Efficient multi‐fidelity design optimization of microwave filters using adjoint sensitivity

A simple and robust algorithm for computationally efficient design optimization of microwave filters is presented. Our approach exploits a trust‐region (TR)‐based algorithm that utilizes linear approximation of the filter response obtained using adjoint sensitivity. The algorithm is sequentially executed on a family of electromagnetic (EM)‐simulated models of different fidelities, starting from a coarse‐discretization one, and ending at the original, high‐fidelity filter model to be optimized. Switching between the models is determined using suitably defined convergence criteria. This arrangement allows for substantial cost reduction of the initial stages of the optimization process without compromising the accuracy and resolution of the final design. The performance of our technique is illustrated through the design of a fifth‐order waveguide filter and a coupled iris waveguide filter. We also demonstrate that the multi‐fidelity approach allows for considerable computational savings compared to TR‐based optimization of the high‐fidelity EM model (also utilizing adjoint sensitivity). © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:178–183, 2015.     

Microstructural design of composite materials using fixed-grid modeling and noise-resistant smoothed Kriging-based approximate optimization

This paper discusses a microstructural optimization of composites using a fixed-grid modeling technique and an approximate optimization approach. In particular, we design a microscopic structure of composites to improve its reliability. As the response surface becomes nonlinear and inaccuracies may be included in the sampling results in using the fixed-grid model, applicability of several approximation methods such as a polynomial-based approach, neural network, and Kriging method are investigated. Especially, the inaccuracy is regarded as a noise in sampling data, and applicability of the noise-resistant smoothed Kriging (ns-Kriging) is investigated. As an example, cross-sectional shape of fiber in a unidirectional fiber-reinforced plastics is optimized. By applying several approximate optimization methods to the problem, applicability of those methods is investigated. Next, cross-sectional shape of fibers in a composite plate subject to bending and compression is optimized using the ns-Kriging-based method. Numerical results illustrate applicability of the proposed approach.     

Phase‐spacing optimization of linear microstrip antenna arrays using simulation‐based surrogate superposition models

A technique for simulation‐driven optimization of the phase excitation tapers and spacings for linear arrays of microstrip patch antennas is presented. Our technique exploits two models of the array under optimization: an analytical model which is based on the array factor, as well as an electromagnetic (EM) simulation‐based surrogate model of the entire array. The former is used to provide initial designs which meet the design requirements imposed on the radiation response. The latter is used for tuning of the array radiation response while controlling the array reflection response as well as for validation of the final design. Furthermore, the simulation‐based surrogate model allows for subsequent evaluation of the array responses in the beam scanning operation at negligible computational costs. The simulation‐based surrogate model is constructed with a superposition of simulated radiation and reflection responses of the array under design with only one radiator active at a time. Low computational cost of the surrogate model is ensured by the EM‐simulation data computed with coarse meshes. Reliability of the model is achieved by means of suitable correction carried out with respect to the high‐fidelity array model. The correction is performed iteratively in the optimization process. Performance, numerical efficiency, and accuracy of the technique is demonstrated with radiation pattern synthesis of linear arrays comprising 32 microstrip patch antennas by phase‐spacing optimization. Properties of the optimal designs in the beam scanning operation are then studied using the superposition models and compared to suitably selected reference designs. The proposed technique is versatile as it also can be applied for simulation‐based optimization of antenna arrays comprising other types of individually fed elements. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:536–547, 2015.     

Surrogate‐assisted EM‐driven miniaturization of wideband microwave couplers by means of co‐simulation low‐fidelity models

This article proposes a methodology for rapid design optimization of miniaturized wideband couplers. More specifically, a class of circuits is considered, in which conventional transmission lines are replaced by their abbreviated counterparts referred to as slow‐wave compact cells. Our focus is on explicit reduction of the structure size as well as on reducing the CPU cost of the design process. For the sake of computational feasibility, a surrogate‐based optimization paradigm involving a co‐simulation low‐fidelity model is used. The latter is a fundamental component of the proposed technique. The low‐fidelity model represents cascaded slow‐wave cells replacing the low‐impedance lines of the original coupler circuit. It is implemented in a circuit simulator (here, ADS) and consists of duplicated compact cell EM simulation data as well as circuit theory‐based feeding line models. Our primary optimization routine is a trust‐region‐embedded gradient search algorithm. To further reduce the design cost, the system response Jacobian is estimated at the level of the low‐fidelity model, which is sufficient due to good correlation between the low‐ and high‐fidelity models. The coupler is explicitly optimized for size reduction, whereas electrical performance parameters are controlled using a penalty function approach. The presented methodology is demonstrated through the design of a 1‐GHz wideband microstrip branch‐line coupler. Numerical results are supported by experimental validation of the fabricated coupler prototype.     

