基于差分进化算法的共形阵及多频天线研究
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摘要
电磁问题中的最优化设计作为现代电磁研究领域的一个重要部分，越来越受到研究者的关注。电磁优化问题的目标函数通常具有高度非线性、不可导和多极值的特点，使得经典优化方法在求解实际问题时存在诸多困难。差分进化算法（Differential Evolution, DE）作为一种简单高效的全局搜索算法，非常适合求解复杂的电磁优化问题。尽管如此，由于电磁优化问题的复杂性，目标函数的计算需要较长的时间，如何提高算法的收敛速度，减少目标函数计算次数是当前亟待解决的关键问题。随着微波集成电路的发展和空间技术的需求，能够与载体表面充分吻合的共形天线技术日益受到重视。共形阵的结构特性使其方向图综合非常困难，而传统的阵列综合方法和局部优化方法应用受到了很大限制，所以高效的DE算法成为了共形阵方向图综合的有效手段。无线局域网（WLAN）及全球微波互联接入（WiMAX）的发展使得能满足多种通信标准的高性能、小型化的多频天线成为现代无线通信系统中的迫切需求。传统天线设计过程中的试错法非常依赖设计者的经验枚举可能的参数组合，使得设计过程冗长繁琐。随着高性能计算机的普及，利用差分进化算法和电磁计算方法的结合实现天线的全局优化设计，成为了天线设计者们所期望的设计方式。
本论文以DE算法为基础，对算法性能的改进及其在共形阵设计和多频天线优化中的应用等方面展开研究，论文的主要内容可以概括为以下几个方面：
1.改进DE算法研究。通过在标准DE算法中引入随机最佳变异和随机局部寻优策略，提出了一种改进型的差分进化算法（MDE），在取得收敛速度和种群多样性之间相对平衡的同时增强了算法的局部寻优能力，从而提高了算法的整体性能。然后对7个标准测试函数进行优化并综合了一个直线阵的宽零陷低副瓣方向图，将优化结果与其它算法进行了对比，证明了提出的MDE算法的优越性。
2.共形阵优化设计研究。首先，分析并研究了共形阵中的极化问题，给出了阵列有源区的选择方法。其次，设计了8×12元的圆柱共形阵，用MDE算法综合了三种不同扫描角度下的低副瓣方向图。在设计过程中采用单元的有源方向图，计入了阵元及载体的互耦对阵列方向图的影响；通过改进的Bernstein多项式对阵元幅度进行约束，克服了幅度高度振荡对方向图综合带来的危害并有效地减少了优化变量数目。最后，设计了半球面覆盖的球面共形阵。在选定阵列有源区的范围之后通过调节双极化阵元的馈电改善了阵列的极化状况，采用MDE算法综合了阵列的低副瓣方向图，实现了阵列的大范围扫描。
3.多目标DE算法及多目标方向图综合研究。首先，在广义多目标DE算法（GDE3）的基础上，通过引入新的变异算子和个体保留机制，提出一种改进型的多目标DE算法（IGDE）。5个标准测试函数的优化结果表明该算法得到的Pareto解集收敛性更好，分布更均匀。然后，将该算法应用于两个不同的阵列方向图综合中，有效地克服了单目标算法处理此类问题时的缺陷，得到了波束宽度和副瓣电平的Pareto前沿面，一次性优化出了满足约束条件的所有可能的阵列优化设计形式。
4.平面印刷多频天线优化设计研究。依照试错法分别研究并设计了三种不同工作机理的印刷多频天线。首先，在矩形环上延伸出相应的枝节形成新的谐振多枝节结构，设计了一种多枝节矩形环天线，设计思路简单、模型调节方便。其次，利用叉子形馈线结构激励微带宽缝隙，在不需改变缝隙外形和引入寄生单元的情况下，设计了一种工作于WLAN/WiMAX系统的多频天线；再次，利用宽带加陷波的形式设计了一种小型化的多频天线。通过新颖的加载缝隙和非对称馈电结构使天线尺寸减少了约二分之一。最后，将MDE算法和商用电磁仿真软件相结合对一款工作于WLAN/WiMAX系统的双频天线进行了优化设计。
As an important part of the modern electromagnetic research field， the optimaldesign in electromagnetic research is being paid more and more attention by researchers.The cost functions in the optimization of electromagnetic problems are always highlynonlinear, nondifferentiable and have multiple peaks, which bring many challenges tothe classical optimization methods in solving the practical problems. As a simple andefficient global search algorithm, differential evolution algorithm (DE) is very suitablefor dealing with the complex optimization problems in the electromagnetic field. Evenso, because of the complexity in the practical electromagnetic applications, thecomputation of the object functions needs noticeable amount of time. How to acceleratethe convergence speed of the algorithm and reduce the total time consumption of theoptimization process is a key problem requiring to be solved at present. As the greatachievements in microwave integrated circuit and the growing demands for the spacetechnology, the conformal array antennas which fully conform to the surfaces of thecarriers have attracted more and more attentions. Since the structure of a conformalarray makes it difficult to synthesize the pattern of the array, the traditional synthesismethods and the local optimization techniques are not applicable anymore, but the highefficient DE algorithm becomes a very effective method for the synthesis of conformalarrays. The development of Wireless Local Area Networks (WLAN) and WorldwideInteroperability for Microwave Access (WiMAX) makes the antennas which satisfyseveral kinds of communication standards with high performance and compact sizegreatly demanded. The trial-and-error procedure in the traditional antenna designprocess is very dependent on the enumeration of possible parameter combinations bythe experience of designers, which makes the design process very complex and timeconsuming. As previously unimaginable computational resources become commonplace,the optimization of antenna design by the combination of DE and computationalelectromagnetism method is imminently desired by the antenna designers.
