Robust topology optimization of phononic crystals with random field uncertainty

The uncertain spatial variation of material properties can remarkably affect the band gap characteristics of phononic crystals (PnCs). It is necessary to consider this issue when designing and manufacturing PnC materials/structures. This paper investigates a robust topology optimization method for designing the microstructures of PnCs by considering random‐field material properties. Herein, the spatial distribution of the material properties is first represented by a random field and then discretized into uncorrelated stochastic variables with the expansion optimal linear estimation method; stochastic band gap analysis is then conducted with polynomial chaos expansion. Furthermore, a robust topology optimization formulation of PnCs is proposed on the basis of the relative elemental density, where a weighted objective function handles the compromise of the mean value and standard deviation of the PnC band gap. The band gap response is analyzed, employing the finite element method for each sample of polynomial chaos expansion. In this context, the sensitivities of the stochastic band gap behaviors to the design variables are also derived. Numerical examples demonstrate that the proposed method can generate meaningful optimal topologies of PnCs with a relatively large width and less sensitive band gap. Additionally, the effects of the weight factors in the objective function and the variation coefficient of material properties are discussed.     

基于蚁群算法的光学膜系初始结构优化设计

本文在分析和研究蚁群算法原理、算法实现过程的基础上,针对多膜料设计,以1200～1600nm波段内带通滤波器、1200～1600nm波段内截止滤波器、600～1000nm波段内截止滤波器和400～800nm波段内截止滤波器等4个滤波器实例为优化对象,以理论反射率和实际反射率之差最小为目标函数,采用蚁群算法和MATLAB语言编制了膜系初始结构优化设计的仿真计算程序,计算机仿真结果准确,证明了蚁群算法应用于膜系设计的可行性.     

Synthesis and applications of new left handed microstrip lines with complementary split-ring resonators etched on the signal strip

A new type of left handed microstrip lines implemented by means of complementary split-ring resonators (CSRRs) is proposed. The CSRRs are etched on the signal strip alternating with series gaps. Additionally, shunt connected stubs are introduced for the first time to the previous structure. The combination of these three elements, that is, the series gaps, the CSRR and the shunt inductance, enhances design flexibility. By this means, the ground plane is left unaltered and narrow band artificial transmission lines with good performance and compact dimensions can be synthesised. The lumped element equivalent circuit model of the structure is proposed and validated. To demonstrate the applicability of these new left handed transmission lines, two compact microwave components have been designed and fabricated: (i) a narrow band power divider and (ii) a band pass filter. The resulting power divider is 75% smaller than the conventional implementation and 50% smaller than previous power dividers implemented by means of CSRRs. The band pass filter performance is comparable to that of previous CSRR-based filters with ground plane etching, whereas its size is smaller. This work represents a significant progress on the design of microwave components based on CSRRs, that is, the approach is opened to those systems where the ground plane cannot be etched.     

Filters in topology optimization based on Helmholtz‐type differential equations

The aim of this paper is to apply a Helmholtz‐type partial differential equation as an alternative to standard density filtering in topology optimization problems. Previously, this approach has been successfully applied as a sensitivity filter. The usual filtering techniques in topology optimization require information about the neighbor cells, which is difficult to obtain for fine meshes or complex domains and geometries. The complexity of the problem increases further in parallel computing, when the design domain is decomposed into multiple non‐overlapping partitions. Obtaining information from the neighbor subdomains is an expensive operation. The proposed filter technique requires only mesh information necessary for the finite element discretization of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz‐type differential equation with homogeneous Neumann boundary conditions. The properties of the filter are demonstrated for various 2D and 3D topology optimization problems in linear elasticity, solved on serial and parallel computers. Copyright © 2010 John Wiley & Sons, Ltd.     

A polynomial‐based method for topology optimization of phononic crystals with unknown‐but‐bounded parameters

The design and analysis of phononic crystals (PnCs) are generally based on the deterministic models without considering the effects of uncertainties. However, uncertainties that existed in PnCs may have a nontrivial impact on their band structure characteristics. In this paper, a sparse point sampling–based Chebyshev polynomial expansion (SPSCPE) method is proposed to estimate the extreme bounds of the band structures of PnCs. In the SPSCPE, the interval model is introduced to handle the unknown‐but‐bounded parameters. Then, the sparse point sampling scheme and the finite element method are used to calculate the coefficients of the Chebyshev polynomial expansion. After that, the SPSCPE method is applied for the band structure analysis of PnCs. Meanwhile, the checkerboard and hinge phenomena are eliminated by the hybrid discretization model. In the end, the genetic algorithm is introduced for the topology optimization of PnCs with unknown‐but‐bounded parameters. The specific frequency constraint is considered. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.     

