## 3 Methodology
### BFRS Detection Algorithm from Multi-Sensor Stream Data
Comparisons with different BFRS detection methods in Area B are depicted in Figure 15. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Length** & **Duration** & **GPS Records** & **Acceleration Records** & **Orientation Records** \\ \hline Area B & 1171 m & 234 s & 234 & 23,233 & 23,233 \\ Area C & 1475 m & 1298 s & 1298 & 129,081 & 129,081 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistic of collected multi-senor stream data in different areas. Figure 15: Comparisons with different BFRS detection methods in Area B. (**a**) Adaptive threshold value. (**b**) CWT. (**c**) Original CNN. (**d**) The proposed method. There are 24 ground truth BFRS in Area B, while the number of detected BFRS varies in different results. In Figure 15a, there are 41 BFRS detected based on the adaptive threshold value method, and 18 BFRS are correctly detected. However, there are 23 wrong BFRS in the result, which holds the highest value compared with other methods. In Figure 15b,c, there are 14 BFRS detected in each result based on the CWT method and the original CNN method, while it performs a little better in the result of the CWT method with nine correct BFRS and five wrong BFRS. In contrast to the result of Figure 15c, the performance of the proposed method is dramatically improved, and 20 BFRS are detected, with 14 correct BFRS and 6 wrong BFRS, since the model is trained with the augmented dataset based on movement feature. The detailed statistics of the experiment results for Area B are depicted in Table 4.

In Table 4, the _precision_, _recall_, and _F-score_ are computed according to the experiment result in Figure 15. Although there are 18 correct BFRS detected by the adaptive threshold value method, the number of wrong BFRS is also the highest among all of the results, and the related _TP_, _FP_, _and FN_ are computed as 18, 23, and 6. Hence, the _precision_, _recall_, and _F-score_ are 43.90%, 75.00%, and 0.5538 for the first method. With the similar detection result by the CWT method and the original CNN method, the related _TP_, _FP_, and _FN_ are computed as CWT: {_TP_: 9, _FP_: 5, _FN_: 15} and original CNN: {_TP_: 8, _FP_: 6, _FN_: 16}, respectively. Moreover, the _precision_, _recall_, and _F-score_ are 64.29%, 37.50%, and 0.4737 for the CWT method, and 57.14%, 33.33%, and 0.4210 for the original method. Finally, the _precision_, _recall_, and _F-score_ for the proposed method {_TP_: 14, _FP_: 6, _FN_: 10} are 70.00%, 58.33%, and 0.6363. With the highest _precision_, _recall_, and _F-score_, the proposed method performs best among all results. As shown in Figure 15 and Table 4 of Area B, where BFRS are more prevalent, detecting all BFRS is challenging. However, the adaptive threshold method detected a higher number of BFRS but resulted in many false detections, leading to low precision. The CWT method applies continuous wavelet transformation to the acceleration data, resulting in complex wavelet coefficient matrixes that are difficult to distinguish using specific thresholds. The original CNN method, lacking training on a dataset enhanced based on movement characteristics, did not perform well in the new experimental area, detecting only 14 BFRS. In contrast, the method proposed in this article, which is based on the analysis and training of vehicle motion characteristics, identified 20 BFRS with a high _precision_ and the best relative _F-score_, demonstrating the superior performance of our method. To further evaluate the performance of the proposed detection method, the BFRS detection operation is conducted in Area C, along with the related comparisons with the adaptive threshold value method, CWT method, and original CNN method, and uses the same parameter as that in Area A. The result is depicted in Figure 16.

In Area C, there are 23 ground truth BFRS spatially distributed, as shown by the gray rectangle in Figure 16. In Figure 16a, 27 BFRS are detected by the adaptive threshold value method, with 14 correct BFRS and 13 wrong BFRS.