Sequential Domain Patching for Computationally Feasible Multi-objective Optimization of Expensive Electromagnetic Simulation Models

AbstractIn this paper, we discuss a simple and efficient technique for multi-objective design optimization of multi-parameter microwave and antenna structures. Our method exploits a stencil-based approach for identification of the Pareto front that does not rely on population-based metaheuristic algorithms, typically used for this purpose. The optimization procedure is realized in two steps. Initially, the initial Pareto-optimal set representing the best possible trade-offs between conflicting objectives is obtained using low-fidelity representation (coarsely-discretized EM model simulations) of the structure at hand. This is realized by sequential construction and relocation of small design space segments (patches) in order to create a path connecting the extreme Pareto front designs identified beforehand. In the second step, the Pareto set is refined to yield the optimal designs at the level of the high-fidelity electromagnetic (EM) model. The appropriate number of patches is determined automatically. The approach is validated by means of two multi-parameter design examples: a compact impedance transformer, and an ultra-wideband monopole antenna. Superiority of the patching method over the state-of-the-art multi-objective optimization techniques is demonstrated in terms of the computational cost of the design process

Low-Cost Unattended Design of Miniaturized 4 × 4 Butler Matrices with Nonstandard Phase Differences

Publisher's version (útgefin grein)Design of Butler matrices dedicated to Internet of Things and 5th generation (5G) mobile systems-where small size and high performance are of primary concern-is a challenging task that often exceeds capabilities of conventional techniques. Lack of appropriate, unified design approaches is a serious bottleneck for the development of Butler structures for contemporary applications. In this work, a low-cost bottom-up procedure for rigorous and unattended design of miniaturized 4 x 4 Butler matrices is proposed. The presented approach exploits numerical algorithms (governed by a set of suitable objective functions) to control synthesis, implementation, optimization, and fine-tuning of the structure and its individual building blocks. The framework is demonstrated using two miniaturized matrices with nonstandard output-port phase differences. Numerical results indicate that the computational cost of the design process using the presented framework is over 80% lower compared to the conventional approach. The footprints of optimized matrices are only 696 and 767 mm(2), respectively. Small size and operation frequency of around 2.6 GHz make the circuits of potential use for mobile devices dedicated to work within a sub-6 GHz 5G spectrum. Both structures have been benchmarked against the state-of-the-art designs from the literature in terms of performance and size. Measurements of the fabricated Butler matrix prototype are also provided.This work was supported in part by the National Science Centre of Poland Grant 2017/27/B/ST7/00563 and by the National Centre for Research and Development Grant NOR/POLNOR/HAPADS/0049/2019-00.Peer reviewe

Recent developments in simulation-driven multi-objective design of antennas

Publisher's version (útgefin grein)This paper addresses computationally feasible multi-objective optimization of antenna structures. We review two recent techniques that utilize the multi-objective evolutionary algorithm (MOEA) working with fast antenna replacement models (surrogates) constructed as Kriging interpolation of coarse-discretization electromagnetic (EM) simulation data. The initial set of Pareto-optimal designs is subsequently refined to elevate it to the high-fidelity EM simulation accuracy. In the first method, this is realized point-by-point through appropriate response correction techniques. In the second method, sparsely sampled high-fidelity simulation data is blended into the surrogate model using Co-kriging. Both methods are illustrated using two design examples: an ultra-wideband (UWB) monocone antenna and a planar Yagi-Uda antenna. Advantages and disadvantages of the methods are also discussed.The authors would like to thank the Computer Simulation Technology AG, Darmstadt, Germany, for making CST Microwave Studio available. This work was supported in part by the Icelandic Centre for Research (RANNIS), the Grant 130450051, and by the National Science Centre of Poland, the Grants 2013/11/B/ST7/04325 and 2014/12/ST7/00045.Peer Reviewe

Accelerated Re-Design of Antenna Structures Using Sensitivity-Based Inverse Surrogates

Publisher's version (útgefin grein)The paper proposes a novel framework for accelerated re-design (dimension scaling) of antenna structures using inverse surrogates. The major contribution of the work is a sensitivity-based model identification procedure, which permits a significant reduction of the number of reference designs required to render the surrogate. Rigorous formulation of the approach is supplemented by its comprehensive numerical validation using a triple-band uniplanar dipole antenna and a dual-band monopole antenna re-designed with respect to operating frequencies as well as the substrate parameters (thickness and dielectric permittivity). It is demonstrated that—for the considered test cases—the reliable inverse model can be set up using a significantly smaller (by a factor of three) number of reference points as compared to the original version of the method, whereas the dimension scaling process itself requires up to four EM simulations of the antenna structure.This work was supported in part by the Icelandic Centre for Research (RANNIS) under Grant 174573051, and in part by the NationalScience Centre of Poland under Grant 2017/27/B/ST7/00563.Peer reviewe

On Rapid Re-Design of UWB Antennas with Respect to Substrate Permittivity

Re-design of a given antenna structure for various substrates is a practically important issue yet non trivial, particularly for wideband and ultra-wideband antennas. In this work, a technique for expedited redesign of ultra-wideband antennas for various substrates is presented. The proposed approach is based on inverse surrogate modeling with the scaling model constructed for several reference designs that are optimized for selected values of the substrate permittivity. The surrogate is set up at the level of coarse-discretization EM simulation model of the antenna and, subsequently, corrected to provide prediction at the high-fidelity EM model level. The dimensions of the antenna scaled to any substrate permittivity within the region of validity of the surrogate are obtained instantly, without any additional EM simulation necessary. The proposed approach is demonstrated using an ultra-wideband monopole with the permittivity scaling range from 2.2 to 4.5. Numerical validation is supported by physical measurements of the fabricated prototypes of the re-designed antennas.The authors would like to thank Computer Simulation Technology AG, Darmstadt, Germany, for making CST Microwave Studio available. This work is partially supported by the Icelandic Centre for Research (RANNIS) Grant 141272051 and by National Science Centre of Poland Grant 2014/15/B/ST7/04683.Peer Reviewe

