DOI QR코드

DOI QR Code

Nonlinear damage detection using linear ARMA models with classification algorithms

  • Chen, Liujie (School of Civil Engineering, Guangzhou University) ;
  • Yu, Ling (MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University) ;
  • Fu, Jiyang (Guangzhou University-Tamkang University Joint Research Center for Engineering Structure Disasters Prevention and Control) ;
  • Ng, Ching-Tai (School of Civil, Environmental & Mining Engineering, The University of Adelaide)
  • 투고 : 2019.08.08
  • 심사 : 2020.04.20
  • 발행 : 2020.07.25

초록

Majority of the damage in engineering structures is nonlinear. Damage sensitive features (DSFs) extracted by traditional methods from linear time series models cannot effectively handle nonlinearity induced by structural damage. A new DSF is proposed based on vector space cosine similarity (VSCS), which combines K-means cluster analysis and Bayesian discrimination to detect nonlinear structural damage. A reference autoregressive moving average (ARMA) model is built based on measured acceleration data. This study first considers an existing DSF, residual standard deviation (RSD). The DSF is further advanced using the VSCS, and then the advanced VSCS is classified using K-means cluster analysis and Bayes discriminant analysis, respectively. The performance of the proposed approach is then verified using experimental data from a three-story shear building structure, and compared with the results of existing RSD. It is demonstrated that combining the linear ARMA model and the advanced VSCS, with cluster analysis and Bayes discriminant analysis, respectively, is an effective approach for detection of nonlinear damage. This approach improves the reliability and accuracy of the nonlinear damage detection using the linear model and significantly reduces the computational cost. The results indicate that the proposed approach is potential to be a promising damage detection technique.

키워드

과제정보

The research described in this paper was financially supported by the open project foundation (Grant No. 20160626005) from MOE Key Lab of Disaster Forecast and Control in Engineering at Jinan University in China.

