Response Correction Techniques Research Articles

Expedited EM‐driven generation of Pareto‐optimal trade‐off curves for variable‐turn on‐chip inductors

This work presents a novel approach to computationally efficient Pareto front identification for variable-turn on-chip inductors. The final outcome is a set of solutions that correspond to the best trade-offs between conflicting design objectives. Here, we consider minimising inductor area and, simultaneously, maximising its quality factor, while maintaining a specified inductance value at a given operating frequency. As opposed to the typically used population-based metaheuristics requiring massive computational resources to generate the entire Pareto front in a single algorithm run, the proposed method reduces the number of necessary structure evaluations by exploiting a point-by-point strategy for determining the consecutive trade-off designs. The original design problem is a mixed-integer task involving integer and non-integer variables (here, the number of inductor windings and its geometry parameters). For the sake of computational efficiency, we develop a separate kriging interpolation model for each considered case of winding turns, and use it, instead of expensive electromagnetic simulations, to obtain the initial Pareto fronts. The non-dominated part of the concatenated initial Pareto sets is subsequently elevated (accuracy-wise) to the level of an electromagnetic analysis by means of a response correction technique. Our considerations are illustrated using a 3.5-nH variable-turn on-chip inductor realised in 65-nm CMOS technology.

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.

Multi-objective design optimization of antenna structures using sequential domain patching with automated patch size determination

ABSTRACTIn this article, a simple yet efficient and reliable technique for fully automated multi-objective design optimization of antenna structures using sequential domain patching (SDP) is discussed. The optimization procedure according to SDP is a two-step process: (i) obtaining the initial set of Pareto-optimal designs representing the best possible trade-offs between considered conflicting objectives, and (ii) Pareto set refinement for yielding the optimal designs at the high-fidelity electromagnetic (EM) simulation model level. For the sake of computational efficiency, the first step is realized at the level of a low-fidelity (coarse-discretization) EM model by sequential construction and relocation of small design space segments (patches) in order to create a path connecting the extreme Pareto front designs obtained beforehand. The second stage involves response correction techniques and local response surface approximation models constructed by reusing EM simulation data acquired in the first step. A major contribution of this work is an automated procedure for determining the patch dimensions. It allows for appropriate selection of the number of patches for each geometry variable so as to ensure reliability of the optimization process while maintaining its low cost. The importance of this procedure is demonstrated by comparing it with uniform patch dimensions.

On deterministic procedures for low-cost multi-objective design optimization of miniaturized impedance matching transformers

PurposeThis paper aims to investigate deterministic strategies for low-cost multi-objective design optimization of compact microwave structures, specifically, impedance matching transformers. The considered methods involve surrogate modeling techniques and variable-fidelity electromagnetic (EM) simulations. In contrary to majority of conventional approaches, they do not rely on population-based metaheuristics, which permit lowering the design cost and improve reliability.Design/methodology/approachThere are two algorithmic frameworks presented, both fully deterministic. The first algorithm involves creating a path covering the Pareto front and arranged as a sequence of patches relocated in the course of optimization. Response correction techniques are used to find the Pareto front representation at the high-fidelity EM simulation level. The second algorithm exploits Pareto front exploration where subsequent Pareto-optimal designs are obtained by moving along the front by means of solving appropriately defined local constrained optimization problems. Numerical case studies are provided demonstrating feasibility of solving real-world problems involving expensive EM-simulation models of impedance transformer structures.FindingsIt is possible, by means of combining surrogate modeling techniques and constrained local optimization, to identify the set of alternative designs representing Pareto-optimal solutions, in a realistic time frame corresponding to a few dozen of high-fidelity EM simulations of the respective structures. Multi-objective optimization for the considered class of structures can be realized using deterministic approaches without defaulting to evolutionary methods.Research limitations/implicationsThe present study can be considered a step toward further studies on expedited optimization of computationally expensive simulation models for miniaturized microwave components.Originality/valueThe proposed algorithmic solutions proved useful for expedited multi-objective design optimization of miniaturized microwave structures. The problem is extremely challenging when using conventional methods, in particular evolutionary algorithms. To the authors’ knowledge, this is one of the first attempts to investigate deterministic surrogate-assisted multi-objective optimization of compact components at the EM-simulation level.

Pareto-Ranking Bisection Algorithm for Expedited Multiobjective Optimization of Antenna Structures

The purpose of this letter is the introduction of a novel methodology for expedited multiobjective design of antenna structures. The key component of the presented approach is fast identification of the initial representation of the Pareto front (i.e., a set of design representing the best possible tradeoffs between conflicting objectives) using a Pareto-ranking bisection algorithm. The algorithm finds a discrete set of Pareto-optimal designs. Its operation principle is sequential partitioning of the line segments connecting the designs found in the previous iterations, and refining the new designs allocated this way by means of poll-type search involving Pareto ranking. Subsequently, the final Pareto set is obtained by means of response correction techniques. Our methodology is demonstrated using an ultrawideband monopole antenna and compared to state-of-the-art multiobjective optimization methods.

