Reduced‐cost surrogate modeling of input characteristics and design optimization of dual‐band antennas using response features

In this article, a procedure for low‐cost surrogate modeling of input characteristics of dual‐band antennas has been discussed. The number of training data required for construction of an accurate model has been reduced by representing the antenna reflection response to the level of suitably defined feature points. The points are allocated to capture the critical features of the reflection characteristic, such as the frequencies and the levels of the resonances, and supplemented by the additions (infill) points, which is necessary to provide sufficient data that allows restoring the entire response through interpolation. Because the coordinates of the feature points exhibit less nonlinear behavior (as a function of antenna geometry parameters) compared to S‐parameters as a function of frequency, surrogate model construction can be realized with a smaller number of data points. The presented modeling approach is demonstrated using an example of a planar dipole antenna. Also, the feature‐based method is favorably compared to direct modeling of reflection characteristics using kriging. The relevance of the technique is further verified by its application for design optimization.     

Response correction techniques for surrogate‐based design optimization of microwave structures

Simulation‐based optimization has become an important design tool in microwave engineering. However, using electromagnetic (EM) solvers in the design process is a challenging task, primarily due to a high‐computational cost of an accurate EM simulation. In this article, we present a review of EM‐based design optimization techniques exploiting response‐corrected physically based low‐fidelity models. The surrogate models created through such a correction can be used to yield a reasonable approximation of the optimal design of the computationally expensive structure under consideration (high‐fidelity model). Several approaches using this idea are reviewed including output space mapping, manifold mapping, adaptive response correction, and shape‐preserving response prediction. A common feature of these methods is that they are easy to implement and computationally efficient. Application examples are provided. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.     

Reliable design optimization of microwave structures using multipoint‐response‐correction space mapping and trust regions

Space mapping (SM) is one of the most efficient simulation‐driven design technologies used in microwave engineering to date. It includes so‐called output SM that ensures exact matching between the EM‐evaluated microwave structure under consideration (fine model) and its surrogate at the current design. The standard, single‐point output SM exploits the fine model data at a single design and is not able to align the models' sensitivity. Here, a multipoint response correction is proposed that generalizes the concept of output SM. By using a design‐variable‐dependent correction term and exploiting all available fine model information, the proposed technique provides exact match between the surrogate and the fine model at several designs. This retains the benefits of output SM but also enhances sensitivity matching between the two models, which results in improved performance of the SM optimization process. The efficiency of the propose approach is demonstrated using several microwave design problems. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

Multi‐objective design optimization of antennas for reflection,size, and gain variability using kriging surrogates and generalized domain segmentation

Cost‐efficient multi‐objective design optimization of antennas is presented. The framework exploits auxiliary data‐driven surrogates, a multi‐objective evolutionary algorithm for initial Pareto front identification, response correction techniques for design refinement, as well as generalized domain segmentation. The purpose of this last mechanism is to reduce the volume of the design space region that needs to be sampled in order to construct the surrogate model, and, consequently, limit the number of training data points required. The recently introduced segmentation concept is generalized here to allow for handling an arbitrary number of design objectives. Its operation is illustrated using an ultra‐wideband monopole optimized for best in‐band reflection, minimum gain variability, and minimum size. When compared with conventional surrogate‐based approach, segmentation leads to reduction of the initial Pareto identification cost by over 20%. Numerical results are supported by experimental validation of the selected Pareto‐optimal antenna designs.     

