变分模态分解与时间序列模型相结合的结构损伤识别方法研究

PDF(6672 KB)

振动与冲击 ›› 2025, Vol. 44 ›› Issue (5) : 131-139.

土木工程

变分模态分解与时间序列模型相结合的结构损伤识别方法研究

姚小俊*1，孙守鹏1，王强1，杨小梅2

作者信息 +

Structural damage identification method combining VMD and ARIMA model

YAO Xiaojun*1, SUN Shoupeng1, WANG Qiang1, YANG Xiaomei2

Author information +

文章历史 +

摘要

针对准确定位土木工程结构突变损伤的损伤时刻和损伤位置问题，提出了基于变分模态分解与差分整合移动平均自回归模型（autoregressive integration moving average ，ARIMA）的突变损伤识别方法。首先利用自回归模型功率谱确定初始频率及需要分解的模态数量，接着通过变分模态分解方法将振动非平稳信号初步分解为多个平稳的分量信号。然后利用ARIMA模型来拟合各阶信号分量，获取模型残差。利用ARIMA拟合信号分量得到的模型残差确定损伤的具体时刻。最后利用主成分分析法获取结构的模态振型，构造一个基于频率与振型的损伤指标，结合损伤阈值定位出损伤位置。该方法通过地震激励下十自由度框架模拟算例以及实际简支钢桁梁桥数据进行分析。结果证实，该方法能够用于平稳及非平稳激励下的结构损伤时刻和损伤位置的定位。

Abstract

To locate the instant and location of abrupt structural damage accurately, this paper proposes a damage identification method based on variational mode decomposition (VMD) and the autoregressive integrated moving average model (ARIMA). Initially, the method accurately selects the initial central frequencies of high-energy modes and the number of modes to be decomposed using the autoregressive model power spectrum. Then, the variational mode decomposition method is applied to decompose the vibration non-stationary signal into several stationary signal components, followed by fitting each order signal component using the ARIMA model to obtain model residuals. The specific time of damage is determined by analyzing the residuals obtained from fitting the signal components with ARIMA. Finally, the structural modal shapes are obtained using principal component analysis (PCA), and a damage index that integrates frequency and modal shape is constructed. Combined with a damage threshold, the location of the damage is pinpointed. Furthermore, the method is analyzed using numerical examples of a ten-degree-of-freedom structure under seismic excitation and the monitoring acceleration data of an actual steel bridge. The results demonstrate that the proposed method can accurately locate the occurrence time and location of structural damage under both stationary and non-stationary excitations.

导出引用

姚小俊1, 孙守鹏1, 王强1, 杨小梅2. 变分模态分解与时间序列模型相结合的结构损伤识别方法研究[J]. 振动与冲击, 2025, 44(5): 131-139

YAO Xiaojun1, SUN Shoupeng1, WANG Qiang1, YANG Xiaomei2. Structural damage identification method combining VMD and ARIMA model[J]. Journal of Vibration and Shock, 2025, 44(5): 131-139

