Design of contemporary antenna structures needs to account for several and often conflicting objectives. These are pertinent to both electrical and field properties of the antenna but also its geometry (e.g., footprint minimization). For practical reasons, especially to facilitate efficient optimization, single-objective formulations are most often employed, through either a priori preference articulation, objective aggregation, or casting all but one (primary) objective into constraints. Notwithstanding, the knowledge of the best possible design trade-offs provides a more comprehensive insight into the properties of the antenna structure at hand. Genuine multi-objective optimization is a proper way of acquiring such data, typically rendered in the form of a Pareto set that represents the mentioned trade-off solutions. In antenna design, the fundamental challenge is high computational cost of multi-objective optimization, normally carried out using population-based metaheuristic algorithms. In most practical cases, the use of reliable, yet costly, full-wave electromagnetic models is imperative to ensure evaluation reliability, which makes conventional multi-objective optimization procedures prohibitively expensive. The employment of fast surrogates (or metamodels) can alleviate these difficulties, yet, construction of metamodels faces considerable challenges by itself, mostly related to the curse of dimensionality. This work proposes a novel surrogate-assisted approach to multi-objective optimization, where the data-driven model is only rendered in a small region spanned by the selected principal components of the extreme Pareto-optimal design set obtained using local search routines. The region is limited in terms of parameter ranges but also dimensionality, yet contains the majority of Pareto front, therefore surrogate construction therein does not incur considerable costs. The typical cost of identifying the Pareto set is just a few hundred of full-wave analyses of the antenna under design. Our technique is validated using two antenna examples (a planar Yagi and an ultra-wideband monopole antenna) and favorably compared to state-of-the-art surrogate-assisted multi-objective optimization methods.

/pdf/fast-multi-objective-optimization-of-antenna-structures-by-aey4rqjykp.pdf

Fast Multi-Objective Optimization of Antenna Structures by Means of Data-Driven Surrogates and Dimensionality Reduction

Constrained multi-objective optimization of compact microwave circuits by design triangulation and pareto front interpolation

Design automation, including reliable optimization of engineering systems, is of paramount importance for both academia and industry. This includes the design of high-frequency structures (antennas, microwave circuits, integrated photonic components), where the appropriate adjustment of geometry and material parameters is crucial to meet stringent performance requirements dictated by practical applications. Realistic design has to account for multiple objectives, which are often conflicting. Identification of available trade-offs (e.g., electrical/field properties vs. physical size and cost), otherwise essential from industry standpoint, requires multi-objective optimization. It is a computationally expensive endeavor as in most cases – for the sake of accuracy – the system evaluation has to be carried out using full-wave electromagnetic (EM) analysis. Attempting to solve EM-driven multi-objective (MO) tasks directly using population-based nature-inspired techniques may be prohibitive in terms of cost. Employing surrogate modeling techniques can lead to mitigation of the cost issue; however, construction of fast replacement models over broad ranges of the system parameters is expensive by itself, especially in higher-dimensional spaces. Recently, several approaches involving knowledge-based surrogate modeling approach have been proposed with the metamodels constructed over small regions of the parameter space containing the Pareto front. The latter are approximated using the sets of pre-optimized reference designs and permit a dramatic reduction of the number of training points required to set up a reliable surrogate, thus reducing the overall cost of the MO process. This paper reviews the recent advancements in these methodologies, and demonstrates the benefits of domain confinement using the various techniques such as reference design triangulation, nested kriging, and modeling with explicit dimensionality reduction using spectral analysis of the reference set. Demonstration examples of multi-objective design of antenna and miniaturized microwave components are provided as well.