Phase‐spacing optimization of linear microstrip antenna arrays using simulation‐based surrogate superposition models

A technique for simulation‐driven optimization of the phase excitation tapers and spacings for linear arrays of microstrip patch antennas is presented. Our technique exploits two models of the array under optimization: an analytical model which is based on the array factor, as well as an electromagnetic (EM) simulation‐based surrogate model of the entire array. The former is used to provide initial designs which meet the design requirements imposed on the radiation response. The latter is used for tuning of the array radiation response while controlling the array reflection response as well as for validation of the final design. Furthermore, the simulation‐based surrogate model allows for subsequent evaluation of the array responses in the beam scanning operation at negligible computational costs. The simulation‐based surrogate model is constructed with a superposition of simulated radiation and reflection responses of the array under design with only one radiator active at a time. Low computational cost of the surrogate model is ensured by the EM‐simulation data computed with coarse meshes. Reliability of the model is achieved by means of suitable correction carried out with respect to the high‐fidelity array model. The correction is performed iteratively in the optimization process. Performance, numerical efficiency, and accuracy of the technique is demonstrated with radiation pattern synthesis of linear arrays comprising 32 microstrip patch antennas by phase‐spacing optimization. Properties of the optimal designs in the beam scanning operation are then studied using the superposition models and compared to suitably selected reference designs. The proposed technique is versatile as it also can be applied for simulation‐based optimization of antenna arrays comprising other types of individually fed elements. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:536–547, 2015.     

Improved trust‐region gradient‐search algorithm for accelerated optimization of wideband antenna input characteristics

Full‐wave electromagnetic (EM) simulation models are ubiquitous in carrying out design closure of antenna structures. Yet, EM‐based design is expensive due to a large number of analyses necessary to yield an optimized design. Computational savings can be achieved using, for example, adjoint sensitivities, surrogate‐assisted procedures, design space dimensionality reduction, or similar sophisticated means. In this article, a simple modification of a rudimentary trust‐region‐embedded gradient search with numerical derivatives is proposed for reduced‐cost optimization of input characteristics of wideband antennas. The approach exploits information and history of relative changes of the design (as compared with the trust region size) during algorithm iterations to control the updates of components of the antenna response Jacobian, specifically, to execute them only if necessary. It is demonstrated that the proposed framework may lead to over 50% savings over the reference algorithm with only minor degradation of the design quality, specifically, up to 0.3 dB (or <3%). Numerical results are supported by experimental validation of the optimized antenna designs. The presented algorithm can be utilized as a stand‐alone optimization routine or as a building block of surrogate‐assisted procedures.     

Fast simulation‐driven antenna design using response‐feature surrogates

In this article, a computationally efficient procedure for electromagnetic (EM)‐simulation‐driven design of antennas is presented. Our methodology is based on local approximation models of the antenna response, established using a set of suitably selected characteristic features rather than the entire response (such as reflection versus frequency). The approximation model is utilized to verify the level of satisfying/violating given performance requirements, and to guide the optimization process towards a better design. By exploiting the fact that the dependence of the response features on the designable parameters of the antenna of interest is simple (close to linear or quadratic), the feature‐based optimization converges faster than conventional optimization of frequency‐based EM‐simulated responses. In order to further speed up the design, coarse‐discretization simulations are utilized to estimate the feature gradients with respect to adjustable parameters of the problem at hand. The optimization algorithm is embedded in the trust‐region framework for safeguarding convergence. The proposed technique is demonstrated using two antenna examples. In both the cases, the optimum design is obtained at the computational cost corresponding to a few high‐fidelity EM antenna simulations. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:394–402, 2015.     

Precise control of reflection response in bandwidth‐enhanced planar antennas

In this work, the issues of bandwidth enhancement of planar antennas and the relevance of precise and automated response control through numerical optimization have been investigated. Using an example of a planar antenna with parasitic radiator we illustrate possible effects of even minor modifications of the antenna geometry (here, applied to the ground plane) on its reflection performance. In particular, a proper handling of geometry parameters may lead to considerable broadening of the antenna bandwidth. For the sake of computational efficiency, the adjustment of geometry parameters is carried out using surrogate‐based optimization methods exploiting coarse‐discretization EM simulations as the underlying low‐fidelity antenna model. Additionally, suitably defined penalty function allows us to precisely control the maximum in‐band reflection so that sufficient margin to accommodate possible manufacturing tolerances can be achieved. The optimized designs of the two antenna structures considered in this work exhibit over 1.75 GHz (>31%) and 2.15 GHz (>38%) bandwidth, respectively, for the center frequency of 5.6 GHz. Simulation results are validated using measurements of the fabricated prototypes. Comparison with state‐of‐the‐art designs is also provided. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:653–659, 2016.     