Integration of topology and shape optimization for design of structural components

This paper presents an integrated approach that supports the topology optimization and CAD-based shape optimization. The main contribution of the paper is using the geometric reconstruction technique that is mathematically sound and error bounded for creating solid models of the topologically optimized structures with smooth geometric boundary. This geometric reconstruction method extends the integration to 3-D applications. In addition, commercial Computer-Aided Design (CAD), finite element analysis (FEA), optimization, and application software tools are incorporated to support the integrated optimization process. The integration is carried out by first converting the geometry of the topologically optimized structure into smooth and parametric B-spline curves and surfaces. The B-spline curves and surfaces are then imported into a parametric CAD environment to build solid models of the structure. The control point movements of the B-spline curves or surfaces are defined as design variables for shape optimization, in which CAD-based design velocity field computations, design sensitivity analysis (DSA), and nonlinear programming are performed. Both 2-D plane stress and 3-D solid examples are presented to demonstrate the proposed approach. Received January 27, 2000 Communicated by J. Sobieski     

Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique

The aim of this work is to illustrate how a space mapping technique using surrogate models together with response surfaces can be used for structural optimization of crashworthiness problems. To determine the response surfaces, several functional evaluations must be performed and each evaluation can be computationally demanding. The space mapping technique uses surrogate models, i.e. less costly models, to determine these surfaces and their associated gradients. The full model is used to correct the gradients from the surrogate model for the next iteration. Thus, the space mapping technique makes it possible to reduce the total computing time needed to find the optimal solution. First, two analytical functions and one analytical structural optimization problem are presented to exemplify the idea of space mapping and to compare the efficiency of space mapping to traditional response surface optimization. Secondly, a sub-model of a complete vehicle finite element (FE) model is used to study different objective functions in vehicle crashworthiness optimization. Finally, the space mapping technique is applied to a structural optimization problem of a large industrial FE vehicle model, consisting of 350.000 shell elements and a computing time of 100 h. In this problem the intrusion in the passenger compartment area was reduced by 32% without compromising other crashworthiness parameters.     

Climate Change: Optimization of Response Strategies

The development of climate change response strategies is expected to remain an important issue in the next few decades. The use of optimization techniques might serve as a helpful guide in this process. Although, in recent years, a number of studies have focused on optimization techniques, the optimization models do not fully employ the dynamics of climatic and economic systems. In this paper a heuristic is introduced that combines an integrated simulation model and an optimization technique (local search). This approach may be considered as a first step towards a more comprehensive and systematic analysis of climate change response strategies in a dynamic setting described by a simulation model. Results of a number of experiments in which the heuristic is applied to the integrated global assessment model TARGETS are discussed.     

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.     

Research on optimization design of the heating/cooling channels for rapid heat cycle molding based on response surface methodology and constrained particle swarm optimization

The aim of this work is to optimize the layout of the heating/cooling channels for rapid heat cycle molding with hot medium heating and coolant cooling by using response surface methodology and optimization technique. By means of a Box–Behnken experiment design technique, an experiment matrix with three factors and three levels was designed. The design variables including the diameter of the heating/cooling channels, distances from the wall of heating/cooling channel to the cavity surface and between the adjacent heating/cooling channels were used to describe the layout and shape of the heating/cooling channels. The heating efficiency, standard deviation of the cavity surface temperature and the maximum von-mises stress were considered as the model variables. Thermal response and structural strength analyses of the mold based on FEM were conducted to acquire the objective variables for combination of process parameters. Some mathematical models of response surface were created by the mixed regression model and response surface method. The analysis of variance (ANOVA) method was used to check the accuracy of the developed mathematical models. With these mathematical models, the layout of the heating/cooling channels was then optimized to minimize the required heating time within reasonable temperature distribution and structural strength of the cavity by coupling the developed response surface (RS) models with the particle swarm optimization (PSO) method.     

