Structural Engineering and Mechanics

  • 제47권3호
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  • Pages.361-381
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  • 2013
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Online estimation of noise parameters for Kalman filter

  • Yuen, Ka-Veng (Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau) ;
  • Liang, Peng-Fei (Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau) ;
  • Kuok, Sin-Chi (Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau)
  • 투고 : 2013.04.15
  • 심사 : 2013.07.30
  • 발행 : 2013.08.10
⟨ 이전 논문 다음 논문 ⟩

초록

A Bayesian probabilistic method is proposed for online estimation of the process noise and measurement noise parameters for Kalman filter. Kalman filter is a well-known recursive algorithm for state estimation of dynamical systems. In this algorithm, it is required to prescribe the covariance matrices of the process noise and measurement noise. However, inappropriate choice of these covariance matrices substantially deteriorates the performance of the Kalman filter. In this paper, a probabilistic method is proposed for online estimation of the noise parameters which govern the noise covariance matrices. The proposed Bayesian method not only estimates the optimal noise parameters but also quantifies the associated estimation uncertainty in an online manner. By utilizing the estimated noise parameters, reliable state estimation can be accomplished. Moreover, the proposed method does not assume any stationarity condition of the process noise and/or measurement noise. By removing the stationarity constraint, the proposed method enhances the applicability of the state estimation algorithm for nonstationary circumstances generally encountered in practice. To illustrate the efficacy and efficiency of the proposed method, examples using a fifty-story building with different stationarity scenarios of the process noise and measurement noise are presented.