Recent advances in accelerated multi-objective design of high-frequency structures using knowledge-based constrained modeling approach

Multiobjective Shape Design In Electricity And Magnetism

Fast replacement models (or surrogates) have been widely applied in the recent years to accelerate simulation-driven design procedures in microwave engineering. The fundamental reason is a considerable—and often prohibitive—CPU cost of massive full-wave electromagnetic (EM) analyses related to solving common tasks such as parametric optimization or uncertainty quantification. The most popular class of surrogates are data-driven models, which are fast to evaluate, versatile, and easy to handle. Notwithstanding, the curse of dimensionality as well as the utility demands (e.g., so that the model covers sufficiently broad ranges of the system operating conditions), limit the applicability of conventional methods. A performance-driven modeling paradigm allows for mitigating these issue by focusing the surrogate setup process in a constrained domain encapsulating designs being of high quality w.r.t. the assumed figures of interest. The nested kriging framework capitalizing on this idea, renders the constrained surrogate using kriging interpolation, and has been shown to surpass traditional approaches. In pursuit of further accuracy improvements, this work incorporates the performance-driven concept into the fully-connected regression model (FRCM). The latter has been recently introduced in the context of frequency selective surfaces, and combined deep neural networks with Bayesian optimization, the latter employed to determine the network architecture and hyper-parameters. Using two examples of miniaturized microstrip couplers, our methodology is demonstrated to outperform both conventional modeling techniques and nested kriging, with reliable models constructed over multi-dimensional parameters spaces using just a few hundreds of samples.

/pdf/improved-modeling-of-microwave-structures-using-performance-3ssu91ntgi.pdf

Improved Modeling of Microwave Structures Using Performance-Driven Fully-Connected Regression Surrogate

The paper focuses on resolving the storage issue of correlation matrices generated by kriging surrogate models in the context of electromagnetic optimization problems with many design variables and multiple objectives. A hybrid kriging approach that involves a direct algorithm in kriging is able to maintain memory requirements at a nearly constant level while offering high efficiency of searching for a global optimum. The feasibility and efficiency of this proposed methodology is demonstrated using an example of a classic two-variable analytic function and a new proposed benchmark TEAM multi-objective pareto optimization problem.

Multiobjective Pareto optimization of electromagnetic devices exploiting hybrid kriging

This paper optimizes mathematical model of the electromagnetic suspension system (EMS) by introducing voltage, current and airgap constraints. The model order is reduced using cascade control theory and PID controller parameters given with the method of pole placement. Then, an ideal simulation model (ISM) and an optimization simulation model (OSM) of suspension system are set up based on matlab/simulink. The simulation results show that OSM's output current is always positive in various working conditions. Moreover, the current ripple in every switch period can be obtained from the waveforms, which is consistent with actual working condition of the system. So, the OSM can not only simulate system's static and dynamic states well, but also reflect performances of the maglev chopper. Finally, the experiment waveforms are given and compared with simulation results of two models. The results show that the OSM can simulate real system better than the ISM.

Mathematical Model Optimization of Electromagnetic Suspension System Based on Additional Constraints

The invention discloses a linear induction motor system for a magnetic levitation train and a control method for the linear induction motor system. The motor system comprises a short stator, a three-phase winding, a rotor track, a controller and the like of a linear induction motor. All windings are coupled through a plurality of switches controlled by the controller, and the controller is used for operating the switches to change a connection mode of the windings by detecting the magnitude of the output phase current and the voltage of an inverter as an instruction. The system and the methodhave the beneficial effects that a plurality of different winding connection states are distributed, so that the motor can obtain larger thrust and acceleration through overload in a starting and low-speed running stage, and the output capacity of the inverter can be fully utilized in an acceleration stage, so that the train can be accelerated to the maximum speed at a shorter time, and meanwhile,a higher residual acceleration is generated at the maximum speed.

Linear induction motor system for magnetic levitation train and control method for linear induction motor system

An Efficient Multi-objective Optimization Algorithm Exploiting Gradient Enhanced Kriging with Optimally Selected Basis Functions for Electromagnetic Design

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Papers

Multiobjective Pareto optimization of electromagnetic devices exploiting hybrid kriging

Mathematical Model Optimization of Electromagnetic Suspension System Based on Additional Constraints

Linear induction motor system for magnetic levitation train and control method for linear induction motor system

An Efficient Multi-objective Optimization Algorithm Exploiting Gradient Enhanced Kriging with Optimally Selected Basis Functions for Electromagnetic Design