An Adaptive Interpolating MLS Based Response Surface Model Applied to Design Optimizations of Electromagnetic Devices

Ho, S. L.; Yang, Shiyou; Ni, Peihong; Wong, K.F.

doi:10.1109/tmag.2006.892107

Cited by 7 publications

(4 citation statements)

References 8 publications

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“…This was the motivation behind the new approach based on adaptive correlation matrices division described in Section 3. The initial sampling points are set as in Table 4, whereas the settings for the test ranges and step sizes Radial basis functions (RBF) [16]; AWEI (Kriging) [10]. shown in Table 5 are initialised to preserve the test conditions originally suggested in [14].…”

Section: Three-parameter Test Resultsmentioning

confidence: 99%

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: Three-parameter Test Resultsmentioning

confidence: 99%

Robust design optimisation of electromagnetic devices exploiting gradient indices and Kriging

Xiao

Rotaru

Sykulski

2015

IET Science, Measurement & Technology

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“…The size of these matrices is directly linked to the number of variables, hence in this case of eight variables and using modest 10 steps for each variable vector, a 10 8 parameter set needs to be stored. Since the kriging predictor produces the response surface at each Genetic algorithm (GA) [10]; Tabu search (HuTS) [11]; improved Tabu search (ITS) [12]; simulated annealing algorithm (SA) [13]; New Tabu Search (NTS) [14]; Population-based Incremental Learning (PBIL) [15]. Results for GA, HuTS, ITS, SA, NTS and PBIL taken from [14].…”

Section: -Parameter Team 22mentioning

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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“…5. We considered the three-parameter problem presented in [2,16,17]. For this problem, the shape of SMES can be defined using three design variables that are modeled by a vector x = {R 2 , H 2 , D 2 }.…”

Section: Electromagnetic Applicationmentioning

confidence: 99%

A Robust Optimization Method Utilizing the Variance Decomposition Method for Electromagnetic Devices

Wang¹,

Li²,

Chen³

2014

Journal of Magnetics

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Uncertainties in loads, materials and manufacturing quality must be considered during electromagnetic devices design. This paper presents an effective methodology for robust optimization design based on the variance decomposition in order to keep higher accuracy of the robustness prediction. Sobol' theory is employed to estimate the response variance under some specific tolerance in design variables. Then, an optimal design is obtained by adding a criterion of response variance upon typical optimization problems as a constraint of the optimization. The main contribution of this paper is that the proposed method applies the variance decomposition to obtain a more accurate variance of the response, as well save the computational cost. The performance and robustness of the proposed algorithms are investigated through a numerical experiment with both an analytic function and the TEAM 22 problem.

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An Adaptive Interpolating MLS Based Response Surface Model Applied to Design Optimizations of Electromagnetic Devices

Cited by 7 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

A Robust Optimization Method Utilizing the Variance Decomposition Method for Electromagnetic Devices

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