Application of model order reduction with Cauer ladder networks to industrial inductors

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Niels Koester ◽  
Oliver Koenig ◽  
Alexander Thaler ◽  
Oszkár Bíró
Keyword(s):  
Model Order Reduction ◽  
Skin Effect ◽  
A Priori ◽  
Order Reduction ◽  
Skin Depth ◽  
Uniform Mesh ◽  
Stopping Criterion ◽  
Model Order ◽  
Content Type ◽  
Ladder Network

Purpose The Cauer ladder network (CLN) model order reduction (MOR) method is applied to an industrial inductor. This paper aims to to anaylse the influence of different meshes on the CLN method and their parameters. Design/methodology/approach The industrial inductor is simulated with the CLN method for different meshes. Meshes considering skin effect are compared with equidistant meshes. The inductor is also simulated with the eddy current finite element method (ECFEM) for frequencies 1 kHz to 1 MHz. The solution of the CLN method is compared with the ECFEM solutions for the current density in the conductor and the total impedance. Findings The increase of resistance resulting from the skin effect can be modelled with the CLN method, using a uniform mesh with elements much larger than the skin depth. Meshes taking account of the skin depth are only needed if the electromagnetic fields have to be reconstructed. Additionally, the convergence of the impedance is used to define a stopping criterion without the need for a benchmark solution. Originality/value The work shows that the CLN method can generate a network, which is capable of mimicking the increase of resistance usually accompanied by the skin effect without using a mesh that takes the skin depth into account. In addition, the proposed stopping criterion makes it possible to use the CLN method as an a priori MOR technique.

Model of induction brazing of nonmagnetic metals using model order reduction approach

2018 ◽  
Vol 37 (4) ◽  
pp. 1515-1524 ◽  
Author(s):  
Pavel Karban ◽  
David Pánek ◽  
Ivo Doležel
Keyword(s):  
Heat Treatment ◽  
Model Order Reduction ◽  
Computation Time ◽  
Order Reduction ◽  
Nonlinear Problems ◽  
Model Order ◽  
Content Type ◽  
Weakly Nonlinear ◽  
Induction Brazing ◽  
Multiphysics Problems

Purpose A novel technique for control of complex physical processes based on the solution of their sufficiently accurate models is presented. The technique works with the model order reduction (MOR), which significantly accelerates the solution at a still acceptable uncertainty. Its advantages are illustrated with an example of induction brazing. Design/methodology/approach The complete mathematical model of the above heat treatment process is presented. Considering all relevant nonlinearities, the numerical model is reduced using the orthogonal decomposition and solved by the finite element method (FEM). It is cheap compared with classical FEM. Findings The proposed technique is applicable in a wide variety of linear and weakly nonlinear problems and exhibits a good degree of robustness and reliability. Research limitations/implications The quality of obtained results strongly depends on the temperature dependencies of material properties and degree of nonlinearities involved. In case of multiphysics problems characterized by low nonlinearities, the results of solved problems differ only negligibly from those solved on the full model, but the computation time is lower by two and more orders. Yet, however, application of the technique in problems with stronger nonlinearities was not fully evaluated. Practical implications The presented model and methodology of its solution may represent a basis for design of complex technologies connected with induction-based heat treatment of metal materials. Originality/value Proposal of a sophisticated methodology for solution of complex multiphysics problems established the MOR technology that significantly accelerates their solution at still acceptable errors.

Model order reduction of nonlinear eddy-current field using parameterized CLN

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Miwa Tobita ◽  
Hamed Eskandari ◽  
Tetsuji Matsuo
Keyword(s):  
Model Order Reduction ◽  
Dynamical Behavior ◽  
Order Reduction ◽  
Parameter Variation ◽  
Computational Time ◽  
State Equations ◽  
Model Order ◽  
Content Type ◽  
Parameter Variations ◽  
Nonlinear State

Purpose The authors derive a nonlinear MOR based on the Cauer ladder network (CLN) representation, which serves as an application of the parameterized MOR. Two parametrized CLN representations were developed to handle the nonlinear magnetic field. Simulations using the parameterized CLN were also conducted using an iron-cored inductor model under the first-order approximation. Design/methodology/approach This work studies the effect of parameter variations on reduced systems and aims at developing a general formulation for parametrized model order reduction (MOR) methods with the dynamical transition of parameterized state. Findings Terms including time derivatives of basis vectors appear in nonlinear state equations, in addition to the linear network equations of the CLN method. The terms are newly derived by an exact formulation of the parameterized CLN and are named parameter variation terms in this study. According to the simulation results, the parameter variation terms play a significant role in the nonlinear state equations when reluctivity is used, while they can be neglected when differential reluctivity is used. Practical implications The computational time of nonlinear transient analyses can be greatly reduced by applying the parameterized CLN when the number of time steps is large. Originality/value The authors introduced a general representation for the dynamical behavior of the reduced system with time-varying parameters, which has not been theoretically discussed in previous studies. The effect of the parameter variations is numerically given as a form of parameter variation terms by the exact derivation of the nonlinear state equations. The influence of parameter variation terms was confirmed by simulation.

