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含外部输入的非线性自回归模型及其在实时混合模拟中的应用

陈梦晖 徐伟杰 高小殊 郭彤 陈城

陈梦晖, 徐伟杰, 高小殊, 郭彤, 陈城. 含外部输入的非线性自回归模型及其在实时混合模拟中的应用[J]. 工程力学, 2022, 39(9): 40-47, 71. doi: 10.6052/j.issn.1000-4750.2021.05.0365
引用本文: 陈梦晖, 徐伟杰, 高小殊, 郭彤, 陈城. 含外部输入的非线性自回归模型及其在实时混合模拟中的应用[J]. 工程力学, 2022, 39(9): 40-47, 71. doi: 10.6052/j.issn.1000-4750.2021.05.0365
CHEN Meng-hui, XU Wei-jie, GAO Xiao-shu, GUO Tong, CHEN Cheng. EXPERIMENTAL STUDY ON NONLINEAR AUTOREGRESSIVE WITH EXOGENOUS INPUT FOR REAL-TIME HYBRID SIMULATION[J]. Engineering Mechanics, 2022, 39(9): 40-47, 71. doi: 10.6052/j.issn.1000-4750.2021.05.0365
Citation: CHEN Meng-hui, XU Wei-jie, GAO Xiao-shu, GUO Tong, CHEN Cheng. EXPERIMENTAL STUDY ON NONLINEAR AUTOREGRESSIVE WITH EXOGENOUS INPUT FOR REAL-TIME HYBRID SIMULATION[J]. Engineering Mechanics, 2022, 39(9): 40-47, 71. doi: 10.6052/j.issn.1000-4750.2021.05.0365

含外部输入的非线性自回归模型及其在实时混合模拟中的应用

doi: 10.6052/j.issn.1000-4750.2021.05.0365
基金项目: 国家自然科学基金项目(51808111,52178114);国家重点研发计划战略性国际科技创新合作重点专项项目(2018YFE0206100);江苏省科协青年科技人才托举工程项目(2021-077)
详细信息
    作者简介:

    陈梦晖(1993−),男,安徽芜湖人,博士生,主要从事抗震试验方法研究(E-mail: 230189096@seu.edu.cn)

    徐伟杰(1990−),男,山东临沂人,博士,主要从事抗震试验方法研究(E-mail: 1224418158@qq.com)

    高小殊(1994−),男,安徽池州人,硕士生,主要从事抗震试验方法研究(E-mail: gxshu1994@gmail.com)

    陈 城(1977−),男,上海人,教授,博士,主要从事抗震试验方法研究(E-mail: chcsfsu@sfsu.edu)

    通讯作者:

    郭 彤(1977−),男,山东青岛人,教授,博士,主要从事新型抗震结构体系、结构健康检测与评价研究(E-mail: guotong@seu.edu.cn)

  • 中图分类号: TU317;O242.2

EXPERIMENTAL STUDY ON NONLINEAR AUTOREGRESSIVE WITH EXOGENOUS INPUT FOR REAL-TIME HYBRID SIMULATION

  • 摘要: 传统实时混合模拟对数值子结构多采用有限元计算,对于较复杂或自由度较多的结构,容易导致计算机在指定积分步长内无法完成结构下一步响应的计算。为了提高计算效率,该文提出一种基于代理模型的实时混合模拟方法,采用含外部输入的非线性自回归模型代替有限元计算。以非线性数值子结构和自复位阻尼器试验子结构组成的单自由度体系为对象,使用数值模拟的数据来训练代理模型,并对该模型进行实时混合模拟试验验证。试验结果表明,基于代理模型的实时混合模拟与传统实时混合模拟结果十分接近,具有替代后者的潜力。
  • 图  1  单自由度实时混合模拟

    Figure  1.  Single-degree-of-freedom RTHS

    图  2  训练随机地震波

    Figure  2.  Stochastic ground motions for training

    图  3  试验子结构的数值模型与实测滞回曲线

    Figure  3.  Numerical model and tested hysteretic curve of experimental substructure

