Identification of Nonlinearity Using Transfer Entropy Combined with Surrogate Data Algorithm
Publication: Journal of Engineering Mechanics
Volume 145, Issue 2
Abstract
A numerical time-delayed transfer entropy method combined with a surrogate data algorithm is proposed to identify the nonlinearities in the vibration data of structures with damages without the use of baseline data. Semianalytical methods based on the Galerkin method are used to precisely predict the linear and nonlinear response of structures. The proposed method can identify nonlinearities in vibration data well. A new nonlinearity index is also proposed. Computation results for different loads indicate that the nonlinearity index increases as load increases. Subsequently, a new discreteness degree index for transfer entropy is additionally proposed. The responses of a plate with different loads are calculated and linear relationships between the discreteness degree index and the nonlinearity index are obtained. Numerical examples with different geometries but similar nonlinearity indexes are also carried out. It is shown that the discreteness degree index for transfer entropy can quantitatively measure nonlinearity degree. As verified, the proposed methodology can be used for structure nonlinearity identification in areas such as civil engineering, mechanical engineering, and ocean engineering.
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Acknowledgments
The authors gratefully acknowledge the financial support provided by the 973 Program of China (No. 2013CB035901), the Fundamental Research Funds for the Central Universities, and the National Natural Science Foundation of China (Nos. 51379185 and 51679214).
References
Achenbach, J. D. 2009. “Structural health monitoring—What is the prescription.” Mech. Res. Commun. 36 (2): 137–142. https://doi.org/10.1016/j.mechrescom.2008.08.011.
Bagchi, A., J. Humar, and H. P. Xu. 2010. “Model-based damage identification in a continuous bridge using vibration data.” J. Perform. Constr. Facil. 24 (2): 148–158. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000071.
Chen, S., M. Zang, D. Wang, Z. Zheng, and C. Zhao. 2016. “Finite element modeling of impact damage in polyvinyl butyral laminated glass.” Compos. Struct. 138 (3): 1–11. https://doi.org/10.1016/j.compstruct.2015.11.042.
Del Linz, P., P. A. Hooper, H. Arora, D. Smith, L. Pascoe, D. Cormie, B. R. K. Blackman, and J. P. Dear. 2015. “Reaction forces of laminated glass windows subject to blast loads.” Compos. Struct. 131 (11): 193–206. https://doi.org/10.1016/j.compstruct.2015.04.050.
Del Linz, P., X. Liang, P. A. Hooper, L. Z. Wang, and J. P. Dear. 2016. “An analytical solution for pre-crack behavior of laminated glass under blast loading.” Compos. Struct. 144 (6): 156–164. https://doi.org/10.1016/j.compstruct.2016.02.058.
Duan, P., F. Yang, T. W. Chen, and S. L. Shah. 2013. “Direct causality detection via the transfer entropy approach.” IEEE Trans. Control. Syst. Technol. 21 (6): 2052–2066. https://doi.org/10.1109/TCST.2012.2233476.
Hooper, P., and B. Blackman. 2012. “The mechanical behavior of poly(vinyl butyral) at different strain magnitudes and strain rates.” J. Mater. Sci. 47 (8): 3564–3576. https://doi.org/10.1007/s10853-011-6202-4.
Hooper, P. A., R. A. M. Sukhram, B. R. K. Blackman, and J. P. Dear. 2012. “On the blast resistance of laminated glass.” Int. J. Solids. Struct. 49 (6): 899–918. https://doi.org/10.1016/j.ijsolstr.2011.12.008.
Ito, S. 2016. “Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality.” Sci. Rep.-UK. 6 (11): 36831. https://doi.org/10.1038/srep36831.
Liebert, W., and H. G. Schuster. 1989. “Proper choice of the time delay for the analysis of chaotic time series.” Phys. Lett. A 142 (2–3): 107–111. https://doi.org/10.1016/0375-9601(89)90169-2.
Nichols, J. M., M. Seaver, and S. T. Trickey. 2006. “A method for detecting damage-induced nonlinearities in structures using information theory.” J. Sound Vib. 297 (7): 1–16. https://doi.org/10.1016/j.jsv.2006.01.025.
Nichols, J. M., M. Seaver, S. T. Trickey, M. D. Todd, C. Olson, and L. Overbey. 2005. “Detecting nonlinearity in structural systems using the transfer entropy.” Phys. Rev. E 72 (4): 1–11. https://doi.org/10.1103/PhysRevE.72.046217.
Overbey, L. A., and M. D. Todd. 2009a. “Dynamic system change detection using a modification of the transfer entropy.” J. Sound Vib. 322 (1–2): 438–453. https://doi.org/10.1016/j.jsv.2008.11.025.
Overbey, L. A., and M. D. Todd. 2009b. “Effects of noise on transfer entropy estimation for damage detection.” Mech. Syst. Signal Process. 23 (7): 2178–2191. https://doi.org/10.1016/j.ymssp.2009.03.016.
Prichard, D., and J. Theiler. 1994. “Generating surrogate data for time series with several simultaneously measured variables.” Phys. Rev. Lett. 73 (7): 951–954. https://doi.org/10.1103/PhysRevLett.73.951.
Schreiber, T. 2000. “Measuring information transfer.” Phys. Rev. Lett. 85 (3): 461–464. https://doi.org/10.1103/PhysRevLett.85.461.
Schreiber, T., and A. Schmitz. 1996. “Improved surrogate data for nonlinearity tests.” Phys. Rev. Lett. 77 (4): 635–638. https://doi.org/10.1103/PhysRevLett.77.635.
Theiler, J., S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer. 1992. “Testing for nonlinearity in time series: The method of surrogate data.” Phys. D 58 (1–4): 77–94. https://doi.org/10.1016/0167-2789(92)90102-S.
Wu, Z. G., G. H. Liu, and Z. H. Zhang. 2011. “Experimental study of structural damage identification based on modal parameters and decay ratio of acceleration signals.” Front. Archit. Civ. Eng. China 5 (1): 112–120. https://doi.org/10.1007/s11709-010-0069-3.
Xie, Z. K., G. H. Liu, and Z. G. Wu. 2012. “Dynamic damage identification for beam structures based on transfer entropy.” [In Chinese.] J. Zhejiang Univ. 46 (10): 1880–1886. https://doi.org/10.3785/j.issn.1008-973X.2012.10.022.
Zeinoddini, M., M. Mo’tamedi, S. A. Gharebaghi, and G. A. R. Parke. 2016. “On the ratcheting response of circular steel pipes subject to cyclic inelastic bending: A closed-form analytical solution.” Int. J. Mech. Sci. 117 (9): 243–257. https://doi.org/10.1016/j.ijmecsci.2016.09.004.
Zembaty, Z., M. Kowalski, and S. Pospisil. 2006. “Dynamic identification of a reinforced concrete frame in progressive states of damage.” Eng. Struct. 28 (5): 668–681. https://doi.org/10.1016/j.engstruct.2005.09.025.
Zou, Y., L. Tong, and G. Steven. 2000. “Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures—A review.” J. Sound Vib. 230 (2): 357–378. https://doi.org/10.1006/jsvi.1999.2624.
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©2018 American Society of Civil Engineers.
History
Received: Sep 13, 2017
Accepted: Aug 17, 2018
Published online: Dec 11, 2018
Published in print: Feb 1, 2019
Discussion open until: May 11, 2019
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