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The transverse flux heating (TFH) concept offers very high electrical efficiency in combination with unique technological flexibility. Numerous advantages make this method beyond competition to be applied in e.g. processing lines. However, all potential advantages of TFH can be realized in practice only by optimal design of the inductor shape using numerical modelling and optimization techniques. This paper aims to describe a hierarchical approach to the optimal design of a one-sided induction coil, which will be used for one-sided TFH of continuous moving thin metal strip to achieve a homogeneous temperature distribution along the strip width.

Depending on the design step, 2D or 3D FEM simulations using ANSYS® Mechanical including the electromagnetics package are used. The harmonic electromagnetic solution is coupled to a transient thermal model which takes the strip movement into account. All models use the symmetries of the inductor workpiece arrangement to keep the calculation times as low as possible.

Due to the geometry of a TFH coil, the models can image a quarter or half of the arrangement. Preliminary investigations of different inductor head shapes can be carried out quickly and then further improved on more complex models in combination with the use of optimization algorithms.

Using hierarchical structure for designing a one-sided TFH coil, offers an efficient and quick way to create a coil which is adapted to the application.

The one-sided inductor design is considered, and the results are generally valid.

The purpose of this paper is to the study the multiphase bubbles flow motion in a vertical channel with an electroconducting liquid without and under the influence of a magnetic field.

For numerical calculations, the lattice Boltzmann method (LBM) is used, which is based on the kinetic theory for solving fluid mechanics and other physical problems. The phase-field lattice Boltzmann model is developed to simulate the behaviour of multiphase bubble–bubble interaction while rising in the fluid with high density ratios.

The behaviour of the rising bubble flow in a rectangular column of two phases is investigated with the two-dimensional LBM.

The multiphase flow in electroconducting liquids with high ratio of density is studied using the LBM.

This paper aims to investigate different multi-objective optimization (MOO) approaches for design and control of electromagnetic devices. The main goal of MOO is to find the set of design variables or control parameters which will provide the best possible values of typical conflicting objective functions.

In the research studies, standard genetic algorithm (GA), non-dominated sorting GA (NSGA-II), migration NSGA algorithm and alternance method of optimal control theory are discussed and compared.

The test practical problems of multi-criteria optimization of induction heating processes with respect to chosen quality criteria confirm the effectiveness of application of considered MOO approaches both for the problems of design and control.

This paper represents and investigates different MOO approaches for design and control of electrotechnological systems.

Reliable modeling of induction hardening requires a multi-physical approach, which makes it time-consuming. In designing an induction hardening system, combining such model with an optimization technique allows managing a high number of design variables. However, this could lead to a tremendous overall computational cost. This paper aims to reduce the computational time of an optimal design problem by making use of multi-fidelity modeling and parallel computing.

In the multi-fidelity framework, the “high-fidelity” model couples the electromagnetic, thermal and metallurgical fields. It predicts the phase transformations during both the heating and cooling stages. The “low-fidelity” model is instead limited to the heating step. Its inaccuracy is counterbalanced by its cheapness, which makes it suitable for exploring the design space in optimization. Then, the use of co-Kriging allows merging information from different fidelity models and predicting good design candidates. Field evaluations of both models occur in parallel.

In the design of an induction heating system, the synergy between the “high-fidelity” and “low-fidelity” model, together with use of surrogates and parallel computing could reduce up to one order of magnitude the overall computational cost.

On one hand, multi-physical modeling of induction hardening implies a better understanding of the process, resulting in further potential process improvements. On the other hand, the optimization technique could be applied to many other computationally intensive real-life problems.

This paper highlights how parallel multi-fidelity optimization could be used in designing an induction hardening system.

The purpose of this paper is to describe main ideas and demonstrate results of the research activities carried out by the authors in the field of design concepts of induction mass heating technology based on multiple-criteria optimization. The main goal of the studies is the application of different optimization methods and numerical finite element method (FEM) codes for field analysis to solve the multi-objective optimization problem that is mathematically formulated in terms of the most important optimization criteria, for example, maximum temperature uniformity, maximum energy efficiency and minimum scale formation.

Standard genetic algorithm (GA), non-dominated sorting genetic algorithm (NSGA) and alternance method of parametric optimization based on the optimal control theory are applied as effective tools for the practice-oriented problems for multiple-criteria optimization of induction heaters’ design based on non-linear coupled electromagnetic and temperature field analysis. Different approaches are used for combining FEM codes for interconnected field analysis and optimization algorithms into the automated optimization procedure.

Optimization procedures are tested and investigated for two- and three-criteria optimization problems solution on the examples of induction heating of a graphite disk, induction heating of aluminum and steel billets prior to hot forming.

Solved problems are based on the design of practical industrial applications. The developed optimization procedures are planned to be applied to the wide range of real-life problems of the optimal design and control of different electromagnetic devices and systems.

The paper describes main ideas and results of the research activities carried out by the authors during past years in the field of multiple-criteria optimization of induction heaters’ design based on numerical coupled electromagnetic and temperature field analysis. Implementing the automated procedure that combines a numerical FEM code for coupled field analysis with an optimization algorithm and its subsequent application for designing induction heaters makes the proposed approach specific and original. The paper also demonstrates that different optimization strategies used (standard GA, NSGA-II and the alternance method of optimal control theory) are effective for real-life industrial applications for multiple-criteria optimization of induction heaters design.