Based on the DE algorithm, this dissertation is mainly concerned with theimprovements of DE and its applications in synthesis of conformal arrays and optimaldesign of multiband antennas. The author’s major contributions can be summarized asfollows:
1. The study of DE algorithm. A modified DE (MDE) algorithm is proposed by introducing the strategies of random best mutation and random local search in thestandard DE algorithm. The proposed algorithm can make a relative balance betweenthe convergence speed and the diversity of the population as well as enhance the localsearch ability, and then improves the overall performance. After that, seven standardbenchmark functions are optimized and a linear array with wide null and low sidelobelevel pattern is synthesized, the optimization results are compared with several otherevolution algorithms, which demonstrate the superiority of the proposed MDEalgorithm.
2. The study of optimal design and synthesis of conformal arrays. Firstly, thepolarization problem in conformal arrays is analyzed and studied, and the selectionmethod of active region is given. Secondly, a cylindrical conformal array with8×12elements is designed, and its patterns with low sidelobe levels when the main beamscans to three different directions are synthesized by the MDE. During this process, theapplication of active-element-pattern can take the influence of mutual coupling betweenthe elements and carrier to the array pattern into consideration. The modified Bernsteinpolynomial is employed to obtain the excitation amplitudes of the cylindrical conformalarray, which can overcome the drawbacks of high oscillation of amplitude weightsacross the phased array and significantly reduce the optimization variables in thesynthesis process. Finally, a hemispherically covered sphere conformal array is designed.The dual polarized array elements are adjusted to improve the polarization of the arrayafter the selection of the active region, and then the proposed MDE is applied tosynthesize the array patterns for low sidelobe levels, which can scan over a wide scope.
3. The study of multi-objective DE and array synthesis. Firstly, an improvedmulti-objective differential evolution algorithm (IGDE) is proposed by introducingnovel mutation strategies and individual preservation mechanism in the GeneralizedDifferential Evolution (GDE3). The optimal results of five standard benchmarkfunctions demonstrate that the obtained Pareto solutions by the proposed algorithm arebetter than the original algorithm both in convergence and diversity. Then, the proposedIGDE is applied in two different synthesis problems, which effectively overcome thedefects in single objective evolution algorithm, the Pareto front of the beamwidths andsidelobe levels are obtained, and all the possible optimal results satisfied the constraintsare optimized at once.
