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摘要:
外形隐身是决定飞行器隐身性能的首要因素，军用飞行器在开展外形设计时需综合考虑气动性能和隐身性能，优化设计时需考虑气动学科和隐身学科的特点。基于Multi-start算法对翼型、布局外形隐身的设计空间特性进行分析，研究结果表明，外形隐身设计是复杂的多峰问题。针对优化问题的多峰性，在经典全局多峰粒子群优化算法的基础上引入局部搜索策略，提出适应值-距离比环形粒子群优化(FER-R3PSO)算法，采用标准函数算例对所提算法的搜索效果进行验证。在此基础上，将全局多峰算法与梯度优化方法结合，提出全局/梯度耦合的气动隐身设计方法，采用飞翼布局气动/隐身优化问题对所提方法的优化效果进行验证。优化结果表明：相对于梯度优化，所提方法能够以较少的计算代价获得气动、隐身特性更加优秀的外形。
Abstract:Shape stealth is the primary factor determining the stealth performance of an aircraft. In the shape design of modern military aircraft, both aerodynamic performance and stealth performance need to be comprehensively considered. Aerodynamic stealth optimization is a complex multimodal problem. Given the high computational cost of global optimization and the tendency of gradient optimization to fall into local optima, an optimal design method combining global multimodal optimization for airfoils and gradient optimization for layouts is proposed. To address the insufficient local search capability of the classical multimodal particle swarm optimization algorithm, the fitness-euclidean distance ratio ring topology local-best particle swarm optimization (FER-R3PSO) algorithm is introduced by combining the ring topology particle swarm optimization algorithm with the fitness-euclidean distance particle swarm optimization algorithm, which enhances the local search capability of the classical multimodal particle swarm optimization algorithm. To combine the multimodal search algorithm with surrogate models and reduce the computational burden of using the multimodal algorithm in engineering applications, a surrogate model point addition strategy and a peak extraction method suitable for the multimodal search algorithm are proposed. Function tests, airfoil stealth optimization, and standard aerodynamic examples are used to verify the effectiveness of the multimodal algorithm. The global/gradient coupling design for the flying wing layout is proposed, and aerodynamic stealth optimization based on the adjoint method is carried out using the three-dimensional shape obtained through global multimodal algorithm optimization of the airfoil assembly as the initial stage. The optimization results show that, compared to gradient optimization, the proposed method can achieve a shape with superior aerodynamic and stealth characteristics at a lower computational cost.
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图 1 Multi-start隐身优化翼型对比
Figure 1. Comparisons of Multi-start stealth optimization airfoils
图 2 Multi-start优化结果的设计变量值
Figure 2. Design variable values of Multi-start optimization results
图 4 优化结果在Y=4.5 m、Y=8.0 m剖面外形
Figure 4. Optimized airfoil geometry at Y=4.5 m and Y=8.0 m
图 5 Multi-start优化外形各剖面设计变量值
Figure 5. Optimized design variable values at different slices
图 7 全局/梯度耦合的气动隐身优化设计方法
Figure 7. Global/gradient coupled aero/stealth optimization design approach
图 8 NACA65016翼型全局和梯度优化外形几何对比
Figure 8. Geometry comparisons of global and gradient optimization of NACA65016 airfoil
图 9 NACA65016翼型全局和梯度优化外形压力分布
Figure 9. Pressure distribution comparisons of global and gradient optimization of NACA65016 airfoil
图 11 GlobalOpt1近场散射电场强度
Figure 11. Near-field scattering characteristics of GlobalOpt1
图 12 初始外形表面及剖面压力系数
Figure 12. Pressure coefficient distribution of initial geometry and slices
图 13 X47B1、X47B2和X47B3的${\sigma _{{\mathrm{ave}}}} $对比（f=1 GHz，垂直极化）
Figure 13. ${\sigma _{{\mathrm{ave}}}} $ comparisons of X47B1, X47B2 and X47B3 (f=1 GHz, vertical polarization)
图 14 梯度优化外形各剖面几何及压力分布对比
