Rapid Optimization of Compact Microwave Passives Using Kriging Surrogates and Iterative Correction

Publisher's version (útgefin grein)Design of contemporary microwave components is & x2014;in a large part & x2014;based on full-wave electromagnetic (EM) simulation tools. The primary reasons for this include reliability and versatility of EM analysis. In fact, for many microwave structures, notably compact components, EM-driven parameter tuning is virtually imperative because traditional models (analytical or network equivalents) are unable to account for the cross-coupling effects, strongly present in miniaturized layouts. At the same time, the cost of simulation-based design procedures may be significant due to a typically large number of evaluations of the circuit at hand involved. In this paper, a novel approach to expedited design closure of compact microwave passives is presented. The proposed procedure incorporates available designs (e.g., existing from the previous design work on the same structure) in the form of the kriging interpolation models, utilized to yield a reasonable initial design and to accelerate its further refinement. An important component of the framework is an iterative correction procedure that feeds the accumulated discrepancies between the target and the actual design objective values back to the kriging surrogate to produce improved predictions. The efficacy of our methodology is demonstrated using two miniaturized impedance matching transformers with the optimized designs obtained at the cost of a few EM simulations of the respective circuits. The relevance of the iterative correction is corroborated through the comparative studies showing its superiority over rudimentary gradient-based refinement.This work was supported in part by the Icelandic Centre for Research (RANNIS) under Grant 174114051, and in part by the National Science Centre of Poland under 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

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

Design centering of compact microwave components using response features and trust regions

Funding Information: Funding: This work was supported in part by the Icelandic Centre for Research (RANNIS) Grant 217771, and by National Science Centre of Poland Grant 2018/31/B/ST7/02369. Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Fabrication tolerances, as well as uncertainties of other kinds, e.g., concerning material parameters or operating conditions, are detrimental to the performance of microwave circuits. Mit-igating their impact requires accounting for possible parameter deviations already at the design stage. This involves optimization of appropriately defined statistical figures of merit such as yield. Although important, robust (or tolerance-aware) design is an intricate endeavor because manufacturing inaccuracies are normally described using probability distributions, and their quantification has to be based on statistical analysis. The major bottleneck here is high computational cost: for reliability reasons, miniaturized microwave components are evaluated using full-wave electromagnetic (EM) models, whereas conventionally utilized analysis methods (e.g., Monte Carlo simulation) are associated with massive circuit evaluations. A practical approach that allows for circumventing the aforementioned obstacles offers surrogate modeling techniques, which have been a dominant trend over the recent years. Notwithstanding, a construction of accurate metamodels may require considerable computational investments, especially for higher-dimensional cases. This paper brings in a novel design-centering approach, which assembles forward surrogates founded at the level of response features and trust-region framework for direct optimization of the system yield. Formu-lating the problem with the use of characteristic points of the system response alleviates the issues related to response nonlinearities. At the same time, as the surrogate is a linear regression model, a rapid yield estimation is possible through numerical integration of the input probability distributions. As a result, expenditures related to design centering equal merely few dozens of EM analyses. The introduced technique is demonstrated using three microstrip couplers. It is compared to recently reported techniques, and its reliability is corroborated using EM-based Monte Carlo analysis.Peer reviewe

On Inadequacy of Sequential Design of Experiments for Performance-Driven Surrogate Modeling of Antenna Input Characteristics

Publisher's version (útgefin grein)Design of contemporary antennas necessarily involves electromagnetic (EM) simulation tools. Their employment is imperative to ensure evaluation reliability but also to carry out the design process itself, especially, the adjustment of antenna dimensions. For the latter, traditionally used parameter sweeping is more and more often replaced by rigorous numerical optimization, which entails considerable computational expenses, sometimes prohibitive. A potentially attractive way of expediting the simulation-based design procedures is the replacement of expensive EM analysis by fast surrogate models (or metamodels). Unfortunately, due to the curse of dimensionality and considerable nonlinearity of antenna characteristics, applicability of conventional modeling methods is limited to structures described by small numbers of parameters within narrow ranges thereof. A recently proposed nested kriging technique works around these issues by allocating the surrogate model domain within the regions containing designs that are of high quality with respect to the selected performance figures. This paper investigates whether sequential design of experiments (DoE) is capable of enhancing the modeling accuracy over one-shot space-filling data sampling originally implemented in the nested kriging framework. Numerical verification carried out for two microstrip antennas indicates that no noticeable benefits can be achieved, which contradicts the common-sense expectations. This result can be explained by a particular geometry of the confined domain of the performance-driven surrogate. As this set consists of nearly-optimum designs, the average nonlinearity of the antenna responses therein is almost location independent, therefore optimum training data allocation should be close to uniform. This is indeed corroborated by our experiments.This work was supported in part by the Icelandic Centre for Research (RANNIS) under Grant 174114051 and Grant174573051, and in part by the National Science Centre of Poland under Grant 2018/31/B/ST7/02369.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

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

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 Yield Optimization of Narrow- and Multi-Band Antennas Using Performance-Driven Surrogates

Publisher's version (útgefin grein)Uncertainty quantification is an important aspect of engineering design, also pertaining to the development and performance evaluation of antenna systems. Manufacturing tolerances as well as other types of uncertainties, related to material parameters (e.g., substrate permittivity) or operating conditions (e.g., bending) may affect the antenna characteristics. In the case of narrow- or multi-band antennas, this usually leads to frequency shifts of the operating bands. Quantifying these effects is imperative to adequately assess the design quality, either in terms of the statistical moments of the performance parameters or the yield. Reducing the antenna sensitivity to parameter deviations is even more essential when increasing the probability of the system satisfying the prescribed requirements is of concern. The prerequisite of such procedures is statistical analysis, normally carried out at the level of full-wave electromagnetic (EM) analysis. While necessary to ensure reliability, it entails considerable computational expenses, often prohibitive. Following the recently fostered concept of constrained modeling, this paper proposes a simple technique for rapid surrogate-assisted yield optimization of narrow- and multi-band antennas. The keystone of the approach is an appropriate definition of the optimization domain. This is realized by considering a few pre-optimized designs that represent the directions of the major changes of the antenna resonant frequencies and operating bands. Due to a small volume of such a domain, an accurate replacement model can be established therein using a small number of training samples, and employed to improve the antenna yield. Verification results obtained for a ring-slot antenna, a dual-band and a triple-band uniplanar dipoles indicate that the optimization process can be accomplished at low cost of a few dozen of EM simulations: 62, 74 and 132 EM simulations, respectively. Result reliability is validated through comparisons with EM-based Monte Carlo simulations.This work was supported in part by the Icelandic Centre for Research (RANNIS) under Grant 206606051, in part by the National Science Centre of Poland under Grant 2017/27/B/ST7/00563, 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

EM‐driven tolerance optimization of compact microwave components using response feature surrogates

Improving microwave component immunity to parameter deviations is of high importance, especially in the case of stringent performance specifications. This paper proposes a computationally efficient algorithm for robustness enhancement of compact microwave circuits. The objective is to increase the acceptable levels of geometry parameter deviations under which the prescribed performance specifications are still fulfilled. Our approach incorporates feature-based surrogate models utilized for low-cost prediction of the fabrication yield, as well as the trustregion framework for adaptive control of design relocation and ensuring convergence of the optimization process. The efficacy of our technique is demonstrated using a broadband microstrip filter.ITESO, A.C