Optimal Design Of Electromagnetic Devices Research Articles

Physics-Informed Generative Adversarial Network-Based Modeling and Simulation of Linear Electric Machines

The demand for fast magnetic field approximation for the optimal design of electromagnetic devices is urgent nowadays. However, due to the lack of a publicly available dataset and the unclear definition of each parameter in the magnetic field dataset, the expansion of data-driven magnetic field approximation is severely limited. This study presents a physics-informed generative adversarial network (PIGAN), as well as a permanent magnet linear synchronous motor (PMLSM)-based magnetic field dataset, for fast magnetic field approximation. It includes the current density, material distribution, electromagnetic material properties, and other parameters of the electric machine. Physics-informed loss functions are utilized in the training process, making the output governed by Maxwell’s equation. Different slot-pole combinations of the PMLSM are involved in the dataset to extend the generalization of PIGAN. Some indicators for the further evaluation of magnetic approximation performance, including image-based metrics and calculation methods for the performance of electric motors, are presented in this study. Some challenges of magnetic field approximation using PIGAN are also discussed. The effectiveness of the physics-informed method is verified by comparing the magnetic field approximation results and the performance analysis results of the PMLSM with FEM, and the speed of PIGAN is approximately 40 times faster than that of FEM, while the accuracy is similar.

A hybrid Jiles–Atherton and Preisach model of dynamic magnetic hysteresis based on backpropagation neural networks

Ferromagnetic materials are widely used for magnetic cores in electromagnetic devices such as inductors, transformers, generators, and motors. In a magnetic core, as the magnetic field varies with time, core loss is generated due to magnetic hysteresis and eddy currents. For performance analysis and design optimization of electromagnetic devices, it is essential to model the dynamic magnetization processes and associated core losses accurately. This paper proposes a hybrid model of dynamic magnetic hysteresis, which incorporates the effects of both hysteresis and eddy currents, by combining the dynamic Jiles-Atherton and Preisach models based on backpropagation neural networks. This model can accurately reproduce the dynamic hysteresis loops and core losses under different excitations. The numerical simulations are verified by experimental measurements.

Optimization of a 3D-Printed Permanent Magnet Coupling Using Genetic Algorithm and Taguchi Method

In recent decades, the genetic algorithm (GA) has been extensively used in the design optimization of electromagnetic devices. Despite the great merits possessed by the GA, its processing procedure is highly time-consuming. On the contrary, the widely applied Taguchi optimization method is faster with comparable effectiveness in certain optimization problems. This study explores the abilities of both methods within the optimization of a permanent magnet coupling, where the optimization objectives are the minimization of coupling volume and maximization of transmitted torque. The optimal geometry of the coupling and the obtained characteristics achieved by both methods are nearly identical. The magnetic torque density is enhanced by more than 20%, while the volume is reduced by 17%. Yet, the Taguchi method is found to be more time-efficient and effective within the considered optimization problem. Thanks to the additive manufacturing techniques, the initial design and the sophisticated geometry of the Taguchi optimal designs are precisely fabricated. The performances of the coupling designs are validated using an experimental setup.

Machine Learning for Design Optimization of Electromagnetic Devices: Recent Developments and Future Directions

This paper reviews the recent developments of design optimization methods for electromagnetic devices, with a focus on machine learning methods. First, the recent advances in multi-objective, multidisciplinary, multilevel, topology, fuzzy, and robust design optimization of electromagnetic devices are overviewed. Second, a review is presented to the performance prediction and design optimization of electromagnetic devices based on the machine learning algorithms, including artificial neural network, support vector machine, extreme learning machine, random forest, and deep learning. Last, to meet modern requirements of high manufacturing/production quality and lifetime reliability, several promising topics, including the application of cloud services and digital twin, are discussed as future directions for design optimization of electromagnetic devices.

