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基于非支配排序的并行加点方法研究及应用

刘睿 白俊强 邱亚松

刘睿,白俊强,邱亚松. 基于非支配排序的并行加点方法研究及应用[J]. 北京航空航天大学学报,2023,49(6):1446-1459 doi: 10.13700/j.bh.1001-5965.2022.0831
引用本文: 刘睿,白俊强,邱亚松. 基于非支配排序的并行加点方法研究及应用[J]. 北京航空航天大学学报,2023,49(6):1446-1459 doi: 10.13700/j.bh.1001-5965.2022.0831
LIU R,BAI J Q,QIU Y S. Research and application of parallel infill sampling method based on non-dominated sorting[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(6):1446-1459 (in Chinese) doi: 10.13700/j.bh.1001-5965.2022.0831
Citation: LIU R,BAI J Q,QIU Y S. Research and application of parallel infill sampling method based on non-dominated sorting[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(6):1446-1459 (in Chinese) doi: 10.13700/j.bh.1001-5965.2022.0831

基于非支配排序的并行加点方法研究及应用

doi: 10.13700/j.bh.1001-5965.2022.0831
详细信息
    通讯作者:

    E-mail:lr300150@163.com

  • 中图分类号: V221

Research and application of parallel infill sampling method based on non-dominated sorting

More Information
  • 摘要:

    代理优化方法可以大幅提升高精度数值优化的效率,而加点方法对于优化结果和效率非常重要。并行加点方法一次可以添加多个训练样本,从而可以充分发挥计算资源的利用率,并且提高效率。在包含子优化的紧密式代理优化框架上将预测值、预测方差和期望改善(EI)函数值两两结合作为子优化目标,构建3种多目标并行加点方法,提出基于非支配排序的并行加点样本的策略。以SC(six-hump camel back)函数和2维GN(Griewank)函数、5维Rosenbrock函数及10维HD1(high-dimension 1)函数作为无约束优化算例,以7维G9函数作为约束优化算例,将构建的3种多目标并行加点方法与混合并行加点方法进行对比分析,结果表明:多目标并行加点方法效果较好。采用多目标并行加点方法、混合并行加点方法及基于计算流体力学(CFD)的遗传算法开展了二维多段翼型起飞状态的升阻比优化。优化结果表明:在升力系数不减小的约束下,多目标并行加点方法经过少量CFD评估,得到的优化结果使升阻比提升了14%,证明多目标并行加点方法在工程问题中的适用性。

     