    图  4  模型训练流程

    Figure  4.  Procedure of training NARX model

    图  5  试验子结构与作动器

    Figure  5.  RTHS experimental substructure and actuator

    图  6  传统实时混合模拟

    Figure  6.  Flow chart of traditional RTHS

    图  7  基于NARX模型的实时混合模拟

    Figure  7.  Flow chart of NARX surrogate model RTHS

    图  8  验证随机地震波

    Figure  8.  Stochastic ground motions for validation

    图  9  作动器位移追踪效果(IC补偿后)

    Figure  9.  Actuator tracking error (after IC compensation)

    图  10  基于NARX的与传统的RTHS测量位移比较

    Figure  10.  Comparison between traditional and NARX RTHS

    图  11  试验子结构滞回曲线

    Figure  11.  Hysteretic curve of experimental substructure

    图  12  试验子结构能量耗散

    Figure  12.  Energy dissipation of experimental substructure

    表  1  NARX模型回归项和系数

    Table  1.   Terms and coefficients of NARX model

    单项式数学表达式
    回归项x(t)x(t−1)x(t−2)x(t−3)x(t−4)
    系数 −9.7626×10−4 −3.6631×10−7 4.8844×10−4 4.8704×10−4 9.0902×10−7
    回归项 F(t) F(t−1) F(t−2) F(t−3) F(t−4)
    系数 4.8743×10−6 8.6668×10−9 −2.4426×10−6 −2.4375×10−6 −2.3216×10−9
    回归项 y(t−1) y(t−2) y(t−3) y(t−4) x(t)×|cos(y(t−1))|3
    系数 0.99961 0.49998 1.7748×10−4 −0.49979 −6.7406×10−7
    回归项 x(t−1)× |cos(y(t−1))|3 x(t−2)× |cos(y(t−1))|3 x(t−3)× |cos(y(t−1))|3 x(t−4)× |cos(y(t−1))|3 F(t)× |cos(y(t−1))|3
    系数 1.0865×10−6 −7.1231×10−7 1.9195×10−6 −1.6538×10−6 1.1095×10−8
    回归项 F(t−1)× |cos(y(t−1))|3 F(t−2)× |cos(y(t−1))|3 F(t−3)× |cos(y(t−1))|3 F(t−4)× |cos(y(t−1))|3 y(t−1)× |cos(y(t−1))|3
    系数 −1.0848×10−8 6.553×10−9 −6.5151×10−9 −1.7233×10−5
    回归项 y(t−2)× |cos(y(t−1))|3 y(t−3)× |cos(y(t−1))|3 y(t−4)× |cos(y(t−1))|3 |cos(y(t−1))|3 1
    系数 2.977×10−5 −3.5679×10−5 2.328×10−5 −1.1399×10−6
    注:NARX模型回归项是100个NARX全模型中筛选出的第7号模型的回归项(28项),系数是由第8号验证随机地震波的验证数据算得。
    下载: 导出CSV

    表  2  实时混合模拟试验工况

    Table  2.   RTHS test cases

    验证随机
    地震波
    实时混合
    模拟试验方法
    强度$ {\overline I _{\rm{a}}} $/
    (s·g2)
    频率$\omega'$/
    (Hz·s−1)
    峰值加速度
    PGA/g
    vGM-8传统的0.01030.08460.053
    基于NARX的
    vGM-17传统的0.0074−0.30820.042
    基于NARX的
    vGM-20传统的0.0166−0.20960.064
    基于NARX的
    注:在实时混合模拟试验进行前,相应的虚拟实时混合模拟需要在Simulink中运行以预演试验情况从而确保试验安全。
    下载: 导出CSV

    表  3  两种RTHS试验结果误差

    Table  3.   Error indices of two types of RTHS

    验证随机
    地震波
    实时混合
    模拟试验方法
    PE/mmRPE/(%)RMSE/mm
    vGM-8传统的0.12781.140.2873
    基于NARX的
    vGM-17传统的0.03270.230.3503
    基于NARX的
    vGM-20传统的0.29671.550.3594
    基于NARX的
    注:在实时混合模拟试验进行前,相应的虚拟实时混合模拟需要在Simulink中运行以预演试验情况从而确保试验安全。
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-05-16
  • 修回日期:  2021-08-18
  • 网络出版日期:  2021-08-27
  • 刊出日期:  2022-09-01

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