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
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火箭軍工程大學(xué) 西安 710025
Synthesis of Sparse Rectangular Planar Arrays with Multiple Constraints Based on Dynamic Parameters Differential Evolution Algorithm
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Rocket Force University of Engineering, Xi’an 710025, China
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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。
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關(guān)鍵詞:
- 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.
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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 下載: 導(dǎo)出CSV
表 2 實(shí)驗(yàn)參數(shù)設(shè)置
縮放因子 交叉概率Cr 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Mr DPDE $1/\sqrt t $ 自適應(yīng) 50 10000 100/200 0.5 0.5 DE (無(wú)) 0.5 下載: 導(dǎo)出CSV
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 下載: 導(dǎo)出CSV
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 – – 下載: 導(dǎo)出CSV
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