基于EBG结构的基片集成波导超宽带带通滤波器

为拓展带通滤波器的通带带宽,设计了一种基于EBG结构的基片集成波导（SIW）超宽带带通滤波器．该滤波器利用箭头形电磁带隙结构的阻波特性,将不同大小箭头形结构单元蚀刻在SIW上金属面,以获得超宽带通带．所设计的滤波器中心频率在985 GHz,相对带宽为3959%,通带内的最大插入损耗约为154 dB,相比于类似结构的带通滤波器,其带内回波损耗较大,且整体电路面积较小．测量结果与仿真结果基本吻合,有效地验证了该设计方法的有效性．     

A Robust Framework for Multi‐Response Surface Optimization Methodology

A robust multi‐response optimization framework is proposed for simultaneously optimizing multiple conflicting quality characteristics. Unlike prior methods, the proposed approach is insensitive to subjective inputs like target specifications and improves optimization process for correlated responses. The effectiveness of the proposed approach is demonstrated and compared with existing methods considering two examples from the literature. The proposed method yields similar results consistently for different assigned target values demonstrating repeatability of the model, hence demonstrating insensitivity to assigned subjective target values. Furthermore, the study also considers multiple correlated design characteristics issue to achieve better trade‐off during design optimization. Copyright © 2013 John Wiley & Sons, Ltd.     

Wide-field-of-view GaAs/AlxOy one-dimensional photonic crystal filter

The design, fabrication, and characterization of a one-dimensional photonic crystal optical filter that has a relatively narrow, flat-topped passband within a wide stop band and small angular sensitivity is presented. The filter is based on a one-dimensional photonic crystal structure that has multiple defects, facilitating simultaneous minimization of the angular sensitivity and optimization of the passband's characteristics. We use epitaxially grown and selectively oxidized GaAs/AlxOy multilayers to achieve a high-index-contrast material system and incorporate the experimentally determined optical and material properties into the design of the device. A flat-topped bandpass filter with a bandwidth of 65 nm and a wide field of view of 50 degrees is experimentally characterized and compared with the design predictions.     

An integration design optimization framework of robust design,axiomatic design,and reliability‐based design

Robust design, axiomatic design, and reliability‐based design provide effective approaches to deal with quality problems, and their integration will achieve better quality improvement. An integration design optimization framework of robust design, axiomatic design, and reliability‐based design is proposed in this paper. First, the fitted response model of each quality characteristic is obtained by response surface methodology and the mean square error (MSE) estimation is given by a second‐order Taylor series approximation expansion. Then the multiple quality characteristics robust design model is developed by the MSE criteria. Finally, the independence axiom constraints for decoupling and reliability constraints are integrated into the multiple quality characteristics robust design model, and the integration design optimization framework is formulated, where the weighted Tchebycheff approach is adopted to solve the multiple objective programming. An illustrative example is presented at the end, and the results show that the proposed approach can obtain better trade‐offs among conflicting quality characteristics, variability, coupling degree and reliability requirements. Copyright © 2011 John Wiley & Sons, Ltd.     

An effective approach for wavelet lifting based on filter optimization and median operator

In JPEG2000, the Cohen–Daubechies–Feauveau (CDF) 9/7‐tap wavelet filter implemented by using the conventional lifting scheme has two problems. The first problem is that the filter coefficients are remaining complex; second, the conventional lifting scheme ignores image edges in the coding process. In this article, we propose an effective wavelet lifting scheme to solve these problems. For this purpose, we design the optimal 9/7‐tap wavelet filters in two steps. In the first step, we select the appropriate filter coefficients; in the second step, we employ a median operator to consider image edges. Experimental results from using the median lifting scheme and combining filter optimization and median lifting show that our proposed methods outperform the well‐known CDF 9/7‐tap wavelet filter of JPEG2000 on edge‐dominant images. © 2010 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 20, 359–366, 2010     

Ultrabroad Band Microwave Absorption of Carbonized Waxberry with Hierarchical Structure

