A space-mapping interpolating surrogate algorithm for highly optimized EM-based design of microwave devices

We justify and elaborate in detail on a powerful new optimization algorithm that combines space mapping (SM) with a novel output SM. In a handful of fine-model evaluations, it delivers for the first time the accuracy expected from classical direct optimization using sequential linear programming. Our new method employs a space-mapping-based interpolating surrogate (SMIS) framework that aims at locally matching the surrogate with the fine model. Accuracy and convergence properties are demonstrated using a seven-section capacitively loaded impedance transformer. In comparing our algorithm with major minimax optimization algorithms, the SMIS algorithm yields the same minimax solution within an error of 10/sup -15/ as the Hald-Madsen algorithm. A highly optimized six-section H-plane waveguide filter design emerges after only four HFSS electromagnetic simulations, excluding necessary Jacobian estimations, using our algorithm with sparse frequency sweeps.     

A Space-Mapping Framework for Engineering Optimization—Theory and Implementation

This paper presents a comprehensive approach to engineering design optimization exploiting space mapping (SM). The algorithms employ input SM and a new generalization of implicit SM to minimize the misalignment between the coarse and fine models of the optimized object over a region of interest. Output SM ensures the matching of responses and first-order derivatives between the mapped coarse model and the fine model at the current iteration point in the optimization process. We provide theoretical results that show the importance of the explicit use of sensitivity information to the convergence properties of our family of algorithms. Our algorithm is demonstrated on the optimization of a microstrip bandpass filter, a bandpass filter with double-coupled resonators, and a seven-section impedance transformer. We describe the novel user-oriented software package SMF that implements the new family of SM optimization algorithms.     

新型高收敛隐式空间映射算法设计微波滤波器

该文介绍了一种高收敛隐式空间映射算法,改进了隐式空间映射算法中粗糙模型到精细模型之间参数映射。它加入粗糙模型参数选择过程,避免了粗糙模型优化中的假收敛情况,加快精细模型与设计目标的逼近速度。参数选择过程不需要增加精细模型的计算次数,提高了优化效率。该文通过设计一个发卡形滤波器,并与以前的隐式空间映射算法计算结果进行比较,优化得到了比指标性能更优越的结果。同时证明了新算法比旧算法具有更快的逼近速度和更高的优化效率的优点。     

TLM-based modeling and design exploiting space mapping

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 space-mapping design framework

We present a comprehensive microwave design framework for implementing the original, aggressive, implicit, and response residual space-mapping (SM) approaches through widely available software. General steps and tools for possible SM implementations are elaborated. Our presentation is a reference guide for microwave designers using the SM technique. An instructive "multiple cheese-cutting" example demonstrates the SM approach to engineering design and some possible pitfalls. For the first time, an ADS framework implements the SM steps interactively. A three-section transformer example illustrates the approach, step by step. A six-section H-plane waveguide filter design emerges after four iterations, using the implicit SM and the response-residual space-mapping (RRSM) optimization entirely within the design framework. An RRSM surrogate is developed to match the fine (HFSS) model. We use sparse frequency sweeps and do not require Jacobians of the fine model.     

采用快速空间映射算法多模超宽带滤波器有效设计方法

文章用快速空间映射算法（ASM）来优化和设计多模（MMR）超宽带滤波器。快速空间映射算法需要一个粗糙物理模型以及一个精确物理模型。文中用MATLAB来建立粗糙物理模型,使用商业仿真软件HFSS10来建立精确物理模型。快速空间映射算法就是用来找到粗糙模型和精确模型之间的映射关系,从而达到快速和精准设计超宽带滤波器的目的。     

改进的隐式空间映射算法的研究

介绍了一种快速收敛空间映射算法,改进了隐式空间映射算法中粗糙模型到精细模型之间参数映射。通过增加限定参数提取的方式,减少粗糙模型的参数空间而实现粗糙模型响应高效准确逼近精细模型响应。通过设计一个交叉耦合滤波器,与之前的隐式空间算法进行比较,更容易达到优化目标,证明了限定参数提取算法具有更快的逼近速度和更高的优化效率的优点。     

EM-based optimization exploiting partial space mapping and exact sensitivities

We present a family of robust techniques for exploiting sensitivities in electromagnetic (EM)-based circuit optimization through space mapping (SM) technology. We utilize derivative information for parameter extractions and mapping updates. We exploit a partial SM (PSM) concept, where a reduced set of parameters is sufficient for parameter extraction optimization. It reflects the idea of tuning and execution time is reduced. Upfront gradients of both EM (fine) model and coarse surrogates can initialize possible mapping approximations. We introduce several effective approaches for updating the mapping during the optimization iterations. Examples include the classical Rosenbrock function, modified to illustrate the approach, a two-section transmission-line 10:1 impedance transformer and a microstrip bandstop filter with open stubs.     

