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基于置信区间的约束多精度序贯代理模型优化方法及应用

钱家昌 程远胜 张锦岚

钱家昌, 程远胜, 张锦岚. 基于置信区间的约束多精度序贯代理模型优化方法及应用[J]. 中国舰船研究, 2021, 16(4): 37–43 doi: 10.19693/j.issn.1673-3185.02025
引用本文: 钱家昌, 程远胜, 张锦岚. 基于置信区间的约束多精度序贯代理模型优化方法及应用[J]. 中国舰船研究, 2021, 16(4): 37–43 doi: 10.19693/j.issn.1673-3185.02025
QIAN J C, CHENG Y S, ZHANG J L. Multi-fidelity sequential constraint updating optimization approach based on confidence intervals and its application[J]. Chinese Journal of Ship Research, 2021, 16(4): 37–43 doi: 10.19693/j.issn.1673-3185.02025
Citation: QIAN J C, CHENG Y S, ZHANG J L. Multi-fidelity sequential constraint updating optimization approach based on confidence intervals and its application[J]. Chinese Journal of Ship Research, 2021, 16(4): 37–43 doi: 10.19693/j.issn.1673-3185.02025

基于置信区间的约束多精度序贯代理模型优化方法及应用

doi: 10.19693/j.issn.1673-3185.02025
基金项目: 国防科技工业海洋防务技术创新中心创新基金资助项目(YT19201701)
详细信息
    作者简介:

    钱家昌,男,1983年生,博士,高级工程师

    程远胜,男,1962年生,博士,教授,博士生导师。研究方向:结构分析与轻量化设计,结构冲击动力学与防护设计,基于代理模型的优化方法。E-mail:yscheng@hust.edu.cn

    张锦岚,男,1963年生,硕士,研究员,博士生导师

    通信作者:

    张锦岚

  • 中图分类号: U662.2

Multi-fidelity sequential constraint updating optimization approach based on confidence intervals and its application

  • 摘要:   目的  水下结构物优化设计领域面临着仿真耗时优化的难题。针对目标不耗时、约束耗时这类优化问题,开展多精度数据来源情况下的约束序贯代理模型优化方法研究。  方法  提出一种基于置信区间的约束多精度序贯Co-Kriging代理模型优化方法(MF-SCU-CI),建立能综合评估代理模型不确定性水平、高/低精度模型相关程度以及成本系数的Co-H函数,用于指导序贯优化过程。然后,通过3个典型的数值测试函数和纵横加筋圆锥壳结构振动优化工程案例进行应用研究。  结果  结果表明,所提出的MF-SCU-CI方法较基于置信区间的约束单精度序贯代理模型优化方法(SCU-CI)具有更优的可行性比率,且优化求解效率更高,能够进一步减少耗时的仿真次数。  结论  该方法适用性好,具有良好的工程应用前景。
  • 图  1  MF-SCU-CI算法流程图

    Figure  1.  Flowchart of the proposed MF-SCU-CI algorithm

    图  2  纵横加筋圆锥壳结构模型

    Figure  2.  The model of longitudinal and transverse stiffened conical shell structure

    图  3  GA,SCU-CI和MF-SCU-CI方法收敛曲线

    Figure  3.  Convergence curves of three methods

    表  1  多精度测试函数参数设置

    Table  1.   Parameters setting of the multi-fidelity functions

    测试函数初始样本点数/个收敛准则
    相对误差/%最大进化代数
    Constrained Branin6+120.2100
    qcp412+240.2100
    G415+500.2100
    下载: 导出CSV

    表  2  数值测试算例在不同方法下的可行性比率

    Table  2.   Feasibility ratios of numerical test examples under different benchmark funcitons

    测试函数可行性比率总样本点数/个
    SCU-CIMF-SCU-CISCU-CIMF-SCU-CI
    Constrained Branin1.0001.00084.36736.83+52.83/10=42.11
    qcp40.8331.000113.66721.33+33.00/10=24.63
    G40.7331.00079.53332.33+77.77/10=40.11
    下载: 导出CSV