4. The study of optimal design in planar printed multiband antennas. Threeprinted multiband antennas with different work mechanisms are studied and designedby the trial-and-error procedure. Firstly, by extending strips from the rectangular ring, a rectangular ring monopole antenna with multiple resonation strips is designed, thisdesign is simple and easy to tune. Secondly, a wide slot is excited by a fork-shaped strip,then a multiband antenna for WLAN/WiMAX applications is designed withoutchanging the shape of slot or introducing coupling strips. Thirdly, a compact multibandantenna is designed by introducing several notches in a wide frequency band, the noveletched slots and the asymmetric coplanar strip (ACS) fed structure used in this designcan reduce the overall antenna size to only one half of the original design. Finally, theMDE and the commercial electromagnetic simulation software are combined to design adual band printed antenna for WLAN/WiMAX applications.
本论文以DE算法为基础，对算法性能的改进及其在共形阵设计和多频天线优化中的应用等方面展开研究，论文的主要内容可以概括为以下几个方面：
1.改进DE算法研究。通过在标准DE算法中引入随机最佳变异和随机局部寻优策略，提出了一种改进型的差分进化算法（MDE），在取得收敛速度和种群多样性之间相对平衡的同时增强了算法的局部寻优能力，从而提高了算法的整体性能。然后对7个标准测试函数进行优化并综合了一个直线阵的宽零陷低副瓣方向图，将优化结果与其它算法进行了对比，证明了提出的MDE算法的优越性。
2.共形阵优化设计研究。首先，分析并研究了共形阵中的极化问题，给出了阵列有源区的选择方法。其次，设计了8×12元的圆柱共形阵，用MDE算法综合了三种不同扫描角度下的低副瓣方向图。在设计过程中采用单元的有源方向图，计入了阵元及载体的互耦对阵列方向图的影响；通过改进的Bernstein多项式对阵元幅度进行约束，克服了幅度高度振荡对方向图综合带来的危害并有效地减少了优化变量数目。最后，设计了半球面覆盖的球面共形阵。在选定阵列有源区的范围之后通过调节双极化阵元的馈电改善了阵列的极化状况，采用MDE算法综合了阵列的低副瓣方向图，实现了阵列的大范围扫描。
3.多目标DE算法及多目标方向图综合研究。首先，在广义多目标DE算法（GDE3）的基础上，通过引入新的变异算子和个体保留机制，提出一种改进型的多目标DE算法（IGDE）。5个标准测试函数的优化结果表明该算法得到的Pareto解集收敛性更好，分布更均匀。然后，将该算法应用于两个不同的阵列方向图综合中，有效地克服了单目标算法处理此类问题时的缺陷，得到了波束宽度和副瓣电平的Pareto前沿面，一次性优化出了满足约束条件的所有可能的阵列优化设计形式。
4.平面印刷多频天线优化设计研究。依照试错法分别研究并设计了三种不同工作机理的印刷多频天线。首先，在矩形环上延伸出相应的枝节形成新的谐振多枝节结构，设计了一种多枝节矩形环天线，设计思路简单、模型调节方便。其次，利用叉子形馈线结构激励微带宽缝隙，在不需改变缝隙外形和引入寄生单元的情况下，设计了一种工作于WLAN/WiMAX系统的多频天线；再次，利用宽带加陷波的形式设计了一种小型化的多频天线。通过新颖的加载缝隙和非对称馈电结构使天线尺寸减少了约二分之一。最后，将MDE算法和商用电磁仿真软件相结合对一款工作于WLAN/WiMAX系统的双频天线进行了优化设计。
As an important part of the modern electromagnetic research field， the optimaldesign in electromagnetic research is being paid more and more attention by researchers.The cost functions in the optimization of electromagnetic problems are always highlynonlinear, nondifferentiable and have multiple peaks, which bring many challenges tothe classical optimization methods in solving the practical problems. As a simple andefficient global search algorithm, differential evolution algorithm (DE) is very suitablefor dealing with the complex optimization problems in the electromagnetic field. Evenso, because of the complexity in the practical electromagnetic applications, thecomputation of the object functions needs noticeable amount of time. How to acceleratethe convergence speed of the algorithm and reduce the total time consumption of theoptimization process is a key problem requiring to be solved at present. As the greatachievements in microwave integrated circuit and the growing demands for the spacetechnology, the conformal array antennas which fully conform to the surfaces of thecarriers have attracted more and more attentions. Since the structure of a conformalarray makes it difficult to synthesize the pattern of the array, the traditional synthesismethods and the local optimization techniques are not applicable anymore, but the highefficient DE algorithm becomes a very effective method for the synthesis of conformalarrays. The development of Wireless Local Area Networks (WLAN) and WorldwideInteroperability for Microwave Access (WiMAX) makes the antennas which satisfyseveral kinds of communication standards with high performance and compact sizegreatly demanded. The trial-and-error procedure in the traditional antenna designprocess is very dependent on the enumeration of possible parameter combinations bythe experience of designers, which makes the design process very complex and timeconsuming. As previously unimaginable computational resources become commonplace,the optimization of antenna design by the combination of DE and computationalelectromagnetism method is imminently desired by the antenna designers.
