Efficient Design of Inline E-Plane Waveguide Extracted Pole Filters Through Enhanced Equivalent Circuits and Space Mapping

The space mapping (SM) technique is applied to conformal antenna design for the first time. A planar microstrip antenna printed on a finite ground-plane with a coarse-mesh is solved as the coarse model and aligned with a conformal microstrip antenna placed on a platform's surface with a fine-mesh through space mapping. When some conformal antennas have the same planar configuration, being able to share a common coarse model is an important advantage of this technique in these conformal antenna optimizations. The S-parameters of conformal antennas are optimized. The function responses in this example are chosen as "e S11". The comparisons of efficiency and accuracy with the commercial software CST MWS 5.0 are made. The final results demonstrate that the SM technique can reduce the overall design process by an order of magnitude (10 times). Therefore, the proposed technique is particularly suitable for conformal antenna optimization. As a demonstration, examples of a planar broadband E-shape microstrip antenna placed on two different platform' surfaces are introduced in this communication.

In this paper, space mapping (SM) technique is combined with response surface methodology (RSM). SM is an optimization method well suited for very costly problems to find an improved design with fulfilled constraints. The SM technique use less costly models, which complements the correct models. The theory is established and compared to the corrected RSM. A multipoint version of SM is presented, where a separate evaluation is done in each iteration to improve the mapping function. Using this additional evaluation to update the mapping function, generally, the number of iterations to find the optimum solution can be reduced. Thus, the elapsed time to solve the optimization problem can be reduced if a parallel computer is utilized. Finally, one engineering optimization problem is solved to illustrate the application of SM in vehicle crashworthiness structural optimization.

Space mapping (SM) is a recognized method for speeding up electromagnetic (EM) optimization. The SM technique often requires an equivalent circuit as the coarse model. In practical cases, equivalent circuit coarse models are not always available. This letter addresses this situation and proposes a new coarse- and fine-mesh SM technique for EM optimization incorporating mesh deformation. By incorporating mesh deformation into coarse-mesh EM optimization, the coarse-mesh EM responses change continuously as the values of the geometrical design variables change. The incorporation of mesh deformation also improves the consistency between the coarse-mesh EM sensitivities and the changes in the coarse-mesh EM responses. This results in the speedup of the coarse-mesh EM optimization and potentially less SM iterations, therefore accelerating the overall SM optimization. This technique is illustrated by two microwave examples.

PurposeOptimisation in electromagnetics, based on finite element models, is often very time‐consuming. In this paper, we present the space‐mapping (SM) technique which aims at speeding up such procedures by exploiting auxiliary models that are less accurate but much cheaper to compute.Design/methodology/approachThe key element in this technique is the SM function. Its purpose is to relate the two models. The SM function, combined with the low accuracy model, makes a surrogate model that can be optimised more efficiently.FindingsBy two examples we show that the SM technique is effective. Further we show how the choice of the low accuracy model can influence the acceleration process. On one hand, taking into account more essential features of the problem helps speeding up the whole procedure. On the other hand, extremely simple auxiliary models can already yield a significant acceleration.Research limitations/implicationsObtaining the low accuracy model is not always straightforward. Some research could be done in this direction. The SM technique can also be applied iteratively, i.e. the auxiliary model is optimised aided by a coarser one. Thus, the generation of hierarchies of models seems to be a promising venue for the SM technique.Originality/valueOptimisation in electromagnetics, based on finite element models, is often very time‐consuming. The results given show that the SM technique is effective for speeding up such procedures.

In this paper, we study the use of space-mapping (SM) techniques within the transmission-line matrix (TLM) method environment. Previous work on SM relies on an idealized coarse model in the design process of a computationally expensive fine model. For the first time, we examine the case when the coarse model is not capable of providing an ideal optimal response. We exploit a coarse-grid TLM solver with relaxed boundary conditions. Such a coarse model may be incapable of satisfying design specifications and traditional SM may fail. Our approach, which exploits implicit SM (ISM) and the novel output SM (OSM), overcomes this failure. Dielectric constant, an expedient preassigned parameter, is first calibrated to roughly align the coarse and fine TLM models. Our OSM scheme absorbs the remaining deviation between the implicitly mapped coarse-grid and fine-grid TLM responses. Because the TLM simulations are on a fixed grid, response interpolation is crucial. We also create a database system to avoid repeating simulations unnecessarily. Our optimization routine employs a trust region methodology. The TLM-based design of an inductive post, a single-resonator filter, and a six-section H-plane waveguide filter illustrate our approach. In a few iterations, our coarse-grid TLM surrogate, with approximate boundary conditions, achieves a good design of the fine-grid TLM model in spite of poor initial responses. Our results are verified with MEFiSTo simulations.

Space mapping (SM) is one of the most popular surrogate- based optimization techniques in microwave engineering. The most critical component in SM is the low-fldelity (or coarse) model | a physically-based representation of the structure being optimized (high-fldelity or flne model), typically evaluated using CPU-intensive electromagnetic (EM) simulation. The coarse model should be fast and reasonably accurate. A popular choice for the coarse models are equivalent circuits, which are computationally cheap, but not always accurate, and in many cases even not available, limiting the practical range of applications of SM. Relatively accurate coarse models that are available for all structures can be obtained through coarsely- discretized EM simulations. Unfortunately, such models are typically computationally too expensive to be e-ciently used in SM algorithms. Here, a study of SM algorithms with coarsely-discretized EM coarse models is presented. More speciflcally, novel and e-cient parameter extraction and surrogate optimization schemes are proposed that make the use of coarsely-discretized EM models feasible for SM algorithms. Robustness of our approach is demonstrated through the design of three microstrip fllters and one double annular ring antenna.