Optimal Design of Electromagnetic Devices Assisted by Black Hole and Differential Evolution Algorithms

Recently, many design problems in the field of electrical engineering tend to be more complex, which are characterized by large scale in size, strong nonlinearity for performance analysis, and multi-dimensional design parameters. Therefore, it is not easy to seek for optimum effectively by traditional optimization algorithms. In order to solve optimal design of complex practical problems, in this paper, a novel hybrid optimization algorithm based on the differential evolution algorithm and the black hole theory is proposed and investigated. The differential evolution (DE) algorithm owns good diversity and flexibility, while the black-hole based optimization algorithm (BHBO) possesses faster convergence. In addition, these two algorithms have simple structures. The proposed algorithm with better merits combination may guarantee better convergence and stronger robustness than its independent counterparts of DE and BHBO. The searching performance is deeply investigated through numerical experiments on benchmark functions and practical electromagnetic applications.

Resonant Frequency Modeling of Microwave Antennas Using Gaussian Process Based on Semisupervised Learning

For the optimal design of electromagnetic devices, it is the most time consuming to obtain the training samples from full wave electromagnetic simulation software, including HFSS, CST, and IE3D. Traditional machine learning methods usually use only labeled samples or unlabeled samples, but in practical problems, labeled samples and unlabeled samples coexist, and the acquisition cost of labeled samples is relatively high. This paper proposes a semisupervised learning Gaussian Process (GP), which combines unlabeled samples to improve the accuracy of the GP model and reduce the number of labeled training samples required. The proposed GP model consists two parts: initial training and self-training. In the process of initial training, a small number of labeled samples obtained by full wave electromagnetic simulation are used for training the initial GP model. Afterwards, the trained GP model is copied to another GP model in the process of self-training, and then the two GP models will update after crosstraining with different unlabeled samples. Using the same test samples for testing and updating, a model with a smaller error will replace another. Repeat the self-training process until a predefined stopping criterion is met. Four different benchmark functions and resonant frequency modeling problems of three different microstrip antennas are used to evaluate the effectiveness of the GP model. The results show that the proposed GP model has a good fitting effectiveness on benchmark functions. For microstrip antennas resonant frequency modeling problems, in the case of using the same labeled samples, its predictive ability is better than that of the traditional supervised GP model.

Proposal of a Bi-Objective Kriging Adapted Output Space Mapping Technique for Electromagnetic Design Optimization

Multi-objective optimization with finite-element model (FEM) for the optimal design of electromagnetic devices is a complex task and also time costly. Output space mapping (OSM) techniques allow having an affordable computation cost with a minimum number of computationally expensive FEM evaluations. In this paper, a bi-objective Kriging adapted OSM, an original space-mapping technique based on adaptive nonlinear corrective projection, is proposed. First, the proposed technique is validated using a mathematical test function; Second, it is applied on a three-phase brushless dc motor, which is represented through two modeling levels: 1) coarse (analytical model) and 2) fine (2-D FEM). An advantage of this new technique is its ability to make the coarse model converge effectively toward the fine model.

A Novel Reliability-Based Optimal Design of Electromagnetic Devices Based on Adaptive Dynamic Taylor Kriging

This paper proposes an efficient reliability-based optimization algorithm based on adaptive dynamic Taylor Kriging (ADTK). In the ADTK model, the basis functions are optimally selected by the binary particle swarm optimization algorithm and the minimal number of sampling data with a desired fitting error is decided. To evaluate performance of reliability calculation, the Monte Carlo simulation method is employed, where the performance constraint functions are constructed by the ADTK surrogate model. Overall, an electromagnetic application-superconducting magnetic energy storage device (TEAM problem 22) is used to investigate performances of the proposed method.

A Novel Subregion-Based Multidimensional Optimization of Electromagnetic Devices Assisted by Kriging Surrogate Model

A novel subregion-based optimization strategy utilizing an adaptive dynamic Taylor Kriging (ADTK) surrogate model is developed for a multidimensional optimal design of electromagnetic devices. In the algorithm, the whole design space is divided into a series of subregion, which has its own local ADTK model with optimal set of basis functions. For all subregions, a global optimal solution is found by using particle swarm optimization with the help of the local ADTK models of the objective and constraint functions. The proposed algorithm improves remarkably the accuracy of the ADTK model by reducing the computational complexity. It also significantly reduces the computational cost especially for an optimal design of large-scale multidimensional problems. Finally, the effectiveness of the proposed method is demonstrated through applications to two benchmark problems: TEAM problems 22 and 25.