  • 图 1  紧密式代理优化框架

    Figure 1.  Framework of inseparable surrogate-based optimization

    图 2  SC函数样本点分布

    Figure 2.  Sample distributions of SC function

    图 3  SC函数收敛历程

    Figure 3.  Convergence histories of SC function

    图 4  SC函数所有样本函数值

    Figure 4.  SC function values for all samples

    图 5  GN函数样本分布

    Figure 5.  Sample distributions of GN function

    图 6  GN函数收敛历程

    Figure 6.  Convergence histories of GN function

    图 7  GN函数所有样本函数值

    Figure 7.  GN function values for all samples

    图 8  RB5函数收敛历程

    Figure 8.  Convergence histories of RB5 function

    图 9  RB5函数所有样本函数值

    Figure 9.  RB5 function values for all samples

    图 10  HD1函数收敛历程

    Figure 10.  Convergence histories of HD1 function

    图 11  HD1函数所有样本函数值

    Figure 11.  HD1 function values for all samples

    图 12  G9函数收敛历程

    Figure 12.  Convergence histories of G9 function

    图 13  G9函数所有样本函数值

    Figure 13.  G9 function values for all samples

    图 14  多段翼型形状参数

    Figure 14.  Shape parameters of multi-foil

    图 15  二维多段翼型收敛历程

    Figure 15.  Convergence histories of multi-foil

    图 16  气动外形

    Figure 16.  Aerodynamic shapes

    图 17  压力分布

    Figure 17.  Pressure distributions

    表  1  SC函数优化结果

    Table  1.   SC function optimization results

    加点方法最大最优解最小最优解平均最优解方差
    多目标MSP+MSE−1.031585−1.031608−1.0315867.919×10−11
    多目标MSP+EI−1.031620−1.031628−1.0316248.500×10−12
    多目标MSE+EI−1.031565−1.031616−1.0315933.525×10−10
    混合MSP+MSE−1.031546−1.031587−1.0315622.527×10−10
    混合MSP+EI−1.031606−1.031617−1.0316121.219×10−11
    混合MSE+EI−1.031502−1.031547−1.0315253.977×10−10
    下载: 导出CSV

    表  2  GN函数优化结果对比

    Table  2.   Comparison of GN function optimization results

    加点方法最大最优解最小最优解平均最优解方差
    多目标MSP+MSE0.1336×10−20.3400×10−40.5942×10−32.7742×10−7
    多目标MSP+EI0.3015×10−20.3191×10−30.2035×10−21.0961×10−6
    多目标MSE+EI0.1632×10−10.5207×10−30.9236×10−24.4510×10−5
    混合MSP+MSE0.3238×10−20.1116×10−30.1305×10−21.4331×10−6
    混合MSP+EI0.7878×10−10.1462×10−20.3933×10−18.8700×10−4
    混合MSE+EI0.1889×10−10.3288×10−20.1033×10−13.1375×10−5
    下载: 导出CSV

    表  3  RB5函数优化结果

    Table  3.   RB5 function optimization results

    加点方法最大最优解最小最优解平均最优解方差
    多目标MSP+MSE0.3688×1000.1346×1000.2380×1009.2365×10−3
    多目标MSP+EI0.1383×10−10.3822×10−20.8861×10−21.9272×10−5
    多目标MSE+EI0.6197×10−10.2293×10−10.4350×10−13.3689×10−4
    混合MSP+MSE0.5963×1000.3502×1000.4553×1008.1918×10−3
    混合MSP+EI0.3270×10−10.5230×10−20.2063×10−11.2910×10−4
    混合MSE+EI0.2858×1000.1793×1000.2326×1001.4606×10−3
    下载: 导出CSV

    表  4  HD1函数优化结果

    Table  4.   HD1 function optimization results

    加点方法最大最优解最小最优解平均最优解方差
    多目标MSP+MSE31.72722.36327.27911.692
    多目标MSP+EI9.2784.4926.72653.308
    多目标MSE+EI26.87917.88522.35412.197
    混合MSP+MSE42.14532.42737.04212.072
    混合MSP+EI12.6584.9309.0657.995
    混合MSE+EI58.52748.08453.35614.805
    下载: 导出CSV

    表  5  G9函数优化结果对比

    Table  5.   Comparison of G9 function optimization results

    加点方法最大最优解最小最优解平均最优解方差
    多目标MSP+MSE743.90732.96737.9016.750
    多目标MSP+EI703.80697.39700.985.393
    多目标MSE+EI773.57760.60767.1823.478
    混合MSP+MSE792.20779.59784.8322.643
    混合MSP+EI734.87722.61728.2115.863
    混合MSE+EI783.39768.96776.2927.633
    下载: 导出CSV

    表  6  二维多段翼型优化设计空间

    Table  6.   Design space of multi-foil

    参数数值
    上边界下边界
    z方向/mS11.045841.09584
    S21.095841.15584
    S31.189221.22922
    S41.251721.27172
    S51.289721.30572
    F11.097201.16073
    F21.160731.21073
    F31.223831.26383
    F41.271701.30170
    F51.295201.31020
    搭接量缝翼−0.010.01
    襟翼−0.010.01
    缝道宽度缝翼0.0050.02
    襟翼0.0050.02
    偏转角度/(°)缝翼1723
    襟翼2026
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-10-04
  • 录用日期:  2022-12-30
  • 网络出版日期:  2023-01-20
  • 整期出版日期:  2023-06-30

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