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Article
Publication date: 11 May 2020

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

Fabian Müller, Lucas Crampen, Thomas Henneron, Stephane Clénet and Kay Hameyer

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…

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Abstract

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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 5
Type: Research Article
DOI: https://doi.org/10.1108/COMPEL-01-2020-0025
ISSN: 0332-1649

Keywords

  • Model order reduction
  • Proper generalized decomposition
  • Proper orthogonal decomposition
  • T-Ω-formulation
  • Finite element method

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Article
Publication date: 5 August 2019

Galerkin proper orthogonal decomposition-reduced order method (POD-ROM) for solving generalized Swift-Hohenberg equation

Mehdi Dehghan, Mostafa Abbaszadeh, Amirreza Khodadadian and Clemens Heitzinger

The current paper aims to develop a reduced order discontinuous Galerkin method for solving the generalized Swift–Hohenberg equation with application in biological science…

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Abstract

Purpose

The current paper aims to develop a reduced order discontinuous Galerkin method for solving the generalized Swift–Hohenberg equation with application in biological science and mechanical engineering. The generalized Swift–Hohenberg equation is a fourth-order PDE; thus, this paper uses the local discontinuous Galerkin (LDG) method for it.

Design/methodology/approach

At first, the spatial direction has been discretized by the LDG technique, as this process results in a nonlinear system of equations based on the time variable. Thus, to achieve more accurate outcomes, this paper uses an exponential time differencing scheme for solving the obtained system of ordinary differential equations. Finally, to decrease the used CPU time, this study combines the proper orthogonal decomposition approach with the LDG method and obtains a reduced order LDG method. The circular and rectangular computational domains have been selected to solve the generalized Swift–Hohenberg equation. Furthermore, the energy stability for the semi-discrete LDG scheme has been discussed.

Findings

The results show that the new numerical procedure has not only suitable and acceptable accuracy but also less computational cost compared to the local DG without the proper orthogonal decomposition (POD) approach.

Originality/value

The local DG technique is an efficient numerical procedure for solving models in the fluid flow. The current paper combines the POD approach and the local LDG technique to solve the generalized Swift–Hohenberg equation with application in the fluid mechanics. In the new technique, the computational cost and the used CPU time of the local DG have been reduced.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 8
Type: Research Article
DOI: https://doi.org/10.1108/HFF-11-2018-0647
ISSN: 0961-5539

Keywords

  • Exponential time differencing (ETD) scheme
  • Local discontinuous Galerkin method
  • Swift–Hohenberg equation
  • 65M70
  • 34A34

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Article
Publication date: 29 April 2014

Absorption line black body distribution function evaluated with proper orthogonal decomposition for mixture of CO2 and H2O

Gabriel Węcel, Ziemowit Ostrowski and Pawel Kozołub

The purpose of this paper is to present a new approach of evaluation of the absorption line black body distribution function (ALBDF) for a mixture of gases. Currently…

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Abstract

Purpose

The purpose of this paper is to present a new approach of evaluation of the absorption line black body distribution function (ALBDF) for a mixture of gases. Currently published correlations, which are used to reproduce the ALBDF, treat only single gases.

Design/methodology/approach

A discrete form of the ALBDF is generated using line by line (LBL) calculations. The latest spectroscopic database HITEMP 2010 is used for the generation of the absorption coefficient histogram, which is cumulated later in order to produce a tabulated form of the ALBDF. The proper orthogonal decomposition (POD) statistical method is employed for the reproduction of the ALBDF. Interpolation property of the POD allows to reproduce the ALBDF for arbitrary gas mixture parameters.

Findings

POD proved to possess optimal interpolation properties. Results obtained by using POD are in very good agreement with LBL integration.

Research limitations/implications

One have to be aware that the model generated with the POD method can be used only within the range of parameters used to build the model. The POD does not perform any property extrapolation. The model is limited to a mixture of two gases, namely CO2 and H2O. Expanding the number of gases used in the mixture may lead to a relatively large matrix system, which is difficult to process with the POD approach.

Practical implications

The presented approach can be used to produce absorption coefficients values and their weights, which can be applied in the gas radiative properties description using the weighted sum of gray gas (WSGG) concept. The proposed model can be used with any radiative transfer equation solver which employs the WSGG approach.