Proposal of a Kriging Output Space Mapping Technique for Electromagnetic Design Optimization

Using the finite-element model (FEM) to achieve the optimal design of electromagnetic devices is a complex and time-consuming process. Space-mapping techniques reduce computation cost by aligning two models with different granularities, namely, a coarse model and a fine model. In this paper, Kriging output space mapping (OSM), an original space-mapping technique based on adaptive nonlinear corrective projection, is proposed and compared with a conventional OSM technique. The device for optimal sizing is a five-phase linear induction motor, which is represented through two modeling levels: 1) coarse (Kriging model) and 2) fine (2-D FEM). An advantage of this new technique is its ability to provide a sufficiently accurate model for each objective and constraint function and make the coarse model converge effectively toward the fine model.

A Novel Adaptive Dynamic Taylor Kriging and Its Application to Optimal Design of Electromagnetic Devices

An adaptive dynamic Taylor Kriging (ADTK) is developed and combined with the particle swarm optimization algorithm to get a numerically efficient optimization strategy. For given sampling data, the ADTK always minimizes its fitting error without regard to a problem through optimal selection of basis functions among Taylor polynomials. An adaptive sampling method is also proposed based on the fitting error estimation, through which a minimum number of sampling data for a desired level of fitting error can be controlled. The proposed approaches are tested with an analytic function and the TEAM 25.

A Hybridized Vector Optimal Algorithm for Multi-Objective Optimal Designs of Electromagnetic Devices

Multiple-objective designs exist in most real-world engineering problems in different disciplines. A multi-objective evolutionary algorithm will face a challenge to obtain a series of compromises of different objectives, called Pareto optimal solutions, and to distribute them uniformly. In this regard, it is essential to keep the balance of local and global search abilities of such algorithms. Quantum-behaved particle swarm optimization (QPSO) is a population-based swarm intelligence algorithm, and differential evolutionary (DE) is another simple population-based stochastic search one for global optimization with real-valued parameters. Although the two optimizers have been successfully employed to solve a wide range of design problems, they also suffer from premature convergence and insufficient diversity in the later searching stages. This is probably due to the insufficient dimensional searching strength, especially for problems with many decision parameters. In this paper, a new multi-objective non-dominated optimal methodology combining QPSO, DE, and tabu search algorithm (QPSO-DET) is proposed to guarantee the balance between the local and global searches. The performances of the proposed QPSO-DET are compared with those of other two widely recognized vector optimizers using different case studies.

A Possibility-Based Robust Optimal Design Algorithm in Preliminary Design Stage of Electromagnetic Devices

In the early design stage of an electromagnetic device, sufficient information on uncertainties of design variables is not available. Therefore, a reliable optimal design cannot be achieved by the conventional reliability analysis, in which the probabilistic method is applied. This paper, considering the insufficient uncertainty data, proposes a possibility-based optimal design algorithm to get a robust and reliable optimal design of electromagnetic devices. The suggested algorithm adopts a possibility analysis utilizing the fuzzy set theory. In addition, to mitigate the expensive performance analysis during possibility analysis, the design sensitivity analysis is employed to construct a surrogate model. Finally, the developed algorithm is validated through applications to several examples.

Investigation of reliability analysis algorithms for effective reliability‐based optimal design of electromagnetic devices

To extend the reliability-based optimal design to engineering electromagnetic problems, the essential prerequisite is to develop a numerically efficient method of reliability calculation. From a practical point of view, this study presents a comparative study on different algorithms of reliability analysis. For reliability analysis of electromagnetic problems, the author proposed one sensitivity-assisted Monte Carlo simulation (SA-MCS) method in the previous research. To seek a higher accuracy of reliability analysis, in this study, the second-order derivatives are incorporated into the SA-MCS method. About calculation of second-order derivatives (also called sensitivity analysis in the finite element analysis), a hybrid direct differentiation–adjoint variable method is applied. Finally, analysis performances of the suggested SA-MCS and traditional methods such as the reliability index approach and the performance measure approach are investigated through applications to analytic examples and a superconducting magnetic energy storage system.