The growing complexity of engineering modeling and design problems demands effective strategies for optimization of computationally expensive objective functions. To this end, we focus on knowledge-based, variable-fidelity optimization of expensive functions through a tried and tested, yet still rapidly evolving art called space mapping optimization. Fitting into the arena of surrogatebased optimization, space-mapping optimization is a model-driven optimization process where the model is an iteratively updated surrogate derived from a valid, low-fidelity or physics-based coarse model. Space mapping takes several forms. Here, we present and formulate the original input space mapping concept, as well as the more recent implicit and output space mapping concepts. Corresponding surrogate models are presented, classified, and discussed. A proposed optimization flow is explained. Then we illustrate both input space mapping and implicit space mapping through the space mapping optimization of a simple, technology-free wedgecutting problem. We also present tuning space mapping, a powerful methodology, but one that requires extra engineering knowledge of the problem under investigation. To confirm our work, we select representative examples from the fields of microwave and antenna engineering, including filter and antenna designs.

Surrogate-based Airfoil Design with Space Mapping and Adjoint Sensitivity

Do all roads lead to Rome? A comparison of knowledge-based, data-driven, and physics-based surrogate models for performance-based early design

The Monte Carlo (MC) method is most exact but computationally expensive for uncertainty quantification (UQ). Instead, surrogate models can approximate UQ at a lower computational cost. However, as the input uncertainty dimensionality increases, the number of samples required to construct the surrogate models also increases rapidly; thus, the advantage of using surrogate models disappears. Therefore, it is necessary to combine the surrogate models with dimensionality reduction for effective UQ. This study compares the performance of UQ for the direct MC method and four different combinations of surrogate models and dimensionality reduction methods in benchmark test functions. The results clarify the effectiveness of training a surrogate model and a dimensionality reduction technique simultaneously rather than separately.

A fully automated direct EM design approach for all-pole filters is proposed by integrating the reflected group delay design procedure with a novel sequential parameter extraction method. This approach contains a number of design stages in which 2–3 resonance frequencies of individual resonators or adjacent couplings are extracted from the simulated reflected group delay response of a one-port network separated from the entire filter. The space mapping technique is used to estimate geometric parameters from the extracted elements. Lagrange interpolation is exploited during the design process to estimate a few design parameters using mapping information from previous stages. A Matlab program is created to automate the design of a 6-pole interdigital microstrip band pass filter.

A computationally efficient procedure for multiobjective design optimization with variable-fidelity models and response surface surrogates is presented. The proposed approach uses the multiobjective evolutionary algorithm that works with a fast surrogate model, obtained with kriging interpolation of the low-fidelity model data enhanced by space-mapping correction exploiting a few high-fidelity training points. The initial Pareto front generated by multiobjective optimization of the surrogate using the multiobjective evolutionary algorithm can be iteratively refined by local enhancements of the surrogate model. The latter are realized with a space-mapping response correction based on a limited number of high-fidelity training points allocated along the initial Pareto front. The proposed method allows us to obtain, at a low computational cost, a set of designs representing tradeoffs between the conflicting objectives. The current approach is illustrated using examples of airfoil design: one in transonic flow, involving aerodynamics tradeoffs; and another one in low-speed flow, involving tradeoffs between the aerodynamic and the aeroacoustic performances.

ABSTRACTThis work presents a substrate integrated waveguide (SIW) bandpass filter with wide and precipitous stopband, which is different from filters with a direct input/output coupling structure. Higher modes in the SIW cavities are used to generate the finite transmission zeros for improved stopband performance. The design of SIW filters requires full wave electromagnetic simulation and extensive optimisation. If a full wave solver is used for optimisation, the design process is very time consuming. The space mapping (SM) approach has been called upon to alleviate this problem. In this case, the coarse model is optimised using an equivalent circuit model-based representation of the structure for fast computations. On the other hand, the verification of the design is completed with an accurate fine model full wave simulation. A fourth-order filter with a passband of 12.0–12.5 GHz is fabricated on a single layer Rogers RT/Duroid 5880 substrate. The return loss is better than 17.4 dB in the passband and the rejection is more than 40 dB in the stopband. The stopband is from 2 to 11 GHz and 13.5 to 17.3 GHz, demonstrating a wide bandwidth performance.

Seepage criteria based optimal design of water retaining structures with reliability quantification utilizing surrogate model linked simulation-optimization approach

In order to minimize the number of evaluations of high-fidelity (“fine”) model in the optimization process, to increase the optimization speed, and to improve optimal solution accuracy, a robust and computational-efficient multi-fidelity local surrogate-model optimization method is proposed. Based on the principle of response surface approximation, the proposed method exploits the multi-fidelity coarse models and polynomial interpolation to construct a series of local surrogate models. In the optimization process, local region modeling and optimization are performed iteratively. A judgment factor is introduced to provide information for local region size update. The last local surrogate model is refined by space mapping techniques to obtain the optimal design with high accuracy. The operation and efficiency of the approach are demonstrated through design of a bandpass filter and a compact ultra-wide-band (UWB) multiple-in multiple-out (MIMO) antenna. The response of the optimized design of the fine model meet the design specification. The proposed method not only has better convergence compared to an existing local surrogate method, but also reduces the computational cost substantially.