Space-Mapping Optimization With Adaptive Surrogate Model

The proper choice of mapping used in space-mapping optimization algorithms is typically problem dependent. The number of parameters of the space-mapping surrogate model must be adjusted so that the model is flexible enough to reflect the features of the fine model, but at the same time is not over flexible. Its extrapolation capability should allow the prediction of the fine model response in the neighborhood of the current iteration point. A wrong choice of space-mapping type may lead to poor performance of the space-mapping optimization algorithm. In this paper, we consider a space-mapping optimization algorithm with an adaptive surrogate model. This allows us to adjust the type of space-mapping surrogate model used in a given iteration based on the approximation/extrapolation capability of the model. The technique does not require any additional fine model evaluations     

An explicit knowledge-embedded space mapping technique and its application to optimization of LTCC RF passive circuits

A novel explicit knowledge embedded space mapping (SM) optimization technique is presented in this paper. It generalizes the implementation procedure of the efficient SM technique by introducing a buffer space called embedded knowledge space between the original coarse model space and the fine model space, where the ingredients of the coarse model space can be completely different from those of the fine model space. Therefore, this generic scheme can be used to map the coarse model space of arbitrary physical content to the fine model space of different physical content through the embedded knowledge space that is built up with the available radio frequency (RF) circuit CAD formula. The emphasis of the application of the proposed scheme is put on the design of low temperature cofired ceramic (LTCC) RF passive circuits in this paper, along with the required CAD formulas (knowledge) for typical embedded multilayer passives. The effectiveness of the proposed new scheme is demonstrated through two design examples of LTCC lumped element band pass filters for wireless applications. The detailed procedure and flowchart of the proposed implementation scheme are also given in the paper.     

基于空间映射的RF MEMS 开关建模研究

空间映射的思想是通过构造粗糙模型设计变量与精确模型设计变量之间的映射关系,获得合适的替代模型（校准后的粗糙模型）,从而简化优化过程。本文针对电容耦合式RF MEMS 开关使用初始空间映射算法进行计算和优化,经过迭代,建立了精确空间和粗糙空间的映射关系,最终得到了精确空间优化设计值,利用此映射关系,可将精确空间的优化工作放到粗糙空间进行,从而大大节省时间和电脑资源。计算结果验证了该方法的可行性和高效性。     

Interpolated Coarse Models for Microwave Design Optimization With Space Mapping

The efficiency of space-mapping optimization depends on the quality of the underlying coarse model, which should be sufficiently close to the fine model and cheap to evaluate. In practice, available coarse models are often cheap, but inaccurate (e.g., a circuit equivalent of the microwave structure) or accurate, but too expensive (e.g., a coarse-mesh model). In either case, the space-mapping optimization process exhibits substantial computational overhead due to the excessive fine model evaluations necessary to find a good solution if the coarse model is inaccurate, or due to the cost of the parameter extraction and surrogate optimization sub-problems if the coarse model is too expensive. In this paper, we use an interpolation technique, which allows us to create coarse models that are both accurate and cheap. This overcomes the accuracy/cost dilemma described above, permitting significant reduction of the space-mapping optimization time. Examples verify the performance of our approach.     

基于空间映射算法的微带滤波器优化设计

考虑到传统电磁优化仿真方法的低效性,在原始空间映射算法的基础上,构造一种有效的输入一输出空间映射算法,并用于优化设计一个微带带通滤波器,其替代模型和精确模型分别采用了基于电路原理的AgilentADS和基于矩量法的全波电磁仿真软件FEKO进行计算分析。仿真结果表明,该算法能够有效增加所设计器件的优化自由度,大大减少计算机优化时间,有效提高了微波器件的设计效率。     

Enhancing the Convergence Speed of Space Mapping Technique in Cylinder Conformal Antennas Optimization

Space mapping (SM) technique is applied in conformal antenna design. The main idea of this technique is to map the coarse model of a planar layer structure microstip antenna to fine structure of a conformal antenna including platform through space mapping. This technique is very suitable for conformal antenna optimization where long computational time is required to achieve an accurate solution. As the convergence speed of this technique is related to the response functions, some response functions are researching for accelerating the optimization. Two examples are studied to validate the advantages of the feasible response functions for accelerating the convergence speed of SM technique.     

