Volume 22 Issue 2
Apr.  2022
Turn off MathJax
Article Contents
Article Navigation >  Journal of Traffic and Transportation Engineering  > 2022  >  22(2): 59-75
WANG Zuo-cai, DING Ya-jie, GE Bi, YUAN Zi-qing, XIN Yu. Review on nonlinear model updating for bridge structures[J]. Journal of Traffic and Transportation Engineering, 2022, 22(2): 59-75. doi: 10.19818/j.cnki.1671-1637.2022.02.004
Citation: WANG Zuo-cai, DING Ya-jie, GE Bi, YUAN Zi-qing, XIN Yu. Review on nonlinear model updating for bridge structures[J]. Journal of Traffic and Transportation Engineering, 2022, 22(2): 59-75. doi: 10.19818/j.cnki.1671-1637.2022.02.004
shu

Review on nonlinear model updating for bridge structures

doi: 10.19818/j.cnki.1671-1637.2022.02.004
  • 1.

    College of Civil Engineering, Hefei University of Technology, Hefei 230009, Anhui, China

  • 2.

    Engineering Technology Research Center of Disaster Prevention and Mitigation of Civil Engineering of Anhui Province, Hefei University of Technology, Hefei 230009, Anhui, China

  • 3.

    Anhui Province Infrastructure Safety Inspection and Monitoring Engineering Laboratory, Hefei University of Technology, Hefei 230009, Anhui, China

Funds:

National Natural Science Foundation of China 51922036

Key Research and Development Project of Anhui Province 1804a0802204

Fundamental Research Funds for the Central Universities JZ2020HGPB0117

More Information
    Abstract
  • Due to the weakening of the structural mechanical properties during the service period of bridges, the nonlinear vibration with time-varying characteristics occurs. Considering this, the development of nonlinear model updating was reviewed, and on this basis, some critical problems existing in nonlinear model updating technologies were summarized from the aspects of nonlinear system identification, nonlinear model updating methods, and uncertainty quantification of nonlinear models. In addition, in view of the damage identification, performance assessment, and safety monitoring of complex structures, the application of nonlinear model updating in bridge structures was further discussed. Research results indicate that the response characteristic quantities represented by natural frequencies and modes of vibration can only reflect the physical characteristics of time-invariant structures. However, for nonlinear structures, their mechanical properties change with the external excitation, and thus the model updating methods based on characteristic quantities of linear systems are not suitable for nonlinear structures with obvious time-varying characteristics. The instantaneous frequency and amplitude of the principal component of structural dynamic response contain the phase and amplitude information of vibration response signals. They can comprehensively reflect the non-stationary characteristics of structural responses under dynamic loads. The dynamic characteristics of nonlinear structures can be properly represented by using the instantaneous characteristic quantities with time-varying characteristics to construct the objective function. With the consideration of uncertainty factors, such as the measurement noise, model errors, and numerical calculation methods, the uncertainty model updating method can improve the model updating result by comprehensively using the measured response data. Since many parameters and massive computations are involved in the nonlinear model updating of complex structures, its application in the practical engineering structures is greatly limited. Therefore, the reasonable selection of representative nonlinear model parameters and improving the computational efficiency are urgent problems to be solved. 12 figs, 95 refs.

     

    • FullText(HTML)
  • loading
    • References(95)
  • [1]
    GIRARDI M, PADOVANI C, PELLEGRINI D, et al. Finite element model updating for structural applications[J]. Journal of Computational and Applied Mathematics, 2020, 370: 112675. doi: 10.1016/j.cam.2019.112675
    [2]
    宗周红, 高铭霖, 夏樟华. 基于健康监测的连续刚构桥有限元模型确认(Ⅰ)—基于响应面法的有限元模型修正[J]. 土木工程学报, 2011, 44(2): 90-98. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201102015.htm

    ZONG Zhou-hong, GAO Ming-lin, XIA Zhang-hua. Finite element model validation of the continuous rigid frame bridge based on structural health monitoring. Part Ⅰ : FE model updating based on the response surface method[J]. China Civil Engineering Journal, 2011, 44(2): 90-98. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201102015.htm
    [3]
    朱劲松, 肖汝诚. 桥梁损伤识别的实用模型修正方法研究[J]. 工业建筑, 2006, 36(增1): 219-224. https://www.cnki.com.cn/Article/CJFDTOTAL-GYJZ2006S1065.htm

