## 3 Methodology
### BFRS Detection Algorithm from Multi-Sensor Stream Data
The experiment is reconducted based on the proposed method with the same parameter as that of the original CNN model, and the result is depicted in Figure 8.0

In the test dataset of Area A, there are four ground truth BFRS distributed along the road, as depicted by the gray square in Figure 8.1 In Figure 12a, it is the BFRS detection result based on the original CNN model [17] without augmentation information. Although four BFRS are covered by the detected BFRS groups, the results are over-detected, i.e., there

Figure 8.2 Comparison with and without augmentation information. (**a**) BFRS detected results without augmentation. (**b**) BFRS detected results with augmentation. are seven BFRS groups detected and three are falsely detected. In comparison with the result in Figure 12a, the BFRS detection result in Figure 12b seems better; four BFRS are successfully covered by the detected BFRS group, and no more false-BFRS results are further detected. The over-detected BFRS result in Figure 12a is mainly caused by the insufficient training dataset, and it cannot detect BFRS in different movement situations. Hence, the proposed BFRS detection method turns out to be effective with augmentation information. With the result in Figure 12, the BFRS detection results are further represented by the method in Section 3.6. Secondly, BFRS detection experiments are further conducted and compared with the adaptive threshold-based method [34] and the CWT-based method [7], as depicted in Figure 8.3

Figure 8.4 Comparisons between different BFRS detection methods. (**a**) Adaptive threshold value. (**b**) CWT. (**c**) Original CNN. (**d**) The proposed method. In the result, the BFRS within the distance of 10 m is considered to be the correct BFRS, and the one out of the distance is taken as the wrong BFRS. In Figure 12(a), it is the result by adaptive threshold value, computed based on the abnormal acceleration changes in its neighborhood. The first derivative of acceleration recordings is computed and taken as the abnormal change, along with the total standard deviation of the dataset. Then, the abnormal change larger than the standard deviation is adaptively selected as BFRS. Finally, seven BFRS are detected, with two correct BFRS and five wrong BFRS. In Figure 12(b), the BFRS is computed based on the CWT method, with the parameters {wave name: 'db3', total scale: 256}, and the threshold value adaptively computed based on the absolute mean value of the coefficient matrix. The acceleration recording with a related coefficient larger than ten times the threshold value is selected as BFRS, and four BFRS are detected, with two correct BFRS and two wrong BFRS. Consistent with the experiment in Figure 12, the BFRS detection results of the original CNN and the proposed method are depicted in Figure 12(c),d. In Figure 12(c), seven BFRS are detected by the original CNN, with four correct BFRS and three wrong BFRS, while in Figure 12(d), four BFRS are all correctly detected by the proposed method. Figure 8.5

Figure 8.6

To evaluate the performances of different methods, precision and _recall_ are computed based on (17) and (18). In the equation above, _TP_ is the true positive BFRS (the true BFRS that successfully detected), _FP_ is the false positive BFRS (the BFRS that falsely detected), and _FN_ is the false negative BFRS (the true BFRS that are not detected). Finally, the _F-score_ is further computed based on these two quality indexes, as denoted in (19), and the statistical result is depicted in Figure 8.7

Figure 8.8

In Table 2, the _precision_, _recall_, and _F-score_ are also computed, with the number of correct BFRS and wrong BFRS. For example, the number of detected BFRS, correct BFRS, and wrong BFRS by the adaptive threshold value are 7, 2, and 5, respectively, and the related _TP_, _FP_, and _FN_ can be computed as 2, 5, and 2. Hence, the _precision_ and _recall_ are 28.51% and 50.00% based on (17) and (18), and the _F-score_ is computed as 0.3636.