Low-cost multi-objective optimization and experimental validation of UWB MIMO antenna

Purpose – The purpose of this paper is to validate methodologies for expedited multi-objective design optimization of complex antenna structures both numerically and experimentally. Design/methodology/approach – The task of identifying the best possible trade-offs between the antenna size and its electrical performance is formulated as multi-objective optimization problem. Algorithmic frameworks are described for finding Pareto-optimal designs using auxiliary surrogate models and two alternative approaches to design refinement: response correction techniques and co-kriging. Numerical and experimental case studies are provided to demonstrate feasibility of solving real-world and complex antenna design tasks. Findings – It is possible, through appropriate combination of the surrogate modeling techniques (both data driven and physics based) and response correction methods, to find the set of alternative designs representing the best possible trade-offs between conflicting design objectives, here, electrical performance and size. Design optimization can be performed at practically feasible computational costs. Research limitations/implications – The study demonstrates feasibility of automated multi-objective design optimization of antennas at low computational cost. The presented techniques reach beyond the commonly used design approaches based on parameter sweeps and similar hands-on methods, particularly in terms of automation, reliability and reduction of the computational costs of the design processes. Originality/value – Multi-objective design of antenna structures is very challenging when high-fidelity electromagnetic simulations are utilized for performance evaluation of the structure at hand. The proposed design framework permits rapid optimization of complex structures (here, MIMO antenna), which is hardly possible using conventional methods.

Expedited constrained multi-objective aerodynamic shape optimization by means of physics-based surrogates

In the paper, computationally efficient constrained multi-objective design optimization of transonic airfoil profiles is considered. Our methodology focuses on fixed-lift design aimed at finding the best possible trade-offs between the two objectives: minimization of the drag coefficient and maximization of the pitching moment. The algorithm presented here exploits the surrogate-based optimization principle, variable-fidelity computational fluid dynamics (CFD) models, as well as auxiliary data-driven surrogates (here, using Kriging). In order to permit computationally feasible construction of the Kriging models, initial design space reduction is also utilized. The design process has three major stages: (i) identification of the extreme points of the Pareto front through single-objective optimization (one objective at a time), (ii) construction of the Kriging model and initial Pareto front generation using multi-objective evolutionary algorithm (MOEA), and (iii) Pareto front refinement using response correction techniques and local response surface approximation (RSA) models. For the sake of computational efficiency, stages (i) and (ii) are realized at the level of coarse-discretization CFD model. The RSA models are also utilized to predict the angle of attack necessary to achieve the target lift coefficient, which considerably reduces the CFD simulation effort involved in the design process. Two design case studies are considered involving B-spline-parameterized airfoil shapes with 8 and 12 design variables. The 10-element Pareto front representations are obtained at the cost corresponding to just over two hundred of high-fidelity CFD model evaluations. This cost is not only considerably lower (up to two orders of magnitude) than the cost of direct high-fidelity model optimization using metaheuristics but, more importantly, renders multi-objective optimization of aerodynamic components computationally tractable even at the level of accurate CFD models.

Cost-Efficient Design Optimization of Compact Patch Antennas With Improved Bandwidth

In this letter, a surrogate-assisted optimization procedure for fast design of compact patch antennas with enhanced bandwidth is presented. The procedure aims at addressing a fundamental challenge of the design of antenna structures with complex topologies, which is simultaneous adjustment of numerous geometry parameters. The latter is necessary in order to find a truly optimum design and cannot be executed—at the level of high-fidelity electromagnetic (EM)-simulation models—using conventional numerical optimization procedures due to prohibitive computational cost. Here, we employ coarse-discretization EM simulations as faster representation of the antenna under design (referred to as a low-fidelity model). The low-fidelity model is enhanced using a combination of frequency scaling and response correction techniques. Frequency scaling is particularly suitable for reducing misalignment between EM models of various fidelities in case of narrowband structures. Iterative correction-prediction loop is capable to identify an optimum design at a reasonably low computational cost while adjusting all relevant geometry parameters at the same time. For the sake of illustration, we consider a modified patch antenna based on transversal signal-interference feed and additional slots in the radiator. Upon optimization, the antenna provided 29% bandwidth while maintaining a compact footprint of 645 $~\hbox{mm}^2$ . Experimental validation is also provided.

