Phenomenological and algorithmic methods for the solution of inverse problems of electromagnetic testing

Modern methods for the solution of inverse problems of nondestructive testing are described. The discussion is mainly focused on the methods based on a mathematical model of the respective physical phenomenon (so-called phenomenological methods) and the methods based on the algorithms for the analysis of digital signals (so-called algorithmic methods). The phenomenological methods involving a mathematical model assume that the configuration of the flaws in a tested specimen is varied until the norm of the mismatch between the model solution and the experimentally obtained signal is minimized. A good result is only guaranteed if the physics of the phenomenon in the model is close to reality. In algorithmic methods, the inversion procedure applied to experimental data is considered as an image-recognition problem. In this case, the signal is identified as a representative of the classes associated with known types of flaws. The classification algorithms, which are most frequently used for electromagnetic testing, are developed through identification of diagnostic signatures. This approach assumes the use of an artificial neural network trained with the signals from a predefined database that corresponds to a broad variety of flaws.