基于動(dòng)態(tài)參數(shù)差分進(jìn)化算法的多約束稀布矩形面陣優(yōu)化

姚敏立; 王旭健; 張峰干; 戴定成

doi:10.11999/JEIT190346

基于動(dòng)態(tài)參數(shù)差分進(jìn)化算法的多約束稀布矩形面陣優(yōu)化

doi: 10.11999/JEIT190346

火箭軍工程大學(xué) 西安 710025

詳細(xì)信息

作者簡(jiǎn)介:
姚敏立：男，1966年生，教授，研究方向?yàn)閷拵б苿?dòng)衛(wèi)星通信、陣列信號(hào)處理

王旭?。耗?，1994年生，碩士生，研究方向?yàn)殛嚵刑炀€優(yōu)化設(shè)計(jì)

張峰干：男，1985年生，博士，研究方向?yàn)殛嚵行盘?hào)處理、陣列天線優(yōu)化

戴定成：男，1991年生，博士生，研究方向?yàn)殛嚵刑炀€優(yōu)化設(shè)計(jì)

通訊作者:
王旭健　wxj_903@163.com

中圖分類(lèi)號(hào): TN820
計(jì)量
- 文章訪問(wèn)數(shù): 2943
- HTML全文瀏覽量: 1216
- PDF下載量: 67
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2019-05-16
- 修回日期: 2019-09-06
- 網(wǎng)絡(luò)出版日期: 2020-01-31
- 刊出日期: 2020-06-04

Synthesis of Sparse Rectangular Planar Arrays with Multiple Constraints Based on Dynamic Parameters Differential Evolution Algorithm

Rocket Force University of Engineering, Xi’an 710025, China

摘要

摘要:
針對(duì)多約束條件下稀布矩形平面陣列天線的優(yōu)化問(wèn)題，該文提出一種基于動(dòng)態(tài)參數(shù)差分進(jìn)化(DPDE)算法的方向圖綜合方法。首先，對(duì)差分進(jìn)化(DE)算法中的縮放因子和交叉概率引入動(dòng)態(tài)變化控制策略，提高搜索效率和搜索精度。其次，改進(jìn)矩陣映射方法，重新定義映射法則，改善現(xiàn)有方法隨機(jī)性強(qiáng)和搜索精度低的不足。最后，為檢驗(yàn)所提方法的有效性進(jìn)行仿真實(shí)驗(yàn)，實(shí)驗(yàn)數(shù)據(jù)表明，該方法可以提高天線優(yōu)化性能，有效降低天線的峰值旁瓣電平。
- 陣列天線 /
- 稀布平面陣列 /
- 約束優(yōu)化 /
- 差分進(jìn)化算法
Abstract:
For solving the problem of the synthesis of sparse rectangular planar arrays with multiple constraints, this paper proposes a Dynamic Parameters Differential Evolution (DPDE) based algorithm. Firstly, to improve searching efficiency and accuracy of Differential Evolution (DE), the proposed method introduces dynamically changing strategies to the scaling factor and the crossover probability of the traditional Differential Evolution algorithm. Secondly, a modified matrix mapping method and the redefinition of mapping principles are presented to make up the defects of strong randomness and low accuracy in existing methods. Finally, simulation experiments of antenna arrays are performed to validate the effectiveness of the proposed method, and the results demonstrate that the proposed method performs out the existing methods in the respect of reducing peak sidelobe level of antenna arrays.
- Antenna arrays /
- Sparse planar arrays /
- Constrained optimization /
- Differential Evolution (DE) algorithm

HTML全文

圖 1 矩形面陣結(jié)構(gòu)示意圖

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圖 2 $\varphi = {0^{\rm{^\circ }}}$和$\varphi = {90^{\rm{^\circ }}}$平面的方向圖

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圖 3 實(shí)驗(yàn)1的PSLL實(shí)驗(yàn)結(jié)果

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圖 4 全平面遠(yuǎn)場(chǎng)方向圖

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圖 5 實(shí)驗(yàn)2的PSLL實(shí)驗(yàn)結(jié)果

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圖 6 實(shí)驗(yàn)1陣元分布

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圖 7 實(shí)驗(yàn)2陣元分布

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表 1 標(biāo)準(zhǔn)測(cè)試函數(shù)

