Fast Multi-objective Antenna Design Based on Improved Back Propagation Neural Network Surrogate Model
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摘要: 针对传统天线设计方法计算代价较大的缺陷，该文构建基于反向传播神经网络(BPNN)的新型天线代理模型。为解决BPNN训练易陷入局部最优的问题，采用粒子群优化(PSO)算法来改善神经网络初始结构参数，进而构建PSO-BPNN天线代理模型，并基于该模型提出多参数天线结构的快速多目标设计方法。设计实例表明，该方法在预测精度以及计算代价等方面优于现有的常用天线设计方法。所提方法对处理复杂高维参数空间天线设计问题具有实用价值。Abstract: Focusing on the problem of reducing the large computation cost of traditional antenna design methods, a new surrogate model based on Back Propagation Neural Networks (BPNN) is constructed. In order to solve the problem of easily falling into local optimum in BPNN, a PSO-BPNN surrogate model is developed by improving initial structural parameters of neural networks and applied to fast multi-objective optimization design of multi-parameter antenna structures. The design results show that the proposed PSO-BPNN outperforms other existing antenna surrogate models in terms of prediction accuracy and prediction speed. The proposed method is of value in dealing with complex antenna designs with high-dimensional parameter space.
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表 1 设计参数初始范围
参数 d l l1 l2 l3 范围(mm) [7,10] [26,34] [11,14] [8,10] [6,8] 参数 l4 w w1 w2 w3 范围(mm) [10,14] [17,23] [2,4] [2,4] [0.5,1.5] 
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表 4 平面3频带天线的的Pareto最优设计
设计 ${{{x}}^{(1)}}$ ${{{x}}^{(2)}}$ ${{{x}}^{(3)}}$ ${{{x}}^{(4)}}$ ${{{x}}^{(5)}}$ ${{{x}}^{(6)}}$ F1(dB) –17.57 –16.18 –15.19 –14.19 –13.27 –12.35 F2(mm2) 629.28 608.94 590.00 580.14 555.84 533.90 d 8.7 8.8 8.4 8.6 8.3 9.4 l 30.4 30.6 29.5 29.3 28.8 28.1 l1 11.8 12.9 12.8 12.4 10.9 11.2 l2 9.0 8.8 9.0 9.2 8.8 9.7 l3 6.4 6.8 6.8 6.8 7.0 6.6 l4 11.5 11.5 11.1 12.3 10.9 11.0 w 20.7 19.9 20.0 19.8 19.3 19.0 w1 3.1 3.3 3.2 3.4 3.0 2.9 w2 3.0 3.1 3.8 3.4 3.2 3.4 w3 1.0 1.0 0.9 0.8 1.1 1.2
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表 5 代理模型与HFSS所获得的Pareto最优解集的目标值F1比较
代理模型 ${{{x}}^{(1)}}$ ${{{x}}^{(2)}}$ ${{{x}}^{(3)}}$ ${{{x}}^{(4)}}$ ${{{x}}^{(5)}}$ ${{{x}}^{(6)}}$ HFSS –17.46 –15.75 –15.01 –14.69 –13.50 –12.53 BPNN –19.19 –17.90 –16.97 –16.04 –15.13 –14.36 PSO-BPNN –17.57 –16.18 –15.19 –14.19 –13.27 –12.35 误差率1(%) 9.91 13.65 13.06 9.19 12.07 14.60 误差率2(%) 0.63 2.73 1.20 3.40 1.70 1.44
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