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On the observability and identifiability of nonlinear structural and mechanical systems: OBSERVABILITY AND IDENTIFIABILITY OF NL STRUCT. AND MECH. SYSTEMS

Chatzis, Manolis N., Chatzi, Eleni N., Smyth, Andrew W.·2015·Structural Control and Health Monitoring
DOI 10.1002/stc.1690
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Abstract

The question of a priori observability of a dynamic system, that is, whether the states of a system can be identified given a particular set of measured quantities is of utmost importance in multiple disciplines including biology, economics, and engineering. More often than not, some of the parameters of the system need to be identified, and thus the issue of identifiability, that is, whether the measurements result in unique or finite solutions for the values of the parameters, is of interest. Identifiability arises in conjunction with the question of observability, when the notion of states may be augmented to include both the actual state variables of the dynamic system and its parameters. This results in the formulation of a nonlinear augmented system even though the dynamic equations of motion of the original system might be linear. In this work, three methods for the observability and identifiability of nonlinear dynamic systems are considered. More specifically, for a system whose state and measurement equations are analytic, the geometric Observability Rank Condition, which is based on Lie derivatives may be used. If the equations are rational, algebraic methods are also available. These include the algebraic observability methods and the algebraic identifiability algorithms which determine the finiteness or uniqueness of the solutions for the parameters. The aforementioned methods are used to study the observability and identifiability of suitable problems in civil e…

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Research works printed but not linked: 37

