Document Type : Article

**Authors**

Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, P.O. Box 91775-1111, Iran

**Abstract**

Feature extraction by time series modeling based on statistical pattern recognition is a powerful approach to structural health monitoring. Determination of an adequate order and identification of an appropriate model play prominent roles in extracting sensitive features to damage from time series representations. Early damage detection under statistical decision-making via high-dimensional features is another significant issue. The main objectives of this article are to improve a residual-based feature extraction method by time series modeling and propose a multivariate data visualization approach to early damage detection. A simple graphical tool based on Box-Jenkins methodology is presented to identify the most compatible time series model with vibration time-domain measurements. Furthermore, k-Means and Gaussian mixture model clustering techniques are utilized to examine the performance of the residuals of the identified model in damage detection. A numerical concrete beam and an experimental benchmark model are applied to verify the improved and proposed methods along with comparative analyses. Results will show that these approaches are successful in obtaining a sufficient order superior to a state-of-the-art order determination technique, generating uncorrelated residuals, extracting sensitive features to damage, and accurately detecting early damage by high-dimensional data.

**Keywords**

- structural health monitoring
- statistical pattern recognition
- feature extraction
- time series modeling
- residual extraction
- unsupervised learning
- Andrew plot
- clustering analysis

**Main Subjects**

References:

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29. Newmark, N.M. "A method of computation for structural dynamics", J. Eng. Mech. Div. ASCE, 85(3), pp. 67-94 (1959).

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31. Figueiredo, E., Park, G., Figueiras, J., Farrar, C., and Worden, K., Structural Health Monitoring Algorithm Comparisons Using Standard Data Sets, LA-14393, Los Alamos National Laboratory, Los Alamos, NM (2009).

2. Amezquita-Sanchez, J. and Adeli, H. "Feature extraction and classification techniques for health monitoring of structures", Sci. Iran., A., 22(6), pp. 1931-1940 (2015).

3. Qarib, H. and Adeli, H. "Recent advances in health monitoring of civil structures", Sci. Iran., A., 21(6), pp. 1733-1742 (2014).

4. Amezquita-Sanchez, J.P. and Adeli, H. "Signal processing techniques for vibration-based health monitoring of smart structures", Arch. Comput. Methods Eng., 23(1), pp. 1-15 (2016).

5. Gul, M. and Necati Catbas, F. "Statistical pattern recognition for structural health monitoring using time series modeling: Theory and experimental verifications", Mech. Syst. Sig. Process., 23(7), pp. 2192-2204 (2009).

6. Yao, R. and Pakzad, S.N. "Autoregressive statistical pattern recognition algorithms for damage detection in civil structures", Mech. Syst. Sig. Process., 31, pp. 355-368 (2012).

7. Park, S., Lee, J.-J., Yun, C.-B., and Inman, D.J. "Electro-mechanical impedance-based wireless structural health monitoring using PCA-data compression and k-means clustering algorithms", J. Intell. Mater. Syst. Struct., 19(4), pp. 509-520 (2008).

8. Silva, M., Santos, A., Santos, R., Figueiredo, E., Sales, C., and Costa, J.C.W.A. "Agglomerative concentric hypersphere clustering applied to structural damage detection", Mech. Syst. Sig. Process., 92, pp. 196-212 (2017).

9. Kopsaftopoulos, F. and Fassois, S. "Vibration based health monitoring for a lightweight truss structure: experimental assessment of several statistical time series methods", Mech. Syst. Sig. Process., 24(7), pp. 1977-1997 (2010).

10. Datteo, A. and Luca, F. "Statistical pattern recognition approach for long-time monitoring of the G. Meazza stadium by means of AR models and PCA", Eng. Struct., 153, pp. 317-333 (2017).

11. de Lautour, O.R. and Omenzetter, P. "Nearest neighbor and learning vector quantization classification for damage detection using time series analysis", Struct. Control Health Monit., 17(6), pp. 614-631 (2010).

12. Farahani, R.V. and Penumadu, D. "Full-scale bridge damage identification using time series analysis of a dense array of geophones excited by drop weight", Struct. Control Health Monit., 23(7), pp. 982-997 (2016).

13. Carden, E.P. and Brownjohn, J.M. "ARMA modelled time-series classification for structural health monitoring of civil infrastructure", Mech. Syst. Sig. Process., 22(2), pp. 295-314 (2008).

14. Mei, L., Mita, A., and Zhou, J. "An improved substructural damage detection approach of shear structure based on ARMAX model residual", Struct. Control Health Monit., 23, pp. 218-236 (2016).

15. Box, G.E., Jenkins, G.M., and Reinsel, G.C., Time Series Analysis: Forecasting and Control, 4th Edn., John Wiley & Sons, Inc, New Jersey (2008).

16. Figueiredo, E., Figueiras, J., Park, G., Farrar, C.R., and Worden, K. "Influence of the autoregressive model order on damage detection", Comput.-Aided Civ. Infrastruct. Eng., 26(3), pp. 225-238 (2011).

17. Mosavi, A.A., Dickey, D., Seracino, R., and Rizkalla, S. "Identifying damage locations under ambient vibrations utilizing vector autoregressive models and Mahalanobis distances", Mech. Syst. Sig. Process., 26, pp. 254-267 (2012).

18. Farrar, C.R. and Jauregui, D.A. "Comparative study of damage identification algorithms applied to a bridge: I. Experiment", Smart Mater. Struct., 7(5), p. 704 (1998).

19. Farrar, C.R. and Jauregui, D.A. "Comparative study of damage identification algorithms applied to a bridge: II. Numerical study", Smart Mater. Struct., 7(5), p. 720 (1998).

20. Fugate, M.L., Sohn, H., and Farrar, C.R. Vibrationbased damage detection using statistical process control", Mech. Syst. Sig. Process., 15(4), pp. 707-721 (2001).

21. Gul, M. and Necati Catbas, F. "Structural health monitoring and damage assessment using a novel time series analysis methodology with sensor clustering", J. Sound Vib., 330(6), pp. 1196-1210 (2011).

22. Roy, K., Bhattacharya, B., and Ray-Chaudhuri, S. "ARX model-based damage sensitive features for structural damage localization using output-only measurements", J. Sound Vib., 349, pp. 99-122 (2015).

23. Kitagawa, G., Introduction to Time Series Modeling, CRC Press, Taylor & Francis Group, Boca Raton (2010).

24. Andrews, D.F. "Plots of high-dimensional data", Biometrics, 28(1), pp. 125-136 (1972).

25. Izenman, A.J., Modern Multivariate Statistical Techniques: Regression, Classification and Manifold Learning, Springer, New York, NY (2008).

26. Wu, J., Advances in k-Means Clustering: A Data Mining Thinking, Springer, Science & Business Media (2012).

27. McLachlan, G. and Peel, D., Finite Mixture Models, John Wiley & Sons (2004).

28. Kaufman, L. and Rousseeuw, P.J., Finding Groups in Data: An Introduction to Cluster Analysis, John Wiley & Sons (2009).

29. Newmark, N.M. "A method of computation for structural dynamics", J. Eng. Mech. Div. ASCE, 85(3), pp. 67-94 (1959).

30. Friswell, M.I. and Penny, J.E. "Crack modeling for structural health monitoring", Struct. Health Monit., 1(2), pp. 139-148 (2002).

31. Figueiredo, E., Park, G., Figueiras, J., Farrar, C., and Worden, K., Structural Health Monitoring Algorithm Comparisons Using Standard Data Sets, LA-14393, Los Alamos National Laboratory, Los Alamos, NM (2009).

Transactions on Civil Engineering (A)

May and June 2020Pages 1001-1018