1. School of Civil Engineering, Hunan City University, Yiyang Hunan 413000, China;
2. School of Civil Engineering, Central South University, Changsha Hunan 410075, China;
3. School of Civil Engineering, Hefei University of Technology, Hefei Anhui 230009, China
Extraction of the Bridge Temperature Strain Effect Based on EMD and IMF Energy
LI Miao1,2, REN Wei-xin3, HUANG Tian-li2, WANG Ning-bo2
1. School of Civil Engineering, Hunan City University, Yiyang Hunan 413000, China;
2. School of Civil Engineering, Central South University, Changsha Hunan 410075, China;
3. School of Civil Engineering, Hefei University of Technology, Hefei Anhui 230009, China
摘要To extract the temperature effect component of the dynamic strain signal through empirical mode decomposition(EMD), which presents the shape of a cycle trend measured from a bridge, the intrinsic mode function (IMF) order number by which temperature strain is constructed should be ascertained. The problem is solved on the basis of the selection of the IMF order threshold. The energy of signal of the IMF is analyzed in the time and frequency domains, and the threshold of the IMF order is acquired through a synthetic analysis of the energy catastrophe order and the correlation coefficient of the Hilbert marginal spectrum. Finally, the temperature effect component of the strain data is extracted by selecting the cycle trend of the IMF according to the IMF order threshold. The result shows that (1) the periodic trend component of a dynamic strain leads to the order catastrophe of the IMF energy from which the value range of the IMF order threshold is preliminarily determined; (2) the correlation coefficient of the IMF marginal spectrum increases rapidly to over 0.8 by analyzing the energy distribution in the frequency domain of the IMF located in a preliminarily determined range. The energy distribution patterns of last-order IMFs were consistent. By applying the method to the in-situ data, the result demonstrates that the IMF order threshold can be precisely obtained by the first correlation coefficient of the IMFs marginal spectrum of over 0.8. After the temperature effect component is extracted based on the threshold, the live load information in the dynamic strain is properly retained.
Abstract:To extract the temperature effect component of the dynamic strain signal through empirical mode decomposition(EMD), which presents the shape of a cycle trend measured from a bridge, the intrinsic mode function (IMF) order number by which temperature strain is constructed should be ascertained. The problem is solved on the basis of the selection of the IMF order threshold. The energy of signal of the IMF is analyzed in the time and frequency domains, and the threshold of the IMF order is acquired through a synthetic analysis of the energy catastrophe order and the correlation coefficient of the Hilbert marginal spectrum. Finally, the temperature effect component of the strain data is extracted by selecting the cycle trend of the IMF according to the IMF order threshold. The result shows that (1) the periodic trend component of a dynamic strain leads to the order catastrophe of the IMF energy from which the value range of the IMF order threshold is preliminarily determined; (2) the correlation coefficient of the IMF marginal spectrum increases rapidly to over 0.8 by analyzing the energy distribution in the frequency domain of the IMF located in a preliminarily determined range. The energy distribution patterns of last-order IMFs were consistent. By applying the method to the in-situ data, the result demonstrates that the IMF order threshold can be precisely obtained by the first correlation coefficient of the IMFs marginal spectrum of over 0.8. After the temperature effect component is extracted based on the threshold, the live load information in the dynamic strain is properly retained.
基金资助:Supported by the National Natural Science Foundation of China (No.51478472);the General Project of Hunan Provincial Department of Education (No.14C0214);and the Youth Project of Hunan Provincial Department of Education (No.13B010)
通讯作者:
LI Miao,E-mail address:lm_hncu@163.com
E-mail: lm_hncu@163.com
引用本文:
李苗, 任伟新, 黄天立, 王宁波. 基于EMD与IMF能量的桥梁应变温度效应成分的提取[J]. Journal of Highway and Transportation Research and Development, 2016, 10(1): 41-48.
LI Miao, REN Wei-xin, HUANG Tian-li, WANG Ning-bo. Extraction of the Bridge Temperature Strain Effect Based on EMD and IMF Energy. Journal of Highway and Transportation Research and Development, 2016, 10(1): 41-48.
[1] CATBAS F N,SUSOY M,FRANGOPOL D M. Structural Health Monitoring and Reliability Estimation:Long Span Truss Bridge Application with Environmental Monitoring Data[J]. Engineering Structures,2008,30(9):2347-2359.
[2] HELMICKI A,HUNT V,SHELL M,et al. Multidimensional Performance Monitoring of a Recently Constructed Steel-stringer Bridge[C]//Proceedings of the 2nd International Workshop on Structural Health Monitoring. Palo Alto:Stanford University,1999:408-416.
[3] BENDAT J S,PIERSOL A G. Random Data:Analysis and Measurement Procedures[M]. New York:John Wiley and Sons,1986:396-398.
[4] POLLOCK D S G. Methodology for Trend Estimation[J]. Economic Modelling,2001,18(1):75-96.
[5] POLLOCK D S G. Filters for Short Non-stationary Sequences[J]. Journal of Forecasting,2001,20(5):341-355.
[6] CHRISTIANO L J, FITZGERALD T J. The Band Pass Filter[J]. International Economic Review,2003,44:435-465.
[7] HUANG N E,SHEN Z,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 A:Mathematical Physical and Engineering Scienceo, 1998,454(1971):903-995.
[8] YE Gui-ru,XU Xin. Appliance of Hilbert-Huang Transform in Bridge Health Monitoring[J]. Journal of Highway and Transportation Research and Development,2009,26(9):97-101. (in Chinese)
[9] WU Z,HUANG N E,LONG S R,et al. On the Trend,Detrending,and Variability of Nonlinear and Nonstationary Time Series[J]. Proceedings of National Academy of Sciences,2007,104(38):14889-14894.
[10] CHEN Jun,LI Jie. Methods for Signal Trend Extraction and Their Comparison[J]. Journal of Fuzhou University:Natural Science Edition:2005,33(S1):42-45. (in Chinese)
[11] ZHOU Yi,SUN Li-min,MIN Zhi-hua. Girder Strain Analysis of a Cable-stayed Bridge[J]. Journal of Vibration and Shock,2011,30(4):230-235. (in Chinese)
[12] WU Z,HUANG N E. A Study of the Characteristics of White Noise Using the Empirical Mode Decomposition Method[J]. Proceedings of the Royal Society of London A:Mathematical, Physical and Engineering Science,2004,460(2046):1597-1611.
[13] RILLING G,FLANDRINl P,GONCALVES P. Empirical Mode Decomposition,Fractional Gaussian Noise and Hurst Exponent Estimation[C]//ICASSP 2005 IEEE International Conference on Acoustics, Speech and Signal Processing. Philadelphia:IEEE, 2005:489-492.
[14] MOGHTADERI A,FLANDRIN P,BORGNAT P. Trend Filtering Via Empirical Mode Decompositions[J]. Computational Statistics and Data Analysis,2013,58:114-126.
[15] ZHONG You-ming,QIN Shu-ren,TANG Bao-ping. Study on the Marginal Spectrum in Hilbert-huang Transform[J]. Systems Engineering and Electronics,2004,26(9):1323-1326. (in Chinese)
[16] LIU Jian,GUI Xun,LI Chuan-xi. Study on Fatigue Reliability of Details of Steel Box Girders of a Self-anchored Suspension Bridge Based on Health Monitoring[J]. Journal of Highway and Transportation Research and Development,2015,32(1):69-75. (in Chinese)
[1]
常柱刚, 王林凯, 夏飞龙. 基于CV NewMark-b法桥梁风致振动FSI数值模拟[J]. Journal of Highway and Transportation Research and Development, 2019, 13(2): 28-37.