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无参数自适应罚函数的高效代理模型优化设计方法

张伟 高正红 王超 夏露

张伟,高正红,王超,等. 无参数自适应罚函数的高效代理模型优化设计方法[J]. 北京航空航天大学学报,2024,50(4):1262-1272 doi: 10.13700/j.bh.1001-5965.2022.0451
引用本文: 张伟,高正红,王超,等. 无参数自适应罚函数的高效代理模型优化设计方法[J]. 北京航空航天大学学报,2024,50(4):1262-1272 doi: 10.13700/j.bh.1001-5965.2022.0451
ZHANG W,GAO Z H,WANG C,et al. Efficient surrogate-based aerodynamic optimization with parameter-free adaptive penalty function[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(4):1262-1272 (in Chinese) doi: 10.13700/j.bh.1001-5965.2022.0451
Citation: ZHANG W,GAO Z H,WANG C,et al. Efficient surrogate-based aerodynamic optimization with parameter-free adaptive penalty function[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(4):1262-1272 (in Chinese) doi: 10.13700/j.bh.1001-5965.2022.0451

无参数自适应罚函数的高效代理模型优化设计方法

doi: 10.13700/j.bh.1001-5965.2022.0451
基金项目: 翼型、叶栅空气动力学国家级重点实验室基金(614220121020128)
详细信息
    通讯作者:

    E-mail:zgao@nwpu.edu.cn

  • 中图分类号: V211.3

Efficient surrogate-based aerodynamic optimization with parameter-free adaptive penalty function

Funds: National Key Laboratory Foundation of Airfoil and Blade Grid Aerodynamics (614220121020128)
More Information
  • 摘要:

    在飞行器气动外形优化设计中,复杂约束条件导致设计空间可行域呈现不连续的特征,且理想解大多靠近约束边界,传统高效代理模型方法难以适用。研究了参考点对优化设计的影响,提出了一种考虑约束的参考点选择机制;对于最优解靠近边界的问题,罚函数法更加有效,但惩罚因子的设置对于罚函数方法影响很大,不合适的惩罚因子反而会损害优化效率,分析了优化过程中罚函数方法对惩罚因子的要求,提出了一种无参数自适应罚函数的代理模优化设计方法,引入基于样本分析的惩罚项,结合归一化目标值和约束值,在优化过程中动态调整惩罚因子,使优化能够尽可能地聚焦于可行域内,迅速收敛到最优解,实现样本的高效配置。通过带约束的函数算例和翼型优化算例证实,所提方法可以大幅提高飞行器气动外形优化设计效率。

     

  • 图 1  二维Branin函数

    Figure 1.  Contour of 2 dimensional Branin function

    图 2  约束函数

    Figure 2.  Contour of constraint function

    图 3  二维约束Branin函数

    Figure 3.  Contour of 2 dimensional constrained Branin function

    图 4  加点目标函数值

    Figure 4.  Value of additive objective function

    图 5  EI,max和(EI×PI)max收敛历程

    Figure 5.  Convergence of EI,max and (EI×PI)max

    图 6  改进约束EGO方法目标函数优化趋势

    Figure 6.  Improved constrained EGO method objective function optimisation trends

    图 7  EI,max和(EI*PI)max收敛历程

    Figure 7.  Convergence of EI,max and (EI * PI)max

    图 8  参考点目标值对比

    Figure 8.  Comparison of objective function values of reference points

    图 9  加点目标函数值

    Figure 9.  Objective function values of infill samples

    图 10  RAE2822计算网格

    Figure 10.  Computational grid of RAE2822

    图 11  RAE2822翼型初始设计空间

    Figure 11.  Initial design space of RAE2822 airfoil

    图 12  不同方法阻力系数收敛历程对比

    Figure 12.  Convergence of ${C_d}$ for different methods

    图 13  设计结果外形对比

    Figure 13.  Shape of different optimized results

    图 14  设计压力分布对比

    Figure 14.  Pressure distribution of different optimized results

    图 15  NACA 65,3-018计算网格

    Figure 15.  Computational grid of NACA 65,3-018

    图 16  NACA65, 3-018翼型初始设计空间

    Figure 16.  Initial design space of NACA65, 3-018 airfoil

    图 17  不同约束EGO方法${C_d} $阻力系数收敛历程对比

    Figure 17.  Convergence of ${C_d}$ for different EGO methods

    图 18  RAE2822翼型设计结果外形对比

    Figure 18.  Shape of different optimized results for RAE2822 airfoil

    图 19  NACA65,3-018翼型设计压力分布对比

    Figure 19.  Pressure distribution of different optimized results for NACA65,3-018 airfoil

    表  1  全局优化函数问题

    Table  1.   Benchmark problems for global optimization

    函数 维度 约束数量 设计范围 最优解
    G1 13 9 ${[0,1]^9} \times {[0,100]^3} \times [0,1]$ −15
    G3 10 1 ${[0,10]^{10}}$ −1.0005
    G5 4 5 ${[0,1200]^2} \times {[ - 0.55,0.55]^2}$ 5126.49
    G6 2 2 ${[0,10]^2}$ −6961.8
    G24 2 2 $[0,3] \times [0,4]$ −5.508
    下载: 导出CSV

    表  2  函数测试结果

    Table  2.   Results of benchmark problem

    函数 CEI PCEI APCEI
    G1 200(30) >124.9(2) 115.1(17.48)
    G3 200(30) >191.7(9) 175.3(9.6)
    G5 200(30) 53.6(1.75) 44.8(2.71)
    G6 74.6(3.55) 32.6(1.21) 14.3(0.99)
    G24 22.4(3.08) 13.5(1.11) 8.6(1.35)
    下载: 导出CSV

    表  3  RAE2822翼型计算网格参数

    Table  3.   Parameter settings of computational grid of RAE2822

    参数 数值
    远场大小 50
    网格规模 601×213
    物面第一层网格距离 5×10−6
    物面法向网格增长率 1.13
    翼型前缘网格距离 0.001
    翼型后缘网格距离 0.001
    下载: 导出CSV

    表  4  不同方法设计结果对比

    Table  4.   Comparison of design results for different methods

    方法 Cd /counts Cm A
    RAE2822 203.1 −0.0927 0.07787
    CEI 113.5 −0.0892 0.07787
    PCEI 112.1 −0.0916 0.07787
    APCEI 111.6 −0.0919 0.07787
    下载: 导出CSV

    表  5  NACA 65,3-018翼型计算网格参数

    Table  5.   Parameter settings of computational grid of NACA 65,3-018

    参数 数值
    远场大小 50
    网格规模 401×201
    物面第一层网格距离 5×10−6
    物面法向网格增长率 1.12
    翼型前缘网格距离 0.001
    翼型后缘网格距离 0.0005
    下载: 导出CSV

    表  6  不同约束EGO方法设计结果对比

    Table  6.   Comparison of design results for different EGO methods

    方法 Cd /counts Cm 相对厚度
    RAE2822 114.1 −0.0098 0.18
    CEI 87.9 0.0307 0.18
    PCEI 87.2 0.0303 0.18
    APCEI 86.5 0.0300 0.18
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-05-31
  • 录用日期:  2022-09-18
  • 网络出版日期:  2022-10-10
  • 整期出版日期:  2024-04-29

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