Developing microwave absorption materials with broadband and lightweight characters is of great significance. However, it is still a great challenge for carbonized biomass without loading magnetic particles to cover the broad microwave frequency. Herein, it is proposed to carbonize freeze‐dried waxberry to make full use of its natural hierarchical gradient structure to target the ultrabroad band microwave absorption. The carbonized freeze‐dried waxberry shows radial‐gradient and hierarchical structure. The different components of hierarchical waxberry demonstrate gradient dielectric properties: the outer component shows anisotropic dielectric constants with smaller value, while the inner core shows higher dielectric constants. This gradient dielectric property is beneficial to the impedance matching and strong polarization. As a result, the bandwidth of carbonized waxberry exhibits an ultrabroad band microwave absorption, ranging from 1 to 40 GHz with the reflection loss value below ?8 dB. Meanwhile, the bandwidth can cover from 8 to 40 GHz when the reflection loss is below ?15 dB. The ultrabroad microwave absorption is attributed to the hierarchical radial‐gradient structure of carbonized waxberry, which provides good impedance matching with air media. This achievement paves the way for the exploitation of natural hierarchical biomass as a superlight and broadband high‐performance microwave absorption material.     

Notch filters with novel microstrip, triangle-type resonators

A novel notch filter is designed and fabricated using novel microstrip, triangle-type resonators. The main advantage of the new notch filter is superior microwave characteristics in increasing the frequency of the third harmonic response, as demonstrated in simulations using fullwave electromagnetic (EM) simulators. The novel notch filter is demonstrated using the following frequency characteristics: central frequency f/sub 0/ = 1.975 GHz, a 3 dB bandwidth of 39.5%, and an insertion loss S/sub 21/ of -54.273 dB. The experimental and simulation results closely correspond to each other. The superior features of the proposed filter make it suitable for use in microwave communication systems and other applications.     

Design and implementation of microwave multi-band/multi-level filters using equal-length transmission lines and Yule?Walker scheme

A new method to design microwave filter with multiple-band/multiple-level response is proposed. The modified Yule?Walker equation is used to define the frequency-domain response of filter in the Z domain. To implement a filter having transfer function in the Z domain, an equal-length transmission-line configuration is employed to emulate the filter. A band-pass filter a dual-band band-pass filter and a dual-level band-pass filter are implemented and their frequency responses are measured to illustrate the validity of this design method.     

Evolutionary topology optimization using design space adjustment based on fixed grid

Design space optimization for topology based on fixed grid is proposed and its superiority to conventional topology optimization is shown. In the conventional topology optimization, the design domain is fixed. It is, however, desirable to make the design domain evolve into a better one during optimization process by increasing or decreasing the number of design pixels or variables, which we call design space optimization. A breakthrough in obtaining sensitivities when design space expands has been made recently with necessary mathematical background, but due to coupling effect and others, sensitivity results have not been satisfactory. Three innovative implementations are developed in this paper. Firstly, the proper characteristics of artificial material are defined. The second one is to decouple neighbouring elements for exact design space sensitivities. The previous design space optimization has been tedious because only one layer can be added. So, the third innovation is a new expansion strategy with multi‐layers based on design space sensitivities. As a result, the proposed evolutionary method can get an optimum much faster than ever before especially for large‐scale problems. It is also conjectured that this gives higher probability of getting the global optimum, as confirmed by numerical examples. Copyright © 2005 John Wiley & Sons, Ltd.     

Low‐cost response surface methods from simulation optimization

We propose ‘low‐cost response surface methods’ (LCRSMs) that typically require half the experimental runs of standard response surface methods based on central composite and Box Behnken designs, but yield comparable or lower modeling errors under realistic assumptions. In addition, the LCRSMs have substantially lower modeling errors and greater expected savings compared with alternatives with comparable numbers of runs, including small composite designs and computer‐generated designs based on popular criteria such as D‐optimality. The LCRSM procedures appear to be the first experimental design methods derived as the solution to a simulation optimization problem. Together with modern computers, simulation optimization offers unprecedented opportunities for applying clear, realistic multicriterion objectives and assumptions to produce useful experimental design methods. We compare the proposed LCRSMs with alternatives based on six criteria. We conclude that the proposed methods offer attractive alternatives when the experimenter is considering dropping factors to use standard response surface methods or would like to perform relatively few runs and stop with a second‐order model. Copyright © 2002 John Wiley & Sons, Ltd.     

Synthesis of the low-temperature co-fired ceramic bandpass filters and diplexer with transmission zeros

The multilayered microwave filters are developed with the assistance of two transmission zeros. Besides a coupled line connected to one capacitor, another capacitor cross coupled between the source and load ports is utilised for the proposed filters. By properly adjusting the coupling coefficients between the coupled line and two capacitors, two transmission zeros would appear on the lower side, the higher side or on both sides of the passband skirt. Thus, the characteristics can be employed for diplexers or dual-band filters to make dual-mode portable telephones. Moreover, to miniaturise the circuit sizes and improve their performances, multilayered structure and the low-temperature co-fired ceramic technology are adopted for filter fabrication. The theorem of filter synthesis and procedures of filter design are also presented. Finally, the proposed structure is validated by an agreement between measured results of fabricated filters and the electromagnetic simulation.     

