Open Access

Subspace-Based Algorithms for Structural Identification, Damage Detection, and Sensor Data Fusion

  • Michèle Basseville1, 2Email author,
  • Albert Benveniste1, 3,
  • Maurice Goursat4 and
  • Laurent Mevel1, 3
EURASIP Journal on Advances in Signal Processing20062007:069136

https://doi.org/10.1155/2007/69136

Received: 2 February 2006

Accepted: 27 May 2006

Published: 16 October 2006

Abstract

This paper reports on the theory and practice of covariance-driven output-only and input/output subspace-based identification and detection algorithms. The motivating and investigated application domain is vibration-based structural analysis and health monitoring of mechanical, civil, and aeronautic structures.

[1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677]

Authors’ Affiliations

(1)
IRISA, Campus Universitaire de Beaulieu
(2)
CNRS, Campus Universitaire de Beaulieu
(3)
INRIA, Campus Universitaire de Beaulieu
(4)
INRIA, Domaine de Voluceau Rocquencourt

References

  1. Balageas D, Fritzen C-P, Güemes A (Eds): Structural Health Monitoring. Lavoisier, Paris, France; 2006.Google Scholar
  2. Doebling SW, Farrar CR, Prime MB: A summary review of vibration-based damage identification methods. The Shock and Vibration Digest 1998,30(2):91-105. 10.1177/058310249803000201View ArticleGoogle Scholar
  3. Farrar CR, Doebling SW, Nix DA: Vibration-based structural damage identification. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2001,359(1778):131-149. 10.1098/rsta.2000.0717View ArticleMATHGoogle Scholar
  4. Maeck J: Damage assessment of civil engineering structures by vibration monitoring, Ph.D. thesis. Department of Civil Engineering, Katholieke Universiteit Leuven, Leuven, Belgium; 2003. MarchGoogle Scholar
  5. Zimmerman DC, Kaouk M, Simmermacher T: Structural health monitoring using vibration measurements and engineering insight. Journal of Mechanical Design, Transactions of the ASME 1995, 117 B: 214-221.View ArticleGoogle Scholar
  6. Basseville M, Benveniste A, Goursat M, Hermans L, Mevel L, van der Auweraer H: Output-only subspace-based structural identification: from theory to industrial testing practice. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME 2001,123(4):668-676. special issue on identfication of mechanical systems 10.1115/1.1410919View ArticleGoogle Scholar
  7. Peeters B, De Roeck G: Stochastic system identification for operational modal analysis: a review. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME 2001,123(4):659-667. special issue on identification of mechanical systems 10.1115/1.1410370View ArticleGoogle Scholar
  8. Ewins DJ: Modal Testing: Theory, Practice and Applications. 2nd edition. Research Studies Press, Letchworth, Hertfordshire, UK; 2000.Google Scholar
  9. Heylen W, Lammens S, Sas P: Modal Analysis Theory and Testing. Department of Mechanical Engineering, Katholieke Universiteit Leuven, Leuven, Belgium; 1995.Google Scholar
  10. Juang JN: Applied System Identification. Prentice Hall, Englewood Cliffs, NJ, USA; 1994.MATHGoogle Scholar
  11. Peeters B, De Roeck G: Reference-based stochastic subspace identification for output-only modal analysis. Mechanical Systems and Signal Processing 1999,13(6):855-878. 10.1006/mssp.1999.1249View ArticleGoogle Scholar
  12. Van Overschee P, De Moor B: Subspace Identification for Linear Systems. Kluwer Academic, Boston, Mass, USA; 1996.View ArticleMATHGoogle Scholar
  13. Viberg M: Subspace-based methods for the identification of linear time-invariant systems. Automatica 1995,31(12):1835-1853. 10.1016/0005-1098(95)00107-5MathSciNetView ArticleMATHGoogle Scholar
