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The main goal of the study is to analyze methods and diagnose mechanical damage to the pipeline using functional analysis, neural networks and the finite element method. In the work, mathematical formulations of the corresponding geometrical inverse problems of the theory of shells on reconstruction of defects of lateral surface are formulated according to measurement data obtained from sensors located in a given section of the shell. The statement was given and a method for solving inversedoi:10.13111/2066-8201.2020.12.s.7 fatcat:tl3yhnibxzc2dfmnowbvqlfn54