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Article
Publication date: 8 August 2019

Sohail R. Reddy, Matthias K. Scharrer, Franz Pichler, Daniel Watzenig and George S. Dulikravich

This paper aims to solve the parameter identification problem to estimate the parameters in electrochemical models of the lithium-ion battery.

2289

Abstract

Purpose

This paper aims to solve the parameter identification problem to estimate the parameters in electrochemical models of the lithium-ion battery.

Design/methodology/approach

The parameter estimation framework is applied to the Doyle-Fuller-Newman (DFN) model containing a total of 44 parameters. The DFN model is fit to experimental data obtained through the cycling of Li-ion cells. The parameter estimation is performed by minimizing the least-squares difference between the experimentally measured and numerically computed voltage curves. The minimization is performed using a state-of-the-art hybrid minimization algorithm.

Findings

The DFN model parameter estimation is performed within 14 h, which is a significant improvement over previous works. The mean absolute error for the converged parameters is less than 7 mV.

Originality/value

To the best of the authors’ knowledge, application of a hybrid optimization framework is new in the field of electrical modelling of lithium-ion cells. This approach saves much time in parameterization of models with a high number of parameters while achieving a high-quality fit.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 38 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 15 November 2011

Daniel Watzenig, Markus Neumayer and Colin Fox

The purpose of this paper is to establish a cheap but accurate approximation of the forward map in electrical capacitance tomography in order to approach robust real‐time…

249

Abstract

Purpose

The purpose of this paper is to establish a cheap but accurate approximation of the forward map in electrical capacitance tomography in order to approach robust real‐time inversion in the framework of Bayesian statistics based on Markov chain Monte Carlo (MCMC) sampling.

Design/methodology/approach

Existing formulations and methods to reduce the order of the forward model with focus on electrical tomography are reviewed and compared. In this work, the problem of fast and robust estimation of shape and position of non‐conducting inclusions in an otherwise uniform background is considered. The boundary of the inclusion is represented implicitly using an appropriate interpolation strategy based on radial basis functions. The inverse problem is formulated as Bayesian inference, with MCMC sampling used to efficiently explore the posterior distribution. An affine approximation to the forward map built over the state space is introduced to significantly reduce the reconstruction time, while maintaining spatial accuracy. It is shown that the proposed approximation is unbiased and the variance of the introduced additional model error is even smaller than the measurement error of the tomography instrumentation. Numerical examples are presented, avoiding all inverse crimes.

Findings

Provides a consistent formulation of the affine approximation with application to imaging of binary mixtures in electrical tomography using MCMC sampling with Metropolis‐Hastings‐Green dynamics.

Practical implications

The proposed cheap approximation indicates that accurate real‐time inversion of capacitance data using statistical inversion is possible.

Originality/value

The proposed approach demonstrates that a tolerably small increase in posterior uncertainty of relevant parameters, e.g. inclusion area and contour shape, is traded for a huge reduction in computing time without introducing bias in estimates. Furthermore, the proposed framework – approximated forward map combined with statistical inversion – can be applied to all kinds of soft‐field tomography problems.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 6
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 10 July 2009

Gerald Steiner and Daniel Watzenig

The purpose of this paper is to investigate the achievable improvement in reconstruction accuracy in electrical tomography through the incorporation of physical bound constraints…

275

Abstract

Purpose

The purpose of this paper is to investigate the achievable improvement in reconstruction accuracy in electrical tomography through the incorporation of physical bound constraints as prior knowledge in the inverse problem solution.

Design/methodology/approach

The structure of the nonlinear least squares inverse problem formulation and the importance of prior knowledge are addressed. Several different methods for the incorporation of bound constraints are discussed. The methods are compared by means of reconstructions from simulated and measured data and the computational demands.

Findings

The inclusion of bound constraints on the material values in the inverse problem solution results in a considerable improvement of the reconstructions. The occurrence of artefacts and blurring can be reduced. Among the investigated constraint handling methods, the logarithmic parameter reconstruction approach can be implemented with minimal additional computational effort.

