Abstract
Most of the currently employed vibration-based identification approaches for structural damage detection are based on eigenvalues and/or eigenvectors extracted from dynamic response measurements, and strictly speaking, are only suitable for linear system. However, the inception and growth of damage in engineering structures under severe dynamic loadings are typical nonlinear procedures. Consequently, it is crucial to develop general structural restoring force and excitation identification approaches for nonlinear dynamic systems because the restoring force rather than equivalent stiffness can act as a direct indicator of the extent of the nonlinearity and be used to quantitatively evaluate the absorbed energy during vibration, and the dynamic loading is an important factor for structural remaining life forecast. In this study, based on the instantaneous state vectors and partially unknown excitation, a power series polynomial model (PSPM) was utilized to model the nonlinear restoring force (NRF) of a chain-like nonlinear multi-degree-of-freedom (MDOF) structure. To improve the efficiency and accuracy of the proposed approach, an iterative approach, namely weighted adaptive iterative least-squares estimation with incomplete measured excitations (WAILSE-IME), where a weight coefficient and a learning coefficient were involved, was proposed to identify the restoring force of the structure as well as the unknown dynamic loadings simultaneously. The response measurements of the structure, i.e., the acceleration, velocity, and displacement, and partially known excitations were utilized for identification. The feasibility and robustness of the proposed approach was verified by numerical simulation with a 4 degree-of-freedom (DOF) numerical model incorporating a nonlinear structural member, and by experimental measurements with a four-story frame model equipped with two magneto-rheological (MR) dampers mimicking nonlinear behavior. The results show the proposed approach by combining the PSPM and WAILSE-IME algorithm is capable of effectively representing and identifying the NRF of the chain-like MDOF nonlinear system with partially unknown external excitations, and provide a potential way for damage prognosis and condition evaluation of engineering structures under dynamic loadings which should be regarded as a nonlinear system.
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Abbreviations
- PSPM::
-
Power Series Polynomial Model
- NRF::
-
Nonlinear Restoring Force
- WAILSE-IME::
-
Weighted Adaptive Iterative Least-Squares Estimation with Incomplete Measured Excitations.
References
Ghanem, R., Shinozuka, M.: Structural-system identification I: Theory. J. Eng. Mech. 121(2), 255–264 (1995)
Doebling, S.W., Farrar, C.R., Prime, M.B., Shevitz, D.W.: A review of damage identification methods that examine changes in dynamic properties. Shock Vib. Dig. 30(2), 91–105 (1998)
Wu, Z.S., Xu, B., Harada, T.: Review on structural health monitoring for infrastructure. J. Appl. Mech. 6, 1043–1054 (2003)
Yan, Y.J., Cheng, L., Wu, Z.Y., Yam, L.H.: Development in vibration-based structural damage detection technique. Mech. Syst. Signal Process. 21(5), 2198–2211 (2007)
Farrar, C.R., Lieven, N.A.J.: Damage prognosis: the future of structural health monitoring. Philos. Trans. R. Soc. Lond. A 365, 623–632 (2007)
Ibanez, P.: Identification of dynamic parameters of linear and non-linear structural models from experimental data. Nucl. Eng. Des. 25, 30–41 (1973)
Worden, K., Tomlinson, G.R.: Nonlinearity in Structural Dynamics: Detection, Identification, and Modeling. Inst. Phys. Publ., Bristol and Philadelphia (2001)
Aoun, M., Malti, R., Levron, F., Oustaloup, A.: Numerical Simulations of Fractional Systems: An Overview of Existing Methods and Improvements. Nonlinear Dyn. 38(1–4), 117–131 (2004)
Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.C.: Past, present and future of nonlinear system identification in structural dynamics. Mech. Syst. Signal Process. 20, 505–592 (2006)
Masri, S.F., Caughey, T.K.: A nonparametric identification technique for nonlinear dynamic problems. J. Appl. Mech. 46, 433–447 (1979)
Masri, S.F., Sassi, H., Caughey, T.K.: A nonparametric identification of nearly arbitrary nonlinear systems. J. Appl. Mech. 49, 619–628 (1982)
Yang, Y.X., Ibrahim, S.R.: A nonparametric identification technique for a variety of discrete nonlinear vibrating system. J. Vib. Acoust. Stress 107, 60–66 (1985)
