Microwave Design Optimization Research Articles

Microwave Modeling and Design Optimization: The Legacy of John Bandler

Microwave Modeling and Design Optimization: The Legacy of John Bandler

Compressed Machine Learning-Based Inverse Model for Design Optimization of Microwave Components

This article presents a new noniterative inverse modeling technique based on machine learning regression and its applications to microwave design optimization. The proposed inverse model accepts the high-dimensional S-parameters computed at many frequency points as the input and estimates the optimal geometrical/physical parameters of the microwave component as its output. The least-squares support vector machine regression is combined with the principal component analysis to simultaneously overcome both the high-dimensional input space and ill-posed challenges of the inverse modeling. We also propose a new empirical method to find the optimum number of principal components (i.e., the compression level) for each example in an automated way. This makes our proposed model general and easy to use compared with the existing data-driven inverse modeling techniques. The inverse model is trained by a set of scattering parameters computed via a 2-D/3-D solver for few configurations of the geometrical parameters. The feasibility and the accuracy of the proposed optimization scheme are investigated by comparing its predictions with the corresponding optimal configuration estimated via a commercial solver.

Advanced RF and Microwave Design Optimization: A Journey and a Vision of Future Trends

In this paper, we outline the historical evolution of RF and microwave design optimization and envisage imminent and future challenges that will be addressed by the next generation of optimization developments. Our journey starts in the 1960s, with the emergence of formal numerical optimization algorithms for circuit design. In our fast historical analysis, we emphasize the last two decades of documented microwave design optimization problems and solutions. From that retrospective, we identify a number of prominent scientific and engineering challenges: 1) the reliable and computationally efficient optimization of highly accurate system-level complex models subject to statistical uncertainty and varying operating or environmental conditions; 2) the computationally-efficient EM-driven multi-objective design optimization in high-dimensional design spaces including categorical, conditional, or combinatorial variables; and 3) the manufacturability assessment, statistical design, and yield optimization of high-frequency structures based on high-fidelity multi-physical representations. To address these major challenges, we venture into the development of sophisticated optimization approaches, exploiting confined and dimensionally reduced surrogate vehicles, automated feature-engineering-based optimization, and formal cognition-driven space mapping approaches, assisted by Bayesian and machine learning techniques.

Rapid Microwave Design Optimization in Frequency Domain Using Adaptive Response Scaling

In this paper, a novel methodology for cost-efficient microwave design optimization in the frequency domain is proposed. Our technique, referred to as adaptive response scaling (ARS), has been developed for constructing a fast replacement model (surrogate) of the high-fidelity electromagnetic-simulated model of the microwave structure under design using its equivalent circuit (low-fidelity model). The basic principle of ARS is a nonlinear frequency and amplitude response scaling aimed at accommodating the discrepancies between the low- and high-fidelity models at the reference design and, subsequently, at tracking the low-fidelity model changes that occur during the optimization run. The surrogate model prediction is obtained by applying appropriately composed scaling functions to the high-fidelity model at the reference design. ARS is a parameterless and simple-to-implement method that can be applied to a wide range of microwave structures. The ARS surrogate features excellent generalization capability that translates into improved reliability and reduced design cost. It is demonstrated using an eighth-order microstrip bandpass filter and a miniaturized rat-race coupler. Comparison with several space mapping algorithms is provided. The numerical results are supplemented by measurements of the fabricated optimum designs of the considered structures.

Fast EM-Driven Optimization Using Variable-Fidelity EM Models and Adjoint Sensitivities

A robust and computationally efficient technique for microwave design optimization is presented. Our approach exploits variable-fidelity electromagnetic (EM) simulation models and adjoint sensitivities. The low-fidelity EM model correction is realized by means of space mapping (SM). In the optimization process, the SM parameters are optimized together with the design itself, which allows us to keep the number of both low- and high-fidelity simulations at low levels. The algorithm is demonstrated using two examples. Experimental validation is also provided.