Comparative Study on Kriging Surrogate Models for Metaheuristic Optimization of Multidimensional Electromagnetic Problems

This paper presents a comparative study on different surrogate models for an application to multidimensional optimal design of electromagnetic devices. The surrogate model is combined with a heuristic optimization algorithm, which usually requires a lot of objective function calls. For this, various Kriging surrogate models, including dynamic Kriging (DK) and multiquadric radial basis function with optimal shape parameter, are investigated and discussed. In the DK surrogate model, the optimal combination of the basis functions is obtained using an improved binary particle swarm optimization algorithm.

A Novel Fast Remesh-Free Mesh Deformation Method and Its Application to Optimal Design of Electromagnetic Devices

Optimal shape design of electromagnetic devices using finite-element (FE) parameter sweeping analysis is becoming a routine procedure today. In the optimal design process, different meshes for different device shapes are required for subsequent FE computations to obtain the values of objective function from the field solution. Traditional full or partial remeshing methods usually cost excessive computing time when generating these FE meshes, especially for 3-D problems. The proposed remesh-free method being reported requires only one set of fine computational mesh and an initial coarse mesh, which also forms a convex decomposition of the solution domain. For new geometry shapes, new deformed meshes can be quickly derived using a coordinate mapping technique once the new coordinates of the nodes on the initial boundary mesh are given. In this way, each mesh for each set of parameters can be produced quickly without remeshing, as only the existing fine mesh topological information is needed to update the nodal positions. The method can be applied to both 2-D and 3-D problems. 2-D and 3-D numerical examples are given to showcase the effectiveness of the proposed method.

A New Application of an ANFIS for the Shape Optimal Design of Electromagnetic Devices

This paper presents a new model based on simulated annealing algorithm (ASA) and adaptive neuro-fuzzy inference system (ANFIS) for shape optimization and its applications to electromagnetic devices. The proposed model uses ANFIS system to evaluate the electromagnetic performance of the device. Both the ANFIS and ASA method are applied to the design/optimization of the electromagnetic actuator. The results of the proposed approach are compared with other techniques such as: method of moving asymptotes, penalty method, augmented lagrangian genetic algorithm and simulated annealing method (SA). Among the algorithms, the proposed ANFIS-ASA approach significantly outperforms the other methods.

An Adaptive Optimization Algorithm Based on Kriging Interpolation with Spherical Model and its Application to Optimal Design of Switched Reluctance Motor

In this paper, an adaptive optimization strategy utilizing Kriging model and genetic algorithm is proposed for the optimal design of electromagnetic devices. The ordinary Kriging assisted by the spherical covariance model is used to construct surrogate models. In order to improve the computational efficiency, the adaptive uniform sampling strategy is applied to generate sampling points in design space. Through several iterations and gradual refinement process, the global optimal point can be found by genetic algorithm. The proposed algorithm is validated by application to the optimal design of a switched reluctance motor, where the stator pole face and shape of pole shoe attached to the lateral face of the rotor pole are optimized to reduce the torque ripple.

Minimizing design criterion and sensitivity: Cost-effective evolutionary approach with application in mechatronics

Optimizing against sensitivity is a major issue in optimal design of electromagnetic devices. In the paper, the optimal shape design problem against sensitivity is formulated in terms of Paretian optimality, trading off design criterion and sensi- tivity with respect to large-scale variations in the design space; a cost-effective evaluation of sensitivity, based on evolutionary computing, is proposed. The design optimization of a magnetic MEMS is considered as the case study.

A Paretian Approach to Optimal Design With Uncertainties: Application in Induction Heating

A major issue in optimal design of electromagnetic devices relates to optimizing against uncertainty, in terms of geometric and physical parameters. The induction heating of a graphite disk, with the purpose to obtain a prescribed temperature profile, is considered as the model problem. The novelty of this paper is a cost-effective method enabling the designer to select the Pareto optimal solutions trading off design criterion and sensitivity.