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Reliable data-driven modeling of high-frequency structures by means of nested kriging with enhanced design of experiments

Slawomir Koziel (Gdansk University of Technology, Gdansk, Poland)
Anna Pietrenko-Dabrowska (Department of Microelectronic Systems, Gdansk University of Technology Faculty of Electronics,Telecommunications and Informatics, Gdansk, Poland)

Engineering Computations

ISSN: 0264-4401

Article publication date: 14 June 2019

Issue publication date: 12 September 2019




A framework for reliable modeling of high-frequency structures by nested kriging with an improved sampling procedure is developed and extensively validated. A comprehensive benchmarking including conventional kriging and previously reported design of experiments technique is provided. The proposed technique is also demonstrated in solving parameter optimization task.


The keystone of the proposed approach is to focus the modeling process on a small region of the parameter space (constrained domain containing high-quality designs with respect to the selected performance figures) instead of adopting traditional, hyper-cube-like domain defined by the lower and upper parameter bounds. A specific geometry of the domain is explored to improve a uniformity of the training data set. In consequence, the predictive power of the model is improved.


Building the model in a constrained domain allows for a considerable reduction of a training data set size without a necessity to either narrow down the parameter ranges or to reduce the parameter space dimensionality. Improving uniformity of training data set allocation permits further reduction of the computational cost of setting up the model. The proposed technique can be used to expedite the parameter optimization and enables locating good initial designs in a straightforward manner.

Research limitations/implications

The developed framework opens new possibilities inaccurate surrogate modeling of high-frequency structures described by a large number of geometry and/or material parameters. Further extensions can be investigated such as the inclusion of the sensitivity data into the model or exploration of the particular geometry of the model domain to further reduce the computational overhead of training data acquisition.


The efficiency of the proposed method has been demonstrated for modeling and parameter optimization of high-frequency structures. It has also been shown to outperform conventional kriging and previous constrained modeling approaches. To the authors’ knowledge, this approach to formulate and handle the modeling process is novel and permits the establishment of accurate surrogates in highly dimensional spaces and covering wide ranges of parameters.



The authors would like to thank Dassault Systemes, France, for making CST Microwave Studio available. This work is partially supported by the Icelandic Centre for Research (RANNIS) Grant 174114051 and by National Science Centre of Poland Grant 2017/27/B/ST7/00563.


Koziel, S. and Pietrenko-Dabrowska, A. (2019), "Reliable data-driven modeling of high-frequency structures by means of nested kriging with enhanced design of experiments", Engineering Computations, Vol. 36 No. 7, pp. 2293-2308.



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