Analysis of local state space models for feature extraction in structural health monitoring

Structural Health Monitoring

Volumn 6, Issue 2, 2007, Pages 145-172

  Overbey, L A ^a   Todd, M D ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Damage detection; Local state space; Lyapunov exponents; Nonlinear; Prediction error; State space; Structural health monitoring

Indexed keywords

EID: 34249884207     PISSN: 14759217     EISSN: 17413168     Source Type: Journal    
DOI: 10.1177/1475921706072079     Document Type: Article

References (38)

1. Schreiber, T. (1997). Detecting and analysing nonstationarity in a time series with nonlinear cross predictions. Phys. Rev. Lett., 78, 843-846.
2. Nichols, J.M., Todd, M.D. and Wait, J.R. (2003). Using state space predictive modeling with chaotic interrogation in detecting joint preload loss in a frame structure experiment. Smart Materials and Structures, 12 (4), 580-601.
3. Todd, M.D., Erickson, K., Chang, L., Lee, K. and Nichols, J.M. (2004). Using chaotic interrogation and attractor nonlinear cross-prediction error to detect fastener preload loss in an aluminum frame. Chaos: An Interdisciplinary Journal of Nonlinear Science, 14 (2), 387-399.
4. Doebling, S.W., Farrar, C.R. and Prime, M.B. (1998). A summary review of vibration-based damage identification methods. Shock and Vibration Digest, 30 (2), 91-105.
5. 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. Rep. No. LA-13070-MS, Los Alamos National Laboratory, Los Alamos, N.M.
6. Todd, M.D., Nichols, J.M., Pecora, L.M. and Virgin, L.N. (2001). Vibration-based damage assessment utilizing state space geometry changes: Local attractor variance ratio. Smart Materials and Structures, 10, 1000-1008.
7. Nichols, J.M., Nichols, C.J., Todd, M.D., Seaver, M., Trickey, S.T. and Virgin, L.N. (2004). Use of data driven phase space models in assessing the strength of a bolted connection in a composite beam. Smart Materials and Structures, 13 (2), 241-250.
8. Chelidze, D. and Cusumano, J.P. (2004). A dynamical systems approach to failure prognosis. Journal of Vibration and Acoustics, 126 (1), 1-7.
9. Liu, M. and Chelidze, D. (2005). Local flow variation method for damage identification, In: Proc. IDETC/CIE, Long Beach, CA, USA, September 24-28.
10. Trendafilova, I., Lenaerts, V., Kerschen, G., Golinval, J.-C., Van Brussel, H. and Heylen, W. (2000). Detection, localisation and identification of nonlinearities in structural dynamics. In: ISMA25 Proc., Belgium, Sept. 13-15.
11. Trendafilova, I. and Van Brussel, H. (2001). Non-linear dynamics tools for the motion analysis and condition monitoring of robot joints. Mechanical Systems and Signal Processing, 15 (6), 1141-1164.
12. Stabio, D. and Storer, D. (1999). Development and application of an experimental procedure for detecting damage in gears. In: Gilchrist, M.D., Dulieu-Barton, J.M. and Worden, K. (eds), Damage Assessment of Structures, pp. 189-196, Trans Tech Publications, Switzerland.
13. Adams, D. and Farrar, C.R. (2002). Classifying linear and nonlinear structural damage using frequency domain ARX models. International Journal of Structural Health Monitoring, 1 (2), 183-201.
14. Wang, W.J., Wu, Z.T. and Chen, J. (2000). Fault identification in rotating machinery using the correlation dimension and bispectra. Nonlinear Dynamics, 25, 383-393.
15. Craig, C., Neilson, R.D. and Penman, J. (2000). The use of correlation dimension in condition monitoring of systems with clearance. Journal of Sound and Vibration, 231 (1), 1-17.
