A Dynamical Systems Approach to Failure Prognosis

[+] Author and Article Information
David Chelidze

Department of Mechanical Engineering & Applied Mechanics, University of Rhode Island, Kingston, RI 02881e-mail: chelidze@egr.uri.edu; http://www.mce.uri.edu/chelidze/

Joseph P. Cusumano

Department of Engineering Science & Mechanics, Pennsylvania State University, University Park, PA 16802e-mail: jpc@crash.esm.psu.edu; http://www.esm.psu.edu/nld/

J. Vib. Acoust 126(1), 2-8 (Feb 26, 2004) (7 pages) doi:10.1115/1.1640638 History: Received February 01, 2003; Revised July 01, 2003; Online February 26, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Chelidze,  D., Cusumano,  J. P., and Chatterjee,  A., 2002, “Dynamical Systems Approach to Damage Evolution Tracking, Part 1: Description and Experimental Application,” ASME J. Vibr. Acoust., 124(2), pp. 250–257.
Cusumano,  J. P., Chelidze,  D., and Chatterjee,  A., 2002, “Dynamical Systems Approach to Damage Evolution Tracking, Part 2: Model-Based Validation and Physical Interpretation,” ASME J. Vibr. Acoust., 124(2), pp. 258–264.
Cusumano,  J. P., and Chatterjee,  A., 2000, “Steps Towards a Qualitative Dynamics of Damage Evolution,” Int. J. Solids Struct., 37(44), pp. 6397–6417.
Doebling, A. W., Farrar, C. R., Prime, M. B., and Shevitz, D. W., May 1996, “Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in Their Vibration Characteristics: A Literature Review,” Technical Report LA-13070-MS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545.
Doebling,  S. W., Farrar,  C. R., and Prime,  M. B., 1998, “A Summary Review of Vibration-Based Damage Identification Methods,” Sound Vib., 30, pp. 91–105.
Zou,  Y., Tong,  L., and P.,  S. G., 2000, “Vibration-Based Model-Dependent Damage (Delimination) Identification and Health Monitoring for Composite Structures—A Review,” J. Sound Vib., 230(2), pp. 357–378.
Qu,  L., Xie,  A., and Li,  X., 1993, “Study and Performance Evaluation of Some Nonlinear Diagnostic Methods for Large Rotating Machinery,” J. Mech. Mach. Theory, 28(5), pp. 699–713.
Ma, J., and Li, C. J., 1995, “On Gear Localized Defect Detection by Demodulation of Vibrations—A Comparison Study,” E. Kannatey-Asibu, J., ed., Proc. of Symp. on Mechatronics for Manufacturing in ASME International Mechanical Engineering Congress and Exposition, MED-2-1, New York, NY, ASME, pp. 565–576.
McFadden,  P. D., and Smith,  J. D., 1985, “A Signal Processing Technique for Detecting Local Defects in a Gear from the Signal Averaging of Vibration,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 199 (c4) ImechE-1985.
Robert, T. S., and Lawrence, J. M., 1986, “Detection, Diagnosis and Prognosis of Rotating Machinery,” Proc. of the 41st Meeting of the Mech. Failures Prevention Group, Naval Air Test Center, Patuxent River, Maryland.
McFadden,  P. D., and Wang,  W. J., 1993, “Early Detection of Gear Failure by Vibration Analysis—I. Calculation of the Time-Frequency Distribution,” Mech. Syst. Signal Process., 37(3), pp. 193–203.
Liu,  B., Ling,  S., and Meng,  Q., 1997, “Machinery Diagnisis Based on Wavelet Packets,” J. Vib. Control, 3, pp. 5–17.
Baydar, N., Ball, A., and Kruger, U., 1999, “Detection of Incipient Tooth Defect in Helical Gears Using Principal Components,” Starr, A. G., Leung, A. Y. T., Wright, J. R., and Sandoz, D. J., eds., Integrating Dynamics, Condition Monitoring and Control for the 21st Century, A. A. Balkema, Rotterdam, Brookfield, pp. 93–100.
Isermann,  R., 1984, “Process Fault Detection Based on Modeling and Estimation Methods—A Survey,” Automatica, 20(4), pp. 387–404.
Gertler,  J., 1988, “Survey of Model-Based Failure Detection and Isolation in Complex Plants,” IEEE Control Syst. Mag., 8(6), pp. 3–11.
Natke, H. G., and Campel, C., 1997, Model-Aided Diagnosis of Mechanical Systems: Fundamentals, Detection, Localization, Assesment, Springer-Verlag, Berlin.
Nijmeijer, H., and Fossen, T. I., 1999, “New Directions in Nonlinear Observer Design,” Lecture Notes in Control and Information Sciences, Springer-Verlag, London, pp. 351–466.