  14. Viberg M, Ottersten B: Sensor array processing based on subspace fitting. IEEE Transactions on Signal Processing 1991,39(5):1110-1121. 10.1109/78.80966View ArticleMATHGoogle Scholar
  15. Viberg M, Wahlberg B, Ottersten B: Analysis of state space system identification methods based on instrumental variables and subspace fitting. Automatica 1997,33(9):1603-1616. 10.1016/S0005-1098(97)00097-6MathSciNetView ArticleGoogle Scholar
  16. Ottersten B, Viberg M, Kailath T: Analysis of subspace fitting and ML techniques for parameter estimation from sensor array data. IEEE Transactions on Signal Processing 1992,40(3):590-600. 10.1109/78.120802View ArticleMATHGoogle Scholar
  17. Cardoso J-F, Moulines É: Invariance of subspace based estimators. IEEE Transactions on Signal Processing 2000,48(9):2495-2505. 10.1109/78.863052MathSciNetView ArticleMATHGoogle Scholar
  18. Stoïca P, Moses RL: Introduction to Spectral Analysis. Prentice Hall, Upper Saddle River, NJ, USA; 1997.MATHGoogle Scholar
  19. Akaïke H: Stochastic theory of minimal realization. IEEE Transactions on Automatic Control 1974,19(6):667-674. 10.1109/TAC.1974.1100707View ArticleMathSciNetMATHGoogle Scholar
  20. Mevel L, Basseville M, Benveniste A, Goursat M: Merging sensor data from multiple measurement set-ups for non-stationary subspace-based modal analysis. Journal of Sound and Vibration 2002,249(4):719-741. 10.1006/jsvi.2001.3880View ArticleGoogle Scholar
  21. Akaïke H: Markovian representation of stochastic processes by canonical variables. SIAM Journal on Control and Optimization 1975,13(1):162-173. 10.1137/0313010MathSciNetView ArticleMATHGoogle Scholar
  22. Basseville M, Abdelghani M, Benveniste A: Subspace-based fault detection algorithms for vibration monitoring. Automatica 2000,36(1):101-109. 10.1016/S0005-1098(99)00093-XMathSciNetView ArticleMATHGoogle Scholar
  23. Godambe VP (Ed): Estimating Functions. Clarendon Press, Oxford, UK; 1991.MATHGoogle Scholar
  24. Heyde CC: Quasi-Likelihood and Its Application, Series in Statistics. Springer, New York, NY, USA; 1997.View ArticleGoogle Scholar
  25. Benveniste A, Métivier M, Priouret P: Adaptive Algorithms and Stochastic Approximations, Applications of Mathematics. Volume 22. Springer, New York, NY, USA; 1990.View ArticleMATHGoogle Scholar
  26. Mc Leish DL, Small CG: The Theory and Application of Statistical Inference Functions, Lecture Notes in Statistics. Volume 44. Springer, Berlin, Germany; 1988.View ArticleGoogle Scholar
  27. Mevel L, Benveniste A, Basseville M, et al.: Input/output versus output-only data processing for structural identification—application to in-flight data analysis. Journal of Sound and Vibration 2006,295(3):531-552. 10.1016/j.jsv.2006.01.039View ArticleGoogle Scholar
  28. Benveniste A, Fuchs J-J: Single sample modal identfication of a non-stationary stochastic process. IEEE Transactions on Automatic Control 1985,30(1):66-74. 10.1109/TAC.1985.1103787MathSciNetView ArticleMATHGoogle Scholar
  29. Benveniste A, Mevel L: Nonstationary consistency of subspace methods. In Research Report 1752. IRISA, Rennes, France; 2005. http://hal.inria.fr/inria-00000869Google Scholar
  30. Benveniste A, Mevel L: Nonstationary consistency of subspace methods. In Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC '05), December 2005, Seville, Spain. IEEE & EUCA; 7096-7101.View ArticleGoogle Scholar