16. Eckmann, J.-E. and Ruelle, D. (1985). Ergodic theory of chaos and strange attractors. Rev. Mod. Phys., 57, 617.
17. Oseledec, V.I. (1968). A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trudy Mosk. Mat. Obsc., 19, 197.
18. Eckmann, J.-E., Kamphorst, S.O., Ruelle, D. and Ciliberto, S. (1986). Lyapunov exponents from time series, Phys. Rev., 34A, 4971.
19. Abarbanel, H.D.I. (1996). Invariants of the motion. Analysis of Observed Chaotic Data, pp. 77-89, New York, NY: Springer.
20. Abarbanel, H.D.I., Brown, R. and Bryant, P. (1991). Computing the Lyapunov spectrum of a dynamical system from an observed time series. Physical Review A, 43 (6), 2787-2806.
21. Wolf, A., Swift, J.B., Swinney, H.L. and Vastano, J.A. (1985). Determining Lyapunov exponents from a time series, Physica D, 16, 285-317.
22. Abarbanel, H.D.I., Brown, R. and Kennel, M.B. (1991). Variation of Lyapunov exponents on a strange attractor. Journal of Nonlinear Science, 1, 175-199.
23. Takens, F. (1981). Detecting strange attractors in turbulence. In: Rand, D. and Young, L.S. (eds), Dynamical Systems and Turbulence: Springer Lecture Notes in Mathematics, Vol. 898, pp. 366 - 381, New York, NY: Springer.
24. Fraser, A.M. and Swinney, H.L. (1986). Independent coordinates for strange attractors from mutual information. Physical Review A, 33, 1134-1140.
25. Kennel, M.B., Brown, R. and Abarbanel, H.D.I. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A, 45 (6), 3403-3411.
26. Theiler, J. (1986). Spurious dimension from correlation algorithms applied to limited time-series data. Physical Review A, 34, 2427.
27. Salzmann, B. (1962). Finite amplitude free convection as an initial value problem. Int. J. Atmos. Sci., 19, 329-341.
28. Kaplan, J.L. and Yorke, J.A. (1979). Chaotic behavior of multidimensional difference equations. In: Peitgen, H.-O. and Walther, H.-O (eds), Lecture Notes in Mathematics, Vol. 730, pp.204-227, Berlin: Springer.
29. Bezdek, J.C. (1981). The fuzzy c-varieties clustering algorithms. Pattern Recognition with Fuzzy Objective Function Algorithms, pp. 174-191, New York, NY: Springer.
30. Davies, M.E. and Campbell, K.M. (1996). Linear recursive filters and nonlinear dynamics. Nonlinearity, 9, 487-499.
31. Lorenz, E.N. (1965). A study of the predictability of a 28-variable atmospheric model. Tellus, 17, 321-333.
32. Kennel, M.B. (2005). Private Conversation.
33. Nese, J.M. (1989). Quantifying local predictability in phase space. Physica D, 35, 237-250.
34. Smith, L., Ziehmann, C. and Fraedrich, K. (1999). Uncertainty dynamics and predictability in chaotic systems, Q. J. R. Meteorol. Soc., 125, 2855-2886.
35. Ziehmann, C., Smith, L. and Kurths, J. (2000). Localized Lyapunov exponents and the prediction of predictability. Physics Letters A, 271 (4), 237-251.
36. Nichols, J.M., Todd, M.D., Seaver, M., Trickey, S.T., Pecora, L.M. and Moniz, L. (2003). Controlling system dimension: A class of real systems that obey the Kaplan-Yorke conjecture. Proc. Natl. Acad. Sci. USA, 100 (26), 15299-15303.
37. Nichols, J.M. (2003). Structural health monitoring of offshore structures using ambient excitation. Applied Ocean Research, 25 (3), 101-114.
38. Todd, M.D., Overbey, L.A., Olson, C.C. and Fasel, T.R. (2004). Comparing deterministic and band-limited stochastic excitation with state space models to assess frame joint integrity. Third International Conference on Advances in Structural Engineering and Mechanics, Seoul, Korea, September 2-4.