Masri, S.F., Caffery, J.P., Caughey, T.K., Smyth, A.W., Chassiakos, A.G.: A general data-based approach for developing reduced-order models of non-linear MDOF systems. Nonlinear Dyn. 39, 95–112 (2005)
Masri, S.F., Tasbihgoo, F., Caffery, J.P., Smyth, A.W., Chassiakos, A.G.: Data-based model-free representation of complex hysteretic MDOF systems. Struct. Control Health Monit. 13, 365–387 (2006)
Tasbihgoo, F., Caffrey, J.P., Masri, S.F.: Development of data-based model-free representation of non-conservative dissipative systems. Int. J. Non-Linear Mech. 42, 99–117 (2007)
Haroon, M., Adams, D.E.: Time and frequency domain nonlinear system characterization for mechanical fault identification. Nonlinear Dyn. 50(3), 387–408 (2007)
Paduart, J., Lauwers, L., Sweversb, J., Smolders, K., Schoukens, J., Pintelon, R.: Identification of nonlinear systems using Polynomial Nonlinear State Space models. Automatica 46, 647–656 (2010)
Jamaali, J., Mohammadi, A., Keyvaani, H.: A Novel Nonlinear System Modeling and Identification Method based on Modal Series. J. Appl. Sci. 11(3), 567–572 (2011)
Wang, D., Haldar, A.: Element-level system identification with unknown input. J. Eng. Mech. 120(1), 159–176 (1994)
Li, J., Chen, J.: Inversion of ground motion with unknown structural parameters. Earthq. Eng. Eng. Vib. 17(3), 27–35 (1997)
Chen, J., Li, J.: Study of structural system identification with incomplete input information. Earthq. Eng. Eng. Vib. 18(4), 40–47 (1998)
Li, J., Chen, J.: Compensation method for structural parameter identification with incomplete input information. Chin. J. Comput. Mech. 19(3), 310–314 (2002)
Mohammad, K.S., Worden, K., Tomlinson, G.R.: Direct parameter estimation for linear and nonlinear structures. J. Sound Vib. 152(3), 471–499 (1992)
Wang, D., Haldar, A.: System identification with limited observations and without input. J. Eng. Mech. 123(5), 504–511 (1997)
Yang, J.N., Lin, S.: Identification of parametric variations of structures based on least squares estimation and adaptive tracking techniques. J. Eng. Mech. 131(3), 290–298 (2005)
Yang, J.N., Huang, H.W., Lin, S.: Sequential non-linear least-square estimation for damage identification of structures. Int. J. Non-Linear Mech. 41, 124–140 (2006)
Yang, J.N., Huang, H.W.: Sequential non-linear least-square estimation for damage identification of structures with unknown inputs and unknown outputs. Int. J. Non-Linear Mech. 42, 789–801 (2007)
Lei, Y., Wu, Y., Li, T.: Identification of nonlinear structural parameters under unmeasured excitations. Adv. Build. Mater., 768–772 (2010)
Mariani, S., Ghisi, A.: Unscented Kalman filtering for nonlinear structural dynamics. Nonlinear Dyn. 49(1–2), 131–150 (2007)
He, J., Xu, B., Masri, S.F.: Identification of nonlinear restoring force by using power series power series polynomial modeling. In: Proceedings of the 11th International Symposium on Structural Engineering, Guangzhou, China, Dec., vol. 2, pp. 1362–1368 (2010)
Xu, B., He, J., Masri, S.F.: Data-based identification of nonlinear restoring force under spatially incomplete excitations with power series polynomial model. Nonlinear Dyn. (2011, in press). doi:10.1007/s11071-011-0129-9
Xu, B., He, J., Rovekamp, R., Dyke, S.J.: Structural parameters and dynamic loading identification from incomplete measurements: approach and validation. Mech. Syst. Signal Process. (2011). doi:10.1016/j.ymssp.2011.07.008
Dahl, P.R.: Solid friction damping of mechanical vibrations. AIAA J. 14(12), 1675–1682 (1976)
Spencer, B.F. Jr, Dyke, S.J., Sain, M.K., Carlson, J.D.: Phenomenological model of a magnetorheological damper. J. Eng. Mech. 123(3), 230–238 (1997)
Huang, Z.G., Xu, B., Feinstein, Z., Dyke, S.J.: Nonparametric modeling of magnetorheological damper. In: Proceedings of the Tenth International Symposium on Structural Engineering for Young Experts, Changsha, China, Oct., pp. 1860–1865 (2008)
Zhou, Q., Qu, W.L.: Two mechanic models for magneto-rheological damper and corresponding test verification. Earthq. Eng. Eng. Vib. 22(4), 144–150 (2002)
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He, J., Xu, B. & Masri, S.F. Restoring force and dynamic loadings identification for a nonlinear chain-like structure with partially unknown excitations. Nonlinear Dyn 69, 231–245 (2012). https://doi.org/10.1007/s11071-011-0260-7
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DOI: https://doi.org/10.1007/s11071-011-0260-7