The Construction of Effective Multi-Dimensional Computer Designs of Experiments Based on a Quasi-Random Additive Recursive R_d-sequence

Abstract

Uniform multi-dimensional designs of experiments for effective research in computer modelling are highly demanded. The combinations of several one-dimensional quasi-random sequences with a uniform distribution are used to create designs with high homogeneity, but their optimal choice is a separate problem, the solution of which is not trivial. It is believed that now the best results are achieved using Sobol’s LPτ-sequences, but this is not observed in all cases of their combinations. The authors proposed the creation of effective uniform designs with guaranteed acceptably low discrepancy using recursive Rd-sequences and not requiring additional research to find successful combinations of vectors set distributed in a single hypercube. The authors performed a comparative analysis of both approaches using indicators of centred and wrap-around discrepancies, graphical visualization based on Voronoi diagrams. The conclusion was drawn on the practical use of the proposed approach in cases where the requirements for the designs allowed restricting to its not ideal but close to it variant with low discrepancy, which was obtained automatically without additional research.

Surrogate methods for determining profiles of material properties of planar test objects with accumulation of apriori information about them

“…Using the algorithm for constructing surrogate models proposed by the authors in [22,23,29], metamodels were created taking into account the measurement conditions and possible changes in the ECP signal. To build the metamodels, a volumetric sample is designed for the DFCNN training at the points of the multidimensional DOE [35] based on the Sobol's LP τ -sequences, providing their high accuracy. This sample was obtained by calculation using the "exact" electrodynamic model [5,19] and is presented in Table 1.…”

“…Then the metamodels regarding, for example, the four influencing factors will have the form e metamod = F(σ max , µ max , z, f ), of which σ max = var, µ max = var, z = var, f = var. Using the successful sets of LP τ -sequences calculated for a single hypercube [35], the groups of their combinations of two to nine factors were created. The resulting designs on the sequences were analyzed both by the centered CD and wrap-around WD discrepancies and the newest onesmixed MD and weighted symmetric centered WSCD discrepancies [36,37], which together make it possible to assess the homogeneity of the DOEs created on their basis.…”

Reconstruction of Electrophysical Parameter Distribution During Eddy Current Measurements of Structural Features of Planar Metal Objects

“…These requirements can be met if a perfect DOE is used to create it. To effectively implement the profile reconstruction method, the authors created advanced computer uniform DOEs on quasi-Sobol's sequences [18]. Low discrepancy is their advantage over known designs [19]- [21], and most importantly, in twodimensional projections.…”

Metrology and Measurement Systems

“…The use of DOEs with topology uncertainty of the hypersurface increases the probability of the reference points falling into the areas of extremes and kinds. [23] shows that the best characteristics of the homogeneity of a multidimensional DOE can be achieved on the basis of quasi-random parameterless additive recursive R-sequences and combinations of Sobol's LP τsequences.…”