函數(shù)		變量取值范圍	最小值
f₁	$\displaystyle\sum\limits_{i = 1}^n {x_i^2} $	[–100, 100]	0
f₂	$\displaystyle\sum\limits_{i = 1}^n {\left\| {{x_i}} \right\|} + \prod\limits_{i = 1}^n {{x_i}} $	[–10, 10]	0
f₃	${\displaystyle\sum\limits_{i = 1}^n {\left( {\displaystyle\sum\limits_{j = 1}^i {{x_j}} } \right)} ^2}$	[–100, 100]	0
f₄	$\displaystyle\sum\limits_{i = 1}^D {{{\left( {\left\| {{x_i} + 0.5} \right\|} \right)}^2}\quad } $	[–100, 100]	0
f₅	$\displaystyle\sum\limits_{i = 1}^D {\left[ {x_i^2 - 10\cos \left( {2\pi {x_i}} \right) + 10} \right]} $	[–5.12，5.12]	0
f₆	$ - 20{ {\rm{e} }^{ - 0.2\sqrt {\dfrac{1}{D}\displaystyle\sum\limits_{i = 1}^D {x_i^2} } } } - { {\rm{e} }^{\dfrac{1}{D}\displaystyle\sum\limits_{i = 1}^D {\cos \left( {2\pi {x_i} } \right)} } } + 20 + {\rm{e} }$	[–32, 32]	0
f₇	$\dfrac{1}{ {400} }\displaystyle\sum\limits_{i = 1}^D {x_i^2} - \prod\limits_{i = 1}^D {\cos \left( {\frac{ { {x_i} } }{ {\sqrt i } } } \right)} + 1$	[–600, 600]	0

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表 2 實(shí)驗(yàn)參數(shù)設(shè)置

	縮放因子	交叉概率C_r	種群規(guī)模NP	迭代次數(shù)NI	變量維度D	縮放因子F	變異概率M_r
DPDE	$1/\sqrt t $	自適應(yīng)	50	10000	100/200	0.5	0.5
DE	(無(wú))	0.5	50	10000	100/200	0.5	0.5

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表 3 DPDE和DE的實(shí)驗(yàn)結(jié)果對(duì)比(較好的以*標(biāo)出)

	DPDE (D=100)			DE (D=100)			DPDE (D=200)			DE (D=200)
	MEAN	SD	PSR(%)	MEAN	SD	PSR(%)	MEAN	SD	PSR(%)	MEAN	SD	PSR(%)
f₁	2.72E-28*	5.23E-56	100	1.86E-14	5.94E-29	100	5.16E-17*	6.17E-34	100	1.87E+01	7.91E+00	0
f₂	1.87E-14*	5.83E-29	100	7.97E-09	2.65E-18	0	1.01E-08*	9.34E-18	0	4.73E+00	3.23E-01	0
f₃	1.41E+00*	3.61E-02	0	3.39E+05	5.07E+08	0	9.04E+00*	1.32E+00	0	1.33E+06	1.02E+10	0
f₄	9.25E-28*	9.62E-55	100	1.99E-14	6.35E-29	100	1.97E-16*	1.01E-32	100	1.92E+01	1.12E+01	0
f₅	3.72E+01*	1.77E+02	0	7.67E+02	3.69E+02	0	2.11E+02*	2.14E+03	0	2.04E+03	8.78E+02	0
f₆	1.54E-14*	3.52E-30	100	2.80E-08	3.13E-17	0	1.68E-09*	2.27E-19	0	2.05E+00	9.44E-01	0
f₇	8.66E-17*	2.16E-33	100	1.08E-14	1.55E-29	100	2.33E-16*	1.64E-33	100	2.74E+00	1.12E-01	0

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表 4 仿真實(shí)驗(yàn)結(jié)果對(duì)比(dB)

實(shí)驗(yàn)	方法	最優(yōu)值	均值	最差值	方差
實(shí)驗(yàn)1	本文方法	–62.093	–60.395	–58.141	0.898
	MGA	–45.456	–	–43.864	–
	MMM	–51.499	–	–49.269	–
	AMM	–61.454	–58.922	–	–
實(shí)驗(yàn)2	本文方法	–22.753	–21.287	–19.038	0.363
	MGA	–18.840	–	–	–
	MMM	–20.384	–	–	–
	AMM	–21.886	–20.456	–	–

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