OPTIMAL DESIGN OF EDDY CURRENT PROBES AND METHODS OF ANALYSIS SOLUTIONS OF NONLINEAR INVERSE PROBLEMS
DOI:
https://doi.org/10.32782/KNTU2618-0340/2020.3.2-2.8Keywords:
optimal synthesis, eddy current probe, eddy current density, inverse problem, nonlinear ill-posed problems, regularization methods, surrogate optimization, metamodel, stochastic metaheuristic optimization algorithmAbstract
The implementation of a priori specified characteristics of eddy current probes involves the use of procedures for the optimal synthesis of their structures, in particular, excitation systems at the design stage. The formulation of the optimal design problem of a probe with a predetermined sensitivity characteristic, as an incorrectly posed inverse nonlinear from a mathematical point of view of the problem, is considered. A review and a corresponding analysis of the mathematical methods used to solve problems of this class are carried out, namely, the introduction of the desired solution into the set of correctness regularized using the Tikhonov functional, iterative regularization methods created by the unified scheme of pointwise approximation of the inverse operator, optimization method. The advantages and disadvantages of these methods are indicated. The following features that must be considered when choosing an optimization method are considered: multi-extreme task; the need to search for a global extremum; the complexity of the search hypersurface topology; the presence of restrictions whose introduction into the objective function complicates the topology of the search surface; significant non-linearity and possible non-differentiability of the target function; an algorithmic or complex analytical representation of the objective function. With this in mind, the optimization method for solving the nonlinear inverse problem of designing an eddy current probe excitation system using the modern metaheuristic stochastic global extremum search algorithm was chosen. This algorithm is based on a low-level hybridization of particle swarm optimization methods and the genetic algorithm and provides the evolutionary formation of the swarm composition. The study proved the feasibility of using surrogate optimization to solve the formulated problem in order to reduce the resource consumption of optimization algorithms in calculations using complex objective functions. Effective approximation techniques for constructing metamodels that are necessary for the practical implementation of surrogate optimization are indicated.
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