  31. Mevel L, Benveniste A, Basseville M, Goursat M: Blind subspace-based eigenstructure identification under nonstationary excitation using moving sensors. IEEE Transactions on Signal Processing 2002,50(1):41-48. 10.1109/78.972480View ArticleGoogle Scholar
  32. Jategaonkar R, Fischenberg D, von Gruenhagen W: Aerodynamic modeling and system identification from flight data—recent applications at DLR. AIAA Journal of Aircraft 2004,41(4):681-691. 10.2514/1.3165View ArticleGoogle Scholar
  33. Cauberghe B, Guillaume P, Pintelon R, Verboven P: Frequency-domain subspace identification using FRF data from arbitrary signals. Journal of Sound and Vibration 2006,290(3–5):555-571.View ArticleGoogle Scholar
  34. McKelvey T, Akcay H, Ljung L: Subspace-based multivariable system identification from frequency response data. IEEE Transactions on Automatic Control 1996,41(7):960-979. 10.1109/9.508900MathSciNetView ArticleMATHGoogle Scholar
  35. Vold H, Kundrat J, Rocklin T, Russel R: A multi-input modal parameter estimation algorithm for mini-computers. SAE Transaction 1982,91(1):815-821. SAE paper 820194Google Scholar
  36. Devauchelle B, Basseville M, Benveniste A: Diagnosing mechanical changes in vibrating systems. In Proceedings of the 1st Symposium on Fault Detection, Supervision and Safety for Technical Processes (SAFEPROCESS '91), September 1991, Baden-Baden, FRG, Germany. IFAC /IMACS; 159-164.Google Scholar
  37. Moustakides G: The problem of diagnosis with respect to physical parameters for changes in structures. In Research Report 295. IRISA, Rennes, France; 1986.Google Scholar
  38. Moustakides G, Basseville M, Benveniste A, Vey GL: Diagnosing mechanical changes in vibrating systems. In Research Report 436. IRISA, Rennes, France; 1988.Google Scholar
  39. Basseville M, Mevel L, Goursat M: Statistical model-based damage detection and localization: subspace-based residuals and damage-to-noise sensitivity ratios. Journal of Sound and Vibration 2004,275(3–5):769-794.View ArticleGoogle Scholar
  40. Basawa I: Neyman-Le Cam tests based on estimating functions. In Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer. Volume 2. Edited by: Le Cam L, Olshen R. Wadsworth, Belmont, Calif, USA; 1985:811-825.Google Scholar
  41. Basawa I, Godambe VP, Taylor R (Eds): Selected proceedings of the Symposium on Estimating Functions. Institute of Mathematical Statistics, Hayward, Calif, USA; 1997.Google Scholar
  42. Hall W, Mathiason D: On large sample estimation and testing in parametric models. International Statistical Review 1990,58(1):77-97. 10.2307/1403475View ArticleMATHGoogle Scholar
  43. Basseville M: On-board component fault detection and isolation using the statistical local approach. Automatica 1998,34(11):1391-1415. 10.1016/S0005-1098(98)00086-7View ArticleMATHGoogle Scholar
  44. Basseville M, Nikiforov IV: Detection of Abrupt Changes—Theory and Applications, Information and System Sciences Series. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.Google Scholar
  45. Mevel L, Basseville M, Benveniste A: Fast in-flight detection of flutter onset: a statistical approach. AIAA Journal of Guidance, Control, and Dynamics 2005,28(3):431-438. 10.2514/1.6184View ArticleGoogle Scholar
  46. Benveniste A, Basseville M, Moustakides GV: The asymptotic local approach to change detection and model validation. IEEE Transactions on Automatic Control 1987,32(7):583-592. 10.1109/TAC.1987.1104683MathSciNetView ArticleMATHGoogle Scholar
  47. Delyon B, Juditsky A, Benveniste A: On the relationship between identfication and local tests. In Research Report 1104. IRISA, Rennes, France; 1997. http://www.irisa.fr/bibli/publi/pi/1997/1104/1104.htmlGoogle Scholar