Model order reduction techniques applied to magnetodynamic T-Ω-formulation

2020 ◽  
Vol 39 (5) ◽  
pp. 1057-1069
Author(s):  
Fabian Müller ◽  
Lucas Crampen ◽  
Thomas Henneron ◽  
Stephane Clénet ◽  
Kay Hameyer
Keyword(s):  
Eddy Current ◽  
Model Order Reduction ◽  
Scalar Potential ◽  
Order Reduction ◽  
Computational Effort ◽  
Transient Field ◽  
Model Order ◽  
Field Problem ◽  
Content Type ◽  
Reduction Techniques

Purpose The purpose of this paper is to use different model order reduction techniques to cope with the computational effort of solving large systems of equations. By appropriate decomposition of the electromagnetic field problem, the number of degrees of freedom (DOF) can be efficiently reduced. In this contribution, the Proper Generalized Decomposition (PGD) and the Proper Orthogonal Decomposition (POD) are used in the frame of the T-Ω-formulation, and the feasibility is elaborated. Design/methodology/approach The POD and the PGD are two methods to reduce the model order. Particularly in the context of eddy current problems, conventional time-stepping algorithms can lead to many numerical simulations of the studied problem. To simulate the transient field, the T-Ω-formulation is used which couples the magnetic scalar potential and the electric vector potential. In this paper, both methods are studied on an academic example of an induction furnace in terms of accuracy and computational effort. Findings Using the proposed reduction techniques significantly reduces the DOF and subsequently the computational effort. Further, the feasibility of the combination of both methods with the T-Ω-formulation is given, and a fundamental step toward fast simulation of eddy current problems is shown. Originality/value In this paper, the PGD is combined for the first time with the T-Ω-formulation. The application of the PGD and POD and the following comparison illustrate the great potential of these techniques in combination with the T-Ω-formulation in context of eddy current problems.

scholarly journals Cauer Ladder Network With Multiple Expansion Points for Efficient Model Order Reduction of Eddy-Current Field

2019 ◽  
Vol 55 (6) ◽  
pp. 1-4 ◽  
Author(s):  
Kenta Kuriyama ◽  
Akihisa Kameari ◽  
Hassan Ebrahimi ◽  
Takayuki Fujiwara ◽  
Kengo Sugahara ◽  
...  
Keyword(s):  
Eddy Current ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Current Field ◽  
Model Order ◽  
Ladder Network

scholarly journals Model Order Reduction of an Induction Motor Using a Cauer Ladder Network

2020 ◽  
Vol 56 (3) ◽  
pp. 1-4
Author(s):  
Tetsuji Matsuo ◽  
Kengo Sugahara ◽  
Akihisa Kameari ◽  
Yuji Shindo
Keyword(s):  
Induction Motor ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Model Order ◽  
Ladder Network

Model order reduction for quasi-magnetostatic problems

2017 ◽  
Vol 36 (6) ◽  
pp. 1783-1791
Author(s):  
Yuqing Xie ◽  
Lin Li ◽  
Shuaibing Wang
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Order Method ◽  
Computational Accuracy ◽  
Order Model ◽  
Model Order ◽  
Content Type ◽  
Reduced Order ◽  
Magnetostatic Problem

Purpose To reduce the computational scale for quasi-magnetostatic problems, model order reduction is a good option. Reduced-order modelling techniques based on proper orthogonal decomposition (POD) and centroidal Voronoi tessellation (CVT) have been used to solve many engineering problems. The purpose of this paper is to investigate the computational principle, accuracy and efficiency of the POD-based and the CVT-based reduced-order method when dealing with quasi-magnetostatic problems. Design/methodology/approach The paper investigates computational features of the reduced-order method based on POD and CVT methods for quasi-magnetostatic problems. Firstly the construction method for the POD and the CVT reduced-order basis is introduced. Then, a reduced model is constructed using high-fidelity finite element solutions and a Galerkin projection. Finally, the transient quasi-magnetostatic problem of the TEAM 21a model is studied with the proposed reduced-order method. Findings For the TEAM 21a model, the numerical results show that both POD-based and CVT-based reduced-order approaches can greatly reduce the computational time compared with the full-order finite element method. And the results obtained from both reduced-order models are in good agreement with the results obtained from the full-order model, while the computational accuracy of the POD-based reduced-order model is a little higher than the CVT-based reduced-order model. Originality/value The CVT method is introduced to construct the reduced-order model for a quasi-magnetostatic problem. The computational accuracy and efficiency of the presented approaches are compared.

Nonlinear model order reduction for the fast solution of induction heating problems in time-domain

2017 ◽  
Vol 36 (2) ◽  
pp. 469-475 ◽  
Author(s):  
Lorenzo Codecasa ◽  
Federico Moro ◽  
Piergiorgio Alotto
Keyword(s):  
Induction Heating ◽  
Model Order Reduction ◽  
Computing Time ◽  
Computational Cost ◽  
Order Reduction ◽  
Reduced Model ◽  
Problem Solution ◽  
Model Order ◽  
Content Type ◽  
Time Harmonic

Purpose This paper aims to propose a fast and accurate simulation of large-scale induction heating problems by using nonlinear reduced-order models. Design/methodology/approach A projection space for model order reduction (MOR) is quickly generated from the first kernels of Volterra’s series to the problem solution. The nonlinear reduced model can be solved with time-harmonic phasor approximation, as the nonlinear quadratic structure of the full problem is preserved by the projection. Findings The solution of induction heating problems is still computationally expensive, even with a time-harmonic eddy current approximation. Numerical results show that the construction of the nonlinear reduced model has a computational cost which is orders of magnitude smaller than that required for the solution of the full problem. Research limitations/implications Only linear magnetic materials are considered in the present formulation. Practical implications The proposed MOR approach is suitable for the solution of industrial problems with a computing time which is orders of magnitude smaller than that required for the full unreduced problem, solved by traditional discretization methods such as finite element method. Originality/value The most common technique for MOR is the proper orthogonal decomposition. It requires solving the full nonlinear problem several times. The present MOR approach can be built directly at a negligible computational cost instead. From the reduced model, magnetic and temperature fields can be accurately reconstructed in whole time and space domains.

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