Piezoresistive Cantilever Performance—Part II: Optimization

Piezoresistive silicon cantilevers fabricated by ion implantation are frequently used for force, displacement, and chemical sensors due to their low cost and electronic readout. However, the design of piezoresistive cantilevers is not a straightforward problem due to coupling between the design parameters, constraints, process conditions, and performance. We systematically analyzed the effect of design and process parameters on force resolution and then developed an optimization approach to improve force resolution while satisfying various design constraints using simulation results. The combined simulation and optimization approach is extensible to other doping methods beyond ion implantation in principle. The optimization results were validated by fabricating cantilevers with the optimized conditions and characterizing their performance. The measurement results demonstrate that the analytical model accurately predicts force and displacement resolution, and sensitivity and noise tradeoff in optimal cantilever performance. We also performed a comparison between our optimization technique and existing models and demonstrated eight times improvement in force resolution over simplified models.$hfill$ [2009-0105]      

Comparison of global and local response surface techniques in reliability-based optimization of composite structures

This paper discusses the development and application of two alternative strategies, in the form of global and sequential local response surface (RS) techniques, for the solution of reliability-based optimization (RBO) problems. The problem of a thin-walled composite circular cylinder under axial buckling instability is used as a demonstrative example. In this case, the global technique uses a single second-order RS model to estimate the axial buckling load over the entire feasible design space (FDS), whereas the local technique uses multiple first-order RS models, with each applied to a small subregion of the FDS. Alternative methods for the calculation of unknown coefficients in each RS model are explored prior to the solution of the optimization problem. The example RBO problem is formulated as a function of 23 uncorrelated random variables that include material properties, the thickness and orientation angle of each ply, the diameter and length of the cylinder, as well as the applied load. The mean values of the 8 ply thicknesses are treated as independent design variables. While the coefficients of variation of all random variables are held fixed, the standard deviations of the ply thicknesses can vary during the optimization process as a result of changes in the design variables. The structural reliability analysis is based on the first-order reliability method with the reliability index treated as the design constraint. In addition to the probabilistic sensitivity analysis of the reliability index, the results of the RBO problem are presented for different combinations of cylinder length and diameter and laminate ply patterns. The two strategies are found to produce similar results in terms of accuracy, with the sequential local RS technique having a considerably better computational efficiency.     

Multi-objective optimization design of a complex building based on an artificial neural network and performance evaluation of algorithms

While optimization studies focusing on real-world buildings are somewhat limited, many building optimization studies to date have used simple hypothetical buildings for the following three reasons: (1) the shape and form of real buildings are complex and difficult to mathematically describe; (2) computer models built based on real buildings are computationally expensive, which makes the optimization process time-consuming and impractical and (3) although algorithm performance is crucial for achieving effective building performance optimization (BPO), there is a lack of agreement regarding the proper selection of optimization algorithms and algorithm control parameters. This study applied BPO to the design of a newly built complex building. A number of design variables, including the shape of the building’s eaves, were optimized to improve building energy efficiency and indoor thermal comfort. Instead of using a detailed simulation model, a surrogate model developed by an artificial neural network (ANN) was used to reduce the computing time. In this study, the performance of four multi-objective algorithms was evaluated by using the proposed performance evaluation criteria to select the best algorithm and parameter values for population size and number of generations. The performance evaluation results of the algorithms implied that NSGA-II (with a population size and number of generations of 40 and 45, respectively) performed the best in the case study. The final optimal solution significantly improves building performance, demonstrating the success of the BPO technique in solving complex building design problems. In addition, the findings on the performance evaluation of the algorithms provide guidance for users regarding the selection of suitable algorithms and parameter settings based on the most important performance criteria.     

Rapid design optimization of antennas using space mapping and response surface approximation models

A computationally efficient method for design optimization of antennas is discussed. It combines space mapping, used as the optimization engine, and response surface approximation, used to create the fast surrogate model of the optimized antenna. The surrogate is configured from the response of the coarse‐mesh electromagnetic model of the antenna, and implemented through kriging interpolation. We provide a comprehensive numerical verification of this technique as well as demonstrate its capability to yield a satisfactory design after a few full‐wave simulations of the original structure. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

Improved trust‐region gradient‐search algorithm for accelerated optimization of wideband antenna input characteristics

Full‐wave electromagnetic (EM) simulation models are ubiquitous in carrying out design closure of antenna structures. Yet, EM‐based design is expensive due to a large number of analyses necessary to yield an optimized design. Computational savings can be achieved using, for example, adjoint sensitivities, surrogate‐assisted procedures, design space dimensionality reduction, or similar sophisticated means. In this article, a simple modification of a rudimentary trust‐region‐embedded gradient search with numerical derivatives is proposed for reduced‐cost optimization of input characteristics of wideband antennas. The approach exploits information and history of relative changes of the design (as compared with the trust region size) during algorithm iterations to control the updates of components of the antenna response Jacobian, specifically, to execute them only if necessary. It is demonstrated that the proposed framework may lead to over 50% savings over the reference algorithm with only minor degradation of the design quality, specifically, up to 0.3 dB (or <3%). Numerical results are supported by experimental validation of the optimized antenna designs. The presented algorithm can be utilized as a stand‐alone optimization routine or as a building block of surrogate‐assisted procedures.     