    ZHU Jin-song, XIAO Ru-cheng. Research on damage identification of bridges based on FE model updating[J]. Industrial Construction, 2006, 36(S1): 219-224. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GYJZ2006S1065.htm
    [4]
    贺媛媛, 刘莉. 结构动态模型修正技术[J]. 战术导弹技术, 2008(1): 5-9, 13. doi: 10.3969/j.issn.1009-1300.2008.01.002

    HE Yuan-yuan, LIU Li. Updating techniques of structural dynamic model[J]. Tactical Missile Technology, 2008(1): 5-9, 13. (in Chinese) doi: 10.3969/j.issn.1009-1300.2008.01.002
    [5]
    JAISHI B, KIM H J, KIM M K, et al. Finite element model updating of concrete-filled steel tubular arch bridge under operational condition using modal flexibility[J]. Mechanical Systems and Signal Processing, 2007, 21(6): 2406-2426. doi: 10.1016/j.ymssp.2007.01.003
    [6]
    HUA X G, NI Y Q, CHEN Z Q, et al. Structural damage detection of cable-stayed bridges using changes in cable forces and model updating[J]. Journal of Structural Engineering, 2009, 135(9): 1093-1106. doi: 10.1061/(ASCE)0733-9445(2009)135:9(1093)
    [7]
    范哲. 大跨斜拉桥有限元模型修正与结构损伤监测方法研究[D]. 大连: 大连理工大学, 2013.

    FAN Zhe. Study on the FE model updating and structural damage detection for long-span cable-stayed bridges[D]. Dalian: Dalian University of Technology, 2013. (in Chinese)
    [8]
    单德山, 孙松松, 黄珍, 等. 基于试验数据的吊拉组合模型桥梁有限元模型修正[J]. 土木工程学报, 2014, 47(10): 88-95. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201410013.htm

    SHAN De-shan, SUN Song-song, HUANG Zhen, et al. Finite element model updating of combined cable-stayed suspension model bridge based on experimental data[J]. China Civil Engineering Journal, 2014, 47(10): 88-95. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201410013.htm
    [9]
    宋智, 孙强. 基于模型修正的桥梁极限承载力分析[J]. 水利与建筑工程学报, 2015, 13(5): 228-232. doi: 10.3969/j.issn.1672-1144.2015.05.045

    SONG Zhi, SUN Qiang. An ultimate bearing capacity analysis on bridges based on model updating[J]. Journal of Water Resources and Architectural Engineering, 2015, 13(5): 228-232. (in Chinese) doi: 10.3969/j.issn.1672-1144.2015.05.045
    [10]
    吴多. 基于桥梁全寿命周期的损伤识别及状态评估研究[D]. 西安: 长安大学, 2017.

    WU Duo. Study on damage identification and state evaluation of bridge life cycle[D]. Xi'an: Chang'an University, 2017. (in Chinese)
    [11]
    张明亮. 基于贝叶斯理论的材料非线性桥梁结构模型修正与损伤识别[J]. 长春: 吉林大学, 2011.

    ZHANG Ming-liang. Structural parameters updating and damage identification of material non-linear bridge structure based on Bayesian theory[D]. Changchun: Jilin University, 2011. (in Chinese)
    [12]
    李秉穹. 基于RBF神经网络的曲线斜拉桥不确定性模型修正[D]. 成都: 西南交通大学, 2015.

