Brijesh Upadhaya, Paavo Rasilo, Lauri Perkkiö, Paul Handgruber, Anouar Belahcen and Antero Arkkio
Improperly fitted parameters for the Jiles–Atherton (JA) hysteresis model can lead to non-physical hysteresis loops when ferromagnetic materials are simulated. This can be…
Abstract
Purpose
Improperly fitted parameters for the Jiles–Atherton (JA) hysteresis model can lead to non-physical hysteresis loops when ferromagnetic materials are simulated. This can be remedied by including a proper physical constraint in the parameter-fitting optimization algorithm. This paper aims to implement the constraint in the meta-heuristic simulated annealing (SA) optimization and Nelder–Mead simplex (NMS) algorithms to find JA model parameters that yield a physical hysteresis loop. The quasi-static B(H)-characteristics of a non-oriented (NO) silicon steel sheet are simulated, using existing measurements from a single sheet tester. Hysteresis loops received from the JA model under modified logistic function and piecewise cubic spline fitted to the average M(H) curve are compared against the measured minor and major hysteresis loops.
Design/methodology/approach
A physical constraint takes into account the anhysteretic susceptibility at the origin. This helps in the optimization decision-making, whether to accept or reject randomly generated parameters at a given iteration step. A combination of global and local heuristic optimization methods is used to determine the parameters of the JA hysteresis model. First, the SA method is applied and after that the NMS method is used in the process.
Findings
The implementation of a physical constraint improves the robustness of the parameter fitting and leads to more physical hysteresis loops. Modeling the anhysteretic magnetization by a spline fitted to the average of a measured major hysteresis loop provides a significantly better fit with the data than using analytical functions for the purpose. The results show that a modified logistic function can be considered a suitable anhysteretic (analytical) function for the NO silicon steel used in this paper. At high magnitude excitations, the average M(H) curve yields the proper fitting with the measured hysteresis loop. However, the parameters valid for the major hysteresis loop do not produce proper fitting for minor hysteresis loops.
Originality/value
The physical constraint is added in the SA and NMS optimization algorithms. The optimization algorithms are taken from the GNU Scientific Library, which is available from the GNU project. The methods described in this paper can be applied to estimate the physical parameters of the JA hysteresis model, particularly for the unidirectional alternating B(H) characteristics of NO silicon steel.
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J. Muylle, P. Iványi and B.H.V. Topping
A new point creation scheme is presented for generating unstructured uniform size two‐dimensional triangular meshes using the Delaunay triangulation method. The scheme is shown to…
Abstract
A new point creation scheme is presented for generating unstructured uniform size two‐dimensional triangular meshes using the Delaunay triangulation method. The scheme is shown to be suitable for generating meshes with strict limits on element size, such as that used in acoustic and electromagnetic simulations. In this approach for generating meshes of an exact element size a grid made of regular triangles is used to cover most of the mesh domain. An advanced boundary refinement and alignment procedure is presented for optimal connection of the regular grid with the boundary. A new refinement scheme treats the reconnection triangles, between the regular grid and boundary elements, until all are judged satisfactory. Element quality statistics and edge length distribution graphs compare the new scheme with other triangular mesh generation algorithms.
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This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics…
Abstract
This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.
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Mohammad Rezaiee-Pajand and Hossein Estiri
Numerical experiences reveal that the performances of the dynamic relaxation (DR) method are related to the structural types. This paper is devoted to compare the DR schemes for…
Abstract
Purpose
Numerical experiences reveal that the performances of the dynamic relaxation (DR) method are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells. To achieve this task, 12 famous approaches are briefly introduced. The differences among these schemes are between the estimation of the time step, the mass and the damping matrices. In this study, several benchmark structures are analyzed by using these 12 techniques. Based on the number of iterations and the analysis duration, their performances are graded. Numerical findings reveal the high efficiency of the kinetic DR (kdDR) approach and Underwood’s strategy.
Design/methodology/approach
Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells have not been investigated. In this paper, 12 famous DR methods have been used for solving these structures. It should be noted that the difference between these approaches is in the estimation of the fictitious parameters. The aforementioned techniques are used to solve several numerical samples. Then, the performances of all schemes are graded based on the number of iterations and the analysis duration.
Findings
The final ranking of each strategy will be obtained after studying all numerical examples. It is worth emphasizing that the number of iterations and that of convergence points of the arc length algorithms are dependent on the value of the initial arc length. In other words, a slight change in the magnitude of the arc length may lead to the wrong responses. Contrary to this behavior, the analyzer’s role in the dynamic relaxation techniques is considerably less than the arc length method. In the DR strategies when the answer approaches the limit points, the iteration number increases automatically. As a result, this algorithm can be used to analyze the structures with complex equilibrium paths.
Research limitations/implications
Numerical experiences reveal that the DR method performances are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells.
Practical implications
Geometric nonlinear analysis of shells is a sophisticated procedure. Consequently, extensive research studies have been conducted to analyze the shells efficiently. The most important characteristic of these structures is their high resistance against pressure. This study demonstrates the performances of various DR methods in solving shell structures.