Cost-efficient Microwave Design Optimization Using Adaptive Response Scaling

In this paper, a novel technique for cost-efficient design optimization of microwave structures has been proposed. Our approach exploits an adaptive response scaling that ensures good alignment between an equivalent circuit (used as an underlying low-fidelity model) and an electromagnetic (EM) simulation model of the structure under design. As the adaptive scaling tracks the low-fidelity model changes both in terms of frequency and the response level, it exhibits better generalization capability than traditional (e.g., space mapping) surrogates. This translates into improved design reliability and reduced design cost. Our methodology is demonstrated using two examples of microstrip filters and compared to several variations of conventional space mapping.

Rapid electromagnetic‐based microwave design optimisation exploiting shape‐preserving response prediction and adjoint sensitivities

A new development of the shape-preserving response prediction (SPRP) technique for microwave design optimisation is presented here. The original SPRP method is enhanced by employing low-cost derivative information obtained through adjoint sensitivities. The authors propose using operator notation to simplify the SPRP surrogate description. The enhancement through sensitivity data is twofold: to ensure first-order consistency between the SPRP surrogate and the high-fidelity electromagnetic (EM) model under optimisation and to speed up the surrogate optimisation process. Fast surrogate optimisation allows us to use coarse-discretisation EM simulations as an underlying low-fidelity model and, therefore, efficiently apply SPRP to cases where reliable circuit models are not available (e.g. design of antenna structures). The proposed approach is demonstrated using a dielectric resonator filter and an ultra-wideband monopole antenna. Comparison with three benchmark techniques, including the original SPRP methods, space mapping with sensitivity and direct optimisation of the high-fidelity model, is also provided.

Reliable Space-Mapping Optimization Integrated With EM-Based Adjoint Sensitivities

We present a robust space mapping (SM) algorithm exploiting electromagnetic (EM)-based adjoint sensitivities for microwave design optimization. Our approach utilizes low-cost EM-based adjoint sensitivities and trust region methods to improve an SM algorithm at three levels, which are: 1) to build a better overall surrogate while ensuring convergence; 2) to speed up and safeguard the parameter extraction steps; and 3) to speed up and safeguard the surrogate optimization process. We describe the implementation at each level in detail. We review relevant adjoint sensitivity analysis methods. We also review prior SM methods that exploit both sensitivity and adjoint sensitivity. We summarize these methods in four categories. We compare our proposed approach with them. Efficiency, robustness, and versatility of our method are demonstrated by three design examples: an antenna, a planar filter, and a 3-D resonator filter. We compare the results with those obtained by SM without using adjoint sensitivity information and by direct optimization of the high-fidelity EM models.

Multilevel microwave design optimization with automated model fidelity adjustment

A computationally efficient algorithm for electromagnetic (EM)-simulation-driven design optimization of microwave structures is proposed. Our technique exploits variable-fidelity EM simulations and the multilevel design approach where an approximate optimum of the lower accuracy but faster EM model of the structure under design is used as a starting point for optimizing a more accurate model. Several enhancements of the basic multifidelity method are introduced, including an efficient algorithm of optimizing EM models that is based on local response surface approximations, as well as automated adjustment of model fidelity. Convergence of the procedure to the optimum design is ensured by defaulting to the higher fidelity model whenever the prediction given by the lower fidelity fails to improve the design. Distribution of the computational effort between the models of different fidelity allows for making larger steps in the design space at a low cost, as well as substantial reduction of the number of high-fidelity model evaluations, because the high-fidelity model is only referred to in the last design stage. The article provides comprehensive numerical verification of our technique. Substantial computational savings are demonstrated in comparison to the benchmark methods: over 40% on average as compared to a basic version of the multifidelity optimization approach and over 95% as compared to direct optimization of the high-fidelity model. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:281–288, 2014.

