Two-level refined direct optimization scheme using intermediate surrogate models for electromagnetic optimization of a switched reluctance motor

Crevecoeur, Guillaume; Abdallh, Ahmed Mohamed Abouelyazied; Couckuyt, Ivo; Dupré, Luc; Dhaene, Tom

doi:10.1007/s00366-011-0239-5

Cited by 6 publications

(8 citation statements)

References 35 publications

(42 reference statements)

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“…Moreover, a more advanced technique, i.e. the two-level refined direct method, was presented in Crevecoeur et al (2012) to reduce the modeling error when the FE model with a coarse mesh is used instead of the fine one. Although the results presented in Crevecoeur et al (2012) are acceptable, the implementation of this technique requires advanced computations.…”

Section: Discussionmentioning

confidence: 99%

Stochastic modeling error reduction using Bayesian approach coupled with an adaptive Kriging-based model

Abdallh

Dupré

2014

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Abstract. Magnetic material properties of an electromagnetic device can be recovered by solving an inverse problem where measurements are adequately interpreted by a mathematical forward model. The accuracy of the material properties recovered by the inverse problem is highly dependent on the accuracy of these forward models. In order to ensure the highest possible accuracy of the inverse problem solution, all physics of the electromagnetic device need to be perfectly modeled using for example a complex numerical model. However, the more accurate 'fine' models demand a high computational time and memory storage. Alternatively, less accurate 'coarse' models can be used with a demerit of the high expected recovery errors. Therefore, the Bayesian approximation error approach has been used for reducing the modeling error originating from using a coarse model instead of a fine model in the inverse problem procedure. However, the Bayesian approximation error approach may fail to compensate the modeling error completely when the used model in the inverse problem is too coarse. Therefore, there is a definitely need to use a quite accurate coarse model. In this paper, the electromagnetic device is simulated using an adaptive Kriging based model. The accuracy of this 'coarse' model is a priori assessed using the cross-validation technique. Moreover, the Bayesian approximation error approach is utilized for improving the inverse problem results by compensating the modeling errors. The proposed methodology is validated on both purely numerical and real experimental results. The results show a significant reduction in the recovery error within an acceptable computational time.Keywords: Bayesian approach, inverse problem, Kriging models, modeling error. INTRODUCTIONRecently, the magnetic parameters of the magnetic core material inside an electromagnetic device (EMD), such as rotating electrical machines, have been retrieved using a coupled experimental-numerical electromagnetic inverse problem [1]. In these inverse problems, the measurements are interpreted using a forward model where the difference between the numerical model responses and the measurement quantities is iteratively minimized using a minimization algorithm. In practice, two major aspects can reduce the accuracy of the recovered solution of the inverse problem, specifically: measurement noise and inaccurate modeling. Measurement noise can be reduced to some extent by accurately performing the measurements. On the other hand, modeling errors basically originate from two main sources: the uncertain 'geometrical' model parameters and the way of modeling the physical phenomena of the EMD. The effect of the uncertain geometrical model parameters on the solution of the inverse problem has been extensively investigated by the authors, see [1]. In this reference, the EMD models are assumed to be perfect, i.e. all physical phenomena are modeled, or in other words, the EMD models exactly simulate the reality. To this end, the EMD needs to be modeled using a very complex ...

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Section: Discussionmentioning

confidence: 99%

Stochastic modeling error reduction using Bayesian approach coupled with an adaptive Kriging-based model

Abdallh

Dupré

2014

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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“…Moreover, the authors presented in [8] a two-level refined direct method for electromagnetic inverse problems, in which the coarse model is based on the numerical fine model but with coarse discretizations. Although the results presented in [8] are acceptable, the implementation of these two-level techniques requires advanced computations, such as the computation of Kriging metamodels. Moreover, in the two-level methods, both fine and coarse models are solved in the iterative inverse approach.…”

Section: Methodsmentioning

confidence: 99%

“…The two-or threedimensional finite-element (2D-FE or 3D-FE) models are commonly used with different mesh discretization levels. In general, numerical models are often more accurate than the analytical ones, but much more time consuming: the higher the degree of freedom, the more the time consumed [8].…”

Section: Introductionmentioning

confidence: 99%

A Bayesian approach for the stochastic modeling error reduction of magnetic material identification of an electromagnetic device

Abdallh¹,

Crevecoeur²,

Dupré³

2012

Meas. Sci. Technol.