Supersonic Airfoil Shape Optimization by Variable-fidelity Models and Manifold Mapping

Supersonic vehicles are an important type of potential transports. Analysis of these vehicles requires the use of accurate models, which are also computationally expensive, to capture the highly nonlinear physics. This paper presents results of numerical investigations of using physics-based surrogate models to design supersonic airfoil shapes. Variable-fidelity models are generated using inviscid computational fluid dynamics simulations and analytical models. By using response correction techniques, in particular, the manifold mapping technique, fast surrogate models are constructed. The effectiveness of the approach is investigated using lift-constrained drag minimization problems of supersonic airfoil shapes. Compared with direct optimization, the results show that an order of magnitude speed up can be obtained. Furthermore, we investigate the effectiveness of the variable-fidelity technique in terms of speed and design quality using several combinations of medium-fidelity and low-fidelity models.

A Structure and Simulation-Driven Design of Compact CPW-Fed UWB Antenna

In this letter, a structure of a miniaturized ultrawideband (UWB) coplanar waveguide (CPW)-fed antenna and its design procedure are presented. The antenna is a modified version of the design previously proposed in the literature, with additional degrees of freedom introduced in order to improve the structure flexibility. The small size is achieved by executing a rigorous optimization procedure that consists of two stages: 1) smart random search carried out at the level of coarse-mesh electromagnetic (EM) simulation model that aims at finding an initial design featuring small size and reasonable return loss, and 2) surrogate-assisted optimization exploiting variable-fidelity EM simulations and response correction techniques for expedited design tuning. The final design exhibits return loss below - 13.2 dB in the entire UWB band and a small size of 418 mm 2 . Simulation results are supported by physical measurements of the fabricated antenna prototype.

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

Abstract 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.

Rapid design and size reduction of microwave couplers using variable-fidelity EM-driven optimization

In this article, fast electromagnetic (EM) simulation-driven design optimization of compact microwave couplers is addressed. The main focus is on explicit reduction of the circuit footprint. Our methodology relies on the penalty function approach, which allows us to minimize the circuit area while ensuring equal power split between the output ports and providing a sufficient bandwidth with respect to the return loss and isolation around the operating frequency. Computational efficiency of the design process is achieved by exploiting variable-fidelity EM simulations, local response surface approximation models, as well as suitable response correction techniques for design tuning. The technique described in this work is demonstrated using two examples of compact rat-race couplers. The size-reduction-oriented designs are compared with performance-oriented ones to illustrate available design trade-offs. Final design solutions of the former case illustrate ∼92% of miniaturization for both coupler examples (with corresponding fractional bandwidths of 16%). Alternative design solutions pertaining to the latter case show a lesser size reduction (∼90% for both examples), but present a much wider bandwidths (∼25% for both couplers). The overall computational cost of the design procedure corresponds to about 20 and 10 high-fidelity coupler simulations for the first and second design example, respectively. Numerical results are also validated experimentally. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:27–35, 2016.

Simulation-driven design of low-speed wind tunnel contraction

A low-speed wind tunnel is developed for conducting research on the flow past micro air vehicles. The tunnel is of open suction type and is composed of a square inlet with a honeycomb and turbulence screens, settling chamber, contraction, experimental section housing, diffuser, and axial fan. In this paper, we describe the details of the design optimization procedure of the contraction, which is key to getting a high quality flow in the experimental section. A high-fidelity computational fluid dynamic (CFD) flow solver is used to capture the nonlinear flow physics. Due to the high computational expense of the CFD simulations, surrogate-based optimization (SBO) is used to accelerate the design process. The SBO approach replaces direct optimization of the high-fidelity (accurate but computationally expensive) model by iterative optimization of a properly corrected low-fidelity model. Here, we exploit variable–fidelity CFD simulations, as well as a simple multiplicative response correction technique to construct the surrogate model of the wind tunnel contraction, allowing us to optimize its shape at a low computational cost. To our knowledge, it is the first application of variable–fidelity surrogate modeling to wind tunnel contraction design. The optimum nozzle design is verified using a high-fidelity CFD simulation, as well as by experimental measurements of the fabricated wind tunnel. Experimental validation confirms the correctness of the numerical optimization procedures utilized to design the contraction.

Design optimisation of antennas using electromagnetic simulations and adaptive response correction technique

In this study, the authors describe a simple and reliable procedure for electromagnetic (EM) simulation-based design of antennas. The authors' approach exploits coarse-discretisation EM simulations (the low-fidelity antenna model) and the adaptive response correction (ARC) technique. ARC is used to enhance the low-fidelity model response so that it can serve as a cheap yet accurate representation of the high-fidelity EM model of the antenna under design. The ARC-based iterative correction-prediction process yields an optimised design at a low CPU cost corresponding to a few high-fidelity simulations of the antenna. The proposed approach is compared with direct optimisation of the high-fidelity model and to surrogate-based optimisation exploiting output space mapping. The results obtained for two antenna design cases indicate by reduction of the overall design cost that ARC allows for better utilisation of the knowledge embedded in the low-fidelity model than the simpler correction method.