    表  3  设计变量及其取值范围

    Table  3.   Design variables and their range of values

    设计变量取值范围/mm
    周向肋骨腹板高${x_1}$200~340
    周向肋骨腹板厚${x_2}$10~24
    周向肋骨面板宽${x_3}$100~240
    周向肋骨面板厚${x_4}$10~24
    纵向肋骨腹板高${x_5}$100~240
    纵向肋骨腹板厚${x_6}$6~20
    纵向肋骨面板宽${x_7}$40~180
    纵向肋骨面板厚${x_8}$6~20
    艉段圆锥壳厚${x_9}$6~20
    艏段圆锥壳厚${x_{10}}$6~20
    下载: 导出CSV

    表  4  优化设计方案

    Table  4.   Optimization design results

    设计变量GASCU-CIMF-SCU-CI
    修正前修正后修正前修正后
    ${x_1}$232258245272288
    ${x_{\rm{2}}}$1514151416
    ${x_{\rm{3}}}$119121111109101
    ${x_{\rm{4}}}$1916141814
    ${x_{\rm{5}}}$115110114127105
    ${x_{\rm{6}}}$96987
    ${x_{\rm{7}}}$5952584550
    ${x_{\rm{8}}}$131110711
    ${x_{\rm{9}}}$1719201818
    ${x_{1{\rm{0}}}}$87868
    下载: 导出CSV

    表  5  不同方法结果对比

    Table  5.   Result comparision of different methods

    参数GASCU-CIMF-SCU-CI
    修正前修正后修正前修正后
    w(x)/t8 3998 1338 4248 0708 248
    $\hat g{}_1$−0.012 9−0.010 4−0.002 0−0.025 1
    $\hat g{}_2$−0.007 2−0.005 5−0.012 7−0.004 5
    $g{}_1$00.034 5−0.032 30.024 3−0.011 0
    $g{}_2$−0.000 5−0.005 7−0.007 1−0.010 3−0.005 5
    NS16 000518518382382
    下载: 导出CSV
  • [1] WANG G G, SHAN S. Review of metamodeling techniques in support of engineering design optimization[J]. Journal of Mechanical Design, 2007, 129(4): 370–380. doi: 10.1115/1.2429697
    [2] FORRESTER A I J, KEANE A J. Recent advances in surrogate-based optimization[J]. Progress in Aerospace Sciences, 2009, 45(1/2/3): 50–79.
    [3] PEHERSTORFER B, WILLCOX K, GUNZBURGER M. Survey of multifidelity methods in uncertainty propagation, inference, and optimization[J]. SIAM Review, 2018, 60(3): 550–591. doi: 10.1137/16M1082469
    [4] SHI R H, LIU L, LONG T, et al. Multi-fidelity modeling and adaptive co-Kriging-based optimization for all-electric geostationary orbit satellite systems[J]. Journal of Mechanical Design, 2020, 142(2): 021404. doi: 10.1115/1.4044321
    [5] 赵留平, 詹大为, 程远胜, 等. 船舶结构优化设计技术研究进展[J]. 中国舰船研究, 2014, 9(4): 1–10. doi: 10.3969/j.issn.1673-3185.2014.04.001

    ZHAO L P, ZHAN D W, CHENG Y S, et al. Review on optimum design methods of ship structures[J]. Chinese Journal of Ship Research, 2014, 9(4): 1–10 (in Chinese). doi: 10.3969/j.issn.1673-3185.2014.04.001
    [6] 郑少平, 陈静, 程远胜, 等. 代理模型技术及其在船舶板架强度和稳定性计算中的应用[J]. 中国造船, 2013, 54(1): 40–51. doi: 10.3969/j.issn.1000-4882.2013.01.007

    ZHENG S P, CHEN J, CHENG Y S, et al. Surrogate models and their application in calculation of strength and stability of ship grillage[J]. Shipbuilding of China, 2013, 54(1): 40–51 (in Chinese). doi: 10.3969/j.issn.1000-4882.2013.01.007
    [7] 夏志, 刘均, 程远胜. 基于代理模型的水下结构物基座阻抗特性快速预报[J]. 中国舰船研究, 2020, 15(3): 81–87.