Originality/value

For the first time, radiative properties of gas mixtures are reproduced using the POD approach.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 4
Type: Research Article
DOI: https://doi.org/10.1108/HFF-04-2013-0142
ISSN: 0961-5539

Keywords

  • ALBDF
  • Gas mixture
  • POD
  • Radiative properties

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Article
Publication date: 7 November 2016

Direct synthesis of equivalent circuits from reduced FE models using proper orthogonal decomposition

Toshihito Shimotani, Yuki Sato and Hajime Igarashi

The purpose of this paper is to propose a fast synthesis method of the equivalent circuits of electromagnetic devices using model order reduction. Finite element method…

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Abstract

Purpose

The purpose of this paper is to propose a fast synthesis method of the equivalent circuits of electromagnetic devices using model order reduction. Finite element method (FEM) has been widely used to design electromagnetic devices. For FE analysis of these devices connected to control and deriving circuits, FE equations coupled with the circuit equations have to be solved for many times in their design processes. If the FE models are replaced by equivalent circuit models, computational time could be drastically reduced.

Design/methodology/approach

In the proposed method, a reduced FE model is obtained using proper orthogonal decomposition (POD) in which the size of FE equation is effectively reduced so that the computational time for FE analysis is shortened. Then, the equivalent circuits are directly synthesized from the admittance function of the reduced system.

Findings

Accuracy and computational efficiency of the proposed method are compared with those of another POD-based method in which the equivalent circuits are synthesized from fitting of frequency characteristics using optimization algorithm. There are no significant differences in the accuracy of both methods, while the speedup ratio of the former method is found larger than that for the latter method for the same sampling points.

Originality/value

The equivalent circuits of electric machines and devices have been synthesized on the basis of physical insight of engineers. This paper proposes a novel method by which the equivalent circuits are automatically synthesized from FE model of the electric machines and devices using POD.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 35 no. 6
Type: Research Article
DOI: https://doi.org/10.1108/COMPEL-03-2016-0088
ISSN: 0332-1649

Keywords

  • Finite element method
  • Model order reduction
  • Proper orthogonal decomposition
  • Equivalent circuit

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Article
Publication date: 18 April 2017

A Krylov enhanced proper orthogonal decomposition method for frequency domain model reduction

David Binion and Xiaolin Chen

This paper aims to describe a method for efficient frequency domain model order reduction. The method attempts to combine the desirable attributes of Krylov reduction and…

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Abstract

Purpose

This paper aims to describe a method for efficient frequency domain model order reduction. The method attempts to combine the desirable attributes of Krylov reduction and proper orthogonal decomposition (POD) and is entitled Krylov enhanced POD (KPOD).

Design/methodology/approach

The KPOD method couples Krylov’s moment-matching property with POD’s data generalization ability to construct reduced models capable of maintaining accuracy over wide frequency ranges. The method is based on generating a sequence of state- and frequency-dependent Krylov subspaces and then applying POD to extract a single basis that generalizes the sequence of Krylov bases.

Findings

The frequency response of a pre-stressed microelectromechanical system resonator is used as an example to demonstrate KPOD’s ability in frequency domain model reduction, with KPOD exhibiting a 44 per cent efficiency improvement over POD.

Originality/value

The results indicate that KPOD greatly outperforms POD in accuracy and efficiency, making the proposed method a potential asset in the design of frequency-selective applications.

Details

Engineering Computations, vol. 34 no. 2
Type: Research Article
DOI: https://doi.org/10.1108/EC-11-2015-0344
ISSN: 0264-4401

Keywords

  • Model order reduction
  • Proper orthogonal decomposition
  • Frequency domain response
  • Krylov subspace

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Article
Publication date: 9 September 2013

Model order reduction via proper orthogonal decomposition for a lithium-ion cell

Bettina Suhr and Jelena Rubeša

The simulation of lithium-ion batteries is a challenging research topic. Since there are many electrochemical processes involved in charging and discharging, models which…

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Abstract

Purpose

The simulation of lithium-ion batteries is a challenging research topic. Since there are many electrochemical processes involved in charging and discharging, models which aim to include these processes are in general complex and therefore slow. This paper seeks to address these issues.

