Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Output-error state-space identification of vibrating structures using evolution strategies: a benchmark study

  • Dertimanis, Vasilis K. (Department of Civil Engineering and Geomatics, Faculty of Engineering and Technology, Cyprus University of Technology)
  • Received : 2013.09.11
  • Accepted : 2014.06.25
  • Published : 2014.07.25
⟨ Previous Next ⟩

Abstract

In this study, four widely accepted and used variants of Evolution Strategies (ES) are adapted and applied to the output-error state-space identification problem. The selection of ES is justified by prior strong indication of superior performance to similar problems, over alternatives like Genetic Algorithms (GA) or Evolutionary Programming (EP). The ES variants that are being tested are (i) the (1+1)-ES, (ii) the $({\mu}/{\rho}+{\lambda})-{\sigma}$-SA-ES, (iii) the $({\mu}_I,{\lambda})-{\sigma}$-SA-ES, and (iv) the (${\mu}_w,{\lambda}$)-CMA-ES. The study is based on a six-degree-of-freedom (DOF) structural model of a shear building that is characterized by light damping (up to 5%). The envisaged analysis is taking place through Monte Carlo experiments under two different excitation types (stationary / non-stationary) and the applied ES are assessed in terms of (i) accurate modal parameters extraction, (ii) statistical consistency, (iii) performance under noise-corrupted data, and (iv) performance under non-stationary data. The results of this suggest that ES are indeed competitive alternatives in the non-linear state-space estimation problem and deserve further attention.