    LI Bing-qiong. Uncertainty model updating of a curved cable-stayed bridge based on RBF neural network[D]. Chengdu: Southwest Jiaotong University, 2015. (in Chinese)
    [13]
    WANG Zuo-cai, XIN Yu, REN Wei-xin. Nonlinear structural joint model updating based on instantaneous characteristics of dynamic responses[J]. Mechanical Systems and Signal Processing, 2016, 76/77: 476-496. doi: 10.1016/j.ymssp.2016.01.024
    [14]
    WANG Zuo-cai, XIN Yu, REN Wei-xin. Nonlinear structural model updating based on instantaneous frequencies and amplitudes of the decomposed dynamic responses[J]. Engineering Structures, 2015, 100: 189-200. doi: 10.1016/j.engstruct.2015.06.002
    [15]
    YUAN Ping-ping, REN Wei-xin, ZHANG Jian. Dynamic tests and model updating of nonlinear beam structures with bolted joints[J]. Mechanical Systems and Signal Processing, 2019, 126: 193-210. doi: 10.1016/j.ymssp.2019.02.033
    [16]
    GOEGE D, FUELLEKRUG U, SINAPIUS M, et al. Advanced test strategy for identification and characterization of nonlinearities of aerospace structures[J]. AIAA Journal, 2005, 43(5): 974-986. doi: 10.2514/1.5651
    [17]
    MASRI S F, CAUGHEY T K. A nonparametric identification technique for nonlinear dynamic problems[J]. Journal of Applied Mechanics, 1979, 46(2): 433-447. doi: 10.1115/1.3424568
    [18]
    MASRI S F, SASSI H, CAUGHEY T K. Nonparametric identification of nearly arbitrary nonlinear systems[J]. Journal of Applied Mechanics, 1982, 49(3): 619-628. doi: 10.1115/1.3162537
    [19]
    MASRI S F, MILLER R K, SAUD A F, et al. Identification of nonlinear vibrating structures: Part Ⅱ—applications[J]. Journal of Applied Mechanics, 1987, 54(4): 923-929. doi: 10.1115/1.3173140
    [20]
    MESKELL C, FITZPATRICK J A, RICE H J. Application of force-state mapping to a non-linear fluid-elastic system[J]. Mechanical Systems and Signal Processing, 2001, 15(1): 75-85. doi: 10.1006/mssp.2000.1352
    [21]
    NOëL J P, KERSCHEN G, NEWERLA A. Application of the restoring force surface method to a real-life spacecraft structure[C]//Springer. Conference Proceedings of the Society for Experimental Mechanics Series. Berlin: Springer, 2012: 1-19.
    [22]
    KERSCHEN G. Identification of nonlinear systems using the restoring force surface method[C]//SEM Annual Conference. Student Paper Competition of the SEM Conference. Cincinnati: SEM Annual Conference, 1999: 1-4.
    [23]
    蒋华, 陈前. 恢复力曲面法在颗粒阻尼器研究中的应用[J]. 振动、测试与诊断, 2007, 27(3): 228-231, 259. doi: 10.3969/j.issn.1004-6801.2007.03.012

    JIANG Hua, CHEN Qian. Application of restoring force surface method to particle damping research[J]. Journal of Vibration, Measurement and Diagnosis, 2007, 27(3): 228-231, 259. (in Chinese) doi: 10.3969/j.issn.1004-6801.2007.03.012
    [24]
    WANG Zuo-cai, DING Ya-jie, REN Wei-xin, et al. Structural dynamic nonlinear model and parameter identification based on the stiffness and damping marginal curves[J]. Structural Control and Health Monitoring, 2020, 27(6): e2540.
    [25]
    FELDMAN M. Non-linear system vibration analysis using Hilbert transform—Ⅱ. Forced vibration analysis method 'Forcevib'[J]. Mechanical Systems and Signal Processing, 1994, 8(3): 309-318. doi: 10.1006/mssp.1994.1023
    [26]
    HUANG N E, SHEN Zheng, LONG S R, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J]. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1998, 454(1971): 903-995. doi: 10.1098/rspa.1998.0193
    [27]
    WANG Zuo-cai, CHEN G. Analytical mode decomposition with Hilbert transform for modal parameter identification of buildings under ambient vibration[J]. Engineering Structures, 2014, 59: 173-184. doi: 10.1016/j.engstruct.2013.10.020
    [28]
    STASZEWSKI W. Identification of damping in MDOF systems using time-scale decomposition[J]. Journal of Sound and Vibration, 1997, 203(2): 283-305. doi: 10.1006/jsvi.1996.0864
    [29]
    FRANCO H, PAULETTI R M O. Analysis of nonlinear oscillations by Gabor spectrograms[J]. Nonlinear Dynamics, 1997, 12(3): 215-236. doi: 10.1023/A:1008294918271
    [30]
    LIND R, SNYDER K, BRENNER M. Wavelet analysis to characterise non-linearities and predict limit cycles of an aeroelastic system[J]. Mechanical Systems and Signal Processing, 2001, 15(2): 337-356. doi: 10.1006/mssp.2000.1346
    [31]
    SHI Z Y, LAW S S, XU X. Identification of linear time-varying MDOF dynamic systems from forced excitation using Hilbert transform and EMD method[J]. Journal of Sound and Vibration, 2009, 321(3/4/5): 572-589.
    [32]
    KERSCHEN G, WORDEN K, VAKAKIS A F, et al. Past, present and future of nonlinear system identification in structural dynamics[J]. Mechanical Systems and Signal Processing, 2006, 20(3): 505-592. doi: 10.1016/j.ymssp.2005.04.008
    [33]
    HAROON M, ADAMS D E. A modified H2 algorithm for improved frequency response function and nonlinear parameter estimation[J]. Journal of Sound and Vibration, 2009, 320(4/5): 822-837.
    [34]
    SPOTTSWOOD S M, ALLEMANG R J. Identification of nonlinear parameters for reduced order models[J]. Journal of Sound and Vibration, 2006, 295(1/2): 226-245.
    [35]
    GIFFORD S J, TOMLINSON G R. Recent advances in the application of functional series to non-linear structures[J]. Journal of Soundand Vibration, 1989, 135(2): 289-317. doi: 10.1016/0022-460X(89)90727-X
    [36]
    KHAN A A, VYAS N S. Nonlinear bearing stiffness parameter estimation in flexible rotor-bearing systems using Volterra and Wiener approach[J]. Probabilistic Engineering Mechanics, 2001, 16(2): 137-157. doi: 10.1016/S0266-8920(00)00016-3
    [37]
    YUAN C, FEENY B F. Parametric identification of chaotic systems[J]. Journal of Vibration and Control, 1998, 4(4): 405-426. doi: 10.1177/107754639800400404
    [38]
    NOëL J P, KERSCHEN G. Frequency-domain subspace identification for nonlinear mechanical systems[J]. Mechanical Systems and Signal Processing, 2013, 40(2): 701-717. doi: 10.1016/j.ymssp.2013.06.034
    [39]
    STASZEWSKI W J. Identification of non-linear systems using multi-scale ridges and skeletons of the wavelet transform[J]. Journal of Sound and Vibration, 1998, 214(4): 639-658. doi: 10.1006/jsvi.1998.1616
    [40]
    王超, 任伟新, 黄天立. 基于小波的非线性结构系统识别[J]. 振动与冲击, 2009, 28(3): 10-13, 195. doi: 10.3969/j.issn.1000-3835.2009.03.003

