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基于多链竞争差分进化算法的无砟轨道结构有限元模型修正

叶玲 江宏康 陈华鹏 冯宇轩 王力骋

叶玲, 江宏康, 陈华鹏, 冯宇轩, 王力骋. 基于多链竞争差分进化算法的无砟轨道结构有限元模型修正[J]. 交通运输工程学报, 2024, 24(2): 112-124. doi: 10.19818/j.cnki.1671-1637.2024.02.007
引用本文: 叶玲, 江宏康, 陈华鹏, 冯宇轩, 王力骋. 基于多链竞争差分进化算法的无砟轨道结构有限元模型修正[J]. 交通运输工程学报, 2024, 24(2): 112-124. doi: 10.19818/j.cnki.1671-1637.2024.02.007
YE Ling, JIANG Hong-kang, CHEN Hua-peng, FENG Yu-xuan, WANG Li-cheng. Finite element model correction for ballastless track structure based on multi-chain competition based differential evolution algorithm[J]. Journal of Traffic and Transportation Engineering, 2024, 24(2): 112-124. doi: 10.19818/j.cnki.1671-1637.2024.02.007
Citation: YE Ling, JIANG Hong-kang, CHEN Hua-peng, FENG Yu-xuan, WANG Li-cheng. Finite element model correction for ballastless track structure based on multi-chain competition based differential evolution algorithm[J]. Journal of Traffic and Transportation Engineering, 2024, 24(2): 112-124. doi: 10.19818/j.cnki.1671-1637.2024.02.007

基于多链竞争差分进化算法的无砟轨道结构有限元模型修正

doi: 10.19818/j.cnki.1671-1637.2024.02.007
基金项目: 

国家自然科学基金项目 52008168

详细信息
    作者简介:

    叶玲(1989-),女,湖北京山人,华东交通大学讲师,工学博士,从事结构健康监测与轨道动力学研究

  • 中图分类号: U239.5

Finite element model correction for ballastless track structure based on multi-chain competition based differential evolution algorithm

Funds: 

National Natural Science Foundation of China 52008168

More Information
    Author Bio:

    YE Ling(1989-), female, assistant professor, PhD, 58718070@qq.com

  • 摘要: 为获得更接近真实情况的轨道结构模型,提出了一种基于多链竞争差分进化算法的无砟轨道结构有限元模型修正方法;以频率振型模态为响应建立了适用于无砟轨道结构的目标函数和似然函数,以标准马尔科夫链蒙特卡罗算法为基础,引入多链差分进化算法来解决高维参数模型效率低和收敛难的问题;引进竞争算法,利用竞争决出的失败者向胜利者学习的机制,不断迭代修正钢轨模型以提高修正精度;在此基础上,通过一个无砟轨道结构有限元模型修正数值算例验证所提方法的高效性。分析结果表明:采用Metropolis-Hastings算法和延缓拒绝自适应Metropolis算法修正后,单元参数与真实值间的最大相对误差分别为4.75%和1.35%,而采用多链竞争差分进化算法修正后,单元参数与真实值间的最大相对误差为0.28%,且模态振型向量之间的相关性接近1,说明多链竞争差分进化算法的修正精度优于另外2种算法;在分别加噪5%、10%和15%的噪声测试中,采用Metropolis-Hastings算法和延缓拒绝自适应Metropolis算法修正后,参数误差达到了9%左右,而采用多链竞争差分进化算法模型修正后,参数误差均在5%以内,进一步证明了多链竞争差分进化算法良好的鲁棒性。由此可见,多链竞争差分进化算法可以为解决复杂环境导致测试信息不完备的无砟轨道结构有限元模型修正提供一种新手段。

     

  • 图  1  算法改进过程

    Figure  1.  Algorithm improvement process

    图  2  算法流程

    Figure  2.  Flow of algorithm

    图  3  钢轨模型单元划分

    Figure  3.  Unit division for rail model

    图  4  轨道单元模型

    Figure  4.  Track unit model

    图  5  一阶测试频率均值

    Figure  5.  Mean values of first-order test frequency

    图  6  归一化二阶振型均值

    Figure  6.  Mean values of normalized second-order vibration mode

    图  7  修正前后三阶振型对比

    Figure  7.  Comparison of third-order vibration modes before and after correction

    图  8  DRAM算法和多链CB-DE算法修正后θ7的频数对比

    Figure  8.  Comparison of frequencies of θ7 corrected by DRAM algorithm and multi-chain CB-DE algorithm

    图  9  MH算法修正过程

    Figure  9.  Correction process of MH algorithm

    图  10  DRAM算法修正过程

    Figure  10.  Correction process of DRAM algorithm

    图  11  多链CB-DE算法修正过程

    Figure  11.  Correction process of multi-chain CB-DE algorithm

    图  12  加噪5%、10%和15%的一阶模态频率

    Figure  12.  First-order mode frequencies with 5%, 10%, and 15% noise

    图  13  不同噪声下3种算法修正后参数θ3的误差

    Figure  13.  Errors of parameter θ3 corrected by three algorithms under different noises