Reliable em-driven microwave design optimization using manifold mapping and adjoint sensitivity

A robust and reliable algorithm for computationally efficient design optimization of microwave structures evaluated with electromagnetic (EM) simulations is introduced. The presented approach utilizes a low-fidelity model constructed from coarse-discretization EM simulation of the structure under consideration, as well as cheap derivative information obtained by means of adjoint sensitivity. Adjoint sensitivity is exploited to reduce the misalignment between the low- and high-fidelity models through input space mapping, to construct a first-order consistent surrogate model through manifold mapping, and to optimize the surrogate through a trust-region-based algorithm. This comprehensive use of adjoint sensitivity results in a very low design cost and excellent convergence capability of the proposed algorithm. Efficiency of our approach is demonstrated using two examples: an ultra-wideband antenna and a microstrip bandpass filter. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:809–813, 2013; View this article online at wileyonlinelibrary.com. DOI: 10.1002/mop.27430

Computational-budget-driven automated microwave design optimization using variable-fidelity electromagnetic simulations

A robust technique for microwave design optimization is presented. It is based on variable-fidelity electromagnetic (EM) simulations where the approximate optimum of the “coarser” model becomes an initial design for finding the optimum of the “finer” one. The algorithm automatically switches between the models of different fidelity taking into account the computational budget assumed for the design process. Additional mechanisms enhancing the algorithm include: frequency scaling to reduce the misalignment between the models of different fidelity, as well as the local response surface approximation to reduce the number of EM simulations. The presented technique is particularly suitable for problems where simulation-driven design is the only option, for example, for wideband antennas and dielectric resonator filters. Our method is demonstrated using two filters and one antenna example. In all cases, the optimal design is obtained at a low computational cost corresponding to a few high-fidelity simulations of the structure. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.

Tuning space mapping: The state of the art

The electromagnetic (EM)-simulator-based tuning process for rapid microwave design can combine EM accuracy with circuit-design speed. Our own approach is based on the intuitive engineering idea of “space mapping.” In this article, we explain the art of microwave design optimization through “tuning space mapping” procedures. We list various appropriate types of models (called “surrogates”). We demonstrate the implementation of these surrogates through a simple bandstop filter. We provide application examples using commercial simulation software. Our purpose is to help microwave engineers understand the tuning space mapping methodology and to inspire new implementations and applications. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22: 639–651, 2012.

Comparative study of space-mapping-based techniques for microwave design optimisation

Space mapping (SM) has been used in microwave engineering for some 17 years and demonstrated as one of the most efficient simulation-driven design techniques available to date. By exploiting a fast and physically based surrogate model, SM allows rapid optimisation of an electromagnetic-simulated structure of interest (fine model). Several variations of SM algorithms have been proposed including input, output, implicit and frequency SM, as well as recently introduced tuning space mapping (TSM). However, TSM is an invasive technique that requires modification to the designable structure under consideration (i.e. the ‘cutting’ and inserting of the tuning ports). Here, for the first time, a comparative study of various SM and TSM algorithms is carried out. Advantages and disadvantages of these techniques are discussed and illustrated through design examples. Recommendations for potential users of SM and TSM are given.

Local response surface approximations and variable-fidelity electromagnetic simulations for computationally efficient microwave design optimisation

In this study, the authors propose a robust and computationally efficient algorithm for simulation-driven design optimisation of microwave structures. Our technique exploits variable-fidelity electromagnetic models of the structure under consideration. The low-fidelity model is optimised using its local response surface approximation surrogates. The high-fidelity model is refined by space mapping with polynomial interpolation of the low-fidelity model data used as an underlying coarse model. Our algorithm is carefully developed to minimise the number of evaluations of both the low- and high-fidelity model in the optimisation process. The operation and efficiency of the approach is demonstrated through design of a microstrip filter, a double-ring antenna and an ultra-wideband monopole antenna. A comparison with other design approaches, including the direct high-fidelity model optimisation, is also presented.

Knowledge-Based Response Correction and Adaptive Design Specifications for Microwave Design Optimization

Simulation-based optimization has become an important design tool in microwave engineering. Yet, employing electromagnetic (EM) solvers in the design process is a challenging task, primarily due to a high-computational cost of an accurate EM simulation. This paper is focused on efficient EM-driven design optimization techniques that utilize physically-based low-fidelity models, normally based on coarse-discretization EM simulations. The presented methods attempt to exploit as much of the knowledge about the system or device of interest embedded in the low-fidelity model as possible, so as to reduce the computational cost of the design process. Unlike many other surrogate-based approaches, the techniques discussed here are non-parametric ones, i.e., they are not based on analytical formulas. The paper presents several specific methods, including those based on correcting the low-fidelity model response (adaptive response correction and shape-preserving response prediction), as well as on suitable modification of the design specifications. Formulations, application examples and the discussion of advantages and disadvantages of these techniques are also included.