Originality/value
Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells are not investigated.
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Martin Petrun, Krzysztof Chwastek and Drago Dolinar
The aim of the paper is to provide a simple and reliable hysteresis model for prediction of magnetization curves of a resistance spot welding transformer (RSWT) core, operating in…
Abstract
Purpose
The aim of the paper is to provide a simple and reliable hysteresis model for prediction of magnetization curves of a resistance spot welding transformer (RSWT) core, operating in a wide range of flux densities and excitation frequencies.
Design/methodology/approach
The hysteresis model considered in the paper is the T(x) description advanced by J. Takács. Three options to extend the model to the dynamic magnetization conditions are considered. The excitation conditions differ from those prescribed by international standards.
Findings
The quasi‐static Takács model combined with a fractional viscosity equation similar to that proposed by S.E. Zirka outperforms other considered options. The effect of eddy currents may be considered as a disturbance factor to the frequency‐independent quasi‐static hysteresis loop.
Research limitations/implications
The combined approach yields in most cases a satisfactory agreement between theory and experiment. For highest frequency considered in the paper (1 kHz) excessive “heels” were observed in the modelled loops. This artifact may be reduced by the introduction of a more complicated relationship for the viscous term. Future work shall be devoted to this issue.
Practical implications
The combined Takács‐Zirka model is a useful tool for prediction of magnetization curves of a RSWT core in a wide range of flux densities and excitation frequencies.
Originality/value
The usefulness of the Takács description has been verified in a practical application. The model is able to predict magnetization curves under non‐standard excitation conditions.
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Vesna Rubežić, Luka Lazović and Ana Jovanović
The purpose of this paper is to propose a chaotic optimization method for identifying the parameters of the Jiles–Atherton (J-A) hysteresis model.
Abstract
Purpose
The purpose of this paper is to propose a chaotic optimization method for identifying the parameters of the Jiles–Atherton (J-A) hysteresis model.
Design/methodology/approach
The J-A model has five parameters which are assigned with physical meaning and whose determination is demanding. To determine these parameters, the fitness function, which represents the difference between the measured and the modeled hysteresis loop, is formed. Optimal parameter values are the values that minimize the fitness function.
Findings
The parameters of J-A model for three magnetic materials are determined. The model with the optimal parameters is validated using measured data and comparison with particle swarm optimization algorithm, genetic algorithm, pattern search and simulated annealing algorithm. The results show that the proposed method provides better agreement between measured and modeled hysteresis loop than other methods used for comparison. The proposed method is also suitable for simultaneous optimization of multiple hysteresis loops.
Originality/value
Chaotic optimization method is implemented for the first time for J-A model parameter identification. Numerical comparisons with results obtained with other optimization algorithms demonstrate that this method is a suitable alternative in parameters identification of J-A hysteresis model. Furthermore, this method is easy to implement and set up.
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The paper presents a mathematical model for the hysteresis phenomenon in a multi-winding single-phase core type transformer. The set of loop differential equations was developed…
Abstract
Purpose
The paper presents a mathematical model for the hysteresis phenomenon in a multi-winding single-phase core type transformer. The set of loop differential equations was developed for Kth winding transformer model where the flux linkages of each winding includes a flux common Φ to all windings as function of magneto motive force Θ of all windings. The purpose of this paper is to first determine a hysteresis nonlinearity involved in Φ(Θ) function using modified Preisach theory and second to develop new analytical formula of Preisach distribution function (PDF).
Design/methodology/approach
It is assumed in this paper that flux linkage characteristics Ψ(i) of each winding have nonlinear component due to the magnetization characteristic of the steel core and sum of linear components due to the self and mutual leakage fluxes. This nonlinear component of Ψ(i) characteristic can be expressed as a flux common Φ to all windings vs ampere-turns Θ of all windings. The nonlinear flux linkage characteristics Ψ(i) of the tested transformer are calculated from the set of measured terminal voltages and terminal currents. To simulate magnetic behavior of the iron core the feedback scalar Preisach model of hysteresis is proposed which gives more accurate predictions than classical model. For this hysteresis model the PDF and feedback function are needed. The intend of this paper is to find these function as an analytical formulas which are convenient for numerical simulations. For identification of the PDF and feedback function parameters of the considered iron core of tested transformer the Levenberg-Marquardt optimization algorithm was used.
Findings
The flux common to all windings is calculated by integrating the induced voltages of the appropriate windings. In this paper the PDF is proposed as a functional series including two dimensional Gauss expressions. In order to proper approximation of hysteresis nonlinearity of the tested iron core the first three terms of functional series of the PDF have been used. In the optimization algorithm only initial and descending limiting hysteresis curves Φ(Θ) were utilized. The feedback function for proposed hysteresis model is assumed as third-order polynomial. The hysteresis model has been successfully validated by comparing the calculated and measured results of Φ(Θ) hysteresis curves. This hysteresis model can be used in transient and steady state simulations of tested transformer taking into account the hysteresis phenomenon. The developed hysteresis model can be also used for analysis of the influence of remnant flux on the operation of tested transformer especially in transient states.
