Smart Structures and Systems

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Online correction of drift in structural identification using artificial white noise observations and an unscented Kalman Filter

  • Chatzi, Eleni N. (Institute of Structural Engineering, ETH Zurich) ;
  • Fuggini, Clemente (Industrial Innovation Division, D'Appolonia S.p.A.)
  • Received : 2013.12.15
  • Accepted : 2014.03.16
  • Published : 2015.08.25
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Abstract

In recent years the monitoring of structural behavior through acquisition of vibrational data has become common practice. In addition, recent advances in sensor development have made the collection of diverse dynamic information feasible. Other than the commonly collected acceleration information, Global Position System (GPS) receivers and non-contact, optical techniques have also allowed for the synchronous collection of highly accurate displacement data. The fusion of this heterogeneous information is crucial for the successful monitoring and control of structural systems especially when aiming at real-time estimation. This task is not a straightforward one as measurements are inevitably corrupted with some percentage of noise, often leading to imprecise estimation. Quite commonly, the presence of noise in acceleration signals results in drifting estimates of displacement states, as a result of numerical integration. In this study, a new approach based on a time domain identification method, namely the Unscented Kalman Filter (UKF), is proposed for correcting the "drift effect" in displacement or rotation estimates in an online manner, i.e., on the fly as data is attained. The method relies on the introduction of artificial white noise (WN) observations into the filter equations, which is shown to achieve an online correction of the drift issue, thus yielding highly accurate motion data. The proposed approach is demonstrated for two cases; firstly, the illustrative example of a single degree of freedom linear oscillator is examined, where availability of acceleration measurements is exclusively assumed. Secondly, a field inspired implementation is presented for the torsional identification of a tall tower structure, where acceleration measurements are obtained at a high sampling rate and non-collocated GPS displacement measurements are assumed available at a lower sampling rate. A multi-rate Kalman Filter is incorporated into the analysis in order to successfully fuse data sampled at different rates.

