HOMOGENEOUS PLANS OF MULTI-FACTORY EXPERIMENTS ON QUASI-RANDOM R-ROBERTS SEQUENCES FOR SURROGATE MODELING IN A VORTEX STYLE STRUCTUROSCOPY
Authors: Galchenko V. Ya. , Koshevoy M. D. , Trembovetskaya R .V. 
Published: October 2022

Context. The article is devoted to the creation of multifactorial experimental plans based on quasi-random recursive Roberts Rsequences. The object of the research is the process of creating computer-aided experimental design plans. The aim of the article is to create multifactorial, namely six- and seven-factor, uniform plans of experiments with low discrepancies, study of their projection properties and demonstrate their use on the example of surrogate modeling in eddy current structuroscopy.

Method. An iterative method of unit hypercube even filling with reference points was used for constructing multidimensional experimental plans. It provides acceptable indicators of homogeneity and is realized on the basis of quasi-random nonparametric additive recursive Roberts R-sequences using irrational numbers, which, in turn, are obtained on the basis of the generalized Fibonacci sequence. The criterion for plans perfection is the assessment of homogeneity in terms of differences invariant with respect to the rotation of coordinates and re-marking and ordering of factors and which quantitatively characterize the deviation of the generated distribution from the ideal uniform.

Results. Six- and seven-factor computer uniform experimental plans have been created for cataloging, which are characterized by low discrepancies and sufficiently high-quality projection properties. The tendency, which had been previously proved in the authors' research, for preserving these experimental plans characteristics in multidimensional factor spaces, which is observed with increasing number of plan points, has been confirmed. The evaluation of the quality of the created experimental plans is carried out both by visual analysis of the scattering matrix of all two-dimensional projections and by quantitative indicators of heterogeneity of the set of vectors that form the plan, namely centered and cyclic discrepancies.

The example of the initial stage of creating a surrogate model to solve the problem of identifying profiles of electrophysical parameters in eddy current structuroscopy shows certain features of the application for created plans, in particular the transition from the plan for a unit hypercube to the plan in real factor space in the form of a hyperparallelepiped, which does not significantly affect its characteristics of homogeneity of the distribution of points.

Conclusions. For the first time, the problem of creating six- and seven-factor uniform plans of experiments with low rates of centered and cyclic discrepancies based on R-sequences of Roberts was solved. The projection properties of the created experimental plans for different number of points were investigated. The method of constructing multidimensional computer plans of experiments taking into account the peculiarities of eddy current structuroscopy was improved. The use of six-dimensional experimental plans on the example of surrogate modeling in eddy current structuroscopy was demonstrated. The results of the study can be used in the construction of surrogate mathematical models of physical processes by any known methods of approximation.