Efficient Design Centering of High-Frequency Integrated Continuous-Time Filters

We apply ldquospace-mappingrdquo optimization for design centering high-frequency integrated continuous-time filters. By appropriately choosing the coarse model, a significant simplification of the space mapping technique is possible, since the coarse model design space is almost a translated version of the fine model design space. Graphical intuition is given for the simplified technique. A design example of a fifth-order 71.4-500-MHz constant-C scaled G_m-C Chebyshev ladder filter is presented. Measurement results from fabricated ICs are given.     

多目标神经空间映射算法优化设计微带滤波器

提出了一种多目标形式的空间映射算法,并将其应用于微带滤波器的优化设计问题.该算法没有采用ADS仿真软件进行粗糙模型的计算,而是采用多目标粒子群算法结合矩阵数值计算的形式,优化计算微带线的S参数,并应用神经网络映射粗糙模型与精确模型的仿真结果,由粗糙模型和神经网络推测出精确模型的帕累托最优解集.     

Segmentation of prostate boundaries from ultrasound images using statistical shape model

This paper presents a statistical shape model for the automatic prostate segmentation in transrectal ultrasound images. A Gabor filter bank is first used to characterize the prostate boundaries in ultrasound images in both multiple scales and multiple orientations. The Gabor features are further reconstructed to be invariant to the rotation of the ultrasound probe and incorporated in the prostate model as image attributes for guiding the deformable segmentation. A hierarchical deformation strategy is then employed, in which the model adaptively focuses on the similarity of different Gabor features at different deformation stages using a multiresolution technique, i.e., coarse features first and fine features later. A number of successful experiments validate the algorithm.     

Combining Global and Local Surrogate Models to Accelerate Evolutionary Optimization

In this paper, we present a novel surrogate-assisted evolutionary optimization framework for solving computationally expensive problems. The proposed framework uses computationally cheap hierarchical surrogate models constructed through online learning to replace the exact computationally expensive objective functions during evolutionary search. At the first level, the framework employs a data-parallel Gaussian process based global surrogate model to filter the evolutionary algorithm (EA) population of promising individuals. Subsequently, these potential individuals undergo a memetic search in the form of Lamarckian learning at the second level. The Lamarckian evolution involves a trust-region enabled gradient-based search strategy that employs radial basis function local surrogate models to accelerate convergence. Numerical results are presented on a series of benchmark test functions and on an aerodynamic shape design problem. The results obtained suggest that the proposed optimization framework converges to good designs on a limited computational budget. Furthermore, it is shown that the new algorithm gives significant savings in computational cost when compared to the traditional evolutionary algorithm and other surrogate assisted optimization frameworks     

Space Mapping With Multiple Coarse Models for Optimization of Microwave Components

The performance of space mapping (SM) optimization algorithms depends primarily on the quality of the underlying coarse model. Models available in the microwave area can be cheap but inaccurate or accurate but too expensive. Here, we consider a multicoarse-model technique that allows us to combine the merits of both types of coarse models to substantially reduce the overall computational cost of optimization in comparison to traditional SM.     

交指型MEMS滤波器的优化设计

交指型微机电系统(MEMS)滤波器是采用MEMS工艺制备出的交指型结构滤波器,针对交指型MEMS滤波器电磁优化算法中存在速度慢,占用计算资源大等问题,对交指型MEMS滤波器优化设计方法进行了研究。采用主动空间映射算法,在ADS和HFSS软件中建立滤波器电路结构模型和三维结构电磁模型,并分别将它们用于主动空间映射算法所需的粗糙仿真和精确仿真,仅进行了5次精确仿真就完成了一款Ku波段滤波器的优化设计。结果表明,设计的滤波器中心频率为14 GHz,顶部损耗为1.6 dB,-1 dB带宽为2.2 GHz,满足设计指标要求,同时验证了优化设计方法的可行性。