Figure 14. Geometry and pressure coefficient comparisons at different slices for gradient optimization
图 15 初始外形及X47B3外形梯度优化前后外形${\sigma _{{\mathrm{ave}}}} $对比（f=1 GHz，垂直极化）
Figure 15. ${\sigma _{{\mathrm{ave}}}} $ comparisons of initial and X47B3 geometries before and after gradient optimization (f=1 GHz, vertical polarization)
表 1 Multi-start梯度优化结果
Table 1. Multi-start gradient optimization results
结果编号 10lg(${\sigma _{{\mathrm{ave}}}} $)/m2 tmax NACA65016 13.410 0.0016 Sobol-1 −20.454 0.1618 Sobol-2 −20.715 0.1686 Sobol-3 −21.004 0.1607 Sobol-4 −20.892 0.1601 Sobol-5 −21.004 0.1607 Sobol-6 −20.828 0.1899 Sobol-7 −20.828 0.1899 Sobol-8 −20.635 0.1600 Sobol-9 −21.005 0.1606 Sobol-10 −19.383 0.1600 注：相同颜色认为属于同一峰值。 
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表 2 Multi-start初始外形RCS和优化外形RCS
Table 2. RCS of multi-start initial and optimized geometries
编号 初始${\sigma _{{\mathrm{ave}}}} $/m2 优化${\sigma _{{\mathrm{ave}}}} $/m2 Stealth1 2.5000 1.6840 Stealth2 2.5168 1.6790 Stealth3 2.6127 1.6713 Stealth4 2.4063 1.6777 Stealth5 2.3854 1.6890 Stealth6 2.6902 1.7069 Stealth7 2.5695 1.6796 Stealth8 2.3834 1.6710 Stealth9 2.5077 1.7039 Stealth10 2.4184 1.6785
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表 3 CEC2015测试函数性质及测试参数设置
Table 3. CEC2015 test function properties and parameter settings
编号 维度 全局/局部最优 最优值 粒子数 MaxFES F1 5 1/15 100 100 40000 10 1/55 200 150000 F2 2 4/21 200 100 20000 5 32/0 150 56600 8 256/0 200 256000 F3 2 25/0 300 100 20000 3 125/0 200 67200 4 625/0 800 200000 F4 5 1/15 400 60 40000 10 1/55 150 149700 20 1/210 200 581200 F5 2 25/0 500 100 20000 3 125/0 200 67200 4 625/0 800 200000 F6 4 16/0 600 100 32000 6 64/0 200 96000 8 256/0 400 256000 F7 6 8/0 700 100 34000 10 32/0 150 113280 16 256/0 200 512000 F8 2 36/0 800 100 24000 3 216/0 250 88320 4 1296 /01200 288000
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表 4 CEC2015测试函数评估结果
Table 4. CEC2015 function test results
编号 维度 NPF PR R3PSO FER-R3PSO R3PSO FER-R3PSO F1 5 44 44 0.8627 0.8627 10 3 3 0.0588 0.0588 F2 2 204 204 1.0000 1.0000 5 488 539 0.2990 0.3284 8 286 304 0.0219 0.0233 F3 2 1077 1097 0.8447 0.8604 3 2524 2675 0.3959 0.4196 4 6127 7392 0.1922 0.2319 F4 5 20 21 0.3922 0.4118 10 0 0 0 0 F5 2 1035 1064 0.8118 0.8345 3 2462 2677 0.3862 0.4199 4 6072 7024 0.1905 0.2204 F6 4 475 579 0.5821 0.7096 6 850 1216 0.2604 0.3725 8 1434 2055 0.1098 0.1574 F7 6 338 366 0.8284 0.8971 10 504 587 0.3088 0.3597 16 485 506 0.0371 0.0388 F8 2 678 697 0.3693 0.3796 3 1614 1856 0.1465 0.1685 4 3733 4589 0.0565 0.0694
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表 5 NACA65016外形全局/梯度优化结果
Table 5. Global and gradient optimization results of NACA65016 airfoil
结果编号 CD ${\sigma _{{\mathrm{ave}}}} $/m tmax CM NACA65016 0.007758 0.045612 0.1600 − 0.0064 GlobalOpt1 0.007840 0.005006 0.1600 0.0500 GradOpt1 0.007837 0.003848 0.1601 0.0503 GlobalOpt2 0.007793 0.005540 0.1600 0.0500 GradOpt2 0.007793 0.005540 0.1600 0.0500 GlobalOpt3 0.007841 0.004855 0.1600 0.0500 GradOpt3 0.007840 0.004855 0.1600 0.0500
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表 6 类X47B外形气动隐身优化结果
Table 6. Aero/stealth optimization results of X47B geometry
外形 CD CM ${\sigma _{{\mathrm{ave}}}} $/m2 X47B基础外形 0.019665 − 0.026167 3.79510 AS128-Bezier 0.015582 − 0.040593 0.54040 X47B1 0.018425 − 0.005038 0.44884 X47B2 0.019638 − 0.004940 0.31827 X47B3 0.018707 − 0.001002 0.43848 X47B1-grad 0.014269 − 0.060529 0.05901 X47B2-grad 0.014436 − 0.029866 0.05864 X47B3-grad 0.014214 − 0.047756 0.10260
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