키워드

참고문헌

  1. Beck, J.L. (2010), "Bayesian system identification based on probability logic", Struct. Control Hlth., 17(7), 825-847. https://doi.org/10.1002/stc.424
  2. Beck, J.L. and Katafygiotis, L.S. (1998), "Updating models and their uncertainties, I: Bayesian statistical framework", J. Eng. Mech.-ASCE, 124(4), 455-461. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:4(455)
  3. Beck, J.L. and Yuen, K.V. (2004), "Model selection using response measurements: Bayesian probabilistic approach", J. Eng. Mech.-ASCE, 130(2), 192-203. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:2(192)
  4. Box, G.E.P. and Tiao, G.C. (1973), Bayesian Inference in Statistical Analysis, Addison-Wesley, Reading, MA.
  5. Ching, J., Beck, J.L. and Porter, K.A. (2006), "Bayesian state and parameter estimation of uncertain dynamical systems", Probabilist. Eng. Mech., 21(1), 81-96. https://doi.org/10.1016/j.probengmech.2005.08.003
  6. Ching, J., Porter, K.A. and Beck, J.L. (2009), "Propagating uncertainties for loss estimation in performancebased earthquake engineering using moment matching", Struct. Infrastruct. E., 5(3), 245-262. https://doi.org/10.1080/15732470701298323
  7. Chui, C.K. and Chen, G. (2009), Kalman Filtering with Real-Time Applications, 4th Edition, Springer-Verlag, New York.
  8. Grewal, M.S. and Andrews, A.P. (1993), Kalman Filtering: Theory and Practice, Prentice Hall, Englewood Cliffs, New Jersey.
  9. Hoi, K.I., Yuen, K.V. and Mok, K.M. (2008), "Kalman filter based prediction system for wintertime PM10 concentrations in Macau", Global NEST J., 10(2), 140-150.
  10. Kalman, R.E. (1960), "A new approach to linear filtering and prediction problems", J. Basic Eng.-T. ASME, 82(1), 35-45. https://doi.org/10.1115/1.3662552
  11. Koh, C.G. and See, L.M. (1994), "Identification and uncertainty estimation of structural parameters", J. Eng. Mech.-ASCE, 120(6), 1219-1236. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:6(1219)
  12. Kuok, S.C. and Yuen, K.V. (2012), "Structural health monitoring of Canton tower using Bayesian framework", Smart Struct. Syst., 10(4-5), 375-391. https://doi.org/10.12989/sss.2012.10.4_5.375
  13. Lam, H.F., Yuen, K.V. and Beck, J.L. (2006), "Structural health monitoring via measured Ritz vectors utilizing artificial neural networks", Comput. Aided Civ. Inf., 21(4), 232-241. https://doi.org/10.1111/j.1467-8667.2006.00431.x
  14. Lee, M.H. and Chen, T.C. (2010), "Intelligent fuzzy weighted input estimation method for the input force on the plate structure", Struct. Eng. Mech., 34(1), 1-14. https://doi.org/10.12989/sem.2010.34.1.001
  15. Lei, Y. and Jiang, Y.Q. (2011), "A two-stage Kalman estimation approach for the identification of structural parameters under unknown inputs", Adv. Mat. Res., 243-249, 5394-5398. https://doi.org/10.4028/www.scientific.net/AMR.243-249.5394
  16. Lin, J.W., Chen, C.W. and Hsu, T.C. (2013), "A novel regression prediction model for structural engineering applications", Struct. Eng. Mech., 45(5), 693-702. https://doi.org/10.12989/sem.2013.45.5.693
  17. Mehra, R.K. (1970), "On the identification of variance and adaptive Kalman filtering", IEEE T. Automat. Contr., 15(2), 175-184. https://doi.org/10.1109/TAC.1970.1099422
  18. Mohamed, A.H. and Schwarz, K.P. (1999), "Adaptive Kalman filtering for INS/GPS", J. Geodesy, 73, 193-203. https://doi.org/10.1007/s001900050236
  19. Ni, Y.Q., Ko, J.M., Hua, X.G. and Zhou, H.F. (2007), "Variability of measured modal frequencies of a cablestayed bridge under different wind conditions", Smart Struct. Syst., 3(3), 341-356. https://doi.org/10.12989/sss.2007.3.3.341
  20. Odelson, B.J., Rajamani, M.R. and Rawlings, J.B. (2006), "A new autocovariance least-squares method for estimating noise covariances", Automatica, 42(2), 303-308. https://doi.org/10.1016/j.automatica.2005.09.006
  21. Papadimitriou, C., Beck, J.L. and Au, S.K. (2000), "Entropy-based optimal sensor location for structural model updating", J. Vib. Control, 6(5), 781-800. https://doi.org/10.1177/107754630000600508
  22. Papadimitriou, C., Fritzen, C.P., 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 Hlth., 18(5), 554-573. https://doi.org/10.1002/stc.395
  23. Rosa, L., Tomasini, G., Zasso, A. and Aly, A.M. (2012), "Wind-induced dynamics and loads in a prismatic slender building: modal approach based on unsteady pressure measures", J. Wind Eng. Ind. Aerod., 107-108, 118-130. https://doi.org/10.1016/j.jweia.2012.03.034
  24. Sangsuk-Iam, S. and Bullock, T.E. (1990), "Analysis of discrete time Kalman filtering under incorrect noise covariances", IEEE T. Automat. Contr., 35(12), 1304-1309. https://doi.org/10.1109/9.61006
  25. Schmidt, S.F. (1981), "The Kalman filter: Its recognition and development for aerospace applications", J. Guid. Control Dynam., 4(1), 4-7. https://doi.org/10.2514/3.19713
  26. Simiu, E. and Scanlan, R.H. (1996), Wind Effects on Structures, Fundamentals and Applications to Design, 3rd Edition, John Wiley & Sons.
  27. Sorensen, S.W. and Sacks, J.E. (1971), "Recursive fading memory filters", Inform. Sciences, 3(2), 101-119. https://doi.org/10.1016/S0020-0255(71)80001-4
  28. Taranath, B.S. (2005), Wind and Earthquake Resistant Buildings: Structural Analysis and Design, New York, Marcel Dekker.
  29. Yan, W.M., Yuen, K.V. and Yoon, G.L. (2009), "Bayesian probabilistic approach for correlations of compressibility index for marine clays", J. Geotech. Geoenviron., 135(12), 1932-1940. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000157
  30. Yang, J.N., Lei, Y., Lin, S. and Huang, N. (2004), "Identification of natural frequencies and dampings of in situ tall buildings using ambient wind vibration data", J. Eng. Mech.-ASCE, 130(5), 570-577. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:5(570)
  31. Yuen, K.V. (2010), Bayesian Methods for Structural Dynamics and Civil Engineering, John Wiley and Sons, New York.
  32. Yuen, K.V., Hoi, K.I. and Mok, K.M. (2007), "Selection of noise parameters for Kalman filter", Earthq. Eng. Eng. Vib., 6(1), 49-56. https://doi.org/10.1007/s11803-007-0659-9
  33. Yuen, K.V. and Katafygiotis, L.S. (2001), "Bayesian time-domain approach for modal updating using ambient data", Probabilist. Eng. Mech., 16(3), 219-231. https://doi.org/10.1016/S0266-8920(01)00004-2
  34. Yuen, K.V. and Katafygiotis, L.S. (2005a), "An efficient simulation method for reliability analysis using simple additive rules of probability", Probabilist. Eng. Mech., 20(1), 109-114. https://doi.org/10.1016/j.probengmech.2004.07.003
  35. Yuen, K.V. and Katafygiotis, L.S. (2005b), "Model updating using noisy response measurements without knowledge of the input spectrum", Earthq. Eng. Struct. Dyn., 34(2), 167-187. https://doi.org/10.1002/eqe.415
  36. Yuen, K.V. and Kuok, S.C. (2010), "Ambient interference in long-term monitoring of buildings", Eng. Struct., 32(8), 2379-2386. https://doi.org/10.1016/j.engstruct.2010.04.012
  37. Yuen, K.V. and Kuok, S.C. (2011), "Bayesian methods for updating dynamic models", Appl. Mech. Rev., 64(1), 010802-1-010802-18. https://doi.org/10.1115/1.4004479
  38. Yuen, K.V. and Mu, H.Q. (2012), "A novel probabilistic method for robust parametric identification and outlier detection", Probabilist. Eng. Mech., 30, 48-59. https://doi.org/10.1016/j.probengmech.2012.06.002
  39. Yun, C.B., Abdelrahman, A.M. and Wang, P.C. (1979), "Along-wind gust effect on elevated structures", Eng. Struct., 1(3), 121-124. https://doi.org/10.1016/0141-0296(79)90021-X

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