参考文献

[1] DOEBLING S W F C R P. A Summary Review of Vibration-based Damage Identification Methods[J]. Shock and Vibration Digest, 1998,30(2): 91-105.
[2] 魏巍, 彭涛. 基于EMD和TVAR模型的滚动轴承故障诊断方法[J]. 中国科技论文, 2012,7(04): 317-322.
Wei Wei, Peng Tao, A fault diagnosis approach for rolling bearings based on EMD method and TVAR model [J]. China Science paper, 2012, 7(04): 317-322. (in Chinese)
[3] 张超, 陈建军, 郭迅. 基于EMD能量熵和支持向量机的齿轮故障诊断方法[J]. 振动与冲击, 2010,29(10): 216-220.
Zhang C, Chen J J, Guo X. A gear fault diagnosis method based on EMD energy entropy and SVM [J]. Journal of Vibration and Shock, 2010, 29(10): 216-220.
[4] 董银峰, 李英民, 赖明. 基于EMD和VARMA模型的结构损伤识别[J]. 振动与冲击, 2010,29(12): 141-147.
Dong Yinfeng, Li Yingmin, Lai Ming. EMD and VARMA model based structural damage detection [J]. Journal of Vibration and Shock, 2010, 29(12): 141-147.
[5] SARMADI H, ENTEZAMI A, DANESHVAR KHORRAM M. Energy-based damage localization under ambient vibration and non-stationary signals by ensemble empirical mode decomposition and Mahalanobis-squared distance[J]. Journal of Vibration and Control, 2020,26(11-12): 1012-1027.
[6] DRAGOMIRETSKIY K, ZOSSO D. Variational Mode Decomposition[J]. IEEE Transactions on Signal Processing, 2014,62(3): 531-544.
[7] 杨昊, 朱希安. 基于VMD和小波阈值的谐波检测方法[J]. 计算机仿真, 2017,34(08): 403-407.
Yang Hao, Zhu Xi’an. Harmonic detection method based on VMD and wavelet threshold [J]. Computer Simulation, 2017, 34(08): 403-407.
[8] SEYREK P, ŞENER B, ÖZBAYOĞLU A M, et al. An Evaluation Study of EMD, EEMD, and VMD For Chatter Detection in Milling[J]. Procedia Computer Science, 2022,200: 160-174.
[9] LU Q, SHEN X, WANG X, et al. Fault Diagnosis of Rolling Bearing Based on Improved VMD and KNN[J]. Mathematical problems in engineering, 2021,2021: 1-11.
[10] BAGHERI A, OZBULUT O E, HARRIS D K. Structural system identification based on variational mode decomposition[J]. Journal of Sound and Vibration, 2018,417: 182-197.
[11] XIN Y J L A. Damage Detection in Initially Nonlinear Structures based on Variational Mode Decomposition[J]. International Journal of Structural Stability and Dynamics, 2020,20(10): 2042009.
[12] MOSAVI A A, DICKEY D, SERACINO R, et al. Identifying damage locations under ambient vibrations utilizing vector autoregressive models and Mahalanobis distances[J]. Mechanical Systems and Signal Processing, 2012,26: 254-267.
[13] ENTEZAMI A, SHARIATMADAR H. An unsupervised learning approach by novel damage indices in structural health monitoring for damage localization and quantification[J]. Structural Health Monitoring, 2018,17(2): 325-345.
[14] ENTEZAMI A, SHARIATMADAR H. Damage localization under ambient excitations and non-stationary vibration signals by a new hybrid algorithm for feature extraction and multivariate distance correlation methods[J]. Structural Health Monitoring, 2019,18(2): 347-375.
[15] 赵昕海, 张术臣, 李志深, 等. 基于VMD的故障特征信号提取方法[J]. 振动.测试与诊断, 2018,38(01): 11-19.
Zhao Xinhai, Zhang Shuchen, Li Zhishen, et al. Fault feature extraction method based on VMD[J]. Journal of Vibration, Measurem-ent&Diagnosis, 2018, 38(01):11-19.
[16] 程小龙, 张斌, 刘相杰, 等. 基于CEEMDAN-GMDH-ARIMA的大坝变形预测模型研究[J]. 人民黄河, 2024,46(01): 146-150.
Cheng, X. L., Zhang, B., Liu, X. J., et al. (2024). Research on Dam Deformation Prediction Model Based on CEEMDAN-GMDH-ARIMA. People’s Yellow River, 2024,46(01), 146-150.
[17] LU W, DONG J, PAN Y, et al. Damage identification of bridge structure model based on empirical mode decomposition algorithm and Autoregressive Integrated Moving Average procedure[J]. Archives of Civil Engineering, 2022: 653-667.
[18] 罗亦泳, 姚宜斌, 黄城, 等. 基于改进VMD的变形特征提取与分析[J]. 武汉大学学报(信息科学版), 2020,45(04): 612-619.
Luo Yi Yong, Yao Yi Bin, Huang Cheng, et al. Deformation feature extraction and analysis based on improved variational mode decomposition [J]. Geomatics and Information Science of Wuhan University, 2020, 45(04): 612-619.
[19] 李仙果, 周宇, 叶庆卫, 等. 一种AR模型的稀疏模态参数估计方法[J]. 机械科学与技术, 2016,35(11): 1733-1737.
Li Xianguo, Zhou Yu, Ye Qingwei, et al. A sparse modal parameter estimation method based on AR model[J]. Mechanical Science and Technology for Aerospace Engineering, 2016, 35(11): 1733-1737.
[20] 王孟鸿, 宋春月, 姬晨濛. 基于频响函数与主成分分析的网架结构损伤检测方法研究[J]. 建筑结构, 2017,47(04): 96-101.
WANG Menghong, SONG Chunyue, JI Chenmeng. Researchon damage detection method for grid structures based on frequency response function and principal component analysis[J].Building Structure, 2017, 47(4): 96-101.
[21] DELGADILLO R M, CASAS J R. Bridge damage detection via improved completed ensemble empirical mode decomposition with adaptive noise and machine learning algorithms[J]. Structural Control and Health Monitoring, 2022,29(8).