CMA-ES在电磁设计中的应用：优化超宽带阵列

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"CMA Evolutionary Strategy.pdf - 一篇关于使用CMA-ES优化微波系统天线设计的学术文章" 本文详细介绍了Covariance Matrix Adaptation Evolutionary Strategy（CMA-ES），这是一种在电磁设计领域表现出优越性能的优化算法。传统上，遗传算法（GA）和粒子群优化（PSO）常用于此类设计，但CMA-ES在解决复杂问题时显示出了更高的效率。CMA-ES的核心在于适应性地调整协方差矩阵，从而更好地探索解决方案空间，特别是在面对多模态或非线性优化问题时。文章具体聚焦于超宽带无序阵列的设计，这种阵列采用了现实中的螺旋辐射元件。为了提高阵列的轴比，即改善其方向性，作者提出了一种创新策略：不仅优化每个螺旋元素的位置，还优化它们的机械旋转角度。这种对每个元素位置和旋转角度的联合优化方法显著提升了设计的性能。在实际应用中，强电磁脉冲（EMP）的处理是微波系统设计的一个重要方面，因为它可能对系统的稳定性造成影响。文献中可能包含了如何通过CMA-ES优化设计来增强系统抵御EMP的能力的方法。由于微波传输涉及的能量传播和天线设计密切相关，因此，CMA-ES的使用有助于创建更高效、抗干扰的天线阵列，这对于通信、雷达和空间探测等领域的微波系统至关重要。在电磁设计中，找到最优解通常是一个时间和计算资源密集型的过程。CMA-ES通过动态调整种群的变异性和探索性，能够在较短的时间内找到更优解。此外，通过结合螺旋元素的旋转优化，可以实现更均匀的功率分布和改进的方向图特性，这在超宽带通信系统中尤为关键，因为这些系统需要宽频带响应和低副瓣水平。最后，文章指出，尽管CMA-ES已经在一些领域显示出优势，但在实际应用中，仍需要考虑到硬件限制、成本效益以及与现有技术的兼容性。此外，对CMA-ES算法的进一步改进和调整可能会带来更多的优化可能性，例如引入并行计算加速优化过程，或者开发更适合特定电磁问题的变体。这篇论文揭示了CMA-ES在微波系统天线设计中的潜力，为电磁工程师提供了一个强大的工具，以应对日益复杂的电磁环境和性能需求。对于那些从事微波传输、天线设计和电磁脉冲防护的研究人员来说，这是一个极具价值的参考资源。

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI

10.1109/TAP.2013.2287904, IEEE Transactions on Antennas and Propagation

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

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Abstract—Recently, the covariance matrix adaption

evolutionary strategy (CMA-ES) has received attention for

outperforming conventional optimization algorithms such as the

genetic algorithm (GA) or particle swarm optimization (PSO)

algorithm, often used in electromagnetic designs. Here, CMA-ES

is first applied to the design of ultra-wideband aperiodic arrays

using realistic spiral radiating elements. To improve the axial

ratio of the array, optimization was extended to incorporate a

mechanical rotation of each spiral element. This novel strategy

of optimizing both the location and rotation of each element

provides noticeable improvement in both the axial ratio and

sidelobe level performance.

Index Terms—aperiodic array, axial ratio, CMA-ES,

covariance matrix adaptation, phased array, spiral antenna, ultra-

wideband antennas.

INTRODUCTION

N developing antenna arrays for ultra-wideband

applications, two main approaches can be used to obtain

grating lobe free operation. The first approach is to densely

pack the array elements, with inter-element spacings much

less than λ/2 [1]–[3]. This approach can require an extremely

large number of elements to fill a given aperture, in particular

if a narrow beam width is required, and can thus be very

costly. Moreover, approaches to achieve low relative sidelobe

levels (RSLL) with periodic arrays often require significant

amplitude tapering for outer elements and are thus rather

inefficient [4]. The other approach taken here is to

aperiodically position array elements, which provides a

number of advantages over more traditional periodic arrays.

They develop no grating lobes over arbitrarily large

bandwidths, posses no blind scan angles, require significantly

fewer elements to achieve a desired beam width, and have the

ability to achieve a low RSLL without requiring any amplitude

tapering [5]. Since aperiodic arrangements typically require

relatively sparse apertures with large average inter–element

spacings, they are at a performance disadvantage only when

high directivity is required from a size-constricted aperture.

Manuscript received November 28, 2012.

P. J. Gorman was with The Pennsylvania State University, University Park,

PA 16802 USA. He is now with the RF Communications Division, Harris

Corporation, Rochester, NY 14610 (e-mail: pgorma2@harris.com).

M. D. Gregory and D. H. Werner are with the Electrical Engineering

Department, The Pennsylvania State University, University Park, PA 16802

USA (e-mail: mdg243@psu.edu, dhw@psu.edu).

In the 1960s, when randomly spaced arrays first received

significant attention, the available computational resources and

optimization algorithms were largely insufficient for design

where element positions are directly controlled. Early

aperiodic array designers had to rely on a variety of methods,

such as randomly placing elements with a certain probability

density function [6]–[8] and while this approach was effective,

advances in computers and algorithms have given designers the

ability to quickly design array layouts with significantly better

performance. Some recent approaches that leverage advances

in computing include [9]–[11], which use nature-inspired

optimization techniques such as the genetic algorithm (GA) to

exploit the properties of fractals or aperiodic tilings for array

design.

Recently, the covariance matrix evolutionary strategy

(CMA-ES) has received attention for outperforming

conventional optimization algorithms such as GAs and particle

swarm optimization (PSO), both widely used in the

electromagnetic community [12]. CMA-ES has the advantage

in that it is a self-adaptive algorithm that learns from the

complex optimization parameter dependencies [13], [14]. This

self-adaptive learning combined with minimal reliance on user

defined evolutionary settings (e.g. mutation and crossover rates

in a GA), which can significantly impact optimization

performance, leads to a faster and more robust algorithm

compared to a GAs or PSO, particularly for problems with

large parameter sets.

For aperiodic antenna array design, this means more

flexibility to generate more optimal layouts. With small arrays

(under 100 elements), the aforementioned parameter reduction

or array representation techniques (e.g. aperiodic tilings or

fractals) can be restricting with respect to element arrangement.

Directly optimizing the locations of elements in an array is

impractically slow with traditional algorithms, however, with

the availability of CMA-ES, direct search is possible with

increasingly large arrays, resulting in array designs with

considerably better performance than previously possible [15].

In this paper, CMA-ES is applied to develop low-profile,

ultra-wideband antenna arrays using realistic antenna elements.

Traditional array factor design and optimization [12] is

combined with element patterns and full-wave simulations to

optimize for peak sidelobe level as well as axial ratio. The low-

profile requirement of the array eliminates many potential

candidates for the antenna element such as the log-periodic,

conical variants, and UWB horns. With the aperiodic approach

Design of Ultra-Wideband, Aperiodic Antenna

Arrays with the CMA Evolutionary Strategy

Philip J. Gorman, Student Member, IEEE, Micah D. Gregory, Student Member, IEEE, and

Douglas H. Werner, Fellow, IEEE

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