## 1 Introduction  
With the rapid advancement of smart sensors and the influx of crowdsourced data, geospatial information for road surfaces has become increasingly accessible, crucial for the development of smart cities and, more specifically, for maintaining and optimizing road assets [1, 2]. Roads, a vital component of urban infrastructure [3, 4, 5], endure significant wear due to growing traffic volumes, resulting in various surface irregularities such as bumps, cracks, potholes, and speed breakers--collectively known as bump features of the road surface (BFRS) [6, 7]. Effective collection and analysis of BFRS data are essential not only for maintaining road quality but also for ensuring transportation safety and enhancing the driving experience in urban environments [8, 9]. Vision-based methods, widely used for their ability to capture road surface conditions through cameras, employ techniques such as computing gradients and Haar features from video frames and images to detect BFRS [10, 11]. These methods, alongside advanced machine learning techniques for pothole and crack segmentation [12], and the use of mono and binocular stereo cameras for depth imaging [13, 14, 15], form the core of intuitive vision-based BFRS detection. Recent developments in deep learning have significantly improved these detection methods, tailoring them more effectively to the nuanced challenges of BFRS identification [16]. However, these approaches are susceptible to issues like variable lighting, data noise, and obstructions caused by environmental conditions [10; 11]. Alternative approaches using accelerometers and GPS have been developed to monitor road surface anomalies directly from driving data, offering a robust complement to visual methods [9; 17]. Furthermore, professional settings increasingly utilize advanced sensor technologies like LiDAR to capture precise geometric details of road surfaces, identifying BFRS through deviations from standard models [18; 19; 20]. Additionally, some methods leverage the combination of acceleration sensors, GPS, and auxiliary sensors to capture vehicle vibrations during travel, indirectly detecting BFRS by analyzing unusual sensor data patterns [3; 21]. The integration of Internet of Things (IoT) technologies further enhances these methods by facilitating extensive data collection from a network of sensors, thereby creating multi-source datasets essential for addressing complex BFRS detection challenges [3; 8; 22]. Multi-sensor setups, particularly those incorporating smartphone technologies, offer substantial advantages over traditional methods by enhancing robustness and data diversity. The widespread adoption of smartphones has transformed these devices into powerful tools for crowdsourced data collection on BFRS, which can improve the efficiency of BFRS detection operations and combine user convenience with extensive data coverage [3; 7; 17; 23; 24; 25]. Despite these advancements, challenges remain, including (1) managing discrete-sampled, multi-sensor stream data from smartphones in randomly positioned vehicles, (2) limited dataset coverage, and (3) the complexity of detecting and representing BFRS from non-homogeneous datasets collected under varied driving conditions. To address these challenges and detect BFRS using the widely used motion sensor, this article concentrates on multi-sensor stream data obtained from smartphones positioned in arbitrary poses. The following was carried out: (1) modeling BFRS and augmenting the training dataset with movement features; (2) generating spectral features through fast Fourier transform (FFT) and introducing a deep learning-based BFRS detection method utilizing non-homogeneous, discrete-sampled, multi-sensor data; and (3) representing BFRS using a weighted clustering method.