Low-cost EM-simulation-driven Multi-objective Optimization of Antennas

A surrogate-based method for efficient multi-objective antenna optimization is presented. Our technique exploits response surface approximation (RSA) model constructed from sampled low-fidelity antenna model (here, obtained through coarse-discretization EM simulation). The RSA model enables fast determination of the best available trade-offs between conflicting design goals. A low-cost RSA model construction is possible through initial reduction of the design space. Optimization of the RSA model has been carried out using a multi-objective evolutionary algorithm (MOEA). Additional response correction techniques have been subsequently applied to improve selected designs at the high-fidelity EM antenna model level. The refined designs constitute the final Pareto set representation. The proposed approach has been validated using an ultra-wideband (UWB) monocone and a planar Yagi-Uda antenna.

Multi-Objective Design of Antennas Using Variable-Fidelity Simulations and Surrogate Models

A computationally-efficient procedure for multi-objective design of antenna structures is presented. Our approach exploits the multi-objective evolutionary algorithm (MOEA) working with a fast antenna surrogate model obtained with kriging interpolation of coarse-discretization simulation data. Response correction techniques are subsequently applied to refine the designs obtained by MOEA. Our methodology allows us to obtain-at a low computational cost-a set of designs corresponding to various trade-offs between the antenna size and the refection coefficient. Two illustration examples are considered: (i) an UWB monocone with two objectives being reduction of the antenna size and minimization of the antenna reflection coefficient in the bandwidth of interest, and (ii) a planar Yagi antenna with the objectives being an increase of the end-fire gain and minimization of the reflection coefficient, both in the bandwidth of interest.

Simulation-driven design using surrogate-based optimization and variable-resolution computational fluid dynamic models

Reliable and robust computational fluid dynamics (CFD) solvers are nowadays commonly utilized in the design and analyses of various engineering systems, such as aircraft, turbomachinery, ships, and automotives. Although this has resulted in a drastic decrease of the number of prototype and experimental testing, the use of CFD in the design automation process is still limited. In practice, the geometry parameters that ensure satisfaction of assumed performance requirements are often obtained by repetitive CFD simulations guided by engineering experience. This is a tedious process which does not guarantee optimal results. On the other hand, straight forward automation attempts by employing the CFD solvers directly in the optimization loop are typically impractical, even when using adjoint sensitivity information, because high-fidelity CFD simulations tend to be computationally very expensive. In this paper, we describe a surrogate-based design optimization methodology that shifts the computational burden from the accurate and expensive high-fidelity CFD model to its fast and yet reasonably accurate surrogate. As the surrogate models are computationally much cheaper than the high-fidelity ones, the cost of the design process is greatly reduced. Here, the surrogates are constructed using low-fidelity CFD models and response correction techniques. Application examples, involving the design of axisymmetric hulls in subsonic flow, and airfoils in both subsonic and transonic flows, are presented.

Parameter identification in climate models using surrogate-based optimization

We present initial steps and first results of a surrogate-based optimization (SBO) approach for parameter optimization in climate models. In SBO, a computationally cheap, but yet reasonably accurate representation of the original high-fidelity (or fine) model, the so-called surrogate, replaces the fine model in the optimization process. We choose two representatives, namely two marine ecosystem models, to verify our approach. We present two ways to obtain a physics-based low-fidelity (or coarse) model one based on a coarser time discretization, the other on an inaccurate fixed point iteration. Since in both cases, the low-fidelity model is less accurate, we use a multiplicative response correction technique, aligning the low-and the high-fidelity model output to obtain a reliable surrogate at the current iterate in the optimization process. We verify the approach by using model generated target data. We show that the proposed SBO method leads to a very satisfactory solution at the cost of a few evaluations of the high-fidelity model only.

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. © 2012 Wiley Periodicals, Inc.

Surrogate-based optimization of climate model parameters using response correction

We present a computationally efficient methodology for the optimization of climate model parameters applied to a (one-dimensional) representative of a class of marine ecosystem models. We use a response correction technique to create a surrogate from a temporarily coarser discretized physics-based low-fidelity model. We demonstrate that replacing the direct parameter optimization of the high-fidelity ecosystem model by iteratively updating and re-optimizing the surrogate leads to a very satisfactory solution while yielding significant cost saving – about 84% when compared to the direct high-fidelity model optimization.