참고문헌

  1. Adams, D.E. and Farrar, C.R. (2002), "Classifying linear and nonlinear structural damage using frequency domain ARX models", Struct. Health Monit, 1(2), 185-201. https://dx.doi.org/10.1106/147592102028970
  2. Bao, C.X., Hao, H. and Li, Z.X. (2013), "Integrated ARMA model method for damage detection of subsea pipeline system", Eng. Struct., 48, 176-192. https://doi.org/10.1016/j.engstruct.2012.09.033
  3. Carden, E.P and Brownjohn, J.M.W. (2008), "ARMA modelled time-series classification for structural health monitoring of civil infrastructure", Mech. Syst. Signal Pr., 22(2), 295-314. https://doi.org/10.1016/j.ymssp.2007.07.003
  4. Chen, L.J. and Yu, L. (2013), "Structural nonlinear damage identification algorithm based on time series ARMA/GARCH model", Adv. Struct. Eng., 16(9), 1597-1609. https://doi.org/10.1260%2F1369-4332.16.9.1597 https://doi.org/10.1260/1369-4332.16.9.1597
  5. Chen, L.J., Yu, L. and Xiao, T. (2015), "The structural nonlinear damage detection based on linear time series algorithm", Appl. Mech. Mater., 744-746, 345-350. https://doi.org/10.4028/www.scientific.net/AMM.744-746.345
  6. Ding, Z.H., Li, J., Hao, H. and Lu, Z.R. (2019), "Nonlinear hysteretic parameter identification using an improved tree-seed algorithm", Swarm Evol. Comput., 46, 69-83. https://doi.org/10.1016/j.swevo.2019.02.005
  7. Doebling, S.W., Farrar, C.R., Prime, M.B. and Shevitz, D.W. (1996), "Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a Literature review", Los Alamos National Lab., NM, USA.
  8. Fan, J.Q. and Yao, Q.W. (2006), Nonlinear Time Series: Nonparametric and Parametric Methods, Springer-Verlag, Germany.
  9. Fan, X., Li, J. and Hao, H. (2016), "Piezoelectric impedance based damage detection in truss bridges based on time frequency ARMA model", Smart Struct. Syst., Int. J., 18(3), 501-523. https://doi.org/10.12989/sss.2016.18.3.501
  10. Farrar, C.R. and Lieven, N.A.J. (2007), "Damage prognosis: the future of structural health monitoring", Philosoph. Transact. Royal Soc. A: Math. Phys. Eng. Sci., 365(1851), 623-632. https://doi.org/10.1098/rsta.2006.1927
  11. Fasel, T.R., Hoon, S., Gyuhae, P. and Farrar, C.R. (2010), "Active sensing using impedance-based ARX models and extreme value statistics for damage detection", Earthq. Eng. Struct. D., 34(7), 763-785. https://xs.scihub.ltd/https://doi.org/10.1002/eqe.454
  12. Figueiredo, E., Park, G., Figueiras, J., Farrar, C. and Worden, K. (2009), "Structural health monitoring algorithm comparisons using standard data sets", Los Alamos National Laboratory (LANL), Los Alamos, NM, USA.
  13. Gul, M. and Catbas, F.N. (2009), "Statistical pattern recognition for Structural Health Monitoring using time series modeling: Theory and experimental verifications", Mech. Syst. Signal Pr., 23(7), 2192-2204. https://doi.org/10.1016/j.ymsp.2009.02.013
  14. Gul, M. and Catbas, F.N. (2011), "Structural health monitoring and damage assessment using a novel time series analysis methodology with sensor clustering", J. Sound Vib., 330(6), 1196-1210. https://doi.org/10.1016/j.jsv.2010.09.024
  15. Jayawardhana, M., Zhu, X., Liyanapathirana, R. and Gunawardana, U. (2015), "Statistical damage sensitive feature for structural damage detection using AR model coefficients", Adv. Struct. Eng., 18(10), 1551-1562. https://doi.org/10.1260%2F1369-4332.18.10.1551 https://doi.org/10.1260/1369-4332.18.10.1551
  16. Lam, H.F., Alabi, S.A. and Yang, J.H. (2017), "Identification of rail-sleeper-ballast system through time-domain Markov chain Monte Carlo-based Bayesian approach", Eng. Struct., 140, 421-436. https://doi.org/10.1016/j.engstruct.2017.03.001
  17. Lautour, O.D. and Omenzetter, P. (2010), "Damage classification and estimation in experimental structures using time series analysis and pattern recognition", Mech. Syst. Signal Pr., 24(5), 1556-1569. https://doi.org/10.1016/j.ymssp.2009.12.008
  18. Lu, K.C., Loh, C.H., Yang, Y.S., Lynch, J.P. and Law, K.H. (2008), "Real-time structural damage detection using wireless sensing and monitoring system", Smart Struct. Syst., Int. J., 4(6), 759-778. https://doi.org/10.12989/sss.2008.4.6.759
  19. McQueen, J.B. (1967), "Some methods of classification and analysis of multivariate observations", Proceedings of the 5th Berkeley Symposium on Mathematical Statistics & Probability,. Berkeley, CA, USA.