Design/methodology/approach

For many tasks, e.g. in optimization, a repeated solution of a model is necessary.

Findings

In this paper, a speed up in simulations, with acceptable error in results, is obtained by combining proper orthogonal decomposition with empirical interpolation method.

Originality/value

The authors report a speed up factor between 10 and 15.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 32 no. 5
Type: Research Article
DOI: https://doi.org/10.1108/COMPEL-04-2013-0112
ISSN: 0332-1649

Keywords

  • Electrochemical model
  • Empirical interpolation method
  • Model reduction
  • Proper orthogonal decomposition
  • Electrochemistry
  • Interpolation

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Article
Publication date: 15 June 2010

Reduced order thermal modeling of data centers via proper orthogonal decomposition: a review

Emad Samadiani and Yogendra Joshi

The purpose of this paper is to review the available reduced order modeling approaches in the literature for predicting the flow and specially temperature fields inside…

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Abstract

Purpose

The purpose of this paper is to review the available reduced order modeling approaches in the literature for predicting the flow and specially temperature fields inside data centers in terms of the involved design parameters.

Design/methodology/approach

This paper begins with a motivation for flow/thermal modeling needs for designing an energy‐efficient thermal management system in data centers. Recent studies on air velocity and temperature field simulations in data centers through computational fluid dynamics/heat transfer (CFD/HT) are reviewed. Meta‐modeling and reduced order modeling are tools to generate accurate and rapid surrogate models for a complex system. These tools, with a focus on low‐dimensional models of turbulent flows are reviewed. Reduced order modeling techniques based on turbulent coherent structures identification, in particular the proper orthogonal decomposition (POD) are explained and reviewed in more details. Then, the available approaches for rapid thermal modeling of data centers are reviewed. Finally, recent studies on generating POD‐based reduced order thermal models of data centers are reviewed and representative results are presented and compared for a case study.

Findings

It is concluded that low‐dimensional models are needed in order to predict the multi‐parameter dependent thermal behavior of data centers accurately and rapidly for design and control purposes. POD‐based techniques have shown great approximation for multi‐parameter thermal modeling of data centers. It is believed that wavelet‐based techniques due to the their ability to separate between coherent and incoherent structures – something that POD cannot do – can be considered as new promising tools for reduced order thermal modeling of complex electronic systems such as data centers

Originality/value

The paper reviews different numerical methods and provides the reader with some insight for reduced order thermal modeling of complex convective systems such as data centers.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 5
Type: Research Article
DOI: https://doi.org/10.1108/09615531011048231
ISSN: 0961-5539

Keywords

  • Modelling
  • Flow
  • Temperature measurement
  • Control systems
  • Data handling

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Article
Publication date: 24 May 2013

Adaptive sampling strategies for non‐intrusive POD‐based surrogates

Marc Guénot, Ingrid Lepot, Caroline Sainvitu, Jordan Goblet and Rajan Filomeno Coelho

The purpose of this paper is to propose a novel contribution to adaptive sampling strategies for non‐intrusive reduced order models based on Proper Orthogonal Decomposition…

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Abstract

Purpose

The purpose of this paper is to propose a novel contribution to adaptive sampling strategies for non‐intrusive reduced order models based on Proper Orthogonal Decomposition (POD). These strategies aim at reducing the cost of optimization by improving the efficiency and accuracy of POD data‐fitting surrogate models to be used in an online surrogate‐assisted optimization framework for industrial design.

Design/methodology/approach

The effect of the strategies on the model accuracy is investigated considering the snapshot scaling, the design of experiment size and the truncation level of the POD basis and compared to a state‐of‐the‐art radial basis function network surrogate model on objectives and constraints. The selected test case is a Mach number and angle of attack domain exploration of the well‐known RAE2822 airfoil. Preliminary airfoil shape optimization results are also shown.

Findings

The numerical results demonstrate the potential of the capture/recapture schemes proposed for adequately filling the parametric space and maximizing the surrogates relevance at minimum computational cost.

Originality/value

The proposed approaches help in building POD‐based surrogate models more efficiently.

