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基于自适应多可信度多项式混沌-Kriging模型的高效气动优化方法

赵欢

赵欢. 基于自适应多可信度多项式混沌-Kriging模型的高效气动优化方法. 力学学报, 2023, 55(1): 1-16 doi: 10.6052/0459-1879-22-391
引用本文: 赵欢. 基于自适应多可信度多项式混沌-Kriging模型的高效气动优化方法. 力学学报, 2023, 55(1): 1-16 doi: 10.6052/0459-1879-22-391
Zhao Huan. Adaptive multi-fidelity polynomial chaos-kriging model-based efficient aerodynamic design optimization method. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 1-16 doi: 10.6052/0459-1879-22-391
Citation: Zhao Huan. Adaptive multi-fidelity polynomial chaos-kriging model-based efficient aerodynamic design optimization method. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 1-16 doi: 10.6052/0459-1879-22-391

基于自适应多可信度多项式混沌-Kriging模型的高效气动优化方法

doi: 10.6052/0459-1879-22-391
基金项目: 国家自然科学基金资助项目(12102489)
详细信息
    作者简介:

    赵欢, 博士, 主要研究方向: 飞行器气动与多学科优化设计 . E-mail: huanzhao_aero@163.com

  • 中图分类号: V211

ADAPTIVE MULTI-FIDELITY POLYNOMIAL CHAOS-KRIGING MODEL-BASED EFFICIENT AERODYNAMIC DESIGN OPTIMIZATION METHOD

  • 摘要: 多可信度代理模型已经成为提高基于代理模型的优化算法效率和可信度水平最有效的手段之一. 然而目前流行的co-Kriging和分层Kriging (HK)等多可信度代理模型泛化能力不足, 缺乏对高阶/高非线性建模问题的适应性, 难以广泛应用. 文章基于发展的自适应多可信度多项式混沌-Kriging (MF-PCK)代理模型, 在提高建模效率和对高阶/高非线性问题近似准确率的同时, 建立了基于该自适应MF-PCK模型的高效全局气动优化方法. 在发展的方法中, 提出了基于MF-PCK模型的新型变可信度期望改进加点方法, 使代理优化算法效率进一步提高. 为了验证发展方法的全面表现, 将其应用在经典的数值函数算例以及多个跨音速气动外形的确定性优化和稳健优化设计中, 并与基于Kriging和HK模型的代理优化算法进行了全面比较. 结果表明, 发展的新型多可信度全局气动优化方法其优化效率相对于基于Kriging和HK模型的优化效率显著提高, 结果更好也更加可靠, 并且稳健优化设计效率和结果也更符合工程应用需求, 证明了其相对于基于Kriging和HK模型的代理优化算法的显著优势.

     

  • 图  1  自适应选择最相关的低可信度多项式集合和最优的矫正多项式集合图示说明

    Figure  1.  Sketch map in selecting the optimal cardinalities of the low-fidelity PCE and corresponding correction expansion for the optimal MF-PCK model

    图  2  基于自适应MF-PCK的多可信度气动优化流程图

    Figure  2.  The flow chart of adaptive MF-PCK-based multi-fidelity aerodynamic optimization algorithm.

    图  3  Branin函数及最优值位置

    Figure  3.  The Branin function contour

    图  4  近似Branin函数的低可信度函数

    Figure  4.  The corresponding LF function of Branin function

    图  5  基于Kriging_EI加点过程

    Figure  5.  The infilling process of Kriging_EI optimization method

    图  7  基于MF-PCK_VF-EI的加点过程

    Figure  7.  The infilling process of MF-PCK_VF-EI optimization method

    图  8  函数值收敛过程对比

    Figure  8.  The convergence history of the function values

    图  9  代理模型预测误差收敛过程对比

    Figure  9.  The convergence history of the surrogate prediction errors

    图  6  基于HK_VF-EI的加点过程

    Figure  6.  The infilling process of HK_VF-EI optimization method

    图  10  针对RAE2822翼型的不同可信度水平计算网格

    Figure  10.  Different levels of fidelity grids around RAE2822 airfoil

    图  11  高可信度网格远场图

    Figure  11.  Far view of the high-fidelity grid

    图  12  不同网格量计算压力分布与试验压力分布对比

    Figure  12.  Comparison of pressure distributions among computational and experimental results

