## 3 Methodology
### BFRS Detection Algorithm from Multi-Sensor Stream Data
## 5 Conclusions and Future Work

Road infrastructure is a critical component of the geographic data required for the development of smart cities. It plays a pivotal role in city transportation systems, where the integrity of road surfaces directly influences transportation safety and the quality of the driving experience. The detection and management of road surface irregularities, such as BFRS, are essential due to the stresses imposed by extensive vehicle use and infrastructure wear. To detect BFRS in an economical way, smartphones assembled with multiple sensors are applied in this study. By harnessing the ubiquity and sophisticated sensor capabilities of these devices, discrete-sampled and non-homogeneous datasets are collected. The relationship between BFRS and vehicle speed conditions was analyzed, leading to the development of a robust model that effectively identifies BFRS. Through preprocessing of three-axis acceleration stream data, a comprehensive BFRS model is constructed and augmented by the training dataset with movement features. Then, the deep learning neural network is designed, and the multi-dimensional spectrum feature is input into the neural network. Finally, BFRS are refined and weighted clustered according to detected points and the related probability. Multi-sensor stream data at different areas are collected, training datasets are augmented, spectrum features are constructed based on the modeling result, and the deep learning neural network is trained and validated. The proposed approach not only demonstrated superior performance in detecting BFRS compared to other existing methods, but also provided initial locations of the distress or damages of the road surface, which would contribute to the maintenance of road assets. The flexibility of the CNN model, which can be adapted or replaced with alternative architectures, adds to the scalability of the approach. The smartphone sensors used in this article are highly integrated within the device. However, in IoT sensor application scenarios, especially when dealing with multiple sensors that lack necessary external enclosures and have lower levels of internal integration, calibrating sensors is essential. Additionally, the external environment (such as external magnetic fields) and the impact of different disturbances require in-depth study. Future research aims to improve the performance of BFRS detection results with multi-modal sensors; for example, since video datasets can also be collected using smartphones, the deep learning neural network framework can be improved and redesigned to encode multi-modal stream data. Moreover, for vehicles with different types of tires and suspension systems, it is essential to explore the analysis of forces while overcoming an obstacle. This could provide deeper insights into the interaction between the vehicle's tires, suspension, and road surface, which could be crucial for encoding the BFRS and interpreting the results more accurately. Another aspect that needs to be further explored is BFRS detection with crowdsourced datasets, which collect road surface conditions using volunteered geographic information. [PERSON] was responsible for methodology, analysis, and drafting of the manuscript. [PERSON] contributed to the implementation, programming, and testing. [PERSON] was responsible for literature reviews, background knowledge, and improvement of the writing. [PERSON] contributed to the data collection and visualization of the results. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China [Grant No. 42101466]. Not applicable. The data that were analyzed in this study can be found at [[https://doi.org/10.6084/m9.figshare.26039233.v1](https://doi.org/10.6084/m9.figshare.26039233.v1)]([https://doi.org/10.6084/m9.figshare.26039233.v1](https://doi.org/10.6084/m9.figshare.26039233.v1)). The street map is available from OpenStreetMap, accessed on 19 March 2024.