Details

Engineering Computations, vol. 30 no. 4
Type: Research Article
DOI: https://doi.org/10.1108/02644401311329352
ISSN: 0264-4401

Keywords

  • Adaptive sampling
  • High‐fidelity simulations
  • Non‐intrusive reduced‐order model
  • Proper orthogonal decomposition
  • Surrogate‐based optimization
  • Sampling methods
  • Simulation

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Article
Publication date: 23 November 2019

Modal analysis of trailing edge cutback film cooling

Yuxi Luo, Fengbo Wen, Rui Hou, Shuai Wang, Songtao Wang and Zhongqi Wang

The purpose of this paper devoted to the application of modal analysis to analyze the flow structure of trailing edge cutback film cooling and the effects of vortex…

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Abstract

Purpose

The purpose of this paper devoted to the application of modal analysis to analyze the flow structure of trailing edge cutback film cooling and the effects of vortex structure on the film cooling effectiveness of the cutback surface.

Design/methodology/approach

Large eddy simulation (LES) is used to simulate the trailing edge cutback film cooling. The results of LES are analyzed by proper orthogonal decomposition (POD) method and dynamic mode decomposition (DMD) method. The POD method is used to determine the dominated vortex structure and the energy level of these structures. The DMD method is used to analyze the relationship between vortex structures and wall temperature.

Findings

The POD method shows that the flow field consists of three main vortices – streamwise vortex, lip vortex and coolant vortex. The DMD results show that the lip vortex mainly acts on the middle section of the cutback surface, while the streamwise vortex mainly acts on the back section of the cutback surface.

Research limitations/implications

The modal analysis is only based on numerical simulation but the modal analysis of experimental results will be further studied in the future.

Practical implications

This paper presents the powerful ability of the modal analysis method to study complex flows in trailing edge cutback film cooling. Establishing the relationship between vortex and wall temperature by modal analysis method can provide a new idea for studying convective heat transfer problems.

Originality/value

The role of streamwise vortex in the flow of the trailing edge cutback cooling and its effect on the cooling effectiveness of the cutback surface is found.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 8
Type: Research Article
DOI: https://doi.org/10.1108/HFF-09-2019-0673
ISSN: 0961-5539

Keywords

  • LES
  • POD
  • Film cooling
  • DMD

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Article
Publication date: 1 August 2016

Study on reconstruction and prediction methods of pressure field on blade surfaces for oil-filling process in a hydrodynamic retarder

Hongbin Mu, Wei Wei, Alexandrina Untaroiu and Qingdong Yan

Traditional three-dimensional numerical methods require a long time for transient computational fluid dynamics simulation on oil-filling process of hydrodynamic braking…

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Abstract

Purpose

Traditional three-dimensional numerical methods require a long time for transient computational fluid dynamics simulation on oil-filling process of hydrodynamic braking. The purpose of this paper is to investigate reconstruction and prediction methods for the pressure field on blade surfaces to explore an accurate and rapid numerical method to solve transient internal flow in a hydrodynamic retarder.

Design/methodology/approach

Dynamic braking performance for the oil-filling process was simulated and validated using experimental results. With the proper orthogonal decomposition (POD) method, the dominant modes of transient pressure distribution on blades were extracted using their spatio-temporal structural features from the knowledge of computed flow data. Pressure field on blades was reconstructed. Based on the approximate model (AM), transient pressure field on blades was predicted in combination with POD. The causes of reconstruction and prediction error were, respectively, analyzed.

Findings

Results show that reconstruction with only a few dominant POD modes could represent all flow samples with high accuracy. POD method demonstrates an efficient simplification for accurate prediction of the instantaneous variation of pressure field in a hydrodynamic retarder, especially at the stage of high oil-filling rate.

Originality/value

The paper presents a novel numerical method, which combines POD and AM approaches for rapid and accurate prediction of braking characteristics during the oil-filling period, based on the knowledge of computed flow data.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 6
Type: Research Article
DOI: https://doi.org/10.1108/HFF-05-2015-0166
ISSN: 0961-5539

Keywords

  • Approximate model
  • Hydrodynamic retarder
  • Proper orthogonal decomposition
  • Reconstruction and prediction

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