Expedited Design Closure of Antenna Input Characteristics by Trust Region Gradient Search and Principal Component Analysis

Publisher's version (útgefin grein)Optimization-based parameter tuning has become an inherent part of contemporary antenna design process. For the sake of reliability, it is typically conducted at the level of full-wave electromagnetic (EM) simulation models. This may incur considerable computational expenses depending on the cost of an individual EM analysis, the number of adjustable variables, the type of task (local, global, single-/multi-objective optimization), and the constraints involved. For these reasons, utilization of conventional algorithms is often impractical. This paper proposes a novel gradient-based algorithm with numerical derivatives for expedited antenna optimization. The improvement of computational efficiency is obtained by employing a rank-one Broyden formula and restricting finite differentiation sensitivity updates to the principal directions of the Jacobian matrix, i.e., those corresponding to the most significant changes of the antenna responses. Comprehensive numerical validation carried out using three wideband antennas indicates that the presented methodology offers considerable savings of sixty percent with respect to the reference trust-region algorithm. At the same time, virtually no degradation of the design quality is observed. Furthermore, algorithm reliability is greatly improved (while offering comparable computational efficiency) over the recent state-of-the-art accelerated gradient-based procedures.The Icelandic Centre for Research (RANNIS) Grant 174114051, and in part by the National Science Centre of Poland Grant 2015/17/B/ST6/01857."Peer Reviewed

Expedited Feature-Based Quasi-Global Optimization of Multi-Band Antenna Input Characteristics With Jacobian Variability Tracking

Publisher's version (útgefin grein)Design of modern antennas relies-for reliability reasons-on full-wave electromagnetic simulation tools. In addition, increasingly stringent specifications pertaining to electrical and field performance, growing complexity of antenna topologies, along with the necessity for handling multiple objectives, make numerical optimization of antenna geometry parameters a highly recommended design procedure. Conventional algorithms, particularly global ones, entail often-unmanageable computational costs, so alternative approaches are needed. This work proposes a novel method for cost-efficient globalized design optimization of multi-band antennas incorporating the response feature technology into the trust-region framework. It allows for unequivocal allocation of the antenna resonances even for poor initial designs, where conventional local algorithms fail. Furthermore, the algorithm is accelerated by means of Jacobian variability tracking, which reduces the number of expensive finite-differentiation updates. Two real-world antenna design cases are used for demonstration purposes. The optimization cost is comparable to that of local routines while ensuring nearly global search capabilities.This work was supported in part by the Icelandic Centre for Research (RANNIS) under Grant 206606051, and in part by the National Science Centre of Poland under Grant 2017/27/B/ST7/00563."Peer Reviewed

Expedite Design of Variable-Topology Broadband Hybrid Couplers for Size Reduction using Surrogate-Based Optimization and Co-Simulation Coarse Models

In this paper, we discuss a computationally efficient approach to expedite design optimization of broadband hybrid couplers occupying a minimized substrate area. Structure size reduction is achieved here by decomposing an original coupler circuit into low- and high-impedance components and replacing them with electrically equivalent slow-wave lines with reduced physical dimensions. The main challenge is reliable design of computationally demanding low-impedance slow-wave structures that feature a quasi-periodic circuit topology for wideband operation. Our goal is to determine an adequate number of recurrent unit elements as well as to adjust their designable parameters so that the coupler footprint area is minimal. The proposed method involves using surrogate-based optimization with a reconfigurable co-simulation coarse model as the key component enabling design process acceleration. The latter model is composed in Keysight ADS circuit simulator from multiple EM-evaluated data blocks of the slow-wave unit element and theory-based feeding line models. The embedded optimization algorithm is a trust-region-based gradient search with coarse model Jacobian estimation. We exploit a penalty function approach to ensure that the electrical conditions for the slow-wave lines are accordingly satisfied, apart from explicitly minimizing the area of the coupler. The effectiveness of the proposed technique is demonstrated through a design example of two-section 3-dB branch-line coupler. For the given example, we obtain nine circuit design solutions that correspond to the compact couplers whose multi-element slow-wave lines are composed of unit cells ranging from two to ten

EM-driven miniaturization of high-frequency structures through constrained optimization