    WANG Chao, REN Wei-xin, HUANG Tian-li. System identification of a nonlinear structure based on wavelet transformation[J]. Journal of Vibration and Shock, 2009, 28(3): 10-13, 195. (in Chinese) doi: 10.3969/j.issn.1000-3835.2009.03.003
    [41]
    张淑清, 翟欣沛, 董璇, 等. EMD及Duffing振子在小电流系统故障选线方法中的应用[J]. 中国电机工程学报, 2013, 33(10): 161-167, 5. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGDC201310022.htm

    ZHANG Shu-qing, ZHAI Xin-pei, DONG Xuan, et al. Application of EMD and Duffing oscillator to fault line detection in un-effectively grounded system[J]. Proceedings of the CSEE, 2013, 33(10): 161-167, 5. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGDC201310022.htm
    [42]
    唐贵基, 庞彬. 基于改进的希尔伯特振动分解的机械故障诊断方法研究[J]. 振动与冲击, 2015, 34(3): 167-171, 182. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201503028.htm

    TANG Gui-ji, PANG Bin. A mechanical fault diagnosis method based on improved Hilbert vibration decomposition[J]. Journal of Vibration and Shock, 2015, 34(3): 167-171, 182. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201503028.htm
    [43]
    邓四二, 张言伟, 王恒迪, 等. 基于HVD降噪和多频段频谱叠加的圆柱滚子轴承故障诊断[J]. 振动与冲击, 2018, 37(11): 136-144.

    DENG Si-er, ZHANG Yan-wei, WANG Heng-di, et al. Roller bearings' fault diagnosis based on HVD denoising and multi-band spectra superposition[J]. Journal of Vibration and Shock, 2018, 37(11): 136-144. (in Chinese)
    [44]
    EBRAHIMIAN H, ASTROZA R, CONTE J P. Nonlinear structural finite element model updating and uncertainty quantification[C]//SHULL P J. Structural Health Monitoring and Inspection of Advanced Materials, Aerospace, and Civil Infrastructure. San Diego: SPIE, 2015: 943716.
    [45]
    梁鹏, 李斌, 王秀兰, 等. 基于桥梁健康监测的有限元模型修正研究现状与发展趋势[J]. 长安大学学报(自然科学版), 2014, 34(4): 52-61. doi: 10.3969/j.issn.1671-8879.2014.04.009

    LIANG Peng, LI Bin, WANG Xiu-lan, et al. Present research status and development trend of finite element model updating based on bridge health monitoring[J]. Journal of Chang'an University (Natural Science Edition), 2014, 34(4): 52-61. (in Chinese) doi: 10.3969/j.issn.1671-8879.2014.04.009
    [46]
    续秀忠, 张志谊, 华宏星, 等. 应用时频分析方法辨识时变系统的模态参数[J]. 振动工程学报, 2003, 16(3): 104-108. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC200303021.htm