Originality/value
In this paper the feedback Preisach hysteresis model is involved in the flux common to all windings vs ampere-turns of all windings. The new PDF is proposed as functional series including two dimensional Gauss expressions. For tested transformer the three first terms of this functional series may be used for proper approximation of hysteresis nonlinearities.
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Celine Louche, Suzanne Young and Martin Fougère
The purpose of this paper is to introduce the topic and review the contributions of the special issue papers on cross-sector dialogue for sustainability. The paper also presents…
Abstract
Purpose
The purpose of this paper is to introduce the topic and review the contributions of the special issue papers on cross-sector dialogue for sustainability. The paper also presents avenues for further research.
Design/methodology/approach
The paper is based on a review of the current literature on cross-sector partnership and dialogue. It explores the current issues in cross-sector partnerships through a discussion of the papers accepted for the special issue, their focus, findings and key contributions.
Findings
It highlights three main key research themes and learnings from the special issue papers: a high level of “hybridity” of collaboration forms, which involve important tensions; a need to understand partnership in its context and the importance of the individual level in cross-sector collaboration.
Practical implications
The authors call for attention to be paid to two forms of myopia: a tendency to view partnerships primarily from a resource-based view (without much attempt to measure societal impact) and a reluctance to be explicitly critical (despite empirical evidence of some suboptimal aspects of partnerships).
Social implications
The authors call for researchers to move away from a resource-based approach to one that is situated in exploring the value derived from partnerships in the broader societal context. The authors suggest some avenues for further research to move the discussion beyond the partnership imperative.
Originality/value
The paper outlines the need to critically revisit the very essence of what real partnership means and whether dialogue is really taking place.
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M. Rezaiee-Pajand, Hossein Estiri and Mohammad Mohammadi-Khatami
The purpose of this study is to demonstrate that using appropriate values for fictitious parameters is very important in dynamic relation methods. It will be shown that a better…
Abstract
Purpose
The purpose of this study is to demonstrate that using appropriate values for fictitious parameters is very important in dynamic relation methods. It will be shown that a better scheme can be made by modifying these terms.
Design/methodology/approach
Former research studies have proposed diverse values for fictitious parameters. These factors are very essential and highly affect structural analyses’ abilities. In this paper, the fictitious masses in ten previous well-known schemes are replaced with each other. These formulations lead to the extra 41 different new procedures.
Findings
To compare the skills of the created processes with those of the ten previous ones, 14 benchmark problems with geometrical nonlinear behaviour are analysed. The performances’ evaluations are based on the number of iterations and analysis time. Considering these two criteria, the score of each technique is found for the ranking assessments.
Research limitations/implications
To solve a static problem by using a dynamic relaxation (DR) scheme, it should be first converted to a dynamic space. Using the appropriate values for fictitious terms is very important in this approach. The fictitious mass matrix and damping factor play the most effective role in the process stability. Besides, the fictitious time step is necessary for improving the method convergence rate.
Practical implications
Different famous DR procedures were compared with each other previously. These solvers used their original assumptions for the imaginary mass and damping. So far, no attempt has been made to change the fictitious parameters of the well-known DR methods. As these fictitious factors highly affect structural analyses’ efficiencies, these solvers are formulated again by using new parameters. In this study, the fictitious masses of ten previous famous methods are replaced with each other. These substitutions give 51 different procedures.
Originality/value
It is concluded that the present formulations lead to more effective and favourable methods than the solvers with previous assumptions.
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Ramezan‐Ali Naghizadeh, Behrooz Vahidi and Seyed Hossein Hosseinian
The purpose of this paper is to implement a simple, fast and accurate heuristic method for parameter determination of Jiles‐Atherton (JA) hysteresis model for representing…
Abstract
Purpose
The purpose of this paper is to implement a simple, fast and accurate heuristic method for parameter determination of Jiles‐Atherton (JA) hysteresis model for representing magnetization in electrical steel sheets. The performance of the method is validated using measured data and comparison with previous methods.
Design/methodology/approach
JA model requires five parameters to represent the hysteretic behavior of ferromagnetic materials. In order to determine these parameters, measured hysteresis loop is used here to calculate a fitness function which is defined by comparing the measured and simulated magnetization loops. This fitness function is minimized by optimization algorithms.
Findings
In total, four different measured hysteresis loops are studied in this paper. Each optimization algorithm is executed 50 times to investigate the convergence, speed, and accuracy of six methods. All methods begin with the same randomly generated initial parameters. Physical boundaries are used for parameters to avoid unaccepted results. Thorough examination of results shows that the proposed method is more appropriate than previously implemented methods for the parameter determination of Jiles‐Atherton model in all studied cases. The required parameters for each optimization method are also presented.
Originality/value
Shuffled frog leaping algorithm (SFLA) is implemented for the first time for JA model parameter determination. The results show that SFLA is faster and more accurate in comparison with other methods. Furthermore, this algorithm is easy to implement and tune.