Keywords

References

  1. Basseville, M., Benveniste, A., Goursat, M. and Mevel, L. (2007), "In-flight vibration monitoring of aeronautical structures", IEEE Control Syst. Mag., 27(5), 27-42. https://doi.org/10.1109/MCS.2007.904652
  2. Beck, J., Au, S. and Vanik, M. (1999), "A bayesian probabilistic approach to structural health monitoring", American Control Conference Proceedings, 2, 1119-1123.
  3. Berg, G. and Housner, G.W. (1961), "Integrated velocity and displacement of strong earthquake ground motion", B. Seismol. Soc. Am., 51(2), 175-189.
  4. Boore, D.M. and Bommer, J.J. (2005), "Processing of strong-motion accelerograms: needs, options and consequences", Soil Dyn. Earthq. Eng., 25(2), 93-115. https://doi.org/10.1016/j.soildyn.2004.10.007
  5. Bucharles, A. and Vacher, P. (2002), "Flexible aircraft model identification for control law design", Aerosp. Sci. Technol., 6(8), 591-598. https://doi.org/10.1016/S1270-9638(02)01197-5
  6. Casciati, F., Saleh, R.A. and Fuggini, C. (2009), "GPS-based SHM of a tall building: torsional effects", Proceedings of the 7th International Workshop on Structural Health Monitoring, 9-11 September 2009, Stanford University, Stanford.
  7. Chatzi, E.N. and Smyth, A.W. (2009), "The unscented kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing", Struct. Control Health Monit., 16(1), 99-123. https://doi.org/10.1002/stc.290
  8. Chatzi, E.N., Smyth, A.W. and Masri, S.F. (2010), "Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty", Struct. Saf., 32(5), 326 -337. https://doi.org/10.1016/j.strusafe.2010.03.008
  9. Chen, T., Morris, J. and Martin, E. (2005), "Particle Filters for state and parameter estimation in batch processes", J. Process Contr., 15(6), 665-673. https://doi.org/10.1016/j.jprocont.2005.01.001
  10. Doebling, S.W., Farrar, C.R., Prime, M. and Shevitz, D.W. (2009), Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review, Technical Report, Los Alamos National Lab, NM (United States).
  11. Faravelli, L., Casciati, S. and Fuggini, C. (2009), "Full-scale experiment using GPS sensors for dynamic tests", Proceedings of the XIX Congress AIMETA, September 14-17, 2009, Ancona.
  12. Faravelli, L., Ubertini, F. and Fuggini, C. (2010), "Subspace Identification of the Guangzhou new TV Tower", Proceedings of the 5th World Conference on Structural Control and Monitoring, July 12-14, 2010, Shinjuku, Tokyo.
  13. Faravelli, L., Ubertini, F. and Fuggini, C. (2010), "System identification toward FEM updating of a super high-rise buildings", Proceedings of the 5th European Workshop on Structural Health Monitoring, June 28 July 2, 2010, Sorrento, Italy.
  14. Faravelli, L., Ubertini, F. and Fuggini, C. (2011), "System identification of a super high-rise building via a stochastic subspace approach", Smart Struct. Syst., 7 (2), 133-152. https://doi.org/10.12989/sss.2011.7.2.133
  15. Fraraccio, G.A., Brugger, A. and Betti, R. (2008), "Identification and damage detection in structures subjected to base excitation", Experimental Mech., 48(4), 521-528. https://doi.org/10.1007/s11340-008-9124-6
  16. Fuggini, C. (2009), Using Satellites Systems for Structural Monitoring: Accuracy, Uncertainty and Reliability, PhD Dissertation, University of Pavia, Pavia, Italy.
  17. Gao, Y., Spencer, B.F. and Ruiz-Sandoval, M. (2006), "Distributed computing strategy for structural health monitoring", Struct. Control Health Monit., 13(1), 488-507. https://doi.org/10.1002/stc.117
  18. Hong, A., Ubertini, F. and Betti, R. (2013), "New stochastic subspace approach for system identification and its application to long-span bridges", J. Eng. Mech. - ASCE, 139(6), 724-736. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000524
  19. Julier, S.J. and Uhlmann, J.K. (1997), "A new extension of the Kalman Filter to nonlinear systems", Proceedings of AeroSense: The 11th Int. Symposium on Aerospace/Defense Sensing, Simulation and Controls, Orlando.
  20. Kim, J., Kim, K. and Sohn, H. (2014), "Autonomous dynamic displacement estimation from data fusion of acceleration and intermittent displacement measurements", Mech. Syst. Signal Pr., 42(12), 194-205. https://doi.org/10.1016/j.ymssp.2013.09.014
  21. Lin, J.W., Betti, R., Smyth, A.W. and Longman, R.W. (2001), "On-line identification of non-linear hysteretic structural systems using a variable trace approach", Earthq. Eng. Struct. D., 30(9), 1279-303. https://doi.org/10.1002/eqe.63