    XIA Z, LIU J, CHENG Y S. Fast prediction of mechanical impedance of an underwater foundation based on surrogate models[J]. Chinese Journal of Ship Research, 2020, 15(3): 81–87 (in Chinese).
    [8] QIAN J C, YI J X, CHENG Y S, et al. A sequential constraints updating approach for Kriging surrogate model-assisted engineering optimization design problem[J]. Engineering with Computers, 2020, 36(3): 993–1009. doi: 10.1007/s00366-019-00745-w
    [9] HAN Z H, XU C Z, ZHANG L, et al. Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids[J]. Chinese Journal of Aeronautics, 2020, 33(1): 31–47. doi: 10.1016/j.cja.2019.05.001
    [10] JIANG P, CHENG J, ZHOU Q, et al. Variable-fidelity lower confidence bounding approach for engineering optimization problems with expensive simulations[J]. AIAA Journal, 2019, 57(12): 5416–5430. doi: 10.2514/1.J058283
    [11] YI J X, LIU J, CHENG Y S. A fast forecast method based on high and low fidelity surrogate models for strength and stability of stiffened cylindrical shell with variable ribs[C]//Proceedings of the 2018 IEEE 8th International Conference on Underwater System Technology: Theory and Applications. Wuhan: IEEE, 2018: 1–6.
    [12] 宋保维, 王新晶, 王鹏. 基于变保真度模型的AUV流体动力参数预测[J]. 机械工程学报, 2017, 53(18): 176–182. doi: 10.3901/JME.2017.17.176

    SONG B W, WANG X J, WANG P. Predictions of AUV's hydrodynamic parameters based on variable-fidelity modeling[J]. Journal of Mechanical Engineering, 2017, 53(18): 176–182 (in Chinese). doi: 10.3901/JME.2017.17.176
    [13] 姜哲, 崔维成, 黄小平. 基于响应面的可变复杂度方法在桁架式Spar平台方案设计中的应用[J]. 船舶力学, 2010, 14(7): 771–781. doi: 10.3969/j.issn.1007-7294.2010.07.010

    JIANG Z, CUI W C, HUANG X P. Response surface based variable-complexity method for optimization of truss Spar concept design[J]. Journal of Ship Mechanics, 2010, 14(7): 771–781 (in Chinese). doi: 10.3969/j.issn.1007-7294.2010.07.010
    [14] 张守慧, 谢玲玲, 冯佰威, 等. 基于变复杂度方法的船舶型线优化[J]. 船舶工程, 2018, 40(3): 5–9.

    ZHANG S H, XIE L L, FENG B W, et al. Ship profile optimization based on variable complexity method[J]. Ship Engineering, 2018, 40(3): 5–9 (in Chinese).
    [15] KENNEDY M C, O'HAGAN A. Predicting the output from a complex computer code when fast approximations are available[J]. Biometrika, 2000, 87(1): 1–13. doi: 10.1093/biomet/87.1.1
    [16] LV Z Y, LU Z Z, WANG P. A new learning function for Kriging and its applications to solve reliability problems in engineering[J]. Computers & Mathematics with Applications, 2015, 70(5): 1182–1197.
    [17] WANG Z L, IERAPETRITOU M. Constrained optimization of black-box stochastic systems using a novel feasibility enhanced Kriging-based method[J]. Computers & Chemical Engineering, 2018, 118: 210–223.
    [18] QIAN J C, YI J X, ZHANG J L, et al. An entropy weight-based lower confidence bounding optimization approach for engineering product design[J]. Applied Sciences, 2020, 10(10): 3554. doi: 10.3390/app10103554
    [19] 刘东, 王春旭, 刘均, 等. 纵横加筋圆锥壳振动特性多目标优化设计[J]. 中国舰船研究, 2018, 13(1): 24–30. doi: 10.3969/j.issn.1673-3185.2018.01.004

    LIU D, WANG C X, LIU J, et al. Multi-objective optimization design for vibration characteristics of longitudinal and transverse stiffened conical shells[J]. Chinese Journal of Ship Research, 2018, 13(1): 24–30 (in Chinese). doi: 10.3969/j.issn.1673-3185.2018.01.004
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出版历程
  • 收稿日期:  2020-07-04
  • 修回日期:  2020-09-23
  • 网络出版日期:  2021-06-11
  • 刊出日期:  2021-08-10

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