The trends afoot for miniaturization of high-frequency electronic devices require integration of active and passive high-frequency circuit elements within a single system. This high level of accomplishment not only calls for a cutting-edge integration technology but also necessitates accommodation of the corresponding circuit components within a restricted space in applications such as implantable devices, internet of things (IoT), or 5G communication systems. At the same time, size reduction does not remain the only demand. The performance requirements of the abovementioned systems form a conjugate demand to that of the size reduction, yet with a contrasting nature. A compromise can be achieved through constrained numerical optimization, in which two kinds of constrains may exist: equality and inequality ones. Still, the high cost of electromagnetic-based (EM-based) constraint evaluations remains an obstruction. This issue can be partly mitigated by implicit constraint handling using the penalty function approach. Nevertheless, securing its performance requires expensive guess-work-based identification of the optimum setup of the penalty coefficients. An additional challenge lies in allocating the design within or in the vicinity of a thin feasible region corresponding to equality constraints. Furthermore, multimodal nature of constrained miniaturization problems leads to initial design dependency of the optimization results. Regardless of the constraint type and the corresponding treatment techniques, the computational expenses of the optimization-based size reduction persist as a main challenge. This thesis attempts to address the abovementioned issues specifically pertaining to optimization-driven miniaturization of high frequency structures by developing relevant algorithms in a proper sequence. The first proposed approach with automated adjustment of the penalty functions is based on the concept of sufficient constraint violation improvement, thereby eliminating the costly initial trial-and-error stage for the identification of the optimum setup of the penalty factors. Another introduced approach, i.e., correction-based treatment of the equality constraints alleviates the difficulty of allocating the design within a thin feasible region where designs satisfying the equality constraints reside. The next developed technique allows for global size reduction of high-frequency components. This approach not only eliminates the aforementioned multimodality issues, but also accelerates the overall global optimization process by constructing a dimensionality-reduced surrogate model over a pre-identified feasible region as compared to the complete parameter search space. Further to the latter, an optimization framework employing multi-resolution EM-model management has been proposed to address the high cost issue. The said technique provides nearly 50 percent average acceleration of the optimization-based miniaturization process. The proposed technique pivots upon a newly-defined concept of model-fidelity control based on a combination of algorithmic metrics, namely convergence status and constraint violation level. Numerical validation of the abovementioned algorithms has also been provided using an extensive set of high-frequency benchmark structures. To the best of the author´s knowledge, the presented study is the first investigation of this kind in the literature and can be considered a contribution to the state of the art of automated high-frequency design and miniaturization

Design specification management with automated decision-making for reliable optimization of miniaturized microwave components

Funding Information: The authors would like to thank Dassault Systemes, France, for making CST Microwave Studio available. This work is partially supported by the Icelandic Centre for Research (RANNIS) Grant 217771 and National Science Centre of Poland Grant 2020/37/B/ST7/01448. Publisher Copyright: © 2022, The Author(s). © 2022. The Author(s).The employment of numerical optimization techniques for parameter tuning of microwave components has nowadays become a commonplace. In pursuit of reliability, it is most often carried out at the level of full-wave electromagnetic (EM) simulation models, incurring considerable computational expenses. In the case of miniaturized microstrip circuits, densely arranged layouts with strong cross-coupling effects make EM-driven tuning imperative to achieve the optimum performance. The process is even more challenging due to a typically large number of geometry parameters, and the lack of reasonable initial designs. The latter often encourages the use of global search procedures, which may be prohibitively expensive. In this paper, a novel automated framework for reliable optimization of miniaturized microwave components is proposed. Our methodology is based on design specification management, where the performance requirements imposed on the system are temporarily relaxed if the current design is unlikely to be improved (e.g., due to being away from the target operating frequency). The specifications are re-adjusted at each iteration of the algorithm, and eventually converge to their original values. Using two examples of compact microstrip couplers and a power divider, the presented technique is demonstrated to significantly improve the efficacy of local search routines under challenging design scenarios.Peer reviewe

Reliable Surrogate Modeling of Antenna Input Characteristics by Means of Domain Confinement and Principal Components