    图  13  翼型设计空间展示

    Figure  13.  The design space of airfoil

    图  15  阻力系数代理模型预测误差收敛过程

    Figure  15.  The convergence history of surrogate prediction errors of drag coefficients

    图  16  优化翼型与初始翼型外形对比

    Figure  16.  Comparison of optimized and initial airfoils

    图  14  阻力系数收敛过程

    Figure  14.  The convergence history of drag coefficients

    图  17  优化翼型压力分布对比

    Figure  17.  Comparison of pressure distributions of optimized and initial airfoils

    图  18  单点优化设计翼型在非设计点气动特性对比

    Figure  18.  Comparison of aerodynamic characteristics of optimized airfoil on off-design points

    图  19  优化翼型与初始翼型外形对比

    Figure  19.  Comparison of optimized and initial airfoils

    图  20  优化翼型阻力发散特性对比

    Figure  20.  Comparison of drag-divergence characteristics of optimized and initial airfoils

    图  21  优化翼型与RAE2822翼型在不同状态下压力分布对比

    Figure  21.  Comparison of pressure distributions of optimized and initial airfoils under different Mach numbers

    图  23  不同计算网格量下计算压力分布与试验压力分布对比

    Figure  23.  Comparison of computational and experimental pressure distributions under different number of grids

    图  24  M6机翼FFD框

    Figure  24.  FFD frame of M6 wing

    图  25  两种方法阻力收敛历程对比

    Figure  25.  The convergence history of different optimization algorithms

    图  26  初始机翼和优化后机翼(MF-PCK_VF-EI)上表面压力云图对比

    Figure  26.  Comparison of pressure distribution contours of upper surface of M6 wing using the MF-PCK_VF-EI method

    图  27  初始机翼和优化后的机翼(MF-PCK_VF-EI)各剖面压力分布和翼型对比

    Figure  27.  Comparison of pressure distributions and shapes of initial and optimized wing sections

    图  22  M6 机翼CFD计算空间网格展示

    Figure  22.  Computational grids of M6 wing

    表  1  3种优化方法结果对比

    Table  1.   Comparison of optimization results using three methods

    Optimization methodThe optimal
    locations
    The optimal valuesPrediction errors/10−4
    Kriging_EI[−3.1702579,12.2190345]0.41744748.953
    HK_VF-EI[3.1912351, 2.3199426]0.41666187.642
    MF-PCK_VF-EI[9.4185951, 2.4763138]0.39811353.692
    下载: 导出CSV

    表  2  RAE2822网格收敛结果对比

    Table  2.   Comparison of computational results of different levels of grids

    Grid levelGrid number$ {C}_{l} $$ {C}_{d} $$ {C}_{m} $α/(°)
    $ {L}_{1} $$ 0.4\times {10}^{4} $0.8240.024297−0.0961643.022
    $ {L}_{2} $$ 2.1\times {10}^{4} $0.8240.021261−0.0922842.973
    $ {L}_{3} $$ 8.1\times {10}^{4} $0.8240.020112−0.0928682.917
    $ {L}_{4} $$ 12.7\times {10}^{4} $0.8240.019960−0.0960622.869
    $ {L}_{5} $$ 19.8\times {10}^{4} $0.8240.019729−0.0927782.806
    下载: 导出CSV

    表  3  RAE2822翼型优化设计结果对比

    Table  3.   Comparison of optimization results of RAE2822 airfoil

    Optimization methods$ {C}_{l} $${C}_{d}/10^{-3}$Areas${C}_{m}/10^{-3}$Total time of CFD evaluations
    Kriging_EI0.82411.3750.0779−91.98$ 70{N}_{h} + 40{N}_{h} = 110 t $
    HK_VF-EI0.82411.2820.0779−91.75$ 50{N}_{h} + 15{N}_{h} + 500{N}_{l}\approx 90 t $
    MF-PCK_VF-EI0.82411.1820.0779−91.71$ 30{\mathit{N}}_{\mathit{h}} + 15{\mathit{N}}_{\mathit{h}} + 500{\mathit{N}}_{\mathit{l}}\approx 70\mathit{t} $
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-08-25
  • 录用日期:  2022-11-07
  • 网络出版日期:  2022-11-08

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