Derivative-free microwave design optimisation using shape-preserving response prediction and space mapping

A two-level derivative-free algorithm for electromagnetic-simulation-driven design optimisation is introduced. The technique exploits a fast surrogate model that is created using a modified version of a shape-preserving response prediction (SPRP) methodology and a limited amount of coarse-discretisation electromagnetic (EM) simulation data. The surrogate is subsequently utilised by the space mapping algorithm to find a design satisfying given performance specifications. As demonstrated using two examples of microstrip filters and a planar antenna, the design cost is low and corresponds to a few high-fidelity EM simulations of the optimised structure and it is 30–50% lower than that for the original SPRP technique exploiting coarse-discretisation EM models.

Fast microwave design optimisation using shape-preserving response prediction and coarse-discretisation EM models

An efficient technique for fast design optimisation of microwave structures is discussed. The approach is based on the recently introduced shape-preserving response prediction method (SPRP). SPRP allows us to estimate the response of the computationally expensive structure under consideration using the properly selected set of characteristic points of the physically based coarse model response. Here, the coarse model is implemented in the same electromagnetic solver as the one that evaluated the original structure, but coarse discretisation is used. It is demonstrated that the presented technique yields a satisfactory design after two or three evaluations of the original structure. The efficiency of this approach is illustrated through the design optimisation of a double annular ring antenna and two microstrip filters. Comparison with the direct EM-simulation-based optimisation of the fine model is also given.

Shape-Preserving Response Prediction for Microwave Design Optimization

A shape-preserving response prediction methodology for microwave design optimization is introduced. The presented technique allows us to estimate the response of the microwave structure being optimized (fine model) using a computationally cheap representation of the structure (coarse model). The change of the coarse model response is described by the translation vectors corresponding to certain (finite) number of characteristic points of the response. These translation vectors are subsequently used to predict the response change of the fine model. The presented method has very good generalization capability and it is not based on any extractable parameters, which makes it easy to implement. Applications for microwave design optimization are discussed. The robustness of the proposed approach is demonstrated by extensive comparison with space mapping, which is one of the most efficient optimization approaches in microwave engineering so far.

Space mapping algorithm with improved convergence properties for microwave design optimization

Space mapping is one of the most efficient techniques for microwave design optimization. Still, it is well known that space mapping algorithms may suffer from convergence issues, which are consequences of certain fundamental features. In many cases, the space mapping algorithm quickly finds an acceptable solution, but then falls into oscillations with respect to the design variables and/or the objective function value; as a consequence, there are no clear criteria for terminating the optimization process. In this article, we investigate some techniques for improving the convergence properties of the space mapping algorithm, which are based on the general convergence results for such algorithms. Our approach is verified using several microwave design optimization problems. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.

Implicit space mapping with adaptive selection of preassigned parameters

Implicit space mapping is one of the latest developments in space mapping (SM) technology. Its advantage is that the variables (the so-called preassigned parameters) used to adjust the surrogate model to have it match the fine model are typically separate from the design variables. Also, implicit space mapping offers greater flexibility in creating and enhancing surrogate models. Still, choosing the proper model as well as the right set of preassigned parameters - both being critical for the performance of the space mapping algorithm - is an open problem. Here, the authors apply suitable assessment techniques that help in automatically making the right selection of the model and, consequently, its associated parameters. The assessment is embedded into the SM algorithm so that the choice of the most suitable model is performed before each iteration of the algorithm. Our approach is verified using several microwave design optimisation problems. The authors also present a modified version of the adaptive SM to improve performance. Our examples are repeated using the modified adaptive SM and compared with the basic adaptive SM.