Publisher's version (útgefin grein)A reliable design of contemporary antenna structures necessarily involves full-wave electromagnetic (EM) analysis which is the only tool capable of accounting, for example, for element coupling or the effects of connectors. As EM simulations tend to be CPU-intensive, surrogate modeling allows for relieving the computational overhead of design tasks that require numerous analyses, for example, parametric optimization or uncertainty quantification. Notwithstanding, conventional data-driven surrogates are not suitable for handling highly nonlinear antenna characteristics over multidimensional parameter spaces. This paper proposes a novel modeling approach that employs a recently introduced concept of domain confinement, as well as principal component analysis. In our approach, the modeling process is restricted to the region containing high-quality designs with respect to the performance figures of antennas under design, identified using a set of pre-optimized reference designs. The model domain is spanned by the selected principal components of the reference design set, which reduces both its volume and dimensionality. As a result, a reliable surrogate can be constructed over wide ranges of both operating conditions and antenna parameters, using small training datasets. Our technique is demonstrated using two antenna examples and is favorably compared to both conventional and constrained modeling approaches. Application case studies (antenna optimization) are also discussed.This work was supported in part by the Icelandic Centre for Research (RANNIS) grant 174114051, and by the National Science Centre of Poland grant 2017/27/B/ST7/00563.Peer Reviewe

Supervised-learning-enabled EM-driven development of low scattering metasurfaces

The recent advances in the development of coding metasurfaces created new opportunities to elevate the stealthiness of combat aircrafts. Metasurfaces, composed of optimized geometries of meta-atoms arranged as periodic lattices, are devised to obtain desired electromagnetic (EM) scattering characteristics, and have been extensively exploited in stealth applications to reduce radar cross section (RCS). They rely on the manipulation of backward scattering of electromagnetic (EM) waves into various oblique angles. Despite potential benefits, a practical obstacle hindering widespread metasurface utilization is the lack of systematic design procedures. Conventional approaches are largely intuition-inspired and demand heavy designer’s interaction while exploring the parameter space and pursuing optimum unit cell geometries. Another practical obstacle that hampers efficient design of metasurfaces is implicit handling of RCS performance. To achieve essential RCS reduction, the design task is normally formulated in terms of phase reflection characteristics of the unit cells, whereas their reflection amplitudes—although contributing to the overall performance of the structure—is largely ignored. A further practical issue is insufficiency of the existing performance metrics, specifically, monostatic and bistatic evaluation of the reflectivity, especially at the design stage of metasurfaces. Both provide a limited insight into the RCS reduction properties, with the latter being dependent on the selection of the planes over which the evaluation takes place. As a consequence of raised concerns, the existing design methodologies are still insufficient, especially in the context of controlling the EM wavefront through parameter tuning of unit cells. Furthermore, they are unable to determine truly optimum solutions. Therefore, we have introduced a novel machine-learning-based framework for automated and computationally efficient design of metasurfaces realizing broadband RCS reduction. We have employed a three-stage design procedure involving global surrogate-assisted optimization of the unit cells, followed by their local refinement. In its final stage, a direct EM-driven maximization of the RCS reduction bandwidth has been performed, facilitated by appropriate formulation of the objective function involving regularization terms. Moreover, to handle the combinatorial explosion in the design closure of multi-bit coding metasurfaces, a sequential-search strategy has been developed that enabled global search capability at the concurrent unit cell optimization stage. Latterly, the metasurface design task with explicit handling of RCS reduction at the level of unit cells has been introduced that has accounted for both the phase and reflection amplitudes of the unit cells. The design objective has been defined so as to directly optimize the RCS reduction bandwidth at the specified level (e.g., 10 dB) w.r.t. the metallic surface. The appealing feature of the said framework has consisted in its ability to optimize the RCS reduction bandwidth directly at the level of the entire metasurface as opposed to merely optimizing unit cell geometries. Besides, the obtained design has required minimum amount of tuning at the level of the entire metasurface. Lastly, a new performance metric for evaluating scattering characteristics of a metasurface, referred to as Normalized Partial Scattering Cross Section (NPSCS), has been proposed. The metric involved integration of the scattered energy over a specific solid angle, which allows for a comprehensive assessment of the structure performance in a format largely independent of the particular arrangement of the scattering lobes. Our design methodologies have been utilized to design several instances of novel scattering metasurface structures with the focus on RCS reduction bandwidth enhancement and the level of RCS reduction. Experimental validations confirming the numerical findings have been also provided. To the best of the author’s knowledge, the presented study is the first systematic investigation of this kind in the literature and can be considered a step towards the development of efficient, low-cost, and more high performing scattering structures

