## 3 Methodology
### BFRS Detection Algorithm from Multi-Sensor Stream Data
In Figure 9d-f, it is the comparison result of data augmentation by driving speed; the original recording in Figure 9e is speed increased with 123% of the original speed in Figure 9d, while decreased with 85% of the original speed in Figure 9e. In Figure 9a-c, the spectrum feature keeps steady during the pre-resample and post-resample processes. However, in Figure 9d,e the same spectrum features vary under different speed conditions; the spectrum feature representation of the same BFRS is stretched or squeezed by different vehicle speeds and becomes non-homogenous. In addition, to validate the effectiveness of the data augmentation method, two different spectrum feature maps are generated based on the actual acceleration recording under speed conditions of 18 km/h and 27 km/h, as depicted in Figure 10.

Figure 8: Spatial transformation for the acceleration data. (**a**) Before spatial transformation. (**b**) After spatial transformation. In Figure 10, the actual acceleration recording of the same kind of BFRS is collected under different speed conditions. There is a strong saliency (the light-yellow color in Figure 10b) in the lower frequency domain when recording under the speed of 18 km/h in Figure 10a; however, the strong saliency (the light-yellow color in Figure 10d) moves to the higher frequency domain when recording under the speed of 27 km/h in Figure 10c, which is consistent with the assumption analyzed in Section 3.3. In addition, the augmentation result based on the speed direction is not further experimented with, as the spectrum feature keeps steady during the process. Despite the presence of noise in the original recordings, the method transforms one-dimensional acceleration changes into two-dimensional spectral features. By distinguishing BFRS characteristics from noise across different frequency spectrum coefficients, the proposed method effectively reduces the impact of noise on experimental results. Based on the proposed data augmentation, there are non-homogenous feature representations under different speed conditions, and the feature can be extracted and strengthened based on the spectrum modeling method, which would contribute to the classification of BFRS in the next section. Figure 9: Comparisons of spectrum modeling results. (**a**) Augmented by driving direction: pre-example. (**b**) Augmented by driving direction: original dataset. (**c**) Augmented by driving direction: post-resample. (**d**) Augmented by driving speed: low speed. (**e**) Augmented by driving speed: original dataset. (**f**) Augmented by driving speed: high speed. ### BFRS Detection and Representation

Since BFRS is affected by the abnormal changes in the three-axis acceleration, all the spectra in three dimensions are computed and taken into the CNN model. In addition, the non-homogenous is caused by different driving speeds, as discussed in the previous section. The CNN model to detect BFRS is designed according to Section 3.3, with the spectrum in the three-axis acceleration. The training parameters are set as follows: [number of filters: 12; mini batch size: 50; learning rate: 0.0001; max epochs: 30; dropout probability: 0.2; padding mode: same], with other parameters the same as Section 3.5. During the training process, the dataset is divided into the following two categories: 80% of datasets are taken as training datasets, and 20% datasets are taken into validate datasets. Furthermore, to distinguish the BFRS from the normal road features, 166 segments of normal road segments are randomly selected in the research area and further labeled as \"background\". During the training process, the detection result is validated after each epoch, and the CNN model converges. Then, the BFRS detection operation is conducted on the test dataset of Area A, with the trained learnable parameters.