    XU Xiu-zhong, ZHANG Zhi-yi, HUA Hong-xing, et al. Identification of time-varying modal parameters by a linear time-frequency method[J]. Journal of Vibration Engineering, 2003, 16(3): 104-108. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC200303021.htm
    [47]
    邓杨, 彭志科, 杨扬, 等. 基于参数化时频分析的非线性振动系统参数辨识[J]. 力学学报, 2013, 45(6): 992-996. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201306021.htm

    DENG Yang, PENG Zhi-ke, YANG Yang, et al. Identification of nonlinear vibration systems based on parametric TFA[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(6): 992-996. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201306021.htm
    [48]
    JAISHI B, REN Wei-xin. Damage detection by finite element model updating using modal flexibility residual[J]. Journal of Sound and Vibration, 2006, 290(1/2): 369-387.
    [49]
    ZANG C, FRISWELL M I, IMREGUN M. Structural health monitoring and damage assessment using measured FRFs from multiple sensors, Part Ⅰ: the indicator of correlation criteria[J]. Key Engineering Materials, 2003, 245/246: 131-140. doi: 10.4028/www.scientific.net/KEM.245-246.131
    [50]
    温华兵, 王国治. 基于频响函数灵敏度分析的鱼雷模型有限元模型修正[J]. 鱼雷技术, 2006, 14(3): 10-13. doi: 10.3969/j.issn.1673-1948.2006.03.003

    WEN Hua-bing, WANG Guo-zhi. Revising finite element model of torpedo model based on sensitivity analysis of frequency response function (FRF)[J]. Torpedo Technology, 2006, 14(3): 10-13. (in Chinese) doi: 10.3969/j.issn.1673-1948.2006.03.003
    [51]
    孙国民, 张效忠, 孙延华. 基于特征值分析的多尺度结构优化设计方法[J]. 应用数学和力学, 2019, 40(6): 630-640. https://www.cnki.com.cn/Article/CJFDTOTAL-YYSX201906005.htm

    SUN Guo-min, ZHANG Xiao-zhong, SUN Yan-hua. Multi-scale structure optimization design based on eigenvalue analysis[J]. Applied Mathematics and Mechanics, 2019, 40(6): 630-640. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YYSX201906005.htm
    [52]
    周飞燕, 金林鹏, 董军. 卷积神经网络研究综述[J]. 计算机学报, 2017, 40(6): 1229-1251. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJX201706001.htm

    ZHOU Fei-yan, JIN Lin-peng, DONG Jun. Review of convolutional neural network[J]. Chinese Journal of Computers, 2017, 40(6): 1229-1251. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJX201706001.htm
    [53]
    韩露霜, 李旭东. 基于模拟退火算法的频域受限序列搜索算法[J]. 计算机科学与应用, 2021, 11(3): 543-548.

    HAN Lu-shuang, LI Xu-dong. Spectrally-constrained sequence search based on simulated annealing algorithm[J]. Computer Science and Application, 2021, 11(3): 543-548. (in Chinese)
    [54]
    陈华根, 吴健生, 王家林, 等. 模拟退火算法机理研究[J]. 同济大学学报(自然科学版), 2004, 32(6): 802-805. doi: 10.3321/j.issn:0253-374X.2004.06.023

    CHEN Hua-gen, WU Jian-sheng, WANG Jia-lin, et al. Mechanism study of simulated annealing algorithm[J]. Journal of Tongji University (Natural Science), 2004, 32(6): 802-805. (in Chinese) doi: 10.3321/j.issn:0253-374X.2004.06.023
    [55]
    辛宇. 基于结构动力响应主分量瞬时特性的非线性结构模型修正[D]. 合肥: 合肥工业大学, 2016.

    XIN Yu. Nonlinear structural model updating based on the instantaneous characteristics of decomposed dynamic responses[D]. Hefei: Hefei University of Technology, 2016. (in Chinese)
    [56]
    张长林, 余建星, 杨振国. 非线性约束最优化问题的多目标模拟退火算法[J]. 复旦学报(自然科学版), 2003, 42(1): 93-97. doi: 10.3969/j.issn.0427-7104.2003.01.018

    ZHANG Chang-lin, YU Jian-xing, YANG Zhen-guo. The multi-object simulated annealing algorithm for the nonlinear constraint optimization problem[J]. Journal of Fudan University (Natural Science), 2003, 42(1): 93-97. (in Chinese) doi: 10.3969/j.issn.0427-7104.2003.01.018
    [57]
    赖文龙. 改进的模拟退火算法及其在非线性能量阱减震控制性能优化中的运用[D]. 广州: 广州大学, 2018.