Analysis of circular polarization antenna design trade‐offs using low‐cost EM‐driven multiobjective optimization

Circular polarization (CP) antennas are vital components of modern communication systems. Their design involves handling several requirements such as low reflection and axial ratio (AR) within the frequency range of interest. Small size is an important criterion for antenna mobility which is normally achieved as a by‐product of performance‐oriented modifications of the structure topology. In this work, multiobjective optimization is used in order to identify and analyze design trade‐offs for miniaturized CP antenna including the antenna capability for maintaining small size while retaining acceptable levels of other performance figures. We use a population‐based metaheuristic algorithm to obtain a set of designs which represent the best attainable compromise between the imposed requirements. To maintain a low optimization cost, the algorithm is executed on a cheap approximation model and the results are further corrected to bring them to the EM model accuracy level. Here, the analysis is carried out for a planar CP antenna. Achievable size reduction of the considered structure—while maintaining acceptable performance—is around 11%. Antenna performance in terms of in‐band reflection and AR varies from ?14 to ?10 dB and from 1.3 to 3 dB, respectively. The numerical results are validated by measurements of fabricated antenna prototypes.     

Recent advances in rapid multiobjective optimization of expensive simulation models in microwave and antenna engineering by Pareto front exploration

Practical engineering design problems are inherently multiobjective, that is, require simultaneous control of several (and often conflicting) criteria. In many situations, genuine multiobjective optimization is required to acquire comprehensive information about the system of interest. The most popular solution techniques are population‐based metaheuristics, however, they are not practical for handling expensive electromagnetic (EM)‐simulation models in microwave and antenna engineering. A workaround is to use auxiliary response surface approximation surrogates but it is challenging for higher‐dimensional problems. Recently, a deterministic approach has been proposed for expedited multiobjective design optimization of expensive models in computational EMs. The method relies on variable‐fidelity EM simulations, tracking the Pareto front geometry, as well as response correction. The algorithm sequentially generates Pareto‐optimal designs using a series of constrained single‐objective optimizations. The previously obtained design is used as a starting point for the next iteration. In this work, we review this technique and its modification based on space mapping surrogates. We also propose new variations exploiting adjoint sensitivities, as well as response features, which can be attractive depending on availability of derivatives or the characteristics of the system responses that need to be handled. We also discuss several case studies involving various antenna and microwave components.     

Surrogate‐assisted EM‐driven miniaturization of wideband microwave couplers by means of co‐simulation low‐fidelity models

This article proposes a methodology for rapid design optimization of miniaturized wideband couplers. More specifically, a class of circuits is considered, in which conventional transmission lines are replaced by their abbreviated counterparts referred to as slow‐wave compact cells. Our focus is on explicit reduction of the structure size as well as on reducing the CPU cost of the design process. For the sake of computational feasibility, a surrogate‐based optimization paradigm involving a co‐simulation low‐fidelity model is used. The latter is a fundamental component of the proposed technique. The low‐fidelity model represents cascaded slow‐wave cells replacing the low‐impedance lines of the original coupler circuit. It is implemented in a circuit simulator (here, ADS) and consists of duplicated compact cell EM simulation data as well as circuit theory‐based feeding line models. Our primary optimization routine is a trust‐region‐embedded gradient search algorithm. To further reduce the design cost, the system response Jacobian is estimated at the level of the low‐fidelity model, which is sufficient due to good correlation between the low‐ and high‐fidelity models. The coupler is explicitly optimized for size reduction, whereas electrical performance parameters are controlled using a penalty function approach. The presented methodology is demonstrated through the design of a 1‐GHz wideband microstrip branch‐line coupler. Numerical results are supported by experimental validation of the fabricated coupler prototype.     