    表  1  CRTS Ⅱ型无砟轨道参数

    Table  1.   Parameters of CRTS Ⅱ ballastless track

    部件 参数 取值
    钢轨 质量/(kg·m-1) 60
    弹性模量/MPa 2.06×105
    截面惯性矩/m4 0.321 7×10-4
    横截面积/m2 7.745×10-3
    轨道板 长度/m 6.45
    宽度/m 2.55
    厚度/m 0.2
    密度/(kg·m-3) 2 500
    弹性模量/MPa 3.9×105
    路基 刚度系数/(MN·m) 60
    阻尼系数/(kN·s·m-1) 90
    垫板 刚度系数/(MN·m) 60
    阻尼系数/(kN·s·m-1) 50
    CA砂浆 刚度系数/(MN·m) 900
    阻尼系数/(kN·s·m-1) 83
    混凝土支承层 长度/m 6.45
    宽度/m 2.95
    厚度/m 0.3
    密度/(kg·m-3) 2 500
    弹性模量/MPa 3.0×104
    下载: 导出CSV

    表  2  待修正参数的真实值

    Table  2.   True values of parameters to be corrected

    单元 1 2 3 4 5
    真实值 1.2E0 1.4E0 1.6E0 1.8E0 2.0E0
    单元 6 7 8 9 10
    真实值 2.2E0 2.4E0 2.6E0 2.8E0 3.0E0
    下载: 导出CSV

    表  3  各阶频率均值与标准差

    Table  3.   Mean values and standard deviations of frequencies at different orders

    阶数 均值/Hz 标准差/Hz 变异系数/%
    1 8.985 0.006 3 0.07
    2 10.673 0.018 0 0.17
    3 12.580 0.016 0 0.13
    4 14.174 0.010 0 0.07
    5 15.022 0.035 0 0.23
    6 21.693 0.019 0 0.09
    下载: 导出CSV

    表  4  三种算法的频率修正结果对比

    Table  4.   Comparison of frequency correction results among three algorithms

    阶数 测试均值/Hz MH DRAM 多链CB-DE
    均值/Hz 相对误差/% 均值/Hz 相对误差/% 均值/Hz 相对误差/%
    1 8.985 8.876 1.21 8.981 0.04 8.960 0.28
    2 10.673 10.547 1.18 10.670 0.03 10.678 0.05
    3 12.580 12.476 0.83 12.570 0.08 12.583 0.02
    4 14.174 14.847 4.75 14.344 1.20 14.178 0.03
    5 15.022 14.890 0.88 15.225 1.35 15.008 0.09
    6 21.693 21.561 0.61 21.553 0.65 21.691 0.01
    下载: 导出CSV

    表  5  三种算法修正后振型的MAC对比

    Table  5.   Comparison of MACs of vibration modes corrected by three algorithms

    阶数 1 2 3 4
    MH 0.991 0.993 0.989 0.993
    DRAM 0.998 0.997 0.992 0.995
    多链CB-DE 0.999 0.999 0.998 0.998
    下载: 导出CSV

    表  6  三种算法的参数修正结果对比

    Table  6.   Comparison of parameter correction results among three algorithms

    参数 真实值 初始值 MH DRAM 多链CB-DE
    θ1 1.20E0 4.34E0 1.12E0 1.25E0 1.20E0
    θ2 1.40E0 4.91E0 1.41E0 1.39E0 1.40E0
    θ3 1.60E0 3.75E0 1.46E0 1.58E0 1.62E0
    θ4 1.80E0 2.20E0 1.78E0 1.81E0 1.80E0
    θ5 2.00E0 4.59E0 1.95E0 1.98E0 1.99E0
    θ6 2.20E0 4.53E0 2.16E0 2.19E0 2.19E0
    θ7 2.40E0 3.50E0 2.40E0 2.43E0 2.40E0
    θ8 2.60E0 4.12E0 2.67E0 2.59E0 2.59E0
    θ9 2.80E0 1.80E0 2.80E0 2.82E0 2.80E0
    θ10 3.00E0 4.89E0 3.01E0 2.98E0 3.00E0
    下载: 导出CSV

    表  7  不同噪声下参数θ3的修正误差

    Table  7.   Correction errors of parameter θ3 under different noises  %

    加噪值/% 5 10 15
    MH 1.41 5.20 8.21
    DRAM 1.22 5.03 8.05
    多链CB-DE 0.84 2.61 5.11
    下载: 导出CSV
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  • 收稿日期:  2023-11-08
  • 网络出版日期:  2024-05-16
  • 刊出日期:  2024-04-30

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