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基于Kriging模型和提升小波变换的随机模型修正

吴雨程 殷红 彭珍瑞

吴雨程,殷红,彭珍瑞. 基于Kriging模型和提升小波变换的随机模型修正 [J]. 应用数学和力学,2022,43(7):761-771 doi: 10.21656/1000-0887.420128
引用本文: 吴雨程,殷红,彭珍瑞. 基于Kriging模型和提升小波变换的随机模型修正 [J]. 应用数学和力学,2022,43(7):761-771 doi: 10.21656/1000-0887.420128
WU Yucheng, YIN Hong, PENG Zhenrui. Stochastic Model Updating Based on Kriging Model and Lifting Wavelet Transform[J]. Applied Mathematics and Mechanics, 2022, 43(7): 761-771. doi: 10.21656/1000-0887.420128
Citation: WU Yucheng, YIN Hong, PENG Zhenrui. Stochastic Model Updating Based on Kriging Model and Lifting Wavelet Transform[J]. Applied Mathematics and Mechanics, 2022, 43(7): 761-771. doi: 10.21656/1000-0887.420128

基于Kriging模型和提升小波变换的随机模型修正

doi: 10.21656/1000-0887.420128
基金项目: 国家自然科学基金 (51768035)
详细信息
    作者简介:

    吴雨程(1997—),男,硕士生 (E-mail:821085844@qq.com

    殷红(1978—),女,教授,博士,硕士生导师 (E-mail:yinhong@mail.lzjtu.cn

    彭珍瑞(1972—),男,教授,博士,博士生导师 (通讯作者. E-mail:pzrui@163.com

  • 中图分类号: O327

Stochastic Model Updating Based on Kriging Model and Lifting Wavelet Transform

  • 摘要:

    为提高随机模型修正效率,减小计算量,提出了一种基于Kriging模型和提升小波变换的随机模型修正方法。首先,对加速度频响函数进行提升小波变换,提取第5层近似系数代替原频响函数。其次,采用拉丁超立方抽样抽取待修正样本,将其作为Kriging模型的输入,对应的近似系数作为输出,构建Kriging模型。提出了一种引入莱维飞行(Lévy flight)的蝴蝶优化算法(LBOA),并将其应用于Kriging模型相关参数的寻优中,提高Kriging模型的精度。最后,以最小化Wasserstein距离为目标,通过鲸鱼优化算法求解待修正参数的均值。测试函数结果表明,LBOA在寻优能力、收敛精度和稳定性等方面有了很大的提升。数值算例的修正误差均低于0.4%,验证了所提模型修正方法具有较高的修正精度和效率。

  • 图  1  f6收敛曲线

    Figure  1.  Convergence curves of $ {f_6} $

    图  2  提升小波变换过程

    Figure  2.  The process of the lifting wavelet transform

    图  3  近似系数提取流程

    Figure  3.  The flow chart of extracting approximate coefficients

    图  4  模型修正流程图

    Figure  4.  The flowchart of model updating

    图  5  二维桁架结构

    Figure  5.  The 2D truss structure

    图  6  参数对结构AFRF的灵敏度

    Figure  6.  Sensitivity of structure AFRF to parameters

    图  7  Kriging模型精度评估

    Figure  7.  Accuracy evaluation of the Kriging model

    图  8  修正前后加速度频响函数曲线

    Figure  8.  AFRF curves before and after updating

    图  9  三维桁架结构

    Figure  9.  The 3D truss structure

    图  10  第1、3、5层近似系数

    Figure  10.  Approximate coefficients for the 1st, 3rd and 5th levels

    图  11  Kriging模型参数寻优曲线

    Figure  11.  Optimization curves of the Kriging model parameter

    图  12  Kriging模型精度评估

    Figure  12.  Accuracy evaluation of the Kriging model

    图  13  修正前后加速度频响函数曲线:(a)实部曲线;(b)虚部曲线

    Figure  13.  AFRF curves before and after updating: (a) real part curves; (b) imaginary part curves

    表  1  BOA改进算法寻优结果

    Table  1.   Optimization results of the improved BOA algorithm

    functionBOALBOA
    mean valuestandard deviationsuccessful rate $\delta$/%mean valuestandard deviationsuccessful rate $\delta$/%
    $ {f_1} $1.80E−141.25E−1510000100
    $ {f_2} $9.43E−123.40E−1210000100
    $ {f_3} $7.67E−43.48E−404.37E−54.93E−586
    $ {f_4} $1.81E−152.24E−1510000100
    $ {f_5} $1.90E+15.81E+18000100
    $ {f_6} $1.19E−111.95E−121008.88E−160100
    下载: 导出CSV

    表  2  寻优结果对比

    Table  2.   Comparison of optimization results

    LBOABOA
    ${\theta _k}$4.064 5 × 1033.320 5
    fitting value e7.396 2 × 10146.941 9 × 10−8
    running time t/s27.227.7
    下载: 导出CSV

    表  3  桁架结构修正前后参数均值及误差

    Table  3.   Parameter mean values and errors of the truss structure before and after updating

    updated parametertest valuefinite element valueupdated valuerelative error δ/%
    E/GPa190171189.8810.0626
    E/GPa190209190.0090.0047
    E/GPa190171189.9370.0331
    E/GPa190209189.9710.0155
    下载: 导出CSV

    表  4  不同响应指标下的结果对比

    Table  4.   Comparison of results under different response indicators

    response indicatorrelative error of E
    δ1/%
    relative error of E
    δ2/%
    relative error of E
    δ3/%
    relative error of E
    δ4/%
    time consumed
    t/s
    AFRF1.80921.89070.99210.773992
    approximate coefficient0.06260.00470.03310.015527
    下载: 导出CSV

    表  5  桁架结构修正前后结构参数均值及误差

    Table  5.   Parameter mean values and errors of the truss structure before and after updating

    updated parametertest valuefinite element valueupdated valuerelative error δ/%
    E/GPa190209189.6070.207
    $\rho /({\text{kg} } \cdot { {\text{m} }^{ { { - 3} } } })$780070207773.5620.339
    A/mm285.59585.6620.189
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-05-10
  • 修回日期:  2021-06-17
  • 刊出日期:  2022-07-15

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