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基于响应面法和改进算术优化算法的抱杆优化设计

陶然 周焕林 孟增 杨小猛

陶然,周焕林,孟增,杨小猛. 基于响应面法和改进算术优化算法的抱杆优化设计 [J]. 应用数学和力学,2022,43(10):1-10 doi: 10.21656/1000-0887.420318
引用本文: 陶然,周焕林,孟增,杨小猛. 基于响应面法和改进算术优化算法的抱杆优化设计 [J]. 应用数学和力学,2022,43(10):1-10 doi: 10.21656/1000-0887.420318
Ran TAO, Huanlin ZHOU, Zeng MENG, Xiaomeng YANG. Optimization Design of Holding Pole Based on Response Surface Methodology and Improved Arithmetic Optimization Algorithm[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420318
Citation: Ran TAO, Huanlin ZHOU, Zeng MENG, Xiaomeng YANG. Optimization Design of Holding Pole Based on Response Surface Methodology and Improved Arithmetic Optimization Algorithm[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420318

基于响应面法和改进算术优化算法的抱杆优化设计

doi: 10.21656/1000-0887.420318
基金项目: 国家自然科学基金(11672098)
详细信息
    作者简介:

    陶然(1991—),男,博士生 (E-mail: taoran127@mail.hfut.edu.cn

    周焕林(1973—),男,教授,博士,博士生导师 (通讯作者. E-mail: zhouhl@hfut.edu.cn

    孟增(1986—),男,副教授,博士,博士生导师 (通讯作者. E-mail: mengz@hfut.edu.cn

  • 中图分类号: TM752

Optimization Design of Holding Pole Based on Response Surface Methodology and Improved Arithmetic Optimization Algorithm

  • 摘要: 抱杆优化设计需要耗费大量有限元分析计算时间,难以确定可行域。该文采用响应面法(response surface method,RSM)来模拟抱杆结构真实响应,提出了改进的算术优化算法(improved arithmetic optimization algorithm,IAOA)对抱杆结构进行优化设计。将分数阶积分引入算术优化算法(arithmetic optimization algorithm,AOA),改善了算法的开发能力。采用拉丁超立方抽样选取抱杆结构杆件截面试验样本,利用最小二乘法对样本点进行分析,构建了抱杆结构应力和位移关于杆件截面尺寸的二阶响应面代理模型。建立以抱杆质量最小化为优化目标,许用应力和位移为约束条件的优化模型,采用IAOA对其进行求解。结果表明:二阶响应面模型能够准确预测抱杆结构的响应值,IAOA的求解精度得到显著提升,代理模型可大幅降低有限元分析所需的计算代价,优化后抱杆结构质量减轻了8.2%。联合使用RSM和IAOA可有效求解大型空间杆系结构的优化设计问题。
  • 图  1  AOA优化流程

    Figure  1.  The optimization process of AOA

    图  2  抱杆

    Figure  2.  Holding pole

    图  3  不同算法收敛曲线对比

    Figure  3.  Comparison of convergence curves for different algorithms

    表  1  抱杆结构拉丁超立方试验设计结果

    Table  1.   Latin hypercube experimental design results of holding pole

    No.b1/mmt1/mmb2/mmt2/mmb3/mmt3/mmσ/MPad/mm
    111210413817112.776618.502
    2968468736144.207855.603
    31457877764112.785640.648
    41478564967112.759589.670
    513111944448112.745503.594
    6918854495154.753879.046
    714310866584112.738496.787
    8908778817157.628931.646
    91279656877112.765618.600
    101098936565120.008741.433
    1110410499608112.789672.708
    121156476848158.176925.155
    1314012558674112.725455.399
    141109513605112.800672.017
    151379924795112.755563.238
    1612810635858112.750571.317
    17948847804147.380865.021
    1814112646868112.726472.743
    191219524875112.793623.275
    2012312726544112.746498.627
    211207768997123.901800.895
    221067547889147.233893.174
    239711564946112.787667.220
    241007764685158.786903.924
    2514711454896112.729467.172
    2611910506509112.764590.889
    2712911695493112.746507.854
    281057884959148.844902.907
    2914411985915112.723480.494
    3012710875528112.753558.483
    下载: 导出CSV

    表  2  响应面模型随机样本点检验结果

    Table  2.   Test results of random sample points for the response surface model

    itemδ2δRAAEδRMAE
    σ/MPa0.92570.01150.0635
    d/mm0.97740.01950.0174
    high adaptative interval H0.9 ~ 10 ~ 0.20 ~ 0.3
    下载: 导出CSV

    表  3  响应面模型随机非样本点检验结果

    Table  3.   Test results of random non-sample points for the response surface model

    No.σ/MPa$ \hat \sigma $/MPastress error ε/%d/mm$ \hat d $/mmstress error ε/%
    1112.7705111.01601.56576.5725585.72131.59
    2112.7441115.62232.55515.2002535.58263.96
    下载: 导出CSV

    表  4  各算法的参数值

    Table  4.   Parameter values for each algorithm.

    algorithmparametervalue
    GAtypereal coded
    selectionroulette wheel (proportionate)
    crossoverwhole arithmetic
    (probability = 0.8, α = [−0.5, 1.5])
    mutationGaussian (Probability = 0.05)
    PSOcognitive and social constant inertia weight(C1, C2): (2, 2)
    linear reduction from 0.9 to 0.1
    FAα0.5
    β0.2
    γ1
    AOAα5
    µ0.5
    IAOAα5
    µ0.5
    下载: 导出CSV

    表  5  不同算法抱杆优化结果对比

    Table  5.   Optimization results comparison by different algorithms for holding pole

    algorithmb1/mmt1/mmb2/mmt2/mmb3/mmt3/mmW/kgevaluation number
    GA146114010401040 721.261 000
    PSO15012401040540 773.771 000
    FA1441159985847 689.621 000
    AOA15012401040440 164.251 000
    IAOA150104010401039 780.551 000
    下载: 导出CSV

    表  6  抱杆优化前后结果对比

    Table  6.   Results comparison before and after optimization for holding pole

    situationb1/mmt1/mmb2/mmt2/mmb3/mmt3/mmW/kg
    initial1501270570543 335.21
    IAOA150104010401039 780.55
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-10-25
  • 修回日期:  2022-05-25
  • 网络出版日期:  2022-05-26

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