Keywords

References

  1. Arnold, D.V. (2006), "Weighted multirecombination evolution strategies", Theor. Comput. Sci., 361(1), 18-37. https://doi.org/10.1016/j.tcs.2006.04.003
  2. Arnold, D.V. and Beyer, H.G. (2002), "Performance analysis of evolution strategies with multi-recombination in high-dimensional RN-search spaces disturbed by noise", Theor. Comput. Sci., 289(1), 629-647. https://doi.org/10.1016/S0304-3975(01)00384-X
  3. Auger, A. (2009), "Benchmarking the (1+1) evolution strategy with one-Fifth success rule on the BBOB-2009 function testbed", Proceedings of the GECCO'09, Montreal Quebec, Canada.
  4. Beyer, H.G. and Sendhoff, B. (2008), Covariance matrix adaptation revisited-the CMSA evolution strategy, (Eds., Rudolph, G., Jansen, Th., Lucas, S.M., Poloni, C. and Beume, N. ), Parallel Problem Solving from Nature - PPSN X, Springer.
  5. Beyer, H.G. and Schwefel, H.P. (2002), "Evolution strategies: a comprehensive introduction", Nat. Comput., 1(1), 3-52. https://doi.org/10.1023/A:1015059928466
  6. Casciati, S. (2008), "Stiffness identification and damage localization via differential evolution algorithms", Struct. Control Health Monit., 15(3), 436-449. https://doi.org/10.1002/stc.236
  7. Casciati, S. (2010), "Statistical approach to a SHM benchmark problem", Smart Struct. Syst., 6(1), 17-27. https://doi.org/10.12989/sss.2010.6.1.017
  8. Dertimanis, V.K., Koulocheris, D., Vrazopoulos, H. and Kanarachos, A. (2003), "Time-series parametric modeling using Evolution Strategy with deterministic mutation operators", Proceedings of the International Conference on Intelligent Control Systems and Signal Processing, Faro, Portugal.
  9. Faravelli, L. and Casciati, S. (2004) "Structural damage detection and localization by response change diagnosis", Struct. Saf., 6(2), 104-115.
  10. Fassois, S.D. (2001), "MIMO LMS-ARMAX identification of vibrating structures-Part I: the method", Mech. Syst. Signal Pr., 15(4), 737-758. https://doi.org/10.1006/mssp.2000.1385
  11. Franco, G., Betti, R. and Lus, H. (2004), "Identification of structural systems using an evolutionary strategy", J. Eng. Mech. -ASCE , 130(10), 1125-1139. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:10(1125)
  12. Hansen, N. (2006), The CMA evolution strategy: a comparing review, (Eds., J.A. Lozano, P. Larranga, I. Inza and E. Bengoetxea), Towards a new evolutionary computation: Advances in estimation of distribution algorithms, Springer.
  13. Hansen, N. and Ostermeier, A. (2001), "Completely derandomized self-adaptation in evolution strategies", Evol. Comput., 9(2), 159-195. https://doi.org/10.1162/106365601750190398
  14. Hansen, N. and Ostermeier, A. (1997), "Convergence properties of evolution strategies with the derandomized covariance matrix adaptation: the ($\mu$/$\mu_I$,$\lambda$)-CMA-ES", Proceedings of the 5th European Congress on Intelligent techniques and Soft Computing, Aachen, Germany.
  15. Huang, C.S. (2001), "Structural identification from ambient vibration using the multivariate AR model", J. Sound Vib., 241(3), 337-359. https://doi.org/10.1006/jsvi.2000.3302
  16. Huang, J.N. and Pappa, R.S. (1985), "An eigensystem realization algorithm (ERA) for modal parameter identification and model reduction", J. Guid. Control Dynam., 8, 620-627. https://doi.org/10.2514/3.20031
  17. Katayama, T. (2005), Subspace methods for system identification, Springer-Verlag, Berlin, Germany.
  18. Koulocheris, D., Dertimanis, V.K. and Spentzas, C.N. (2008), "Parametric identification of vehicle structural characteristics", Forsch. Ingenieurwes., 68(4), 173-181.
  19. Koulocheris, D., Dertimanis, V.K. and Vrazopoulos, H. (2004), "Evolutionary parametric identification of dynamic systems", Forsch. Ingenieurwes., 72(1), 39-51.
  20. Koulocheris, D., Dertimanis, V.K. and Vrazopoulos, H. (2003), "Vehicle suspension system identification using evolutionary algorithms", Proceedings of the EUROGEN 2003, Barcelona, Spain.
  21. Kruisselbrink, J.W. (2012), Evolution strategies for robust optimization, PhD Thesis, Leiden University, Leiden, The Netherlands.
  22. Landau, I.D. and Zito, G. (2006), Digital control systems: design, identification and implementation, Springer-Verlag, London, UK.
  23. Ljung, L. (1999), System identification: theory for the user, 2nd Ed., Prentice-Hall Inc., Englewood Cliffs, NJ, USA.
  24. Mc Kelvey, T. and Helmersson, A. (1997), "System identification using an over-parameterized model class - Improving the optimization algorithm", Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, CA.
  25. Ostermeier, A., Gawelczyk, A. and Hansen, N. (1994), "Step-size adaptation based on non-local use of selection information", in Parallel Problem Solving from Nature - PPSN III, Springer.
  26. Tang, H.S., Xue S.T. and Fan. C. (2008), "Differential evolution strategy for structural system identification", Comput. Struct., 86(21-22), 2004-2012. https://doi.org/10.1016/j.compstruc.2008.05.001
  27. Van Overschee, P. and De Moor, B. (1996), Subspace identification for linear systems: theory - Implementation - Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands.
  28. Verhaegen, M. and Dewilde, P. (1992), "Subspace model identification Part 1. the output-error state-space model identification class of algorithms", Int. J. Control, 56(5), 1187-1210. https://doi.org/10.1080/00207179208934363
  29. Verhaegen, M. and Verdult, V. (2007), Filtering and system identification: a least squares approach, 2nd Ed., Prentice-Hall Inc., Englewood Cliffs, NJ, USA.
  30. Viberg, M. (1995), "Subspace-based methods for the identification of linear time-invariant systems", Automatica, 31(12), 1835-1851. https://doi.org/10.1016/0005-1098(95)00107-5
  31. Zhang, Z., Koh, C.G. and Duan, W.H. (2010a), "Uniformly sampled genetic algorithm with gradient search for structural identification - Part I: Global search", Comput. Struct., 88(15-16), 949-962. https://doi.org/10.1016/j.compstruc.2010.05.001
  32. Zhang, Z., Koh, C.G. and Duan, W.H. (2010b), "Uniformly sampled genetic algorithm with gradient search for structural identification - Part II: Local search", Comput. Struct., 88(19-20), 1149-1161. https://doi.org/10.1016/j.compstruc.2010.07.004

Cited by

  1. Hybrid evolutionary identification of output-error state-space models vol.1, pp.4, 2014, https://doi.org/10.12989/smm.2014.1.4.427
  2. Data-driven uncertainty quantification of structural systems via B-spline expansion 2017, https://doi.org/10.1016/j.compstruc.2017.03.006