  48. Zhang Q, Basseville M, Benveniste A: Early warning of slight changes in systems. Automatica 1994,30(1):95-113. 10.1016/0005-1098(94)90231-3MathSciNetView ArticleMATHGoogle Scholar
  49. Zhang Q, Basseville M:Advanced numerical computation of -tests for fault detection and isolation. In Proceedings of the 5th Symposium on Fault Detection, Supervision and Safety for Technical Processes (SAFEPROCESS '03), June 2003, Washington, DC, USA. IFAC /IMACS; 211-216.Google Scholar
  50. Moustakides G, Benveniste A: Detecting changes in the AR parameters of a nonstationary ARMA process. Stochastics 1986, 16: 137-155. 10.1080/17442508608833370MathSciNetView ArticleMATHGoogle Scholar
  51. Basseville M, Benveniste A, Moustakides G, Rougée A: Detection and diagnosis of changes in the eigenstructure of nonstationary multivariable systems. Automatica 1987,23(4):479-489. 10.1016/0005-1098(87)90077-XMathSciNetView ArticleMATHGoogle Scholar
  52. Mevel L, Goursat M, Basseville M: Stochastic subspace-based structural identification and damage detection and localisation—application to the Z24 bridge benchmark. Mechanical Systems and Signal Processing 2003,17(1):143-151. 10.1006/mssp.2002.1552View ArticleGoogle Scholar
  53. Basseville M: An invariance property of some subspace-based detection algorithms. IEEE Transactions on Signal Processing 1999,47(12):3398-3400. 10.1109/78.806083View ArticleMATHGoogle Scholar
  54. Rougée A, Basseville M, Benveniste A, Moustakides G: Optimum robust detection of changes in the AR part of a multivariable ARMA process. IEEE Transactions on Automatic Control 1987,32(12):1116-1120. 10.1109/TAC.1987.1104500View ArticleMATHGoogle Scholar
  55. Ladelli L: Diffusion approximation for a pseudo-likelihood test process with application to detection of change in a stochastic system. Stochastics and Stochastics Reports 1990,32(1):1-25.MathSciNetView ArticleMATHGoogle Scholar
  56. Ljung L: System Identification—Theory for the User. 2nd edition. PTR Prentice Hall, Upper Saddle River, NJ, USA; 1999.MATHGoogle Scholar
  57. Basseville M, Benveniste A, Mevel L: Handling uncertainties in identification and model validation: a statistical approach. In Proceedings of the 24th International Modal Analysis Conference (IMAC '06), January 2006, Saint Louis, Mich, USA. SEM; tutorial paperGoogle Scholar
  58. Mevel L, Goursat M: Model validation by using a damage detection test. In Proceedings of the 24th International Modal Analysis Conference (IMAC '06), January 2006, Saint Louis, Mich, USA. SEM;Google Scholar
  59. Gersch W: On the achievable accuracy of structural parameter estimates. Journal of Sound and Vibration 1974,34(1):63-79. 10.1016/S0022-460X(74)80355-XView ArticleMATHGoogle Scholar
  60. Basseville M, Goursat M, Mevel L: Multiple CUSUM tests for flutter monitoring. In Proceedings of the 14th Symposium on System Identfication (SYSID '06), March 2006, Newcastle, Australia. IFAC /IFORS; 624-629.Google Scholar
  61. Goethals I, Mevel L, Benveniste A, de Moor B: Recursive output-only subspace identification for in-flight flutter monitoring. In Proceedings of the 22nd International Modal Analysis Conference (IMAC '04), January 2004, Dearborn, Mich, USA. SEM;Google Scholar
  62. Mevel L, Coursat M, Basseville M, Benveniste A: On-line monitoring of slow to fast evolving aeronautic structures. Proceedings of the International Conference on Noise and Vibration Engineering (ISMA '04), September 2004, Leuven, Belgium 1033-1047.Google Scholar