Research limitations/implications

The study is performed with discrete two‐phase material distributions as occurring in industrial problems. A further step would be the extension to multiple phases.

Originality/value

The logarithmic transform method is a novel approach for the incorporation of bound constraints in tomography. It outperforms other constraint handling approaches and may be of interest for electrical tomography systems in various applications.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 28 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 19 June 2007

Daniel Watzenig, Gerald Steiner, Anton Fuchs, Hubert Zangl and Bernhard Brandstätter

The investigation of the influence of the modeling error on the solution of the inverse problem given uncertain measured data in electrical capacitance tomography (ECT).

499

Abstract

Purpose

The investigation of the influence of the modeling error on the solution of the inverse problem given uncertain measured data in electrical capacitance tomography (ECT).

Design/methodology/approach

The solution of the nonlinear inverse problem in ECT and hence, the obtainable accuracy of the reconstruction result, highly depends on the numerical modeling of the forward map and on the required regularization. The inherent discretization error propagates through the forward map, the solution of the inverse problem, the subsequent calculation of process parameters and properties and may lead to a substantial estimation error. Within this work different finite element meshes are compared in terms of obtainable reconstruction accuracy. In order to characterize the reconstruction results, two error measures are introduced, a relative integral error and the relative error in material fraction. In addition, the influence of the measurement noise given different meshes is investigated from the statistical point of view using repeated measurements.

Findings

The modeling error, the degree of regularization, and measurement uncertainties are the determining and limiting factors for the obtainable reconstruction accuracy of electrical tomography systems. The impact of these key influence factors on the calculation of process properties given both synthetic as well as measured data is quantified. Practical implications – The obtained results show that especially for measured data, the variability in calculated parameters strongly depends on the efforts put on the forward modeling, i.e. on an appropriate finite element mesh size. Hence, an investigation of the modeling error is highly recommended when real‐world tomography problems have to be solved.

Originality/value

The results presented in this work clearly show how the modeling error as well as inherent measurement uncertainties influence the solution of the inverse problem and the posterior calculation of certain parameters like void fraction in process tomography.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 26 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 September 2003

Bernhard Brandstätter, Gert Holler and Daniel Watzenig

Electrical capacitance tomography (ECT) is a technique for reconstructing information about the spatial distribution of the contents of closed pipes by measuring variations in the…

447

Abstract

Electrical capacitance tomography (ECT) is a technique for reconstructing information about the spatial distribution of the contents of closed pipes by measuring variations in the dielectric properties of the material inside the pipe. In this paper, we propose a method that solves the non‐linear reconstruction problem directly leading to less iterations and higher accuracy than linear back projection algorithms currently in use in most ECT systems.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 22 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 15 November 2011

Markus Neumayer, Daniel Watzenig and Bernhard Brandstätter

The purpose of this paper is to demonstrate an inverse problem approach for the determination of stress zones in steel plates of electrical machines. Steel plates of electrical…

151

Abstract

Purpose

The purpose of this paper is to demonstrate an inverse problem approach for the determination of stress zones in steel plates of electrical machines. Steel plates of electrical machines suffer large mechanical stress by processes like cutting or punching during the fabrication. The mechanical stress has effects on the electrical properties of the steel, and thus on the losses of the machine.

Design/methodology/approach

In this paper, the authors present a sensor arrangement and an appropriate algorithm for determining the spatial permeability distribution in steel plates. The forward problem for stress zone imaging is explained and an appropriate numerical solution technique is proposed. Then an inverse problem formulation is introduced and the nature of the problem is analyzed.

Findings

Based on sensitivity analysis, different measurement procedures are compared and a measurement setup is suggested. Further the ill‐posed nature of the inverse problem is analyzed by the Picard condition.

Practical implications

Because of the increased losses due to stress zones, the quantification of stress effects is of interest to adjust the production process. Stress zone imaging is a first approach for the application of an imaging system to quantify these material defects.

