Variable-fidelity optimization of microwave filters using co-kriging and trust regions

In this paper, a variable-fidelity optimization methodology for simulation-driven design optimization of filters is presented. We exploit electromagnetic (EM) simulations of different accuracy. Densely sampled but cheap low-fidelity EM data is utilized to create a fast kriging interpolation model (the surrogate), subsequently used to find an optimum design of the high-fidelity EM model of the filter under consideration. The high-fidelity data accumulated during the optimization process is combined with the existing surrogate using the co-kriging technique. This allows us to improve the surrogate model accuracy while approaching the optimum. The convergence of the algorithm is ensured by embedding it into the trust region framework that adaptively adjusts the search radius based on the quality of the predictions made by the co-kriging model. Three filter design cases are given for demonstration and verification purposes

Cost-efficient modeling of antenna structures using Gradient Enhanced Kriging

Reliable yet fast surrogate models are indispensable in the design of contemporary antenna structures. Data-driven models, e.g., based on Gaussian Processes or support-vector regression, offer sufficient flexibility and speed, however, their setup cost is large and grows very quickly with the dimensionality of the design space. In this paper, we propose cost-efficient modeling of antenna structures using Gradient-Enhanced Kriging. In our approach, the training data set contains, apart from the EM-simulation responses of the structure at hand, also derivative data at the respective training locations obtained at little extra cost using adjoint sensitivity techniques. We demonstrate that introduction of the derivative information into the model allows for considerable reduction of the model setup cost (in terms of the number of training points required) without compromising its predictive power. The Gradient-Enhanced Kriging technique is illustrated using a dielectric resonator antenna structure. Comparison with conventional Kriging interpolation is also provided

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

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

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.ITESO, A.C

Sensitivity of Equivalent Circuits on the Extraction Procedure

The present paper proposes an approach to evaluate the “quality” of equivalent circuits of complex devices obtained by a novel technique based on constitutive sub circuits and an Particle Swarm Optimization. In particular the robustness of the obtained circuits is evaluated by a sensitivity analysis, which leads to the identification of the range of variation of its frequency response, since different runs of the global extraction procedure lead to slightly different equivalent circuits (yet topologically coincident). The analysis of the numerical results give an insight on the robustness of as single case and at the same time attest the efficiency of the extraction technique