## 3 Methodology
### BFRS Detection Algorithm from Multi-Sensor Stream Data
The multi-dimensional spectrum features of acceleration recordings are sent to the CNN model, output with the detected labels, segmented and refined as consecutive segments, and weight-clustered and represented as BFRS, as depicted in Figure 11.

Figure 10: The actual acceleration recording and related spectrum feature. (**a**) Acceleration recording with actual speed 18 km/h. (**b**) Related spectrum feature of 18 km/h. (**c**) Acceleration recording with speed 27 km/h. (**d**) Related spectrum feature of 27 km/h. In Figure 11a, the BFRS is initially detected based on the CNN model; each recording is assigned the probability of BFRS and further visualized by the graded color in greed (the darker the point, the higher the probability of the BFRS). In Figure 11b, the detection result is further segmented and refined as each segment based on (14) and (15), which are labeled with different colors. Finally, the BFRS is represented as the single BFRS in each group using the weighted clustering process based on (16). In Figure 11, it can be seen that the BFRS are dynamically generated based on the proposed BFRS detection method in Section 3.7. The proposed method primarily aims at the positioning of BFRS, but it can also represent the size of the obstacle. For the horizontal length of BFRS, it can be directly represented by the results of continuous detection, that is, without clustering the BFRS initially (as shown by the different BFRS group in Figure 11). The lateral width can be inferred from multi-source data coverage of the road surface, which helps estimate the lateral width of BFRS. The changes in \(z\)-axis acceleration from the recorded acceleration corresponding to detection results can indicate the vertical dimension (as shown by the actual acceleration recording in Figure 10). Figure 11: BFRS detection results. (**a**) BRFS detected results colored with probability. (**b**) Segmented and refined as different BFRS groups. (**c**) Represented by weighted cluster center. In addition, from the acceleration data recorded, ideally, when a vehicle passes over a hump-type obstacle, it produces an upward acceleration followed by a downward acceleration. Conversely, passing over a hole results in the opposite pattern of acceleration. However, these features are not distinctly clear and are difficult to differentiate due to inherent noise in the acceleration data. Theoretically, since it uses spectrum analysis coefficients to represent BFRS features, and these coefficients are absolute values from the Fourier transform process, the directionality of accelerations caused by hump-type and hole-type obstacles is neutralized by the absolute value operation. Therefore, it is not possible to accurately capture the specific acceleration features of raised and lowered surface elements. What is more, regarding road surface irregularities, such as selected thickness and type of paint, it is possible to sample these characteristics, represent them using the spectrum features, and input them into a neural network model as part of the training set. The network is subsequently trained to learn the subtle variations and distinctions among these features, thereby enabling the detection of these types of BFRS. ### BFRS Detection Comparison with Different Methods

To have an intuitive understanding of the performance of the proposed BFRS detection method, different experiments are conducted, and related comparisons are made with other methods. Firstly, it is the performance comparison between the original CNN model and the proposed BFRS detection method on the test dataset (Area A shown in Figure 7). The BFRS is detected using the original CNN model without the dataset augmented based on the movement feature analyzed in Sections 3.2 and 3.3.