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Magnetic material properties of an electromagnetic device can be recovered by solving an inverse problem where measurements are adequately interpreted by a mathematical forward model. The accuracy of these forward models dramatically affects the accuracy of the material properties recovered by the inverse problem. The more accurate the forward model is, the more accurate recovered data are. However, the more accurate 'fine' models demand a high computational time and memory storage. Alternatively, less accurate 'coarse' models can be used with a demerit of the high expected recovery errors. This paper uses the Bayesian approximation error approach for improving the inverse problem results when coarse models are utilized. The proposed approach adapts the objective function to be minimized with the a priori misfit between fine and coarse forward model responses. In this paper, two different electromagnetic devices, namely a switched reluctance motor and an EI core inductor, are used as case studies. The proposed methodology is validated on both purely numerical and real experimental results. The results show a significant reduction in the recovery error within an acceptable computational time. Q1Keywords: Bayesian approximation error approach, coarse and fine models, inverse problem, magnetic material identification, modeling error

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“…Therefore, additional samples are evaluated close to the current iterate during the sequential optimization procedure to ensure that the process converges to a solution of the original problem. Examples of such schemes in the design optimization literature can be found in the works of Crevecoeur et al…”

Section: Framework For Metamodel‐based Dynamic Optimizationmentioning

confidence: 99%

“…In brief, an MM requires to maximize the metamodel fidelity along the optimization iterates while simultaneously limiting the accumulated number of evaluations. Examples in static context can be found in the works of Crevecoeur et al…”

Section: Introductionmentioning

confidence: 99%

A trajectory‐based sampling strategy for sequentially refined metamodel management of metamodel‐based dynamic optimization in mechatronics

Lefebvre

Belie

Crevecoeur

2018

Optim Control Appl Methods

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Dynamic optimization problems based on computationally expensive models that embody the dynamics of a mechatronic system can result in prohibitively long optimization runs. When facing optimization problems with static models, reduction in the computational time and thus attaining convergence can be established by means of a metamodel placed within a metamodel management scheme. This paper proposes a metamodel management scheme with a dedicated sampling strategy when using computationally demanding dynamic models in a dynamic optimization problem context. The dedicated sampling strategy enables to attain dynamically feasible solutions where the metamodel is locally refined during the optimization process upon satisfying a feasibility-based stopping condition. The samples are distributed along the iterate trajectories of the sequential direct dynamic optimization procedure. Algorithmic implementation of the trajectory-based metamodel management is detailed and applied on two case studies involving dynamic optimization problems. These numerical experiments illustrate the benefits of the presented scheme and its sampling strategy on the convergence properties. It is shown that the acceleration of the solution time of the dynamic optimization problem can be achieved when evaluating the metamodel that is lower than 90% compared to the computationally expensive model. KEYWORDSmetamodel-based optimization, metamodel management, sequential dynamic optimization INTRODUCTIONA recurring task within the area of mechatronics is the identification of a set of time-dependent signals (ie, the optimal state trajectory and the corresponding optimal control [OC] policy) to achieve improved system behavior with respect to a well-defined task or objective. 1-3 Reduction in energy consumption, minimization of the execution time, increased safety of operation, and robust tracking are only a few examples of such tasks. A rigorous framework to formulate such dynamic optimization problems (DOPs) is provided by the OC framework, 1 which requires a dynamic model of the system. Having a high-fidelity dynamic model is key to assure close correspondence between optimized and actual system behavior. Dynamic models may incorporate multidomain physics and subsystem interaction, rendering simulation times that can be much slower than real time (see, eg, other works 4-9 ).

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Two-level refined direct optimization scheme using intermediate surrogate models for electromagnetic optimization of a switched reluctance motor

Cited by 6 publications

References 35 publications

Stochastic modeling error reduction using Bayesian approach coupled with an adaptive Kriging-based model

Stochastic modeling error reduction using Bayesian approach coupled with an adaptive Kriging-based model

A Bayesian approach for the stochastic modeling error reduction of magnetic material identification of an electromagnetic device

A trajectory‐based sampling strategy for sequentially refined metamodel management of metamodel‐based dynamic optimization in mechatronics

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