  1. Papadimitriou, 2012, The effect of prediction error correlation on optimal sensor placement in structural dynamics, Mechanical Systems and Signal Processing, 28, 105, 10.1016/j.ymssp.2011.05.019 · DOI
  2. Papadimitriou, 2000, Entropy-based optimal sensor location for structural model updating, Journal of Vibration and Control, 6, 781, 10.1177/107754630000600508 · DOI
  3. Papadimitriou, 2004, Optimal sensor placement methodology for parametric identification of structural systems, Journal of Sound and Vibration, 278, 923, 10.1016/j.jsv.2003.10.063 · DOI
  4. Kalman, 1963, Mathematical description of linear dynamical systems, Journal of the Society for Industrial and Applied Mathematics Series A Control, 1, 152, 10.1137/0301010 · DOI
  5. Isidori, 1995, Nonlinear Control Systems, 10.1007/978-1-84628-615-5 · DOI
  6. Nijmeijer, 1990, Nonlinear Dynamical Control Systems, 10.1007/978-1-4757-2101-0 · DOI
  7. A Kugi K Schlacher R Novak Symbolic computation for the analysis and synthesis of nonlinear control systems International conference on software for electrical engineering analysis and design 1999 255 264
  8. August, 2009, A new computational tool for establishing model parameter identifiability, Journal of Computational Biology, 16, 875, 10.1089/cmb.2008.0211 · DOI
  9. S Diop M Fliess Nonlinear observability, identifiability, and persistent trajectories Decision and Control, 1991, Proceedings of the 30th IEEE Conference on 1991 714 719 · DOI
  10. ST Glad L Ljung Model structure identifiability and persistence of excitation Decision and Control, 1990., Proceedings of the 29th IEEE Conference on 1990 3236 3240 · DOI
  11. Ljung, 1994, On global identifiability for arbitrary model parametrizations, Automatica, 30, 265, 10.1016/0005-1098(94)90029-9 · DOI
  12. S Diop Y Wang Equivalence between algebraic observability and local generic observability 1993 2864 2865 · DOI
  13. Sedoglavic, 2002, A probabilistic algorithm to test local algebraic observability in polynomial time, Journal of Symbolic Computation, 33, 735, 10.1006/jsco.2002.0532 · DOI
  14. Walter, 1982, Identifiability of State Space Models, 10.1007/978-3-642-61823-9 · DOI
  15. Audoly, 2001, Global identifiability of nonlinear models of biological systems, Biomedical Engineering, IEEE Transactions on, 48, 55, 10.1109/10.900248 · DOI
  16. Pia Saccomani, 2003, Parameter identifiability of nonlinear systems: the role of initial conditions, Automatica, 39, 619, 10.1016/S0005-1098(02)00302-3 · DOI
  17. Bellu, 2007, DAISY: a new software tool to test global identifiability of biological and physiological systems, Computer Methods and Programs in Biomedicine, 88, 52, 10.1016/j.cmpb.2007.07.002 · DOI
  18. Vajda, 1989, Similarity transformation approach to identifiability analysis of nonlinear compartmental models, Mathematical Biosciences, 93, 217, 10.1016/0025-5564(89)90024-2 · DOI
  19. Miao, 2011, On identifiability of nonlinear ode models and applications in viral dynamics, SIAM Review, 53, 3, 10.1137/090757009 · DOI · Paper page
  20. Udwadia, 1978, Some uniqueness results related to building structural identification, SIAM Journal on Applied Mathematics, 34, 104, 10.1137/0134009 · DOI
  21. Udwadia, 1978, Uniqueness of damping and stiffness distributions in the identification of soil and structural systems, Journal of Applied Mechanics, 45, 181, 10.1115/1.3424224 · DOI
  22. Franco, 2006, On the uniqueness of solutions for the identification of linear structural systems, Journal of Applied Mechanics, 73, 153, 10.1115/1.2062829 · DOI
  23. Mukhopadhyay, 2014, Modal parameter based structural identification using inputoutput data: minimal instrumentation and global identifiability issues, Mechanical Systems and Signal Processing, 45, 283, 10.1016/j.ymssp.2013.11.005 · DOI
  24. Katafygiotis, 1998, Updating models and their uncertainties. II: model identifiability, Journal of Engineering Mechanics, 124, 463, 10.1061/(ASCE)0733-9399(1998)124:4(463) · DOI
  25. Ritt, 1950, Differential algebra, American Mathematical Society, 33
  26. Pohjanpalo, 1978, System identifiability based on the power series expansion of the solution, Mathematical Biosciences, 41, 21, 10.1016/0025-5564(78)90063-9 · DOI · Paper page
  27. Bellman, 1970, On structural identifiability, Mathematical Biosciences, 7, 329, 10.1016/0025-5564(70)90132-X · DOI · Paper page
  28. MP Saccomani S Audoly G Bellu L D'Angio A new differential algebra algorithm to test identifiability of nonlinear systems with given initial conditions Decision and Control, 2001. Proceedings of the 40th IEEE Conference on 2001 3108 3113 · DOI
  29. Tunali, 1987, New results for identifiability of nonlinear systems, Automatic Control, IEEE Transactions on, 32, 146, 10.1109/TAC.1987.1104544 · DOI
  30. Margaria, 2004, Structural identifiability analysis of some highly structured families of statespace models using differential algebra, Journal of Mathematical Biology, 49, 433, 10.1007/s00285-003-0261-3 · DOI
  31. Persis, 2000, On the observability codistributions of a nonlinear system, Systems & Control Letters, 40, 297, 10.1016/S0167-6911(00)00014-1 · DOI
  32. Smyth, 2007, Multi-rate Kalman filtering for the data fusion of displacement and acceleration response measurements in dynamic system monitoring, Mechanical Systems and Signal Processing, 21, 706, 10.1016/j.ymssp.2006.03.005 · DOI
  33. Chatzi, 2009, The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing, Structural Control and Health Monitoring, 16, 99, 10.1002/stc.290 · DOI
  34. Kogan, 2008, Load response on a large suspension bridge during the NYC marathon revealed by GPS and accelerometers, Seismological Research Letters, 79, 12, 10.1785/gssrl.79.1.12 · DOI
  35. M Babaali M Egerstedt On the observability of piecewise linear systems Decision and Control, 2004. CDC. 43rd IEEE Conference on 2004 26 31 · DOI
  36. Sontag, 1981, Nonlinear regulation: the piecewise linear approach, Automatic Control, IEEE Transactions on, 26, 346, 10.1109/TAC.1981.1102596 · DOI
  37. Hespanha, 2005, Nonlinear norm-observability notions and stability of switched systems, Automatic Control, IEEE Transactions on, 50, 154, 10.1109/TAC.2004.841937 · DOI

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Metadata

Authors
Chatzis, M. N., Chatzi, E. N., & Smyth, A. W.
Affiliations
  • Dept. of Engineering Science; The University of Oxford; Oxford UK
  • Dept. of Civil Environmental and Geomatic Engineering; ETH; Zurich Switzerland
  • Dept. of Civil Engineering & Engineering Mechanics; Columbia University; New York USA
Venue
Structural Control and Health Monitoring
Publisher
Wiley
Published
2014-09-18
Volume
22
Issue
3
Pages
574-593
ISSN
1545-2255
DOI
10.1002/stc.1690
Cited by
104
References
1
Language
en
Licence
doi.wiley.com/10.1002/tdm_license_1.1 (tdm, 348 d)
Funders
National Science Foundation (CMMI-1100321)

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