Nonlinear Interpolation on Manifold of Reduced-Order Models in Magnetodynamic Problems

Paquay, Yannick; Brüls, Olivier; Geuzaine, Christophe

doi:10.1109/tmag.2015.2477169

Cited by 19 publications

(14 citation statements)

References 13 publications

(2 reference statements)

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“…DEIM approximates a nonlinear function by constructing a subspace through singular value decomposition (SVD) on a snapshot matrix of the nonlinear function and selecting interpolation indices through a recursive interpolation-based projection process. Due to its excellent performance, the DEIM has already been employed for model order reduction in numerous applications [29]- [31].…”

Section: A Reduced Model Using the Deim (Rm-deim)mentioning

confidence: 99%

Reduced Preisach Model: Beyond Discrete Empirical Interpolation Method

Wang

Lü

et al. 2019

IEEE Access

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The Preisach model, which is formulated as a weighted superposition of hysteresis kernels, has been widely used for hysteresis modeling, especially in smart-material-based actuators. However, in the classical Preisach model, a trade-off is always required between the model accuracy and the number of the hysteresis kernels. To deal with this problem, a model order reduction technique based on the discrete empirical interpolation method (DEIM) has recently been proposed. The method can largely reduce the number of the hysteresis kernels while barely losing the model accuracy. It is noted that the kernel weight in the reduced DEIM-based model can be both positive and negative, which means that the monotonicity of the Preisach model could be lost. The monotonicity is a very important property especially when constructing the inverse Preisach model. Furthermore, the loss of the monotonicity can also deteriorate the model predictability. In the current paper, a modification strategy is proposed. In the modified reduced Preisach model, the DEIM is only employed to select the dominant hysteresis kernels while the corresponding weights of the selected hysteresis kernels are re-identified by solving a constraint optimization problem. Systematic simulation studies and experimental validation are carried out to demonstrate the effectiveness of the proposed strategy.INDEX TERMS Discrete empirical interpolation method (DEIM), hysteresis nonlinearity, monotonicity, reduced Preisach model, smart-material-based actuator.

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Section: A Reduced Model Using the Deim (Rm-deim)mentioning

confidence: 99%

Reduced Preisach Model: Beyond Discrete Empirical Interpolation Method

Wang

Lü

et al. 2019

IEEE Access

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“…To overcome this problem, the interpolation method which does not solve the reduced equations has been proposed [5], [6]. In this method, the machine response for arbitrary input is obtained via interpolation of the basis vectors obtained by POD.…”

Section: Introductionmentioning

confidence: 99%

“…In this method, the machine response for arbitrary input is obtained via interpolation of the basis vectors obtained by POD. The nonlinear interpolation is applied to the Grassmann manifold in [5], while the interpolation is adopted for the righthand vector of the singular value decomposition in [6].…”

Section: Introductionmentioning

confidence: 99%

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Fast Analysis of Rotating Machine Using Simplified Model-Order Reduction Based on POD

2020

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This paper proposes a simplified model order reduction for the fast dynamic simulation of electric motors. The magnetic fields are snapshotted for different input currents at each mechanical angle to construct a data matrix. The basis vectors are then computed by the singular value decomposition applied to the data matrix. The interpolation along the mechanical angle is performed by the dynamic mode decomposition. Fast computation of the magnetic field for arbitrary input current and mechanical angle is performed through interpolation of the basis vectors in the space of input currents for the dynamic analysis of motors.

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“…However, these two methods are not valid for cases, in which induced eddy currents are involved. The model order reduction (MOR) technique is capable of considering the eddy-current effects with the advantage of a low computing capacity and a quick transient [21]- [23]. The main drawback is, however, that the MOR is not suitable for applications where a high precision is required especially for the magnetic field distribution.…”

Section: Introductionmentioning

confidence: 99%

Accelerating the Time-Stepping Finite-Element Analysis of Induction Machines in Transient-Magnetic Solutions

Petrov

Pyrhönen

2019

IEEE Access

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Finite-element analysis (FEA) is one of the most significant tools in the designing and analyzing of electrical machines, which mainly includes the transient-magnetic (TM), magnet-static (MS) and time-harmonic (TH) solutions. The transient-magnetic (TM) solution in FEA is capable of considering both the harmonic effects and eddy-current effects accurately, which makes it suitable for the induction machine (IM) simulation. However, the drawback of the TM FEA for the IM modelling is that it takes some time before reaching the steady state because of the longer numerical transient, which is affected by the inherent electromagnetic time constants of the IM directly. In this paper, a new approach is proposed to reduce the duration of the numerical transient of the IM in the time-stepping FEA so that the steady state can be achieved in a short time. The proposed approach is capable of creating an initial condition close to the final steady state for the simulation by eliminating or reducing the stator and rotor electromagnetic time constants separately. The stator electromagnetic time constant is eliminated by an initial current excitation (obtained by the TH solution or the analytical method) and the rotor electromagnetic time constant is reduced by a locked rotor model at the beginning of the simulation. Then the initial current excitation is switched to a voltage excitation and the locked rotor is turned to the rotating state at proper time. Finally, the proposed approach is tested and proved efficient to reduce the transients by two typical cases (a solid-rotor IM and a squirrel-cage IM) with 2D FEA. INDEX TERMS Numerical transient, finite-element analysis (FEA), induction machine (IM), electromagnetic time constant, transient-magnetic (TM) solution.

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Nonlinear Interpolation on Manifold of Reduced-Order Models in Magnetodynamic Problems

Cited by 19 publications

References 13 publications

Reduced Preisach Model: Beyond Discrete Empirical Interpolation Method

Reduced Preisach Model: Beyond Discrete Empirical Interpolation Method

Fast Analysis of Rotating Machine Using Simplified Model-Order Reduction Based on POD

Accelerating the Time-Stepping Finite-Element Analysis of Induction Machines in Transient-Magnetic Solutions

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