|Title:||Numerical methods for topology optimization of electromagnetic devices|
|Advisors:||Ho, Siu-lau (EE)|
Fu, Weinong (EE)
Electromagnetic devices -- Mathematical models
Hong Kong Polytechnic University -- Dissertations
|Department:||Department of Electrical Engineering|
|Pages:||19, 181 pages : color illustrations|
|Abstract:||Topology optimization of a device is the process of determining the material distribution within the device. Compared with the conventional shape and seize optimizations, topology optimization offers more degrees of freedom, and has the potential to produce more possible and promising designs but with a cost of a longer optimization time. Based on the requirement of the design and the nature of the problems involved, different topology optimization algorithms have been developed and applied in fellow disciplines. In the area of electromagnetic device designs, the development of applicable methods and strategies for topology optimization is still very demanding, and topology optimization remains a difficult and challenging problem due to the inherent complex natures of an electromagnetic inverse problem in terms of the geometry and involved multiple types of materials. In this respect, some typical problems and challenges encountered in a topology optimization process of electromagnetic device designs are addressed in this thesis. To deal with the uncertainties in the engineering manufacturing of a device, a direct search methodology for robust topology optimizations is developed based on the quantum evolutionary algorithm, and numerically proved to be efficient when compared with other conventional robust optimizers, such as robust oriented genetic algorithms. Via using a quantum bit or Q-bit to represent the design parameters and an adaptive incremental angle for updating positions, the proposed algorithm is able to extensively exploit the neighbor of the searched space. Via using the stochastic approximation method to compute gradient information, the proposed algorithm realizes computational savings of n (the dimension seize) times, and hence is able to be developed into an extremely fast convergent algorithm. Followed by the development of the algorithm, an engineering robust optimization problem related to the RLC ratio of a metamaterial unit cell for wireless power transmission efficiency enhancement is investigated. As the robustness and the averaged transmission efficiency are two distinctive objectives in this case study, a two-step or phase algorithm is further developed for the corresponding robust multi-objective optimization. At the first phase, the performance of different unit cells is evaluated separately, and at the second stage a regression model is constructed to replace the finite element analysis to reduce the computational time. The best candidate thus would be the one having a balance performance with a strong robustness and a high-power transmission enhancement.|
To combat the extremely computationally expensive problem of a topology optimization procedure, a design-of-experiment (DOE) assisted surrogate model for an improved TABU search based refinement optimal method is introduced. By using the Latin-Hypercube sampling scheme to sample the design space, a Kriging model to interpolate the objective function, and a multi-start technique to reduce the design space; the proposed method is able to accurately predict the objective function of the optimization problem with a much shorter computational time, when compared to that of the conventional finite element method. The proposed algorithm is further investigated and applied to the design optimization of the metamaterial slab in wireless power transmission applications to develop an automatic optimization procedure for a hybrid metamaterial slab. The numerical simulation results agree well with the experimental ones, indicating the accuracy of the proposed algorithm. As a topology optimization problem in electromagnetic applications often contains multiple requirements and objectives, a vector wind driven optimization algorithm for multi-objective topology optimizations is also developed. By removing the inertia terms and adding an adaptive mutation term to the position updating equations, the proposed algorithm can extensively explore the entire design domain; and rather than using the non-dominance method, the proposed method employs a gauging metrics to measure the improvement/reduction of various objective functions for every candidate and chooses the most effective one as the optimum. Numerical results indicate that the proposed algorithm has a faster converge rate when compared with the multi-objective counterparts of the conventional heuristic methods. To address the multi-material issue in a topology optimization, a multiscale TO methodology by combining the sequential element rejection-admission (SERA) and boundary element evolvement is presented. As it is well known, the basic formulation of topology optimization only deals with two types of materials, and hence dealing with problems involving more than two types of materials becomes an obstacle on many occasions. In the proposed SERA approach, only the sensitivities of the boundary elements need to be computed and used, and an adaptive parameter updating strategy is introduced to balance the requirements on both the convergence and the quality performance of the solutions. To eliminate the dependence of the final solution on the initial topology, a new hole generating mechanism is proposed. In addition, a sensitivity filter is designed to remove the checkerboard patterns as well as to further eliminate the mesh-dependent problem. Also, a multi-level meshing method is introduced to help to reduce the design domain at the early stage of the optimization without sacrificing the resolution of the resultant topology. The numerical experiments demonstrate that for both di/tri-material problems, the proposed algorithm has a faster optimization speed. Lastly, in the optimization process of complex structure like electrical motors, the conventional modeling methods require too many control parameters to describe the topology of the device and hence have a complicated optimization procedure. To tackle this problem, a radial-basis function based shuffled frog leaping algorithm (SFLA) is developed and applied to the rotor topology optimization of an interior permanent magnet motor. The Gaussian radial-basis function significantly reduces the number of design parameters, and the modified shuffle frog leaping algorithm is able to efficiently explore and exploit the design apace. The performance of the proposed algorithm is compared with the conventional SFLA method, and the hybrid GA method; and the results indicate that the proposed algorithm has a high efficiency with a good accuracy, when compared to the GA (low efficiency, good accuracy) and conventional SFLA (high efficiency, poor accuracy).
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