Originality/value

This paper presents a simulation study about the applicability of an inverse problem for stress zone imaging and presents first reconstruction results. Further, the paper discusses several issues about stress zone imaging for the ongoing research.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 7 September 2015

Matthias K. Scharrer, Franz Pichler, Martin Cifrain and Daniel Watzenig

The need to optimize and simulate lithium-ion cells is of high importance to their durability. It is possible to use semi-empirical models based on equivalent circuits to model…

165

Abstract

Purpose

The need to optimize and simulate lithium-ion cells is of high importance to their durability. It is possible to use semi-empirical models based on equivalent circuits to model the dynamic behavior. Still, parameter identification is a time consuming task if many equivalent circuits are coupled into a finite element-based simulation. The paper aims to discuss these issues.

Design/methodology/approach

In this paper the authors present an approach to estimate parameters in a very efficient way by using a single equivalent circuit model as a surrogate model on measurement data. The results of the surrogate model are periodically linked back to the original complex model via the so called space mapping method. The authors validate the approach and compare it to the original problem.

Findings

As a remarkable result, the authors report the achieved reduction of computational cost by approximately 87 percent, which equals a speed up factor of 8.

Originality/value

To the best of the authors’ knowledge, using high and low fidelity semi-empirical models combined with space mapping is new in the field of electrical modeling of lithium-ion cells. This approach saves much time in parameterization of coupled models while maintaining high quality results for geometrical and thermal optimization of lithium-ion cells.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 34 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 June 2005

Gerald Steiner, Daniel Watzenig, Christian Magele and Ulrike Baumgartner

To establish a statistical formulation of robust design optimization and to develop a fast optimization algorithm for the solution of the statistical design problem.

722

Abstract

Purpose

To establish a statistical formulation of robust design optimization and to develop a fast optimization algorithm for the solution of the statistical design problem.

Design/methodology/approach

Existing formulations and methods for statistical robust design are reviewed and compared. A consistent problem formulation in terms of statistical parameters of the involved variables is introduced. A novel algorithm for statistical optimization is developed. It is based on the unscented transformation, a fast method for the propagation of random variables through nonlinear functions. The prediction performance of the unscented transformation is demonstrated and compared with other methods by means of an analytical test function. The validity of the proposed approach is shown through the design of the superconducting magnetic energy storage device of the TEAM workshop problem 22.

Findings

Provides a consistent formulation of statistical robust design optimization and an efficient and accurate method for the solution of practical problems.

Originality/value

The proposed approach can be applied to all kinds of design problems and allows to account for the inevitable effects of tolerances and parameter variations occuring in practical realizations of designed devices.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 24 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 22 March 2013

Iliya Tizhe Thuku, Mohd Fua'ad Rahmat, Norhaliza Abdul Wahab, Teimour Tajdari and Abdulrahamam Amuda Yusuf

Circular pipelines are mostly used for pneumatic conveyance in industrial processes. For optimum and efficient production in industries that use a pipeline for conveyance…

318

Abstract

Purpose

Circular pipelines are mostly used for pneumatic conveyance in industrial processes. For optimum and efficient production in industries that use a pipeline for conveyance, tomographic image of the transport particles is paramount. Sensing mechanism plays a vital role in process tomography. The purpose of this paper is to present a two‐dimensional (2‐D) model for sensing the characteristics of electrostatic sensors for electrical charge tomography system. The proposed model uses the finite‐element method.

Design/methodology/approach

The domain is discretized into discrete shapes, called finite elements, by using a MATLAB. Each of these elements is taken as image pixels, on which the electric charges carried by conveyed particles are transformed into equations. The charges' interaction and the sensors installed around the circumference, at the sensing zone of the conveying pipeline are related by the proposed model equations. A matrix compression technique was also introduced to solve the problem of unevenly sensing characteristics of the sensors due to elements' number's concentration. The model equations were used to simulate the modeled electrostatic charge distribution carried by the particles moving in the pipeline.

Findings

The simulated results show that the proposed sensors are highly sensitive to electrostatic charge at any position in the sensing zone, thereby making it a good candidate for tomographic image reconstruction.

Originality/value

Tomographic imaging using finite element method is found to be more accurate and reliable compared to linear and filtered back projection method.

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