## 1 Introduction  
### General Background  
Drilling operations in the oil and gas industry are highly complex and require precise control to ensure safety, efficiency, and cost-effectiveness [1, 2, 3, 4, 5, 6, 7]. One of the most important problems encountered in drilling is pipe sticking, where the drill string becomes lodged in the wellbore and becomes stuck and unable to proceed any further [8, 9, 10, 11, 12]. Pipe sticking can lead to significant delays in operations, additional costs, and abandonment of the well in extreme situations if left unmanaged. Pipe sticking incidents are caused by a number of factors, including geological conditions, wellbore instability, differential pressure, and improper drilling practices. With the advancement in complexity and depths in modern day drilling activities, particularly in offshore and unconventional reservoirs, avoiding the hazards of pipe sticking have become a priority for the industry [13, 14, 15, 16, 17, 18]. Pipe sticking carries implications beyond financial loss, as it affects the efficiency and safety of the entire drilling process. In the event of pipe sticking, operators are forced to undertake costly remedial measures such as jarring, backreaming, or side-tracking the wellbore in an attempt to free the stuck pipe. These remedial measures lead to delays in operations,as well as create risks of formation damage, failure of tools, and additional wear on the drill components. Pipe sticking also leads to non-productive time (NPT), an important parameter in measuring the efficiency of a drill process. Reducing NPT becomes essential in order to maintain cost efficiency, as the costs of drilling continue to rise with increasing depths and challenging well conditions. Several factors contribute to pipe sticking, with mechanical and differential sticking being the most common types. Mechanical sticking results from the physical blockage of the drill string due to wellbore instability, cuttings accumulation, or key seat formation [19; 20; 21; 22]. Differential sticking, however, results from pressure differentials between the drill pipe and the surrounding formation, causing the pipe to adhere to the wellbore wall. Inefficient hole cleaning, high mud weight, and poor drilling fluid properties are some of the factors that can exacerbate the risk of pipe sticking. The interaction of these factors needs to be understood for the formulation of effective prevention and mitigation strategies. With growing technical difficulties in drilling operations, traditional stuck pipe prevention and detection techniques have been found lacking in many cases. Traditional techniques rely on real-time surface monitoring, historical data analysis, and drilling engineer experience to identify early warning signs. While these techniques have been useful, they are often beset by late detection, subjective interpretations, and weak predictive abilities. The dynamic drilling process requires more proactive and data-driven approaches to enhance early detection, improve decision-making, and reduce operational risks associated with stuck pipe incidents. Recent advancements in stuck pipe detection have extended beyond traditional mechanical indicators that incorporated alternative technologies of physical modeling, sensor-based diagnostics, and hybrid signal analysis. For example, magnetic flux leakage analysis has been proposed to detect outer wall defects in bimetal composite pipes with high sensitivity [23]. In a related study, contact property evaluation and friction modeling were used to enhance the predictive understanding of pipe string behavior during pipe jacking operations [24]. Additionally, non-invasive diagnostic techniques, such as radioisotope-based blockage localization in multiproduct pipelines, have been successfully employed to detect obstructions with precision [25]. These alternatives reflect the diverse technological landscape in which stuck pipe detection strategies continue to evolve and strengthen the need for new methodologies.