Compact 4 × 4 butler matrix with non‐standard phase differences for IoT applications

Publisher's version (útgefin grein)Butler matrices represent a popular class of feeding networks for antenna arrays. Large dimensions and the lack of flexibility in terms of achievable output phase difference make conventional Butler structures of limited use for modern communication devices. In this work, a com-pact planar 4×4 matrix with non-standard relative phase shifts of –30,150, –120, and 60° has been proposed. The structure is designed to operate at the centre frequency of 2.45 GHz. Small dimensions of 31.3×22.9 mm make it useful for Internet of Things applications. The structure operates from 2.35 to 2.55 GHz, which covers the industrial, scientific and medical bandwidth. At the centre frequency, the measured amplitude and phase imbalance are 1.65 dB and±4.3°, respectively. The proposed circuit has been compared to the state-of-the-art structures from the literature.This work was supported in part by National Centre for Research and Development Grant NOR/POLNOR/HAPADS/ 0049/2019-00, by National Science Centre of Poland Grant 2017/27/B/ST7/00563, and by Icelandic Centre for Research (RANNIS) Grant 206606051.Peer reviewe

Airfoil Design under Uncertainty using Non-Intrusive Polynomial Chaos Theory and Utility Functions

Fast and accurate airfoil design under uncertainty using non-intrusive polynomial chaos (NIPC) expansions and utility functions is proposed. The NIPC expansions provide a means to efficiently and accurately compute statistical information for a given set of input variables with associated probability distribution. Utility functions provide a way to rigorously formulate the design problem. In this work, these two methods are integrated for the design of airfoil shapes under uncertainty. The proposed approach is illustrated on a numerical example of lift-constrained airfoil drag minimization in transonic viscous flow using the Mach number as an uncertain variable. The results show that compared with the standard problem formulation the proposed approach yields more robust designs. In other words, the designs obtained by the proposed approach are less sensitive to variations in the uncertain variables than those obtained with the standard problem formulation

A Novel Structure and Design Optimization of Compact Spline-Parameterized UWB Slot Antenna

In this paper, a novel structure of a compact UWB slot antenna and its design optimization procedure has been presented. In order to achieve a sufficient number of degrees of freedom necessary to obtain a considerable size reduction rate, the slot is parameterized using spline curves. All antenna dimensions are simultaneously adjusted using numerical optimization procedures. The fundamental bottleneck here is a high cost of the electromagnetic (EM) simulation model of the structure that includes (for reliability) an SMA connector. Another problem is a large number of geometry parameters (nineteen). For the sake of computational efficiency, the optimization process is therefore performed using variable-fidelity EM simulations and surrogate-assisted algorithms. The optimization process is oriented towards explicit reduction of the antenna size and leads to a compact footprint of 199 mm2 as well as acceptable matching within the entire UWB band. The simulation results are validated using physical measurements of the fabricated antenna prototype.The authors would like to thank Computer Simulation Technology AG, Darmstadt, Germany, for making CST Microwave Studio available. This work is partially supported by the Icelandic Centre for Research (RANNIS) Grant 141272051 and by National Science Centre of Poland Grant 2014/15/B/ST7/04683

Pareto Ranking Bisection Algorithm for EM-Driven Multi-Objective Design of Antennas in Highly-Dimensional Parameter Spaces

A deterministic technique for fast surrogate-assisted multi-objective design optimization of antennas in highly-dimensional parameters spaces has been discussed. In this two-stage approach, the initial approximation of the Pareto set representing the best compromise between conflicting objectives is obtained using a bisection algorithm which finds new Pareto-optimal designs by dividing the line segments interconnecting previously found optimal points, and executing poll-type search that involves Pareto ranking. The initial Pareto front is generated at the level of the coarsely-discretized EM model of the antenna. In the second stage of the algorithm, the high-fidelity Pareto designs are obtained through optimization of corrected local-approximation models. The considered optimization method is verified using a 17-variable uniplanar antenna operating in ultra-wideband frequency range. The method is compared to three state-of-the-art surrogate-assisted multi-objective optimization algorithms

Data-driven model based design and analysis of antenna structures

Data-driven models, or metamodels, offer an efficient way to mimic the behaviour of computation-intensive simulators. Subsequently, the usage of such computationally cheap metamodels is indispensable in the design of contemporary antenna structures where computation-intensive simulations are often performed in a large scale. Although metamodels offer sufficient flexibility and speed, they often suffer from an exponential growth of required training samples as the dimensionality of the problem increases. In order to alleviate this issue, a Gaussian process based approach, known as Gradient-Enhanced Kriging (GEK), is proposed in this work to achieve cost-efficient modelling of antenna structures. The GEK approach incorporates adjoint-based sensitivity data in addition to function data obtained from electromagnetic simulations. The approach is illustrated using a dielectric resonator and an ultra-wideband antenna structures. The method demonstrates significant accuracy improvement with the less number of training samples over the Ordinary Kriging (OK) approach which utilises function data only. The discussed technique has been favourably compared with OK in terms of computational cost