  63. Basseville M, Benveniste A, Gach-Devauchelle B, et al.: In situ damage monitoring in vibration mechanics: diagnostics and predictive maintenance. Mechanical Systems and Signal Processing 1993,7(5):401-423. 10.1006/mssp.1993.1023View ArticleGoogle Scholar
  64. Basseville M, Mevel L, Vecchio A, Peeters B, van der Auweraer H: Output-only subspace-based damage detection—application to a reticular structure. Structural Health Monitoring 2003,2(2):161-168. 10.1177/1475921703002002008View ArticleGoogle Scholar
  65. Goursat M, Mevel L: On-line monitoring of bradford stadium. In Proceedings of the 23rd International Modal Analysis Conference (IMAC '05), January 2005, Orlando, Fla, USA. SEM;Google Scholar
  66. Goursat M, Mevel L: On-line monitoring of the crowd influence on manchester stadium. In Proceedings of the 24th International Modal Analysis Conference (IMAC '06), January 2006, Saint Louis, Mich, USA. SEM;Google Scholar
  67. Mevel L, Basseville M, Goursat M: Stochastic subspace-based structural identification and damage detection—application to the steel-quake benchmark. Mechanical Systems and Signal Processing 2003,17(1):91-101. 10.1006/mssp.2002.1544View ArticleGoogle Scholar
  68. Mevel L, Hermans L, van der Auweraer H: On the application of a subspace-based fault detection method to industrial structures. Mechanical Systems and Signal Processing 1999,13(6):823-838. 10.1006/mssp.1999.1247View ArticleGoogle Scholar
  69. Peeters B, Mevel L, Vanlanduit S, et al.: Online vibration-based crack detection during fatigue testing. Key Engineering Materials 2003,245(2):571-578.View ArticleGoogle Scholar
  70. Mevel L, Goursat M, Basseville M, Benveniste A: Subspace-based modal identification and monitoring of large structures, a Scilab toolbox. In Proceedings of the 13th Symposium on System identification (SYSID '03), August 2003, Rotterdam, The Netherlands. IFAC /IFORS; 1405-1410. http://www.irisa.fr/sisthem/cosmad/Google Scholar
  71. Brenner M, Lind R, Voracek D: Overview of recent flight flutter testing research at NASA Dryden. In Technical Memorandum NASA TM-4792. NASA Dryden, Edwards, Calif, USA; 1997.Google Scholar
  72. Pickrel C, White P: Flight flutter testing of transport aircraft: in-flight modal analysis. In Proceedings of the 21st International Modal Analysis Conference (IMAC '03), February 2003, Kissimmee, Fla, USA. SEM;Google Scholar
  73. Lind R: Flight testing with the flutterometer. Journal of Aircraft 2003,40(3):574-579. 10.2514/2.3132MathSciNetView ArticleGoogle Scholar
  74. Peeters B, Maeck J, De Roeck G: Vibration-based damage detection in civil engineering: excitation sources and temperature effects. Smart Materials and Structures 2001,10(3):518-527. 10.1088/0964-1726/10/3/314View ArticleGoogle Scholar
  75. Basseville M: Information criteria for residual generation and fault detection and isolation. Automatica 1997,33(5):783-803. 10.1016/S0005-1098(97)00004-6MathSciNetView ArticleMATHGoogle Scholar
  76. Basseville M, Nikiforov IV: Fault isolation for diagnosis: nuisance rejection and multiple hypothesis testing. Annual Reviews in Control 2002,26(2):189-202. 10.1016/S1367-5788(02)00029-9View ArticleGoogle Scholar
  77. Basseville M, Nikiforov IV: Handling nuisance parameters in systems monitoring. In Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC '05), December 2005, Seville, Spain. IEEE & EUCA; 3832-3837.View ArticleGoogle Scholar

Copyright

© Basseville et al. 2007