基于马氏距离累积量和EMD的结构损伤识别两步法
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摘要
结构损伤识别一直是结构健康监测和安全状态评估的热点问题,损伤信息少、信噪比低等因素极大增加了结构损伤识别的难度。基于马氏距离累积量(MDC)和经验模态分解(EMD)提出一种结构损伤识别的"两步法",首先,利用健康状态监测数据作为参考样本,并利用参考样本的MDC值构造损伤识别向量,其MDC值的均值作为阈值,对待测样本进行初步损伤识别;当监测数据中损伤信息较少、信噪比低,利用直接的监测数据损伤识别困难时,则利用经验模态分解方法将监测数据分解成各阶本征模态函数(IMF),再利用各阶IMF的MDC值构造损伤识别向量,并利用统计学方法对损伤识别向量进行概率密度函数拟合,以概率密度函数95%置信区间的上限值作为阈值对结构进一步损伤识别。通过简支梁数值模拟和工字钢的模型试验验证了该方法的有效性及抗噪性。
Structural damage identification is always a hot topic in structural health monitoring and safe state evaluation. Here, a two-step method for structural damage identification based on Mahalanobis distance accumulation(MDC) and empirical mode decomposition(EMD) was proposed. Firstly, health state monitoring data were taken as the reference sample, and its MDC was used to construct the damage identification vector. This vector's MDC average value was taken as the threshold to do preliminary damage identification for samples to be tested. When damage identification using directly monitored data was difficult due to less damage information and lower signal-to-noise ratio, the EMD method was used to decompose the monitored data into various intrinsic mode functions(IMFs). Then, MDC values of various IMFs were used to construct damage identification vectors, and the statistical method was used to do probability density function fitting for damage identification vectors. The upper limit of the probability density function within its 95% confidence interval was taken as the threshold to do further structural damage identification. Numerical simulation for a simply supported beam and model tests of I-steel verified the effectiveness and anti-noise of the proposed method.
Structural damage identification is always a hot topic in structural health monitoring and safe state evaluation. Here, a two-step method for structural damage identification based on Mahalanobis distance accumulation(MDC) and empirical mode decomposition(EMD) was proposed. Firstly, health state monitoring data were taken as the reference sample, and its MDC was used to construct the damage identification vector. This vector's MDC average value was taken as the threshold to do preliminary damage identification for samples to be tested. When damage identification using directly monitored data was difficult due to less damage information and lower signal-to-noise ratio, the EMD method was used to decompose the monitored data into various intrinsic mode functions(IMFs). Then, MDC values of various IMFs were used to construct damage identification vectors, and the statistical method was used to do probability density function fitting for damage identification vectors. The upper limit of the probability density function within its 95% confidence interval was taken as the threshold to do further structural damage identification. Numerical simulation for a simply supported beam and model tests of I-steel verified the effectiveness and anti-noise of the proposed method.
引文
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[2] 宗周红,钟儒勉,郑沛娟,等.基于健康监测的桥梁结构损伤预后和安全预后研究进展及挑战[J].中国公路学报,2014,27(12):46-57.ZONG Zhouhong,ZHONG Rumian,ZHENG Peijuan,et al.Damage and safety prognosis of bridge structures based on structural health monitoring:progress and challenges[J].China Journal of Highway and Transport,2014,27(12):46-57.
[3] 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 & Signal Processing,2012,26(1):254-267.
[4] 曹军宏,韦灼彬,高屹.独立分量分析结合马氏距离的非监督损伤识别方法[J].计算机应用与软件,2012,29(6):72-75.CAO Junhong,WEI Zhuobin,GAO Yi.Unsupervised damage detection based on combination of independent component analysis and Mahalanobis distance[J].Computer Applications and Software,2012,29(6):72-75.
[5] 骆志高,李旭东,赵俊丽,等.利用马氏距离判别法准确实现对裂纹的识别[J].振动与冲击,2013,32(21):186-188.LUO Zhigao,LI Xudong,ZHAO Junli,et al.Crack identification with Mahalanobis distance discrimination method[J].Journal of Vibration and Shock,2013,32(21):186-188.
[6] ZHOU Y L,FIGUEIREDO E,MAIA N,et al.Damage detection in structures using a transmissibility-based Mahalanobis distance[J].Structural Control & Health Monitoring,2015,22(10):1209-1222.
[7] 刘纲,罗钧,方鹏,等.基于向量自回归模型的损伤识别方法[J].振动.测试与诊断,2015,35(5):873-879.LIU Gang,LUO Jun,FANG Peng,et al.Damage identification method based on vector autoregressive model[J].Journal of Vibration,Measurement & Diagnosis,2015,35(5):873-879.
[8] 王清华,王丹生.基于EMI与马氏距离的木试件损伤检测试验研究[C]//全国结构工程学术会议.长沙,2016.
[9] SZYMON G,DALGAARD M U,MICHAEL D,et al.Statistical methods for damage detection applied to civil structures[J].Procedia Engineering,2017,199:1919-1924.
[10] 罗钧,刘纲,黄宗明.基于子结构模型剪切型框架结构损伤识别[J].振动、测试与诊断,2017,37(2):294-300.LUO Jun,LIU Gang,HUANG Zongming.Damage identification of shear frame structures based on substructure models[J].Journal of Vibration,Measurement & Diagnosis,2017,37(2):294-300.
[11] MAHALANOBIS P C.On the generalised distance in statistics[J].Proceedings of the National Institute of Sciences of India,1936,2:49-55.
[12] HUANG N E,SHEN Z,LONG S R,et al.The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis[J].Proceedings of the Royal Society of London Series A,1998,454:903-995.
[13] 陈隽,徐幼麟,李杰.经验模分解及小波分析在结构损伤识别中的应用:试验研究[J].地震工程与工程振动,2007,27(1):110-116.CHEN Jun,XU Youlin,LI Jie.Structural damage detection using empirical mode decomposition and wavelet analysis:experimental investigation[J].Journal of Earthquake Engineering and Engineering Vibration,2007,27(1):110-116.
[14] 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.
[15] 裴益轩,郭民.滑动平均法的基本原理及应用[J].火炮发射与控制学报,2001(1):21-23.PEI Yixuan,GUO Min.The fundamental principle and application of sliding average method[J].Gun Launch & Control Journal,2001(1):21-23.