Mathematical modeling of the transition resistance of the insulation of the main pipeline according to the data of measurements of the magnetic induction vector modulus

Interpretation of magnetometry data of main pipelines in order to assess the state of their insulating coating is a relevant subtask for automated control systems for the process of pipeline operation. Determining the transient resistance at the "soil / pipe" boundary is an inverse problem of mathematical physics. In the article, a mathematical model of the inverse problem of determining the transient resistance at the "soil / pipe" boundary is constructed according to measurements in air of the modulus of the magnetic induction vector of the magnetic field excited by a direct electric current of the cathodic electrochemical protection of the pipeline. In the class of bounded piecewise constant functions, the solution is sought by A.N. Tikhonov's method as an extremal of the regularizing functional. The results of the computational experiment demonstrate the possibility of determining the transition resistance of the outer insulating coating of the pipeline according to the measurements of the magnetic induction vector in air at heights varying from 2 to 4 lengths of "defective" segments.