FRM滤波器中应用积分梳状滤波器的研究

传统的频率响应屏蔽(Frequency Response Masking,FRM)滤波器由多个含有乘法器的滤波器构成,计算复杂度较高。提出了一种改进窄带低通FRM数字滤波器设计复杂度的方法,使用积分梳状滤波器作为屏蔽滤波器,以达到设计窄过渡带的滤波器的要求。仿真结果表明,在降低窄带低通FRM滤波器计算复杂度方面效果明显,有效地减少了乘法器的使用,降低了目标滤波器设计的阶数。该方法可以应用于窄过渡FRM数字滤波器的设计中。     

Automated structural optimization system for integrated topology and shape optimization

Abstract

This paper combines previously developed techniques for image‐preprocessing and characteristic image‐interpreting together with a newly proposed automated shape‐optimization modeling technique into an integrated topology‐optimization and shape‐optimization system. As a result, structure designers are provided with an efficient and reliable automated structural optimization system (ASOS). The automated shape‐optimization modeling technique, the key technique in ASOS, uses hole‐expanding strategy, interference analysis, and hole shape‐adjusting strategy to automatically define the design variables and side constraints needed for shape optimization. This technique not only eliminates the need to manually define design variables and side constraints for shape optimization, but during the process of shape optimization also prevents interference between the interior holes and the exterior boundary. The ASOS is tested in three different structural configuration design examples.     

ASRSM: A Sequential Experimental Design for Response Surface Optimization

Most preset response surface methodology (RSM) designs offer ease of implementation and good performance over a wide range of process and design optimization applications. These designs often lack the ability to adapt the design on the basis of the characteristics of application and experimental space so as to reduce the number of experiments necessary. Hence, they are not cost‐effective for applications where the cost of experimentation is high or when the experimentation resources are limited. In this paper, we present an adaptive sequential response surface methodology (ASRSM) for industrial experiments with high experimentation cost, limited experimental resources, and high design optimization performance requirement. The proposed approach is a sequential adaptive experimentation approach that combines concepts from nonlinear optimization, design of experiments, and response surface optimization. The ASRSM uses the information gained from the previous experiments to design the subsequent experiment by simultaneously reducing the region of interest and identifying factor combinations for new experiments. Its major advantage is the experimentation efficiency such that for a given response target, it identifies the input factor combination (or containing region) in less number of experiments than the classical single‐shot RSM designs. Through extensive simulated experiments and real‐world case studies, we show that the proposed ASRSM method outperforms the popular central composite design method and compares favorably with optimal designs. Copyright © 2012 John Wiley & Sons, Ltd.     

An enhanced genetic algorithm for structural topology optimization

Genetic algorithms (GAs) have become a popular optimization tool for many areas of research and topology optimization an effective design tool for obtaining efficient and lighter structures. In this paper, a versatile, robust and enhanced GA is proposed for structural topology optimization by using problem‐specific knowledge. The original discrete black‐and‐white (0–1) problem is directly solved by using a bit‐array representation method. To address the related pronounced connectivity issue effectively, the four‐neighbourhood connectivity is used to suppress the occurrence of checkerboard patterns. A simpler version of the perimeter control approach is developed to obtain a well‐posed problem and the total number of hinges of each individual is explicitly penalized to achieve a hinge‐free design. To handle the problem of representation degeneracy effectively, a recessive gene technique is applied to viable topologies while unusable topologies are penalized in a hierarchical manner. An efficient FEM‐based function evaluation method is developed to reduce the computational cost. A dynamic penalty method is presented for the GA to convert the constrained optimization problem into an unconstrained problem without the possible degeneracy. With all these enhancements and appropriate choice of the GA operators, the present GA can achieve significant improvements in evolving into near‐optimum solutions and viable topologies with checkerboard free, mesh independent and hinge‐free characteristics. Numerical results show that the present GA can be more efficient and robust than the conventional GAs in solving the structural topology optimization problems of minimum compliance design, minimum weight design and optimal compliant mechanisms design. It is suggested that the present enhanced GA using problem‐specific knowledge can be a powerful global search tool for structural topology optimization. Copyright © 2005 John Wiley & Sons, Ltd.