Structural Nonlinear Damage Detection Based on ARMA-GARCH Model

Abstract:

Two economic models, i.e. auto-regressive and moving average model (ARMA) and generalized auto-regressive conditional heteroscedasticity model (GARCH), are adopted to assess the conditions of structures and to detect structural nonlinear damage based on time series analysis in this study. To improve the reliability of the method for nonlinear damage detection, a new damage sensitive feature (DSF) for the ARMA-GARCH model is defined as a ratio of the standard deviation of the variance time series of ARMA-GARCH model residual errors in test condition to ones in reference condition. Compared to the traditional DSF defined as the ratio between the deviations of ARMA-GARCH model residual error in two conditions, the successful outcomes of the new DSF can give obvious explanation for the current states of structures and can detect the nonlinear damage exactly, which enhance the worth of structural health monitoring as well as condition-based maintenance in practical applications. This method is finally verified by a series of experimental data of three-story building structure made in Los Alamos National Laboratory USA.

• Periodical: Applied Mechanics and Materials (Volumes 204-208)
• Pages: 2891-2896
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.204-208.2891
• Online since: October 2012
• Authors: Cong Cheng, Ling Yu, Liu Jie Chen
• Keywords: ARMA-GARCH Model, Nonlinear Damage Detection, Structural Health Monitoring (SHM)

References

[1] M.L. Fugate, H. Sohn and C.R. Farrar: Mech. Syst. Sig. Process., Vol. 15(4) (2001), p.707.

[2] H. Sohn and C.R. Farrar: Smart Mater. Struct., Vol. 10 (3) (2001), p.1.

[3] H. Sohn, C.R. Farrar, N.F. Hunter, et al.: J. Dyn. Syst. Meas. Contr., Vol. 123 (4) (2001), p.706.

[4] L.J. Chen: Structural Damage Identification based on Conditional Heteroscedasticity Time Series Model. Master Thesis, Jinan University, 2011. (In Chinese).

[5] H. Thom Pham and B.S. Yang: Mech. Syst. Sig. Process., Vol. 24 (2) (2010), p.546.

[6] E. Figueriedo, G. Park, J. Figuerias, et al: Structural health monitoring algorithm comparisons using standard data sets. Los Alamos, New Mexico: Los Alamos National Laboratory (2009).

DOI: 10.2172/441698

[7] C. Francq and J.M. Zakoian: GARCH models: structure, statistical inference and financial applications (Chichester, West Sussex, U.K.: Wiley, 2010).

DOI: 10.1002/9781119313472

[8] J.H. Zhu and L. Yu: J. Southeast Univ. (Nat. Sci. ), Vol. 42 (1) (2012), p.137 (In Chinese).