Fast simulation‐driven antenna design using response‐feature surrogates

In this article, a computationally efficient procedure for electromagnetic (EM)‐simulation‐driven design of antennas is presented. Our methodology is based on local approximation models of the antenna response, established using a set of suitably selected characteristic features rather than the entire response (such as reflection versus frequency). The approximation model is utilized to verify the level of satisfying/violating given performance requirements, and to guide the optimization process towards a better design. By exploiting the fact that the dependence of the response features on the designable parameters of the antenna of interest is simple (close to linear or quadratic), the feature‐based optimization converges faster than conventional optimization of frequency‐based EM‐simulated responses. In order to further speed up the design, coarse‐discretization simulations are utilized to estimate the feature gradients with respect to adjustable parameters of the problem at hand. The optimization algorithm is embedded in the trust‐region framework for safeguarding convergence. The proposed technique is demonstrated using two antenna examples. In both the cases, the optimum design is obtained at the computational cost corresponding to a few high‐fidelity EM antenna simulations. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:394–402, 2015.     

基于参考模型法的双闭环调速系统参数优化

调节器是双闭环调速系统的核心,传统的工程设计方法不仅烦琐、复杂,而且不够精确.为解决上述问题,提出了基于参考模型法的调节器参数优化方法:首先根据系统指标要求选择典型的最佳模型作为参考,然后以改进单纯形法为优化算法,通过比较控制系统和参考模型在同一输入信号下的输出偏差对调节器参数进行优化,使得在某种意义下偏差尽可能小,实现控制系统的输出响应跟踪或逼近参考模型特征.实验表明,方法不仅使设计工作大为简化,并且使控制系统较好地复现参考模型的特征,有效地提高了系统的性能.     

Efficient multi-criteria optimization on noisy machine learning problems

Recent research revealed that model-assisted parameter tuning can improve the quality of supervised machine learning (ML) models. The tuned models were especially found to generalize better and to be more robust compared to other optimization approaches. However, the advantages of the tuning often came along with high computation times, meaning a real burden for employing tuning algorithms. While the training with a reduced number of patterns can be a solution to this, it is often connected with decreasing model accuracies and increasing instabilities and noise. Hence, we propose a novel approach defined by a two criteria optimization task, where both the runtime and the quality of ML models are optimized. Because the budgets for this optimization task are usually very restricted in ML, the surrogate-assisted Efficient Global Optimization (EGO) algorithm is adapted. In order to cope with noisy experiments, we apply two hypervolume indicator based EGO algorithms with smoothing and re-interpolation of the surrogate models. The techniques do not need replicates. We find that these EGO techniques can outperform traditional approaches such as latin hypercube sampling (LHS), as well as EGO variants with replicates.     

轨道扣件弹性垫板结构优化设计

采用OptiStruct对某型铁路扣件轨下垫板进行拓扑优化和自由形状优化,实现垫板结构轻量化设计.根据优化空间最大化原则,对垂向载荷工况进行拓扑优化、对极限载荷工况进行自由形状优化.使用Abaqus极限载荷扣件系统仿真模型对优化后垫板结构性能进行验证评价.结果表明:优化后的垫板性能基本不变,质量减少约10%,刚度满足设计要求.优化结果可为垫板轻量化设计提供参考.     

Using surrogate models and response surfaces in structural optimization – with application to crashworthiness design and sheet metal forming

The aim of this paper is to determine if the Space Mapping technique using surrogate models together with response surfaces is useful in the optimization of crashworthiness and sheet metal forming. In addition, the efficiency of optimization using Space Mapping will be compared to traditional structural optimization using the Response Surface Methodology (RSM). Five examples are used to study the algorithm: one optimization of an analytic function and four structural optimization problems. All examples are constrained optimization problems. In all examples, the algorithm converged to an improved design with all constraints fulfilled, even when a conventional RSM optimization failed to converge. For the crashworthiness design problems, the total computing time for convergence was reduced by 53% using Space Mapping compared to conventional RSM. For the sheet metal forming problems the total computing time was reduced by 63%. The conclusions are that optimization using Space Mapping and surrogate models can be used for optimization in crashworthiness design and sheet metal forming applications with a significant reduction in computing time.