# The neurocomputing using of the development metamodels stage in the optimal surrogate antennas synthesis process

## DOI:

https://doi.org/10.20535/RADAP.2018.74.60-72## Keywords:

antenna synthesis, surrogate optimization, metamodel, computer experiment plan, LPτ-sequence, response surface, neural network## Abstract

**Introduction**. A computational developing metamodels technology for optimal antenna synthesis problems is proposed. This computational technology is created using methods of data mining, artificial intelligence and modern computer methods of experiment planning. To develop an approximation model, the mathematical apparatus of artificial neural networks, namely the RBF-network, is applied.

**Analysis of metamodels developing research**. The computer experiment plan is performed with the help of Sobol’s $LP_\tau$-sequences $(\xi_1, \xi_2)$, which in the general case uniformly fill the points with the search space in the unit hypercube. Verification of the proposed technology is performed on test functions of the two variables goal. The obtained metamodels have rather high accuracy of approximation and improved computational efficiency. The created computing metamodels developing technology of provides high modeling speed which makes a possible realization of optimum antennas synthesis procedure. This technology is effective and correct for more complex problems of approximating multidimensional hypersurfaces.

**Metamodels developing**. To develop the RBF-metamodel, an automatic and user-defined strategy with random sampling is used in the ratio: 70% - training, 15% - control, 15% - test. Training and control samples were used in the metamodel developing, and the test - for cross-verification. At the stage of training best neural networks selection was carried out by indicators: determination coefficient $R^2$; standard forecast error deviations ratio and learning data $S.D.ratio$; average relative model error magnitude MAPE,%; residual average squared error $MS_R$; residues histogram; scattering diagrams.

**Results of numerical experiments**. Obtained metamodels for test functions $f_1(x,y)$ - RBF-2-130-1 (44); $f_2(x,y)$ - RBF-2-150-1 (6); $f_3(x,y)$ - RBF-2-185-1 (10) have a high enough approximation accuracy and improved computational efficiency. For these metamodels, we checked the adequacy and informativeness of Fisher's criterion. The results of metamodels checking adequacy calculations at the stage of response surface recovery are presented. The created computing metamodels developing technology provides a high simulation speed, which makes possible the implementation of the procedure for optimal antennas synthesis. This technology is effective and correct for more complex problems of multidimensional hypersurfaces approximation.

**Conclusions**. The numerical experiments results analysis is evidence of the high efficiency of the proposed computing developing metamodels technology, which is created using methods of intellectual data analysis, artificial intelligence and modern computer experiment planning methods. The metamodels developing with its use are characterized by fairly high accuracy of approximation and improved computational efficiency. It is these advantages that allow their using with the optimal surrogate antennas synthesis.

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