Multi-objective optimization of expensive electromagnetic simulation models

Vast majority of practical engineering design problems require simultaneous handling of several criteria. For the sake of simplicity and through a priori preference articulation one can turn many design tasks into single-objective problems that can be handled using conventional numerical optimization routines. However, in some situations, acquiring comprehensive knowledge about the system at hand, in particular, about possible trade-offs between conflicting objectives may be necessary. This calls for multi-objective optimization that aims at identifying a set of alternative, Pareto-optimal designs. The most popular solution approaches include population-based metaheuristics. Unfortunately, such methods are not practical for problems involving expensive computational models. This is particularly the case for microwave and antenna engineering where design reliability requires utilization of CPU-intensive electromagnetic (EM) analysis. In this work, we discuss methodologies for expedited multi-objective design optimization of expensive EM simulation models. The solution approaches that we present here rely on surrogate-based optimization (SBO) paradigm, where the design speedup is obtained by shifting the optimization burden into a cheap replacement model (the surrogate). The latter is utilized for generating the initial approximation of the Pareto front representation as well as further front refinement (to elevate it to the high-fidelity EM simulation model level). We demonstrate several application case studies, including a wideband matching transformer, a dielectric resonator antenna and an ultra-wideband monopole antenna. Dimensionality of the design spaces in the considered examples vary from six to fifteen, and the design optimization cost is about one hundred of high-fidelity EM simulations of the respective structure, which is extremely low given the problem complexity.     

Space mapping optimization of handset antennas considering EM effects of mobile phone components and human body

To meet antenna design specifications under realistic conditions, electromagnetic coupling effects between the antenna and its environment must be considered. In this work, an efficient antenna design optimization methodology that considers the influence of the human head and main mobile handset components on the antenna performance is presented. The computational optimization time is dramatically reduced by exploiting a Broyden‐based input space mapping (SM) algorithm. Both coarse and fine models required for the SM algorithm are based on the finite‐element method and are implemented in the same simulator; simplifying the modeling process. However, our coarse model does not consider any object of the actual operational environment. In spite of that and other simplifications applied to the coarse model, the proposed optimization scheme is able to find a solution that meets the specifications in a realistic environment by performing an extremely small number of expensive fine model simulations. Our practical illustration opens up the feasibility of using this CAD methodology to optimize other RF devices that operate in close proximity to objects that affect its desired response, as it is the case for many wearable devices. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:121–128, 2016.     

Neural network optimization of complex microwave structures with a reduced number of full‐wave analyses

An innovative technique of neural network optimization of substantially less computational cost is presented as a procedure suitable for viable computer‐aided design of complex microwave systems. The number of necessary full‐wave simulations in this optimization procedure is dramatically reduced because of a special objective function (OF) and constrained optimization response surface (CORS) sampling in the dynamic training of the decomposed radial‐basis‐function network. A high rate of convergence to an optimization objective is shown to be dependent on the combined effect of the OF and CORS technique. Performance of the algorithm is illustrated by its application to a waveguide band‐pass filter, a loaded microwave oven, and a dielectric resonator antenna; their optimal designs are found from five‐parameter optimizations requiring as little as 167, 177, and 99 analyses, respectively. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

Application of support vector machines to the antenna design

The antenna design is a complicated and time‐consuming procedure. This work explores using support vector machines (SVMs), a statistical learning theory based on the structural risk minimization principle and has a great generalization capability, as a fast and accurate tool in the antenna design. As examples, SVMs is used to design a rectangular patch antenna and a rectangular patch antenna array. Results show, after an appropriate training, SVMs is able to effectively design antennas with high accuracy. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

Generalized Pareto ranking bisection for computationally feasible multiobjective antenna optimization

