## 3 Methodology
### BFRS Detection Algorithm from Multi-Sensor Stream Data
The _precision_, _recall_, and _F-score_ for the CWT method {_TP_: 2, _FP_: 2, _FN_: 2} are 50.00%, 50.00%, and 0.5000, respectively, and these indexes for the original CNN method {_TP_: 4, _FP_: 3, _FN_: 0} are 57.14%, 100.00%, and 0.7272. However, the _precision_, _recall_, _and_ _F-score_ for the proposed method {_TP_: 4, _FP_: 0, _FN_: 0} are 100.00%, 100.00%, and 1.0000, since all BFRS are correctly detected with no wrong result. In the experiment result in Figure 13 and Table 2, more BFRS are detected than other methods by the adaptive threshold method, while most of them are wrong results since the threshold value cannot be adapted to every situation. It seems that the CWT method can perform well with four detected BFRS, while it also faces the similar situation of the adaptive threshold value method, and the threshold only fits limited conditions. In the original CNN method, the detection standard can be learned from the training dataset, with four corrected BFRS detected. However, the performance still depends on the training \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 & 7 & 2 & 5 & 28.57\% & 50.00\% & 0.3636 \\ CWT & 4 & 2 & 2 & 50.00\% & 50.00\% & 0.5000 \\ Original CNN & 7 & 4 & 3 & 57.14\% & 100.00\% & 0.7272 \\ The proposed method & 4 & 4 & 0 & 100.00\% & 100.00\% & 1.0000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistic of the comparison results. dataset, and it performs not so well since there are three wrongly detected BFRS. Finally, four BFRS are successfully detected with the highest _F-score_ by the proposed method with a movement-feature-augmented training dataset. As shown in the experiments, the proposed method achieved superior BFRS detection results, with the detected positions closely aligning with the ground truth BFRS locations. Unlike the CWT method and adaptive threshold method, the proposed method does not require the setting of specific parameters. Furthermore, compared to the original CNN method, the proposed method enhances the data by considering the characteristics of vehicle movements and multi-sensor recordings, resulting in superior experimental outcomes. Hence, it can be concluded that the BFRS detection result computed by the proposed method outperforms other results in the experiment. In addition, variations in tire or suspension systems across different vehicles may impact the BFRS detection results, and BFRS might not be adequately captured just by a single vehicle type. However, it assumes general conditions, and the credibility of BFRS detection results can be further improved through the integration of multi-source data. ### BFRS Detection and Comparison in the Different Areas

To assess the capability of the proposed BFRS detection method, multi-sensor stream data in different areas are collected using smartphones, and experiments are conducted based on the trained deep learning model in the previous section. The sampling rate for the GPS sensor is 1 Hz, and that for the gyroscope and accelerometer is 100 Hz. The research area and discrete-sampled GPS stream data are depicted in Figure 14a,b, with augmentation information visualized by graded color. In Figure 14, different kinds of BFRS in research Area B and C are visualized as the related pictures of (_i_) cracks, (_ii_) speed breaker, (_iii_) transverse gutter, and (_iv_) pothole. The detailed statistics of the collected multi-sensor stream data are depicted in Table 3.

Figure 14: Different research areas. (**a**) Research Area B. (**b**) Research Area C.

With the test dataset in Areas B and C, BFRS are firstly collected using the proposed method, refined and segmented as different BFRS groups, and clustered and represented as BFRS objects. Then, comparisons are conducted using the adaptive threshold value method, CWT method, and original CNN method, using the same parameter as that in Area A.