Kriging: A Useful Tool for Electromagnetic Device Optimization

Lebensztajn, Luiz; Marretto, Carina Alexandra Rondini; Costa, Maria Conceição da; Coulomb, Jean‐Louis

doi:10.1109/tmag.2004.824542

Cited by 178 publications

(102 citation statements)

References 8 publications

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“…The most popular correlation function is given by the Gaussian model where the value of p k is simply taken as equal to 2. For a given set of data, the maximum likelihood estimation optimises the value of θ and then the correlation model is brought into the regression model to evaluate the function with the best linear unbiased predictor [8,12]. Along with the increase in the number of sampling points selected by Kriging during the iterations, the amount of data produced by the correlation matrices accumulates constantly throughout the optimisation process, which may become problematic especially when dealing with largescale multi-parameter problems, leading to a 'combinatorial explosion'.…”

Section: Krigingmentioning

confidence: 99%

“…Finally, rather than calculating the objective function using computationally expensive finite-element software, a Kriging prediction [7] is employed. In other words, the objective function is approximated using Kriging [8], assisted by algorithms balancing exploration and exploitation ( [9,10]) using the concept of rewards [11]. This strategy has been shown previously to be very efficient and has the advantage that it can be linked with any finite-element code, including commercial software.…”

Section: Introductionmentioning

confidence: 99%

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Robust design optimisation of electromagnetic devices exploiting gradient indices and Kriging

Xiao

Rotaru

Sykulski

2015

IET Science, Measurement & Technology

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Since uncertainties in variables are unavoidable, an optimal solution must consider the robustness of the design. The gradient index approach provides a convenient way to evaluate the robustness but is inconclusive when several possible solutions exist. To overcome this limitation, a novel methodology based on the use of first-and second-order gradient indices is proposed introducing the notion of gradient sensitivity. The sensitivity affords a measure of the change in the objective function with respect to the uncertainty of the variables. A Kriging method assisted by algorithms exploiting the concept of rewards is employed to facilitate function predictions for the robust optimisation process. The performance of the proposed algorithm is assessed through a series of numerical experiments. A modification to the correlation model through the introduction of a Kriging predictor and mean square error criterion allows efficient solution of large scale and multi-parameter problems. The three-parameter version of TEAM Workshop Problem 22 has been used for illustration.

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Section: Krigingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust design optimisation of electromagnetic devices exploiting gradient indices and Kriging

Xiao

Rotaru

Sykulski

2015

IET Science, Measurement & Technology

View full text Add to dashboard Cite

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“…Kriging [1][2][3][4] predicts the shape of the objective function by considering the spatial correlation of data based on limited information and thus offers an efficient and inexpensive surrogate to replace the computationally demanding numerical simulation (such as finite elements). The accuracy of the prediction can be estimated by the mean square error in kriging to assist in a decision on where to place the next evaluation point during optimisation iterations.…”

Section: Introductionmentioning

confidence: 99%

“…The most popular correlation function is given by the Gauss model where the value of p k is simply taken as equal to 2. For a given set of data, the maximum likelihood estimation optimises the value of θ and then the correlation model is brought into the regression model to evaluate the function with the best linear unbiased predictor [1]. Although theoretically kriging could be used for any type and size of optimisation, care must be taken with large problems (many variables and multi-objective) as the correlation matrices can grow rapidly.…”

Section: Introductionmentioning

confidence: 99%

Correlation matrices in kriging assisted optimisation of electromagnetic devices

Xiao

Rotaru

Sykulski

2015

IET Science, Measurement & Technology

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Kriging surrogate modelling facilitates efficient decision making regarding where to place the next point for evaluation during optimisation. This is particularly helpful in the design of electromagnetic devices where computationally expensive numerical field modelling needs to be used. The disadvantage, however, is that correlation matrices are required which, for problems with many design variables and multiple objectives, may grow in size leading to the need for page swapping and thus slowing down of what in principle should be a very fast process. In this study several methodologies to reduce the computational resources required in such problems are proposed. The efficiency of the proposed approach is demonstrated using an example of a large multi-parameter optimisation problem where kriging coupled with the average gradient value method is employed.

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“…The SUMO Toolbox is used to solve two complex problems both originating from Electromagnetics (EM). Previously, kriging surrogate models have been used for EM device optimization by creating a global accurate kriging surrogate model [6]. Afterwards, the computational cheap surrogate model is optimized instead of the expensive simulation.…”

Section: Introductionmentioning

confidence: 99%

Surrogate-based infill optimization applied to electromagnetic problems

Couckuyt

Declercq

Dhaene

et al. 2010

Int J RF and Microwave Comp Aid Eng

130

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The increasing use of expensive computer simulations in engineering places a serious computational burden on associated optimization problems. Surrogate-based optimization becomes standard practice in analyzing such expensive black-box problems. This article discusses several approaches that use surrogate models for optimization and highlights one sequential design approach in particular, namely, expected improvement. The expected improvement approach is demonstrated on two electromagnetic problems, namely, a microwave filter and a textile antenna.

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Kriging: A Useful Tool for Electromagnetic Device Optimization

Cited by 178 publications

References 8 publications

Robust design optimisation of electromagnetic devices exploiting gradient indices and Kriging

Robust design optimisation of electromagnetic devices exploiting gradient indices and Kriging

Correlation matrices in kriging assisted optimisation of electromagnetic devices

Surrogate-based infill optimization applied to electromagnetic problems

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