TECHNIQUES FOR CREATING SURROGATE MODELS OF EDDYCURRENT PROBES IN HYPERSPACE BY MEANS OF ADDITIVE NEURAL NETWORK APPROXIMATION
DOI:
https://doi.org/10.32782/KNTU2618-0340/2021.4.1.7Keywords:
homogeneous surface eddy current probe, eddy current density, homogeneous distribution, response hypersurface, multidimensional approximation models, surrogate model, metamodel, computer design of experiment, additive neural network regressionAbstract
The problem of multidimensional approximation of functional approximation dependences of the eddy current density distribution for several structures of excitation systems of surface eddy current probes is formulated.. A universal methodology for the construction of multidimensional approximation models (surrogate models) of various excitation systems of surface eddy current probes is proposed. The method of describing the "exact" mathematical models of the interaction process of a moving eddy current probe with the testing object, which is a mandatory component of the proposed methodology, is considered. The computer design of the computational experiment is proposed to be realized on the basis of quasi-random sequences with minimal difference, namely with the use of Sobol’s LPτ-sequences and additive recursive Rd-sequences of Kronecker. To design multidimensional surrogate models, it is proposed to use a hybrid approach, which consists in dividing the search space into several decomposition areas, in each of which local approximation is carried out, followed by combining the constituent parts of the approximations into one continuous model and the simultaneous use of additive-committee neural network technology. Verification of the created multidimensional surrogate models is carried out by assessing their adequacy and informativeness on a number of statistical indicators, namely the coefficient of determination, the ratio of standard deviations, the mean model error, the residual mean square error and the assessment of recovery using their response surface. Examples of approximation dependences of surface eddy current probes with different geometric shapes of the excitation system, namely circular and frame and different structures, both planar and three-dimensional, are considered. For each of the considered examples the results of reproduction of multidimensional response surfaces in the form of level lines obtained by means of approximation models are given. The quality of the created surrogate models was evaluated by scattering diagrams, the relative value of the approximation error and the histogram of the distribution of these errors.
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