Based on the DE algorithm, this dissertation is mainly concerned with theimprovements of DE and its applications in synthesis of conformal arrays and optimaldesign of multiband antennas. The author’s major contributions can be summarized asfollows:
1. The study of DE algorithm. A modified DE (MDE) algorithm is proposed by introducing the strategies of random best mutation and random local search in thestandard DE algorithm. The proposed algorithm can make a relative balance betweenthe convergence speed and the diversity of the population as well as enhance the localsearch ability, and then improves the overall performance. After that, seven standardbenchmark functions are optimized and a linear array with wide null and low sidelobelevel pattern is synthesized, the optimization results are compared with several otherevolution algorithms, which demonstrate the superiority of the proposed MDEalgorithm.
2. The study of optimal design and synthesis of conformal arrays. Firstly, thepolarization problem in conformal arrays is analyzed and studied, and the selectionmethod of active region is given. Secondly, a cylindrical conformal array with8×12elements is designed, and its patterns with low sidelobe levels when the main beamscans to three different directions are synthesized by the MDE. During this process, theapplication of active-element-pattern can take the influence of mutual coupling betweenthe elements and carrier to the array pattern into consideration. The modified Bernsteinpolynomial is employed to obtain the excitation amplitudes of the cylindrical conformalarray, which can overcome the drawbacks of high oscillation of amplitude weightsacross the phased array and significantly reduce the optimization variables in thesynthesis process. Finally, a hemispherically covered sphere conformal array is designed.The dual polarized array elements are adjusted to improve the polarization of the arrayafter the selection of the active region, and then the proposed MDE is applied tosynthesize the array patterns for low sidelobe levels, which can scan over a wide scope.
3. The study of multi-objective DE and array synthesis. Firstly, an improvedmulti-objective differential evolution algorithm (IGDE) is proposed by introducingnovel mutation strategies and individual preservation mechanism in the GeneralizedDifferential Evolution (GDE3). The optimal results of five standard benchmarkfunctions demonstrate that the obtained Pareto solutions by the proposed algorithm arebetter than the original algorithm both in convergence and diversity. Then, the proposedIGDE is applied in two different synthesis problems, which effectively overcome thedefects in single objective evolution algorithm, the Pareto front of the beamwidths andsidelobe levels are obtained, and all the possible optimal results satisfied the constraintsare optimized at once.
4. The study of optimal design in planar printed multiband antennas. Threeprinted multiband antennas with different work mechanisms are studied and designedby the trial-and-error procedure. Firstly, by extending strips from the rectangular ring, a rectangular ring monopole antenna with multiple resonation strips is designed, thisdesign is simple and easy to tune. Secondly, a wide slot is excited by a fork-shaped strip,then a multiband antenna for WLAN/WiMAX applications is designed withoutchanging the shape of slot or introducing coupling strips. Thirdly, a compact multibandantenna is designed by introducing several notches in a wide frequency band, the noveletched slots and the asymmetric coplanar strip (ACS) fed structure used in this designcan reduce the overall antenna size to only one half of the original design. Finally, theMDE and the commercial electromagnetic simulation software are combined to design adual band printed antenna for WLAN/WiMAX applications.
引文
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