Balancing Exploration and Exploitation using Kriging Surrogate Models in Electromagnetic Design Optimization

The balance between exploration and exploitation is an important issue when attempting to find the global minimum of an objective function. This paper describes how this balance may be carefully controlled when using Kriging surrogate models to approximate the objective function

Automation of finite element aided design of induction motors using multi-slice 2D models

Purpose – To develop a practical design tool employing a general purpose electromagnetic finite element (FE) software package to perform automated simulation and performance analysis of induction motors in a design and optimisation process. Design/methodology/approach – Recent publications identified a suitable approach in applying 2D finite-element analysis to 3D problems. This, together with other similar work carried out on brushless DC motors, set out a framework for program development. Performance of the program was validated against practical test data. Findings – Finite-element analysis-based design tools can be realistically employed within a design office environment and are capable of providing solutions within acceptable time scales. Such tools no longer require user expertise in the underlying FE modelling method. The multiple slice technique was employed to model skew in three-phase induction motors and it was established that a four-slice model provides a good balance between accuracy and speed of computation. Research limitations/implications – Program development was based on one commercial FE software package and comparison with practical test data was not exhaustive. However, the approach outlined confirms the practical application. Future work could consider alternative approaches to optimisation. Practical implications – Computing hardware and commercially available 2D FE software have developed sufficiently to enable multi-slice techniques and optimisation to be employed in the analysis and design of machines. Originality/value – This paper provides a practical illustration of how commercial electromagnetic software can be employed as a design tool, demonstrating to industry that such tools no longer need to be bespoke and can realistically be used within a design office

Considerations of Accuracy and Uncertainty with Kriging Surrogate Models in Single-Objective Electromagnetic Design Optimization

The high computational cost of evaluating objective functions in electromagnetic optimal design problems necessitates the use of cost-effective techniques. This paper discusses the use of one popular technique, surrogate modelling, with emphasis placed on the importance of considering both the accuracy of, and uncertainty in, the surrogate model. After briefly reviewing how such considerations have been made in the single-objective optimization of electromagnetic devices, their use with kriging surrogate models is investigated. Traditionally, space-filling experimental designs are used to construct the initial kriging model, with the aim to maximize the accuracy of the initial surrogate model, from which the optimization search will start. Utility functions, which balance the predictions made by this model with its uncertainty, are often used to select the next point to be evaluated. In this paper, the performances of several different utility functions are examined using experimental designs which yield initial kriging models of varying degrees of accuracy. It is found that no advantage is necessarily achieved through searching for optima using utility functions on initial kriging models of higher accuracy, and that a reduction in the total number of objective function evaluations may be achieved by starting the iterative optimization search earlier with utility functions on kriging models of lower accuracy. The implications for electromagnetic optimal design are discussed

Geometric Formulation of Edge and Nodal Finite Element Equations in Electromagnetics

Finite element equations for electromagnetic fields are examined, in particular nodal elements using scalar potential formulation and edge elements for vector potential formulation. It is shown how the equations usually obtained via variational approach may be more conveniently derived using integral methods employing a geometrical description of the interpolating functions of edge and facet elements. Moreover, the resultant equations describe the equivalent multi-branch circuit models

Electromagnetic Design of Dual Resonant Structures for Improved Sensitivity of Terahertz Label Free Bio-Sensing

A design is proposed exploiting full wave numerical simulation of a dual resonant structure with an aim to sense small amounts of chemical and biochemical materials. The structure is energized with free space radiation in the terahertz regime. Thanks to its asymmetric geometry two close resonances are excited. The interference between these two resonances produces a sharp change in the frequency response of the system. By selectively loading the structure with only small amounts of probe material, a relatively large shift in the frequency response may be achieved. The concept is demonstrated through simulation, while optimization of the structure and the analyte loading is attempted

Scalarizing cost-effective multiobjective optimization algorithms made possible with kriging

The use of kriging in cost-effective single-objective optimization is well established, and a wide variety of different criteria now exist for selecting design vectors to evaluate in the search for the global minimum. Additionly, a large number of methods exist for transforming a multi-objective optimization problem to a single-objective problem. With these two facts in mind, this paper discusses the range of kriging assisted algorithms which are possible (and which remain to be explored) for cost-effective multi-objective optimization