  20. Ng, C.T. and Au, S.K. (2018), "Mode shape scaling and implications in modal identification with known input", Eng. Struct., 156, 411-416. https://xs.scihub.ltd/https://doi.org/10.1016/j.engstruct.2017.11.017
  21. Noh, H.Y., Nair, K.K., Kiremidjian, A.S. and Loh, C.H. (2009), "Application of time series based damage detection algorithms to the benchmark experiment at the National Center for Research on Earthquake Engineering (NCREE) in Taipei, Taiwan", Smart Struct. Syst., Int. J., 5(1), 95-117. https://doi.org/10.12989/sss.2009.5.1.095
  22. Novianti, P., Setyorini, D. and Rafflesia, U. (2017), "K-Means cluster analysis in earthquake epicenter clustering", Int. J. Adv. Intel. Inform., 3(2), 81-89. https://doi.org/10.26555/ijain.v3i2.100
  23. Prawin, J. and Rao, A.R.M. (2018), "Nonlinear Structural Damage Detection Based on Adaptive Volterra Filter Model", Int. J. Struct. Stab. Dyn., 18(2), 1-12. http://dx.doi.org/10.1142/S0219455418710037
  24. Rao, P.S. and Ratnam, C. (2012), "Health monitoring of welded structures using statistical process control", Mech. Syst. Signal Pr., 27(1), 683-695. https://xs.scihub.ltd/https://doi.org/10.1016/j.ymssp.2011.09.023
  25. Roy, K., Bhattacharya, B. and Ray-Chaudhuri, S. (2015), "ARX model-based damage sensitive features for structural damage localization using output-only measurements", J. Sound Vib., 349, 99-122. https://xs.scihub.ltd/https://doi.org/10.1016/j.jsv.2015.03.038
  26. Sohn, H., Farrar, C.R., Hemez, F.M., Shunk, D.D., Stinemates, D.W. and Nadler, B.R. (2003), "A review of structural health monitoring literature: 1996-2001", Los Alamos National Laboratory, NM, USA.
  27. The Mathworks, I. (2014), MATLAB (R2015a), Econometrics Toolbox.
  28. Wang, X.M. (2013), The Study on Movement Characteristics and Non-linear Model of CGCS2000 Framework, Chinese Academy of Surveying and Mapping, Beijing, China.
  29. Weatherill, G. and Burton, P.W. (2009), "Delineation of shallow seismic source zones using K-means cluster analysis, with application to the Aegean region", Geophys. J. Int., 176(2), 565-588. https://doi.org/10.1111/j.1365-246X.2008.03997.x
  30. Worden, K., Farrar, C.R., Manson, G. and Park, G. (2007), "The fundamental axioms of structural health monitoring", Pro. Math. Phy. Eng. Sci., 463(2082), 1639-1664. https://doi.org/10.1098/rspa.2007.1834
  31. Xin, Y., Hao, H., Li, J., Wang, Z.C., Wan, H.P. and Ren, W.X. (2019), "Bayesian based nonlinear model updating using instantaneous characteristics of structural dynamic responses", Eng. Struct., 183, 459-474. http://doi.org/10.1016/j.engstruct.2019.01.043
  32. Yin, T., Jiang, Q.H. and Yuen, K.V. (2017), "Vibration-based damage detection for structural connections using incomplete modal data by Bayesian approach and model reduction technique", Eng. Struct., 132, 260-277. https://xs.scihub.ltd/https://doi.org/10.1016/j.engstruct.2016.11.035
  33. Yuen, K.V. (2010), Bayesian Methods for Structural Dynamics and Civil Engineering, John Wiley & Sons Pte Ltd., Singapore.
  34. Zhang, Q.W. (2007), "Statistical damage identification for bridges using ambient vibration data", Comput. Struct., 85(7-8), 476-485. https://xs.scihub.ltd/https://doi.org/10.1016/j.compstruc.2006.08.071
  35. Zhang, X. (2009), Pattern Recognition, Tsinghua University Press, Beijing, China.
  36. Zheng, H. and Mita, A. (2007), "Two-stage damage diagnosis based on the distance between ARMA models and pre-whitening filters", Smart Mater. Struct., 16(5), 1829-1836. http://dx.doi.org/10.1088/0964-1726/16/5/038
  37. Zheng, H.T. and Mita, A. (2008), "Damage indicator defined as the distance between ARMA models for structural health monitoring", Struct Control Hlth., 15(7), 992-1005. https://doi.org/10.1002/stc.235
  38. Zheng, H.T. and Mita, A. (2009), "Localized damage detection of structures subject to multiple ambient excitations using two distance measures for autoregressive models", Struct. Hlth. Monit., 8(3), 207-222. https://doi.org/10.1177%2F1475921708102145 https://doi.org/10.1177/1475921708102145
  39. Zhu, J.H. and Yu, L. (2012), "Damage detection based on time series analysis and higher statistical moments", J. Southeast U.: Nat. Sci. Ed., 42(1), 137-143. https://doi.org/10.3969/j.issn.1001-0505.2012.01.026
  40. Zhu, S., Wu, J., Xiong, H. and Xia, G. (2011), "Scaling up top-K cosine similarity search", Data Knowl. Eng., 70(1), 60-83. https://xs.scihub.ltd/https://doi.org/10.1016/j.datak.2010.08.004