Optimisation in electromagnetics with the space‐mapping technique

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.

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.

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.

A design procedure for inline waveguide extracted pole filters with all-metal E-plane inserts is presented. To achieve acceptable modeling accuracy for this class of filters, an enhanced schematic-circuit-based surrogate model is developed, accounting for parasitic effects between the neighboring elements of the structure. The proposed circuit representation is used as a coarse model in a surrogate-based optimization of the filter structure with the space mapping technique as the main engine in the optimization process. Feasibility of the modeling approach is demonstrated by two filter design examples. The examples show that a low computational cost (corresponding to a few evaluations of the high-fidelity EM simulations of the filter structure) is required to obtain an optimized design.KeywordsInline filtersE-plane filtersExtracted pole filtersWaveguideModelingSurrogate optimization

This paper presents a quick and reliable methodology for machine design. The methodology is based on Magnetic Equivalent Circuit (MEC) and multi-level, multi-objective optimization. It is applied to design three phase axial flux actuator. The MEC is solved by computing meshes' magnetic flux. It allows taking into account nonlinear operating conditions and its network topology is generated automatically for each rotor position. Multilevel optimization is achieved by means of Space Mapping (SM) method in order to couple linear and non-linear models. Multi-objective optimization problem is solved by means of NSGA-II. This methodology combines final solution accuracy and fast computation/simulation time.

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.

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.

Skull stiffness of children is of great significance to protect brain tissues during traffic accidents. In this paper, the effects of skull stiffness on traumatic brain injury (TBI) are investigated by using a validated 6-year-old child head finite element (FE) model according to Chinese standard GB/T 24550-2009 Results showed that the HIC value, intracranial pressure, Von Mises stress and shear strain of brain tissue increased with the decrease of skull stiffness during the impact of FE model with engine hood. Therefore, the injury risk of the child head decreases with the increase of skull stiffness. And the skull with higher stiffness can provide a better protection for brain tissues during traffic accidents.

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.

In this article, an irregular optimizing design method of wideband and wide-angle scanning array is proposed. The sparsity technology was first extended into the optimization of the arrangement of wideband-connected array components. By virtue of adjusting the width of the edge radiation wall, an optimal radiation distribution of a wideband array can be implemented, which also exploits more freedom of element distribution and characteristic design. Moreover, the advantage is that the connectivity between wideband antenna units and the continuity among array current distribution can be ensured. Though the optimized array layout can accomplish lower sidelobe level (SLL) with equal-amplitude excitation feed, it may also exacerbate the complexity of the mutual coupling (MC), which further affects the radiation characteristics such as bandwidth, voltage standing wave ratio (VSWR), and wide-angle scanning. Hence, the space mapping (SM) technique was introduced to accomplish the wideband irregular optimal design involving the MC effects for higher optimizing efficiency and accuracy. The genetic algorithm (GA) was incorporated with active element pattern (AEP) to further optimize the irregular array distribution for the coarse model of the SM design procedure, which involves the actual array element rather than the only array factor synthesis. A prototype array was made and measured, and the experimental results showed that the design results were in good agreement with the measurement results. Verified the efficiency of synthesizing array patterns with lower SLL and fewer Vivaldi elements in broadband and wide-angle scanning.

We invert InSAR from ascending and descending passes of ENVISAT/ASAR data to estimate the distribution of coseismic slip for the 2008 Mw 7.2 Yutian earthquake by separately using uniform finite element models (FEMs), non-uniform FEMs, and analytical elastic half-space (Okada) models. We use the Steepest Descent method and Laplacian smoothing to regularize and estimate the slip distribution for each of these different models. Fault surface ruptures interpolated from Quickbird optical images constrain the strike of the fault. The uniform FEM and Okada models assume a fault embedded in a homogeneous and elastic finite domain or half-space, respectively, while the non-uniform FEM describes a domain with spatially variable elastic properties according to the geological structure of Tibet plateau and Tarim. We find that the estimated slip distribution of the non-uniform FEM is similar to that of the uniform FEM but has a slightly larger moment (~2 %). However, more noticeable discrepancies occur between the slip distributions of the uniform FEM and Okada model, where the slip pattern estimated with the FEM looks more scattered and locates at a lower depth. We conclude that, for the case of the Yutian earthquake, the improvement brought by simulating the distribution of geologic material properties is insignificant. This suggests that the uniform geologic structure of Okada models may be sufficient for simulating large intra-continental earthquakes.

A computationally efficient procedure for design optimization of slot antennas is presented. We use space mapping as the main optimization engine, the underlying coarse model being coarse-discretization electromagnetic (EM) simulation data of the antenna structure of interest (low-fidelity model). In order to speed up the design process, the low-fidelity model is not used directly in the process; instead, the coarse-discretization simulation data - sampled only in the vicinity of their approximate optimum - are used to create an auxiliary response surface model through Bayesian support vector regression. The latter - after suitable space-mapping-based correction - serves as a prediction tool to find an accurate optimum design of the antenna. The proposed procedure is illustrated using two examples of slot antennas.

There has been a growing demand for nonlinear model updating procedures in the structural dynamics community as advanced vehicles have started to incorporate nonlinearity into their designs. Finite element (FE) model updating is difficult for a nonlinear structure for several reasons: there may be many unknown parameters in the FE model so that multiple solutions may exist, and it is very expensive to compute the structure’s nonlinear normal modes from a full FE model that are an excellent metric to use for nonlinear updating. A recent work showed that some of these challenges can be overcome by updating a nonlinear reduced order model (ROM) rather than the full FE model. The updated ROM can be used to compute response statistics, stresses and ultimately life of the structure. However, one drawback of this approach is that one does not gain physical insight into which parameters in the FE model were in error, and so it is difficult to transfer the lessons learned to future FE models. This work explores the feasibility of updating a FE model to correlate with a ROM with a set of known parameters. The target ROM parameters consist of the linear stiffness and the nonlinear stiffness coefficients which have been identified previously by updating the ROM to correlate with experimental measurements. In this process an optimization routine is setup in which the free parameters are those of the FE model, such as boundary stiffness springs, imperfections, pre-stress, etc. The optimization procedure is wrapped around a ROM creation algorithm that iteratively tunes the FE parameters, creates a ROM, and evaluates the ROM parameters with respect to the target ROM in order to minimize the objective function. This work will demonstrate the procedure on a numerical example of a curved beam in order to verify its effectiveness on the nonlinear model updating.

Modeling of ultra-high performance fiber reinforced concrete columns under eccentric loading

Partial element equivalent circuit (PEEC) is a convenient method for modeling transient behavior of high temperature superconductors (HTS) magnets made of metal-as insulation windings. In HTS coils, especially those made of tapes, screening currents are known to lower the magnetic field, to generate losses, and to contribute to the mechanical stress. Including screening current calculation in PEEC method can be achieved by subdividing the superconducting tape along its width, leading to larger models and much longer computation time. Herein, we propose a finite element (FE) model for screening currents calculation, which can be combined with PEEC model for transport current addition. The FE model is defined as thin shell using formulation with normal component of electric vector potential T as nodal variable, calculated by an iterative procedure. Source term in the FE model is obtained from variation of radial flux density. Critical current densities calculated in the FE model are fed back to the PEEC model at each step of transport current calculation. This work presents in detail the FE model and its coupling with PEEC model. The model is validated by comparison with other 3D FE models and models with axial symmetry. The effect of reducing the size of FE model, by averaging screening currents in adjacent turns, is also presented in this study. Finally, we present simulation results for current ramps and a quench of a double-pancake magnet, obtained by PEEC with and without adding FE screening current model.