    LAI Wen-long. Improved simulated annealing algorithm and its application in seismic control performance optimization of nonlinear energy sinks[D]. Guangzhou: Guangzhou University, 2018. (in Chinese)
    [58]
    卢明奇, 曾风波. 基于自适应遗传算法的钢筋混凝土桥墩抗震设计方法[J]. 土木工程学报, 2020, 53(7): 73-77. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC202007008.htm

    LU Ming-qi, ZENG Feng-bo. Seismic design method for reinforcement concrete piers based on adaptive genetic algorithm[J]. China Civil Engineering Journal, 2020, 53(7): 73-77. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC202007008.htm
    [59]
    蔡颢. 基于遗传算法的装配式混凝土框架建筑优化研究[D]. 成都: 西南交通大学, 2018.

    CAI Hao. Research on optimization of prefabricated construction buildings based on genetic algorithm[D]. Chengdu: Southwest Jiaotong University, 2018. (in Chinese)
    [60]
    LEE K Y, HAN S N, ROH M I. An improved genetic algorithm for facility layout problems having inner structure walls and passages[J]. Computers and Operations Research, 2003, 30(1): 117-138. doi: 10.1016/S0305-0548(01)00085-5
    [61]
    KAMESHKI E S, SAKA M P. Optimum design of nonlinear steel frames with semi-rigid connections using a genetic algorithm[J]. Computers and Structures, 2001, 79(17): 1593-1604. doi: 10.1016/S0045-7949(01)00035-9
    [62]
    任怀庆. 非线性不确定系统的神经网络控制研究[D]. 长春: 吉林大学, 2014.

    REN Huai-qing. Study on control of nonlinear uncertain system by neural network[D]. Changchun: Jilin University, 2014. (in Chinese)
    [63]
    费庆国, 李爱群, 张令弥. 基于神经网络的非线性结构有限元模型修正研究[J]. 宇航学报, 2005, 26(3): 267-269, 281. doi: 10.3321/j.issn:1000-1328.2005.03.005

    FEI Qing-guo, LI Ai-qun, ZHANG Ling-mi. Study on finite element model updating of nonlinear structures using neural network[J]. Journal of Astronautics, 2005, 26(3): 267-269, 281. (in Chinese) doi: 10.3321/j.issn:1000-1328.2005.03.005
    [64]
    肖书敏, 闫云聚, 姜波澜. 基于小波神经网络方法的桥梁结构损伤识别研究[J]. 应用数学和力学, 2016, 37(2): 149-159. https://www.cnki.com.cn/Article/CJFDTOTAL-YYSX201602004.htm

    XIAO Shu-min, YAN Yun-ju, JIANG Bo-lan. Damage identification for bridge structures based on the wavelet neural network method[J]. Applied Mathematics and Mechanics, 2016, 37(2): 149-159. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YYSX201602004.htm
    [65]
    李雪松, 马宏伟, 林逸洲. 基于卷积神经网络的结构损伤识别[J]. 振动与冲击, 2019, 38(1): 167-175. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201901024.htm

    LI Xue-song, MA Hong-wei, LIN Yi-zhou. Structural damage identification based on convolution neural network[J]. Journal of Vibration and Shock, 2019, 38(1): 167-175. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201901024.htm
    [66]
    LU Yong, TU Zhen-guo. A two-level neural network approach for dynamic FE model updating including damping[J]. Journal of Sound and Vibration, 2004, 275(3/4/5): 931-952.
    [67]
    FATHNEJAT H, TORKZADEH P, SALAJEGHEH E, et al. Structural damage detection by model updating method based on cascade feed-forward neural network as an efficient approximation mechanism[J]. International Journal of Optimization in Civil Engineering, 2014, 4(4): 451-472.
    [68]
    MARES C, MOTTERSHEAD J E, FRISWELL M I. Stochastic model updating: Part 1—theory and simulated example[J]. Mechanical Systems and Signal Processing, 2006, 20(7): 1674-1695. doi: 10.1016/j.ymssp.2005.06.006
    [69]
    KHODAPARAST H H, MOTTERSHEAD J E, FRISWELL M I. Perturbation methods for the estimation of parameter variability in stochastic model updating[J]. Mechanical Systems and Signal Processing, 2008, 22(8): 1751-1773. doi: 10.1016/j.ymssp.2008.03.001
    [70]
    MOTTERSHEAD J E, KHODAPARAST H H, DWIGHT R P, et al. Stochastic model updating: perturbation, interval method and Bayesian inference[C]//N'APRSTEK J. The 10th International Conference on Vibration Problems. Berlin: Springer, 2011: 13-23.
    [71]
    FANG Sheng-en, REN Wei-xin, PERERA R. A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation[J]. Mechanical Systems and Signal Processing, 2012, 33: 83-96. doi: 10.1016/j.ymssp.2012.06.028
    [72]
    方圣恩, 林友勤, 夏樟华. 考虑结构参数不确定性的随机模型修正方法[J]. 振动、测试与诊断, 2014, 34(5): 832-837. doi: 10.3969/j.issn.1004-6801.2014.05.008

