## 3 Methodology
### BFRS Detection Algorithm from Multi-Sensor Stream Data
In Area A, the dataset is divided into a training dataset (outside the black dotted rectangle area) and a test dataset (inside the black dotted rectangle area, i.e., Area A), and the training dataset is used to train and validate the CNN model, while the test dataset is used to make validation and comparison with other related methods. The detailed statistics of the collected multi-sensor stream data are depicted in Table 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Length** & **Duration** & **GPS Records** & **Acceleration Records** & **Orientation Records** \\ \hline Area A & 6411 m & 860 s & 860 & 86,662 & 86,662 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistic of collected multi-sensor stream data. ### Non-Homogeneous Analysis and BFRS Modeling

The smartphone is arbitrarily mounted or placed in the vehicle, but there is an extensive abnormal change in the direction vertical to the road surface, and the spatial transformation is necessary to convert the \(z\)-axis acceleration into the vertical direction of the road surface. With timestamp-aligned three-axis acceleration and three-axis orientation recordings, the real-time spatial transformation is applied to the three-axis acceleration. The spatial transformation for the acceleration stream data is depicted in Figure 8.

As shown in Figure 8, there is an obvious change in the three-axis acceleration before and after the spatial transformation. In Figure 8a, both \(x\)-axis, \(y\)-axis, and \(z\)-axis accelerations change during the sampling period, and the average acceleration for the three axes is 2.2278 m/s\({}^{2}\), \(-\)0.6017 m/s\({}^{2}\), and 9.4296 m/s\({}^{2}\), respectively. In Figure 8b, the average \(x\)-axis and \(y\)-axis acceleration becomes 0.0513 m/s\({}^{2}\) and \(-\)0.0533 m/s\({}^{2}\), which is consistent with the actual case (as the vehicle moves forward at a nearly constant speed), and the \(z\)-axis acceleration is to 9.7075 m/s\({}^{2}\); however, abnormal changes are concentrated on the \(z\)-axis, while there are also related slight changes in the \(x\)-axis and \(y\)-axis. It shows strong relations with BFRS after spatial transformation. Additionally, it can be observed that BFRS impacted both the vertical (\(z\)-axis) and horizontal (\(xy\)-axis) directions of the vehicle. In

Figure 7: The research area and related multi-sensor stream data. (a) Research area. (b) Related multi-sensor recordings. the \(z\)-axis direction, the changes in acceleration are quite noticeable, typically fluctuating above \(\pm 3\) m/s\({}^{2}\). In the \(x\)-axis direction (assuming it is the direction of vehicle travel), a noticeable deceleration effect is also presented, although the changes in acceleration were relatively minor. However, employing a threshold method to determine BFRS can lead to significant errors due to the inherent noise in acceleration recordings. Therefore, the proposed method utilizes spectral features to detect BFRS, which also aids in mitigating the impact of acceleration noise to some extent. BFRS is modeled with the relations between the geometric shape and driving speed in this research, and the BFRS training dataset is augmented based on the modeling result since the size and quality of the training dataset have a direct effect on the neural network. To have an intuitive visualization of the augmented results, the experiment is conducted on the actual collected recordings using the proposed augmentation method, as depicted in Figure 9. In the experiment, the spectrum of BFRS is computed using the FFT algorithm based on (10)-(12), with the parameter set as Section 3.3. As seen from the experiments in Figure 9, the spectra of BFRS are computed and visualized for the acceleration of the \(x\)-axis, \(y\)-axis, and \(z\)-axis. In Figure 9a-c, it is the comparison result of data augmentation by driving direction, and the original recording in Figure 9b is pre-resampled with 33 samplings, while post-sampled with 41 samplings.