Computer-economical optimization method for solving inverse problems of determining electrophysical properties of objects in eddy current structroscopy
Authors: Halchenko V. Ya. , Trembovetska R. V. , Tychkov V. V. 
Published: January 2025

Introduction. The problems of determining the profiles of electrophysical material properties are among the inverse problems of electrodynamics. In these studies, the focus is on the creation of a computer-economical method for reconstructing the profiles of electrical conductivity and magnetic permeability of metal planar objects under testing. These parameters can include the information about the results and quality of the production process or the effects of exposure to an aggressive environment. Registration of changes in electrophysical properties by means of eddy current testing allows for prompt adoption of effective management decisions regarding controlled processes. The simultaneous determination of these parameters because of non-contact indirect measurements of the electromotive force (EMF) by surface eddy current probes over the surface object with the subsequent restoration of the parameter distributions along its thickness by numerical methods is an urgent task. Objective. To create a computer-economical method for determining the electrophysical properties of objects by means of surrogate optimization with the accumulation of additional apriori knowledge about them in neural network metamodels with nonlinearly reduced dimensionality to improve the accuracy of simultaneous profile determination. Methodology. The method for determining the electrophysical properties of objects is based on homogeneous designs of experiments, surrogate optimization with the accumulation of apriori knowledge about them in metamodels with nonlinearly reduced dimensionality. Originality. Integration of multiple capabilities in the surrogate model that combine the advantages of high-performance computing and optimization algorithms in the factor space reduced by the Kernel PCA (Principal Component Analysis) method. The accumulated additional apriori knowledge about objects is incorporated into the neural network metamodel. This makes it possible to implicitly identify complex patterns hidden in the data that are characteristic of the eddy current measuring process and take them into account during reconstruction. Results. The reduction of the search space is a considerable result. It was possible due to the nonlinear Kernel-PCA transformations with the analysis of the eigenvalues of the kernel matrix and the restriction on the number of PCA principal components. The results confirmed the validity of a significant reduction in space without major loss of information. Another indicator of the effectiveness of the method is a high precision of the created surrogate models. The accuracy of the reduced dimensional metamodels was achieved by using a homogeneous computer design of experiment and deep learning networks. The adequacy and informativeness of the constructed surrogate models have been proved by numerical indicators. The efficiency of the method is demonstrated on model examples. References 36, table 5, figures 6.