Design-Oriented Two-Stage Surrogate Modeling of Miniaturized Microstrip Circuits With Dimensionality Reduction

Publisher's version (útgefin grein)Contemporary microwave design heavily relies on full-wave electromagnetic (EM) simulation tools. This is especially the case for miniaturized devices where EM cross-coupling effects cannot be adequately accounted for using equivalent network models. Unfortunately, EM analysis incurs considerable computational expenses, which becomes a bottleneck whenever multiple evaluations are required. Common simulation-based design tasks include parametric optimization and uncertainty quantification. These can be accelerated using fast replacement models, among which the data-driven surrogates are the most popular. Notwithstanding, a construction of approximation models for microwave components is hindered by the dimensionality issues as well as high nonlinearity of system characteristics. A partial alleviation of the mentioned difficulties can be achieved with the recently reported performance-driven modeling methods, including the nested kriging framework. Therein, the computational benefits are obtained by appropriate confinement of the surrogate model domain, spanned by a set of pre-optimized reference designs, and by focusing on the parameter space region that contains high quality designs with respect to the considered performance figures. This paper presents a methodology that incorporates the concept of nested kriging and enhances it by explicit dimensionality reduction based on spectral decomposition of the reference design set. Extensive verification studies conducted for a compact rat-race coupler and a three-section impedance matching transformer demonstrate superiority of the presented approach over both the conventional techniques and the nested kriging in terms of modeling accuracy. Design utility of our surrogates is corroborated through application cases studies.The Icelandic Centre for Research (RANNIS) under Grant 206606051, in part by the National Science Centre of Poland under Grant 2018/31/B/ST7/02369, and in part by the Abu-Dhabi Department of Education and Knowledge (ADEK) Award for Research Excellence, in 2019, under Grant AARE19-245."Peer Reviewed

Antenna Modeling Using Variable-Fidelity EM Simulations and Constrained Co-Kriging

Publisher's version (útgefin grein)Utilization of fast surrogate models has become a viable alternative to direct handling of full-wave electromagnetic (EM) simulations in EM-driven design. Their purpose is to alleviate the difficulties related to high computational cost of multiple simulations required by the common numerical procedures such as parametric optimization or uncertainty quantification. Yet, conventional data-driven (or approximation) modeling techniques are severely affected by the curse of dimensionality. This is a serious limitation when it comes to modeling of highly nonlinear antenna characteristics. In practice, general-purpose surrogates can be rendered for the structures described by a few parameters within limited ranges thereof, which is grossly insufficient from the utility point of view. This paper proposes a novel modeling approach involving variable-fidelity EM simulations incorporated into the recently reported nested kriging modeling framework. Combining the information contained in the densely sampled low- and sparsely sampled high-fidelity models is realized using co-kriging. The resulting surrogate exhibits the predictive power comparable to the model constructed using exclusively high-fidelity data while offering significantly reduced setup cost. The advantages over conventional surrogates are pronounced even further. The presented modeling procedure is demonstrated using two antenna examples and further validated through the application case studies.This work was supported in part by the Icelandic Centre for Research (RANNIS) under Grant 206606051, and in part by the National Science Centre of Poland under Grant 2018/31/B/ST7/02369.Peer reviewe

An Early History of Optimization Technology for Automated Design of Microwave Circuits

This paper outlines the early history of optimization technology for the design of microwave circuits—a personal journey filled with aspirations, academic contributions, and commercial innovations. Microwave engineers have evolved from being consumers of mathematical optimization algorithms to originators of exciting concepts and technologies that have spread far beyond the boundaries of microwaves. From the early days of simple direct search algorithms based on heuristic methods through gradient-based electromagnetic optimization to space mapping technology we arrive at today’s surrogate methodologies. Our path finally connects to today’s multi-physics, system-level, and measurement-based optimization challenges exploiting confined and feature-based surrogates, cognition-driven space mapping, Bayesian approaches, and more. Our story recognizes visionaries such as William J. Getsinger of the 1960s and Robert Pucel of the 1980s, and highlights a seminal decades-long collaboration with mathematician Kaj Madsen. We address not only academic contributions that provide proof of concept, but also indicate early formative milestones in the development of commercially competitive software specifically featuring optimization technology.ITESO, A.C