    FANG Sheng-en, LIN You-qin, XIA Zhang-hua. Stochastic model updating method considering the uncertainties of structural parameters[J]. Journal of Vibration, Measurement and Diagnosis, 2014, 34(5): 832-837. (in Chinese) doi: 10.3969/j.issn.1004-6801.2014.05.008
    [73]
    WAN Hua-ping, REN Wei-xin. A residual-based Gaussian process model framework for finite element model updating[J]. Computers and Structures, 2015, 156: 149-159. doi: 10.1016/j.compstruc.2015.05.003
    [74]
    BECK J L, KATAFYGIOTIS L S. Updating models and their uncertainties. Ⅰ : Bayesian statistical framework[J]. Journal of Engineering Mechanics, 1998, 124(4): 455-461. doi: 10.1061/(ASCE)0733-9399(1998)124:4(455)
    [75]
    REBBA R. Model validation and design under uncertainty[D]. Nashville: Vanderbilt University, 2005.
    [76]
    易伟建, 周云, 李浩. 基于贝叶斯统计推断的框架结构损伤诊断研究[J]. 工程力学, 2009, 26(5): 121-129. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200905022.htm

    YI Wei-jian, ZHOU Yun, LI Hao. Damage assessment research on frame structure based on Bayesian statistical inference[J]. Engineering Mechanics, 2009, 26(5): 121-129. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200905022.htm
    [77]
    房长宇, 张耀庭. 基于参数不确定性的预应力混凝土梁模型修正[J]. 华中科技大学学报(自然科学版), 2011, 39(11): 87-91. https://www.cnki.com.cn/Article/CJFDTOTAL-HZLG201111019.htm

    FANG Chang-yu, ZHANG Yao-ting. Model updating of prestressed concrete beams using parameters uncertainty[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2011, 39(11): 87-91. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HZLG201111019.htm
    [78]
    刘纲, 罗钧, 秦阳, 等. 基于改进MCMC方法的有限元模型修正研究[J]. 工程力学, 2016, 33(6): 138-145. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201606018.htm

    LIU Gang, LUO Jun, QIN Yang, et al. A finite element model updating method based on improved MCMC method[J]. Engineering Mechanics, 2016, 33(6): 138-145. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201606018.htm
    [79]
    张建新. 基于贝叶斯方法的有限元模型修正研究[D]. 重庆: 重庆大学, 2014.

    ZHANG Jian-xin. Research on the modification of finite element model based on Bayesian method[D]. Chongqing: Chongqing University, 2014. (in Chinese)
    [80]
    WAN Hua-ping, REN Wei-xin. Stochastic model updating utilizing Bayesian approach and Gaussian process model[J]. Mechanical Systems and Signal Processing, 2016, 70/71: 245-268. doi: 10.1016/j.ymssp.2015.08.011
    [81]
    XIN Yu, HAO Hong, LI Jun, et al. Bayesian based nonlinear model updating using instantaneous characteristics of structural dynamic responses[J]. Engineering Structures, 2019, 183: 459-474. doi: 10.1016/j.engstruct.2019.01.043
    [82]
    ZIMMERMANN H J. Fuzzy set theory[J]. Wiley Interdisciplinary Reviews: Computational Statistics, 2010, 2(3): 317-332. doi: 10.1002/wics.82
    [83]
    SUNAGA T. Theory of an interval algebra and its application to numerical analysis[J]. Japan Journal of Industrial and Applied Mathematics, 2009, 26(2/3): 125-143.
    [84]
    FERSON S, KREINOVICH V, GRINZBURG L, et al. Constructing probability boxes and Dempster-Shafer structures[R]. Albuquerque: U.S. Department of Energy, 2003.
    [85]
    MOENS D, VANDEPITTE D. An interval finite element approach for the calculation of envelope frequency response functions[J]. International Journal for Numerical Methods in Engineering, 2004, 61(14): 2480-2507. doi: 10.1002/nme.1159
    [86]
    KHODAPARAST H H, MOTTERSHEAD J E, BADCOCK K J. Interval model updating with irreducible uncertainty using the Kriging predictor[J]. Mechanical Systems and Signal Processing, 2011, 25(4): 1204-1226. doi: 10.1016/j.ymssp.2010.10.009
    [87]
    朱增青, 陈建军, 宋宗凤, 等. 区间参数杆系结构非概率可靠性指标的改进仿射算法[J]. 工程力学, 2010, 27(2): 49-53, 58. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201002010.htm