Wang,  W., and Wong,  A. K., 2002, “Autoregresive Model-Based Gear Fault Diagnosis,” ASME J. Vibr. Acoust., 124(2), pp. 172–179.
McGhee,  J., Henderson,  I. A., and Baird,  A., 1997, “Neural Networks Applied for the Identification and Fault Diagnosis of Process Valves and Actuators,” J. Int. Measr. Confederation, 20(4), pp. 267–275.
Alessandri, A., and Parisini, T., 1997, “Model-Based Fault Diagnosis Using Nonlinear Estimators: A Neural Approach,” Proceedings of the American Control Conference, Vol. 2, pp. 903–907.
Li, C. J., and Fan, Y., 1997, “Recurrent Neural Networks for Fault Diagnosis and Severity Assessment of a Screw Compressor,” DSC ASME Dynamic Systems & Control Division, Vol. 61, pp. 257–264.
Jeon,  Y. C., and Li,  C. J., 1995, “Non-linear ARX Model Based Kullback Index for Fault Detection of a Screw Compressor,” Mech. Syst. Signal Process., 9(4), pp. 341–358.
Li,  Y., Billington,  S., Zhang,  C., Kurfess,  T., Danyluk,  S., and Liang,  S. Y., 1999, “Adaptive Prognostics for Rolling Element Bearing Condition,” Mech. Syst. Signal Process., 13, pp. 103–113.
Li,  Y., Kurfess,  T. R., and Liang,  S. Y., 2000, “Stochastic Prognostics for Rolling Element Bearings,” Mech. Syst. Signal Process., 14(5), pp. 747–762.
Swanson,  D. C., Spencer,  J. M., and Arzoumanian,  S. H., 2000, “Prognostic Modelling of Crack Growth in a Tensioned Steel Band,” Mech. Syst. Signal Process., 14(5), pp. 789–803.
Takens, F., 1981, “Detecting Strange Attractor in Turbulence,” Rand, D. A. and Young, L. S., eds., Dynamical Systems and Turbulence, Warwick, Springer Lecture Notes in Mathematics, Springer-Verlag, Berlin, pp. 336–381.
Sauer,  T., Yorke,  J. A., and Casdagli,  M., 1991, “Embedology,” J. Stat. Phys., 65(3–4), pp. 579–616.
Fraser,  A. M., and Swinney,  H. L., 1986, “Independent Coordinates for Strange Attractors from Mutual Information,” Phys. Rev. A, 33(2), pp. 1134–1140.
Kennel,  M. B., Brown,  R., and Abarbanel,  H. D. I., 1992, “Determining Embedding Dimension for Phase-Space Reconstruction Using a Geometric Construction,” Phys. Rev. A, 45(6), pp. 3403–3411.
Grewal, M. S., and Angus, P. A., 1993, Kalman Filtering/Theory and Practice, Prentice Hall, Englewood Cliffs, New Jersey.
Ott, E., 1993, Chaos in Dynamical Systems, Cambridge, New York.
Julier, S. J., and Uhlmann, J. K., 1997, “New Extension of Kalman Filter to Nonlinear Systems,” Signal Processing, Sensor Fusion, and Target Recognition VI, 3068, Proc. SPIE, pp. 182–193.
Moon,  F. C., and Holmes,  P., 1979, “A Magnetoelastic Strange Attractor,” J. Sound Vib., 65(2), pp. 275–296.
Cusumano,  J. P., and Kimble,  B., 1995, “A Stochastic Interrogation Method for Experimental Measurements of Global Dynamics and Basin Evolution: Application to a Two-Well Oscillator,” Nonlinear Dyn., 8, pp. 213–235.


Grahic Jump Location
Damage tracking function estimation. Solid black line is the current trajectory of the fast subsystem. Dashed gray line is the corresponding reference trajectory. Model is based on the reference trajectory points shown in gray.
Grahic Jump Location
Schematic diagram of the experimental apparatus of the two-well electro-mechanical oscillator.
Grahic Jump Location
Damage state estimation and failure prognosis: (upper) plot of local mean of measured battery voltage (heavy gray line), fitted nonlinear battery discharge model (dashed black line), and recursively estimated battery state (solid black line) vs. time; (lower) time-to-failure predictions based on damage state estimates. In the time-to-failure predictions, the dashed heavy gray line indicates the true time to failure (known a posteriori), thin black line represents simple time-to-failure estimate using Eq. (20), and thick black line indicates the improved estimate using the failure prognostic filter of Eq. (16).
Grahic Jump Location
Probability distributions of |E5| (upper) and ln|E5| (lower). 214 points were used for histograms.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In