A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Sowa, Marcin

doi:10.1007/s00034-018-0794-8

Cited by 19 publications

(10 citation statements)

References 47 publications

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“…3 Ferromagnetic core coil models applying classical circuit elements Fig. 4 Ferromagnetic core coil models applying a nonlinear fractional coil (symbol as proposed in [65])…”

Section: Measurementsmentioning

confidence: 99%

Ferromagnetic core coil hysteresis modeling using fractional derivatives

Sowa

Majka

2020

Nonlinear Dyn

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The modeling of a ferromagnetic core coil magnetic hysteresis has been considered. The measurement basis consisted of waveforms that have been recorded for various levels of the iron core saturation levels. The investigated models included classical cases as well as models including a nonlinear fractional coil. The possibilities of solutions for transient problems including such models have been recalled. The details of the estimation process have been described next, where each model evaluation made use of an original methodology dealing with periodic steady states. The influence of the model response on parameter changes has also been studied. Further on the parameter estimation procedure has been described, and the results for the various models have been presented.

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“…3 Ferromagnetic core coil models applying classical circuit elements Fig. 4 Ferromagnetic core coil models applying a nonlinear fractional coil (symbol as proposed in [65])…”

Section: Measurementsmentioning

confidence: 99%

Ferromagnetic core coil hysteresis modeling using fractional derivatives

Sowa

Majka

2020

Nonlinear Dyn

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“…Moreover, in this case the fractional derivative turned out to be better for describing the phenomenon. More on the application of the fractional calculus in various fields of science can be found in the papers [ 8 , 9 , 10 , 11 , 12 , 13 , 14 ].…”

Section: Introductionmentioning

confidence: 99%

Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

Brociek

Chmielowska

Słota

2020

Entropy

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This paper presents the algorithms for solving the inverse problems on models with the fractional derivative. The presented algorithm is based on the Real Ant Colony Optimization algorithm. In this paper, the examples of the algorithm application for the inverse heat conduction problem on the model with the fractional derivative of the Caputo type is also presented. Based on those examples, the authors are comparing the proposed algorithm with the iteration method presented in the paper: Zhang, Z. An undetermined coefficient problem for a fractional diffusion equation. Inverse Probl. 2016, 32.

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“…In the articles [7,8] the heat conduction process was considered in composites and porous aluminum. More about the applications of the fractional derivatives can be found in [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Parameter Identification in the Two-Dimensional Riesz Space Fractional Diffusion Equation

2020

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This paper presents the application of the swarm intelligence algorithm for solving the inverse problem concerning the parameter identification. The paper examines the two-dimensional Riesz space fractional diffusion equation. Based on the values of the function (for the fixed points of the domain) which is the solution of the described differential equation, the order of the Riesz derivative and the diffusion coefficient are identified. The paper includes numerical examples illustrating the algorithm’s accuracy.

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A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Cited by 19 publications

References 47 publications

Ferromagnetic core coil hysteresis modeling using fractional derivatives

Ferromagnetic core coil hysteresis modeling using fractional derivatives

Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

Parameter Identification in the Two-Dimensional Riesz Space Fractional Diffusion Equation

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