Linear surrogate synthesis of frame tangential eddy current probes with a volumetric structure of the excitation system
Abstract
A mathematical method of linear surrogate parametric synthesis of frame tangential eddy current probes with a three-dimensional structure of the excitation system is proposed, which provides a uniform eddy current density distribution in the testing object zone. To achieve optimal synthesis, several interrelated tasks are performed in stages. Thus, the design of experiment (DOE) for four-dimensional factor space is proposed to be realized on the basis of a set of nonparametric additive recursive one-dimensional Kronecker’s R-sequences. The use of DOEs with low discrepancies best reproduces the global and local behavior of the four-dimensional response surface. Given the significant nonlinearity and irregular behavior of the response hypersurface, a hybrid approach has been used to design a multidimensional approximation model. This approach involves the simultaneous use of decomposition technologies of the search area and neural network (NN), which are based on the techniques of associative machines, as well as additive NN-regression. To increase the accuracy of additive NN-regression, several methods, namely averaging over the NN ensemble and amplification by forming subsamples (begging), have been used. All this and the additional complication of the structure of additive NN-regression, namely the use of NN committees at each intermediate level of approximation, have allowed to achieve an acceptable MAPE error of a four-dimensional metamodel of a moving frame tangential SECP with a threedimensional excitation system, both at the stage of training and at the stage of reproduction. The paper presents numerical results and graphical material that illustrates the adequacy and informativeness of the obtained metamodel.An example of synthesis of such excitation systems using modern metaheuristic stochastic algorithms for finding the global extremum is considered. Numerical results of the obtained solution and graphical illustrative material of the eddy current density distribution on the surface in the testing object zone are given. The proposed methods and algorithms of linear surrogate optimal parametric synthesis allow to obtain acceptable accuracy of synthesis in the testing area of the frame tangential SECP with the three-dimensional structure of the excitation system
Keywords
frame tangential eddy current probe; volumetric structure of excitation system; eddy current density; uniform sensitivity; additive neural network regression
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