Multiobjective optimization (MO) allows for obtaining comprehensive information about possible design trade‐offs of a given antenna structure. Yet, executing MO using the most popular class of techniques, population‐based metaheuristics, may be computationally prohibitive when full‐wave EM analysis is utilized for antenna evaluation. In this work, a low‐cost and fully deterministic MO methodology is introduced. The proposed generalized Pareto ranking bisection algorithm permits identifying a set of Pareto optimal sets of parameters representing the best trade‐offs between considered objectives. The subsequent designs are found by iterative partitioning of the intervals connecting previously obtained designs and executing Pareto‐ranking‐based poll search. The initial approximation of the Pareto front found using the bisection procedure is subsequently refined to the level of the high‐fidelity EM model of the antenna at hand using local optimization. The proposed framework overcomes a serious limitation of the original, recently reported, bisection algorithm, which was only capable of considering two objectives. The generalized version proposed here allows for handling any number of design goals. An improved poll search procedure has also been developed and incorporated. Our algorithm has been demonstrated using two examples of UWB monopole antennas with four figures of interest taken into account: structure size, reflection response, total efficiency, and gain variability.     

Modeling and design of printed antennas using neural networks

A single neural network is developed to model the resonant frequency of rectangular patch printed on uniaxially anisotropic substrate with air gap using effective parameters in conjunction with spectral dyadic Green's function. Also, the strength of ANN models in antenna design is demonstrated by considering two case studies: the design of circular patch antenna and planar inverted‐F antenna. Results show good agreement with literature. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

Expedited simulation‐driven design optimization of UWB antennas by means of response features

In this work, a method for fast design optimization of broadband antennas is considered. The approach is based on a feature‐based optimization (FBO) concept where reflection characteristics of the structure at hand are formulated in terms of suitably defined feature points. Redefinition of the design problem allows for reducing the design optimization cost, because the dependence of feature point coordinates on antenna dimensions is less nonlinear than for the original frequency characteristics (here, S‐parameters). This results in faster convergence of the optimization algorithm. The cost of the design process is further reduced using variable‐fidelity electromagnetic (EM) simulation models. In case of UWB antennas, the feature points are defined, among others, as the levels of the reflection characteristic at its local in‐band maxima, as well as location of the frequency point which corresponds to acceptable reflection around the lower corner frequency within the UWB band. Also, the number of characteristic points depends on antenna topology and its dimensions. Performance of FBO‐based design optimization is demonstrated using two examples of planar UWB antennas. Moreover, the computational cost of the approach is compared with conventional optimization driven by a pattern search algorithm. Experimental validation of the numerical results is also provided.     

一种基于Kriging模型的天线高维全局优化算法

传统的天线优化设计需要对大量的参数组合进行电磁仿真后才能得到最优结果,使得天线高维优化设计效率普遍较低。针对该问题,使用在参数空间均匀分布的少量样本及其仿真结果构建初始Kriging模型,优化循环中每代种群由高适应度个体和高离散性个体组成,依据Kriging模型预测的个体响应和不确定性,对进化后的下一代种群进行筛选,选择最优个体执行电磁仿真并更新Kriging模型。利用此方法优化一个6变量E形天线的工作频点,相比同类优化算法,所需的电磁仿真次数可减少80%左右。     

Inverse modeling for fast design optimization of small‐size rat‐race couplers incorporating compact cells

In the paper, a framework for computationally‐efficient design optimization of compact rat‐race couplers (RRCs) is discussed. A class of hybrid RRCs with variable operating conditions is investigated, whose size reduction is obtained by replacing ordinary transmission lines with compact microstrip resonant cells (CMRCs). Our approach employs a bottom‐up design strategy leading to the development of compact RRCs through rapid design optimization of its building blocks and a subsequent fine tuning to account for parasitic cross‐coupling effects. The fundamental component of the proposed method is an inverse CMRC surrogate model, covering a wide range of cell electrical parameters, and enabling a convenient adjustment of coupler bandwidth. Having the surrogate model established, it is possible to produce close‐to‐optimum CMRC dimensions at a negligible computational cost. The subsequent correction step requires only up to two electromagnetic simulations of the CMRC. The proposed method is demonstrated by designing an RRC for several operational bandwidths. Experimental results are also provided.