experiment result in Figure 16. With 14 correct BFRS and 13 wrong BFRS by the adaptive threshold value method, the related _TP_, _FP_, _and FN_ are computed as 14, 13, and 9, and the _precision_, _recall_, and _F-score_ are computed according to the experiment result in Figure 16. With 14 correct BFRS and 13 wrong BFRS by the adaptive threshold value method, the related _TP_, _FP_, _and



and _F-score_ are 60.87%, 75.00%, and 0.5600 for the result in Figure 16a. With seven correct BFRS and four wrong BFRS in Figure 16b by the CWT method, the result in Figure 16b {_TP_: 7, _FP_: 4, _FN_: 16} outperforms that of Figure 16c by the original CNN method {_TP_: 5, _FP_: 4, _FN_: 18}. However, the _precision and recall_ of the proposed method are 77.27% and 73.91%, according to the statistic results {_TP_: 15, _FP_: 7, _FN_: 6}; hence, the _F-score_ is the highest among all results {adaptive threshold value: 0.5600; CWT: 0.4117, original CNN: 0.3125; the proposed method: 0.7555}. More correct BFRS and less wrong BFRS are detected based on the proposed method, and it performs best among all experimented results. As shown in Figure 16 and Table 5 of Area C, where the spatial distribution of BFRS is denser compared to the experimental Area B, the adaptive threshold method detected a larger number of BFRS, but many were incorrect, resulting in low _precision_. The CWT method showed higher detection _precision_, yet selecting appropriate BFRS based on wavelet coefficients remains challenging. The original CNN detected 9 BFRS, whereas the proposed method detected 22 BFRS, with 17 being correct BFRS. Therefore, compared to these methods, the _F-score_ performance of the proposed method is the best, consistent with the results from Area B. With experiment results in Figures 15 and 16, Tables 4 and 5, BFRS can be detected with high _precision_, _recall_, and _F-score_ based on the proposed method. Although there are more BFRS detected by the adaptive threshold value method, the _precision_ is not good, as there are also too many wrong BFRS in the result. The CWT method performs better than the adaptive threshold value with a higher _precision_, but the number of detected BFRS is small, as is the result of the original CNN method. However, using an augmented dataset based on the movement feature and the learnable parameters, BFRS are detected with the highest quality index, such as _precision_, _recall_, and _F-score_. Finally, the proposed method performs best in the comparison. The experiments demonstrate that the proposed method described in this article, which establishes a feature representation for BFRS through spectrum modeling, enhances the BFRS training dataset using vehicle motion characteristics, and detects BFRS in different experimental areas using the CNN, achieves relatively superior experimental results compared to other methods. This indicates the applicability and superior performance of the proposed method.