Fractional derivatives for the core losses prediction: State of the art and beyond

Ducharne, Benjamin; Sebald, Gaël

doi:10.1016/j.jmmm.2022.169961

Cited by 8 publications

(7 citation statements)

References 40 publications

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“…Using a fractional derivative of order α, where 0 < α < 1, to model a viscoelastic behavior is grounded in the notion that the actual response lies between that of a 0th and 1st-order derivative, somewhere between an elastic solid and a viscous fluid [29]. The forward Grünwald-Letnikov expression for fractional derivative respects the causality principle [25,30,31]. Therefore, it was used in this study:…”

Section: Fractional Differential Equation: Physical Interpretation An...mentioning

confidence: 99%

“…The nonhomogeneous space distribution of the flux density makes direct inversion impossible. One solution is proposed in [25] and consists of testing, for each step time, a window of field (+/− 3 A•m −1 ) centered around the value of H at t = t − dt. The H value that leads to the targeted B is conserved and becomes H(t).…”

Section: Sinus B-imposed Simulationmentioning

confidence: 99%

“…Recent advancements in fractional calculus present novel avenues for overcoming traditional limitations [25,26], offering precise simulations across considerable frequency bandwidths while providing detailed insights into the local evolution of magnetic quantities. Our study builds upon these advancements, proposing a methodology that combines fractional derivatives with established modeling frameworks to accurately predict loss contributions across diverse frequency regimes.…”

Section: Introductionmentioning

confidence: 99%

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High-Frequency Fractional Predictions and Spatial Distribution of the Magnetic Loss in a Grain-Oriented Magnetic Steel Lamination

Ducharne,

Hamzehbahmani,

Gao

et al. 2024

Fractal Fract

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Grain-oriented silicon steel (GO FeSi) laminations are vital components for efficient energy conversion in electromagnetic devices. While traditionally optimized for power frequencies of 50/60 Hz, the pursuit of higher frequency operation (f ≥ 200 Hz) promises enhanced power density. This paper introduces a model for estimating GO FeSi laminations’ magnetic behavior under these elevated operational frequencies. The proposed model combines the Maxwell diffusion equation and a material law derived from a fractional differential equation, capturing the viscoelastic characteristics of the magnetization process. Remarkably, the model’s dynamical contribution, characterized by only two parameters, achieves a notable 4.8% Euclidean relative distance error across the frequency spectrum from 50 Hz to 1 kHz. The paper’s initial section offers an exhaustive description of the model, featuring comprehensive comparisons between simulated and measured data. Subsequently, a methodology is presented for the localized segregation of magnetic losses into three conventional categories: hysteresis, classical, and excess, delineated across various tested frequencies. Further leveraging the model’s predictive capabilities, the study extends to investigating the very high-frequency regime, elucidating the spatial distribution of loss contributions. The application of proportional–iterative learning control facilitates the model’s adaptation to standard characterization conditions, employing sinusoidal imposed flux density. The paper deliberates on the implications of GO FeSi behavior under extreme operational conditions, offering insights and reflections essential for understanding and optimizing magnetic core performance in high-frequency applications.

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Section: Fractional Differential Equation: Physical Interpretation An...mentioning

confidence: 99%

Section: Sinus B-imposed Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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High-Frequency Fractional Predictions and Spatial Distribution of the Magnetic Loss in a Grain-Oriented Magnetic Steel Lamination

Ducharne,

Hamzehbahmani,

Gao

et al. 2024

Fractal Fract

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“…Relevant statistical data verified the effectiveness of the model for depicting the COVID-19 pandemic. Fractional derivative operators were used for the core loss prediction [34]. The results showed the accuracy of significant frequency bandwidths.…”

Section: Fractional Order Calculusmentioning

confidence: 99%

Fractional Order Sequential Minimal Optimization Classification Method

Zhao,

Dai,

Huang

2023

Fractal Fract

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Sequential minimal optimization (SMO) method is an algorithm for solving optimization problems arising from the training process of support vector machines (SVM). The SMO algorithm is mainly used to solve the optimization problem of the objective function of SVM, and it can have high accuracy. However, its optimization accuracy can be improved. Fractional order calculus is an extension of integer order calculus, which can more accurately describe the actual system and get more accurate results. In this paper, the fractional order sequential minimal optimization (FOSMO) method is proposed based on the SMO method and fractional order calculus for classification. Firstly, an objective function is expressed by a fractional order function using the FOSMO method. The representation and meaning of fractional order terms in the objective function are studied. Then the fractional derivative of Lagrange multipliers is obtained according to fractional order calculus. Lastly, the objective function is optimized based on fractional order Lagrange multipliers, and then some experiments are carried out on the linear and nonlinear classification cases. Some experiments are carried out on two-classification and multi-classification situations, and experimental results show that the FOSMO method can obtain better accuracy than the normal SMO method.

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“…The additional term may possibly be described with a fractional power law. Such relationships have recently been the subject of considerable research [ 65 , 66 , 67 ].…”

Section: Introductionmentioning

confidence: 99%

The Effects of Sheet Thickness and Excitation Frequency on Hysteresis Loops of Non-Oriented Electrical Steel

Chwastek

2022

Sensors

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The paper focuses on modeling the rate dependence of hysteresis loops in conductive magnetic materials. The concept, which was advanced about fifty years ago by Chua, is discussed. It is shown that the viscous-type equation considered by Zirka and co-workers belongs to the class of Chua-type models. The dynamic effects are described with a simple fractional power law. The value of the exponent in the above-mentioned power law may be assessed on the basis of measurements of coercive field strength at different excitation frequencies. To verify the usefulness of the approach, the measurements of hysteresis loops were carried out at several excitation frequencies under standardized conditions for two grades of non-oriented electrical steel. The modeled curves are in a good correspondence with the measured ones. The considered model uses fewer parameters than approaches based on three-term loss separation schemes.

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Fractional derivatives for the core losses prediction: State of the art and beyond

Cited by 8 publications

References 40 publications

High-Frequency Fractional Predictions and Spatial Distribution of the Magnetic Loss in a Grain-Oriented Magnetic Steel Lamination

High-Frequency Fractional Predictions and Spatial Distribution of the Magnetic Loss in a Grain-Oriented Magnetic Steel Lamination

Fractional Order Sequential Minimal Optimization Classification Method

The Effects of Sheet Thickness and Excitation Frequency on Hysteresis Loops of Non-Oriented Electrical Steel

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