    ZHU Zeng-qing, CHEN Jian-jun, SONG Zong-feng, et al. Non-probabilistic reliability index of bar structures with interval parameters based on modified affine arithmetic[J]. Engineering Mechanics, 2010, 27(2): 49-53, 58. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201002010.htm
    [88]
    姜东, 费庆国, 吴邵庆. 基于区间分析的不确定性结构动力学模型修正方法[J]. 振动工程学报, 2015, 28(3): 352-358. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201503003.htm

    JIANG Dong, FEI Qing-guo, WU Shao-qing. Updating of structural dynamics model with uncertainty based on interval analysis[J]. Journal of Vibration Engineering, 2015, 28(3): 352-358. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201503003.htm
    [89]
    单德山, 顾晓宇, 李中辉, 等. 桥梁结构有限元模型的仿射-区间不确定修正[J]. 中国公路学报, 2019, 32(2): 67-76. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201902008.htm

    SHAN De-shan, GU Xiao-yu, LI Zhong-hui, et al. Affine-interval uncertainty updating of finite element model for cable-stayed bridge[J]. China Journal of Highway and Transport, 2019, 32(2): 67-76. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201902008.htm
    [90]
    周建庭, 李晓庆, 辛景舟, 等. 基于Kalman-GARCH模型的结构损伤识别[J]. 振动与冲击, 2020, 39(6): 1-7, 21. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202006001.htm

    ZHOU Jian-ting, LI Xiao-qing, XIN Jing-zhou, et al. Structural damage identification based on a Kalman-GARCH model[J]. Journal of Vibration and Shock, 2020, 39(6): 1-7, 21. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202006001.htm
    [91]
    CHEN Zhao, ZHANG Rui-yang, ZHENG Jing-wei, et al. Sparse Bayesian learning for structural damage identification[J]. Mechanical Systems and Signal Processing, 2020, 140: 106689. doi: 10.1016/j.ymssp.2020.106689
    [92]
    ZHAN J, ZHANG F, SIAHKOUHI M, et al. A damage identification method for connections of adjacent box-beam bridges using vehicle-bridge interaction analysis and model updating[J]. Engineering Structures, 2021, 228: 111551. doi: 10.1016/j.engstruct.2020.111551
    [93]
    勾红叶, 杨彪, 刘雨, 等. 复杂条件下车-轨-桥变形映射关系及行车安全评价研究[J]. 中国公路学报, 2021, 34(4): 162-173. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL202104015.htm

    GOU Hong-ye, YANG Biao, LIU Yu, et al. Deformation mapping relationship and running safety evaluation of train-track-bridge system for high-speed railway in complex conditions[J]. China Journal of Highway and Transport, 2021, 34(4): 162-173. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL202104015.htm
    [94]
    杨颖, 李坤, 王银广. 基于模拟退火算法的BP神经网络在桥梁智能养护中的应用[J]. 智能城市, 2020, 6(21): 12-13. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNCS202021020.htm

    YANG Ying, LI Kun, WANG Yin-guang. Application of BP neural network based on simulated annealing algorithm in intelligent maintenance of bridge[J]. Intelligent City, 2020, 6(21): 12-13. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZNCS202021020.htm
    [95]
    WEI Shi-yin, BAO Yue-quan, LI Hui. Optimal policy for structure maintenance: a deep reinforcement learning framework[J]. Structural Safety, 2020, 83: 101906.
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Get Citation
    PDF
    XML

    Article Metrics

    Article views (1617) PDF downloads(141) Cited by()
    Proportional views
    Related

    Copyright《Journal of Traffic and Transportation Engineering》编辑部陕ICP备05001904号-1

    Address ：Editorial Department of Journal of Traffic and Transportation Engineering, Chang 'an University, Middle Section of South Second Ring Road, Xi 'an, Shaanxi（710064） Tel：029-82334388 Email：jygc@chd.edu.cn

    All visit:Today's visit:

    Supported by: Beijing Renhe Information Technology Co. Ltd    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return