The purpose of this study is now to optimize the coil in a way that its lifetime is increased. In the industry, induction hardening of rotationally symmetrical workpieces in a single-shot process is a common method. Owing to only partial superimposition of the workpiece areas to be heated by the inductor, high power densities are frequently needed there. These lead to local hot spots, amounting to an intensive material stress in the copper and often result in short lifetime of the inductor.

In this elaboration, some numerically analysed approaches are presented that can be used to reduce mechanical stresses in the single-shot inductor and thus increase the service life.

It has been found out that changing the coil profiles has a strong influence on its lifetime. Besides that, the heat transfer coefficient between coil and coolant plays a big role and needs to be considered when the coil is dimensioned.

The lifetime of the coil is an important factor and often requested from the customers. Broken coils create a lot of extra costs and can generate downtime. Therefore, many customers that are struggling with thermal fatigue are interested in approaches that prolong the coil lifetime.

This paper aims to describe main ideas and demonstrates results of the research activities carried out by the authors in the field of optimal design concepts for induction heater for surface hardening. The main goal of the research studies is the application of different optimization methods and numerical finite element method (FEM) codes for field analysis to solve the optimal design problem that is mathematically formulated in terms of the one of the most important optimization criteria for surface hardening technology, e.g. maximum temperature uniformity within the hardening surface layer.

Evolutionary algorithm based on Adaptive Gaussian Process-Assisted Differential Evolution for MEMS Design Optimization (AGDEMO) and alternance method of parametric optimization based on optimal control theory are applied as effective tools for the practice-oriented problem for optimization of induction heater design based on non-linear coupled electromagnetic and temperature field analysis. Different approaches are used for combining FEM codes for interconnected field analysis and optimization algorithms into automated optimization procedure.

Optimization procedures are tested and investigated for optimal design problem solution on the examples of induction hardening of steel cylindrical billet.

Solved problems are based on the design of practical industrial applications. The developed optimization procedures are planned to be applied to the wide range of real-life problems of the optimal design of different electromagnetic devices and systems.

This paper describes main ideas and results of the research activities carried out by the authors in the field of optimal design of induction heaters for hardening based on numerical coupled electromagnetic and temperature field analysis. The implementation of the automated procedure that combines a numerical FEM code for coupled field analysis with an optimization algorithm and its subsequent application for designing induction heaters makes the proposed approach specific and original. This paper also demonstrates that different optimization strategies used (evolutionary algorithm based on AGDEMO and alternance method of optimal control theory) are effective for real-life industrial applications for optimization of induction heaters design.

Most of optimal design or control engineering problems present conflicting objectives that need to be simultaneously minimized or maximized. Often, however, it is a priori known that some functions have greater importance than other. This paper aims to present a novel multi-surrogate, multi-objective, decision-making (DM) optimization algorithm, which is suitable for time-consuming simulations. Its performances have been compared, on the one hand with a standard decision-making algorithm (iTDEA), on the other with a self-adaptive evolutionary algorithm (AMALGAM*). The comparison concerns numerical tests and an optimal control task in induction heating.

In particular, the algorithm makes use of surrogates (meta-models) to concentrate the field evaluations at the most promising areas of the design space. The effect of the decision-maker is instead to drive the search to given regions of the Pareto front. The synergy between surrogates and the decision-maker leads to a greater effectiveness of the optimization search. For the field analysis of the optimal control task, a coupled electromagnetic-thermal FEM model has been developed.

The novel algorithms outperform both iTDEA and AMALGAM* in all done tests.

The algorithm could be applied to other computationally intensive multi-objective real-life problems whenever a preference between the objectives is known.

The combination of surrogates and a decision-maker is beneficial with time-consuming multi-objective optimization problems.

Because of their widespread use in industry, induction through‐heaters of various metal products must be of high effectiveness not only in “quasi” steady‐state operation but in different transient modes as well. Nowadays, they are usually designed to provide the required characteristics in “quasi” steady‐state operation mode mainly. The purpose of this paper is to examine numerical simulation of transient processes in induction through‐heating lines generally and investigate dynamic temperature fields during the first start of the heaters particularly.

The research methodology is based on coupled numerical electromagnetic and thermal analyses using FEM approach. ANSYS simulations are supported with the developed tools for imitation of mass transfer effects in continuous induction heating lines.

The results show that transient temperature fields in the heated strip or slab significantly differ from their “quasi” steady‐state descriptions. Local temperature variations acquired in longitudinal as well as transverse flux induction heaters during the first start have been predicted.

The received results can be used for design of induction through‐heaters and improvement of their characteristics in dynamic operation modes.

Investigation of dynamic characteristics of the heaters in dynamic modes can be only done by numerical modelling based on special algorithms providing a time loop additional to coupling between electromagnetic and thermal analyses. Such algorithms have been developed and used for investigation of two types of induction installations: through‐heaters of cylindrical billets for forging and heating lines of strip or thin slab for rolling mills.