## 1 Introduction  
The sustainable development of any energy industry depends on the ability to ensure the uninterrupted operation of production facilities [1, 2]. This requires ensuring the troubles-free operation of equipment installed on the territory of production [3, 4]. The possibility of trouble-free operation of equipment directly depends on the technologies used and developed in the field to ensure an increase in the lifetime of the equipment operated as well as its repair with the least expenditure of time, labor and explicit costs, while also ensuring a high level of industrial safety [5, 6]. One of the industries that needs the development and implementation of innovative technologies to ensure the smooth operation of equipment is the pipeline transport of oil and gas [7; 8]. This area of research also requires the development of technologies that take into account the influence of oil and gas flow parameters, as well as their composition, on the operation of main pipelines [9; 10]. During the operation of main pipelines, many defects requiring repair of pipelines appear in the pipe body and on its surface [11; 12]. Repair methods include cutting, grinding, welding, the use of couplings of various designs and the use of nozzles with an elliptical bottom [13; 14]. Nevertheless, cutting out a defective area and replacing it with a new one is a universal repair method used to eliminate any type of defects [15; 16]. At the same time, this type of repair is most often used by service departments of companies [17]. The essence of the repair method with cutting out the defective section is to dig out the defective section, cut it out with the help of special pipe cutting machines, perform pipeline space hermetization, weld a new section, process welded joints and isolate and bury the repair area. This method of repair is complicated by the elastic bending of the main pipeline. When the pipeline is cut, its ends, located at the edges of the cutting place, are sharply displaced relative to each other. This can lead to injury and death for workers, as well as tearing out of the pipe metal at the end of the cutting process. To reduce the possible consequences of the displacement of the ends of the pipeline, the pipeline is often pressed with an excavator bucket during the repair work, which does not comply with the rules of industrial safety and regulations for the production of repair works. It is also worth noting that in order to weld a new section, it is necessary to center the ends of the pipeline relative to each other until they are aligned. For this, heavy, expensive pipelayers are used, which require additional costs for acquiring a permit for the transportation of oversized equipment [18]. In addition, speaking about the level of industrial safety, it is worth noting that in organizations involved in transportation and storage, there is one of the highest levels of industrial injuries among industries [19; 20]. In particular, in the repair of main pipelines involving cutting out a defective section, the main share of fatal accidents occur precisely at the stages of making a \"rough\" cut of the pipeline by workers, centering its ends and welding a defect-free section. In this regard, ensuring the safety of repair work, as well as reducing the share of manual labor at these stages, makes the greatest contribution to improving the level of safety and reducing the level of injuries in the repair process as a whole [21; 22]. The elastic bends of the underground pipeline, which are the cause of a sharp displacement of the ends of the pipeline, are quite often encountered along its length and are either calculated at the design stage and implemented during the construction of the pipeline or are formed both in the vertical and horizontal planes due to the characteristics of the natural environment in which the pipeline is laid [23; 24]. They are also formed in the process of operation due to the fact that pipeline comes into operation with almost zero pinching with the ground after commissioning [25].