  22. Lourens, E., Papadimitriou, C., Gillijns, S., Reynders, E., De Roeck, G. and Lombaert, G. (2012), "Joint input-response estimation for structural systems based on reduced-order models and vibration data from a limited number of sensors", Mech. Syst. Signal Pr., 29, 310-327. https://doi.org/10.1016/j.ymssp.2012.01.011
  23. Mani, G., Quinn, D.D. and Kasarda, M.E.F. (2006), "Structural Health Monitoring of Rotordynamic Systems by Wavelet Analysis", ASME Conference Proceedings 2006 (4773X), 685-692.
  24. Mariani, S. and Corigliano, A. (2005), "Impact induced composite delamination: state and parameter identification via joint and dual extended kalman filters", Comput. Method. Appl. M., 194(50-52), 5242-5272. https://doi.org/10.1016/j.cma.2005.01.007
  25. Maskell, S. and Gordon, N.A. (2001), "Tutorial on particle filters for on-line nonlinear/non-gaussian bayesian tracking", IEEE T. Signal Proces., 50(2), 174-188.
  26. Moschas, F. and Stiros, S. (2012), "Phase effect in time-stamped accelerometer measurements: an experimental approach", Int. J. Metrol. Quality Eng., 3, 161-167. https://doi.org/10.1051/ijmqe/2012025
  27. Moaveni, B., He, X., Conte, J.P. and Restrepo, J.I. (2010), "Damage identification study of a seven-story full-scale building slice tested on the UCSD-NEES shake table", Struct. Saf., 32(5), 347-356 https://doi.org/10.1016/j.strusafe.2010.03.006
  28. Naets, F., Pastorino, R., Cuadrado, J. and Desmet, W. (2013), "Online state and input force estimation for multibody models employing extended kalman filtering", Multibody Syst. Dyn., 1-20
  29. Papadimitriou, C., Fritzen, C., Kraemer, P. and Ntotsios, E. (2011), "Fatigue predictions in entire body of metallic structures from a limited number of vibration sensors using kalman filtering", Struct. Control Health Monit., 18(5), 554-573. https://doi.org/10.1002/stc.395
  30. Park, J.W., Sim, S.H. and Jung, H.J. (2013), "Displacement estimation using multimetric data fusion", IEEE/ASME T. Mechatronics, 18(6), 1675-1682. https://doi.org/10.1109/TMECH.2013.2275187
  31. Psimoulis, P.A. and Stiros, S.C. (2008), "Experimental assessment of the accuracy of GPS and RTS for the determination of the parameters of oscillation of major structures", Comput.-Aided Civil Infrastruct. E., 23(5), 389-403. https://doi.org/10.1111/j.1467-8667.2008.00547.x
  32. Rajamani, M.R. (2007), Data-based Techniques to Improve State Estimation in Model Predictive Control, PhD Thesis, University of Wisconsin-Madison, October 2007
  33. Rajamani, M.R. and Rawlings, J.B. (2009), "Estimation of the disturbance structure from data using semidefinite programming and optimal weighting", Automatica, 45,142-148. https://doi.org/10.1016/j.automatica.2008.05.032
  34. Rauch, H.E., Striebel, C.T. and Tung, F. (1965), "Maximum likelihood estimates of linear dynamic systems", J. Am. Inst. Aeronaut. Astronaut., 3(8), 1445-50. https://doi.org/10.2514/3.3166
  35. Ristic, B., Arulampalam, S. and Gordon, N. (2004), "Beyond the Kalman filter: Particle filters for tracking applications", Artech house.
  36. Sarkka, S. (2008), "Unscented Rauch-Tung-Striebel smoother", IEEE T.Automat. Control., 53(3), 845-549. https://doi.org/10.1109/TAC.2008.919531
  37. Smyth, A. and Wu, M. (2007), "Multi-rate kalman filtering for the data fusion of displacement and acceleration response measurements in dynamic system monitoring", Mech. Syst. Signal Pr., 21(2), 706-723. https://doi.org/10.1016/j.ymssp.2006.03.005
  38. Stiros, S., Psimoulis, P. and Kokkinou, E. (2008), "Errors introduced by fluctuations in the sampling rate of automatically recording instruments: Experimental and theoretical approach", J. Surv. Eng. - ASCE, 134(3), 89-93. https://doi.org/10.1061/(ASCE)0733-9453(2008)134:3(89)
  39. Stiros, S.C. (2008), "Errors in velocities and displacements deduced from accelerographs: An approach based on the theory of error propagation", Soil Dynam. Earthq. Eng., 28(5), 415-420. https://doi.org/10.1016/j.soildyn.2007.07.004
  40. Terejanu, G., Singh, T. and Scott, P. (2007), "Unscented kalman filter/smoother for a CBRN puff-based dispersion model", Proceedings of the 10th International Conference on Information Fusion, 9-12 July.
  41. Wan, E. and Van Der Merwe, R. (2000), "The unscented kalman filter for nonlinear estimation", Adaptive Systems for Signal Processing, Communications, and Control Symposium, AS-SPCC, IEEE, Lake Louise, Alberta, Canada. Oct 2000, 153-8.
  42. Yuen, K.V. and Katafygiotis, L.S. (2006), "Substructure identification and health monitoring using noisy response measurements only", Comput. - Aided Civil Infrastruct. E., 21(4), 280-291. https://doi.org/10.1111/j.1467-8667.2006.00435.x

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