한국전산구조공학회논문집 (Journal of the Computational Structural Engineering Institute of Korea)

  • 제32권1호
  • /
  • Pages.45-54
  • /
  • 2019
  • /
  • 1229-3059(pISSN)
  • /
  • 2287-2302(eISSN)
한국전산구조공학회 (Computational Structural Engineering Institute of Korea)
권호 표지
DOI QR코드

DOI QR Code

AEKF(Adaptive Extended Kalman Filter)를 이용하는 건축 구조물의 손상탐지

Damage Detection of Building Structures using AEKF(Adaptive Extended Kalman Filter)

  • Yun, Da Yo (Department of Architectural Engineering, Yonsei Univ.) ;
  • Kim, Yousok (Department of Architectural Engineering, Hongik University) ;
  • Park, Hyo Seon (Department of Architectural Engineering, Yonsei Univ.)
  • 투고 : 2018.11.01
  • 심사 : 2018.11.30
  • 발행 : 2019.02.28
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 EKF기법의 초기 파라미터 설정에 따른 상태벡터의 발산 문제를 해결하고자 AEKF기법을 제시한다. EKF기법의 초기 파라미터는 상태벡터 수렴 및 안정성에 중요한 역할을 함으로 초기 파라미터의 적절한 설정은 EKF를 사용함에 있어 매우 중요하다. AEKF방법은 초기 파라미터인 P행렬을 k스텝마다 업데이트하여 초기 상태벡터의 변화에 민감하게 반응할 수 있으며, 또한 초기 상태벡터와 실제 시스템 모델과의 차이가 크게 발생하여도 적응적으로 P행렬의 값을 조절하여 상태벡터의 수렴을 가능하게 한다. 또한 Q행렬 및 R행렬을 k스텝 업데이트하여 상태벡터의 수렴 안정성을 더욱 확보하였다. 3DOF시스템을 통해서 AEKF기법의 결과와 EKF, UKF기법을 비교 검증하였다.

The damage detection method using the extended Kalman filter(EKF) technique has been continuously used since EKF can estimation the responses of the damaged building structure and the stiffness of the structure. However, in the use of EKF, the requirement of setting the initial paramters P, Q, and R has caused the divergence and instability of the state vector, and various researches have been conducted to determine theses parameters. In this paper, adaptive extended Kalman filter(AEKF) method is proposed to solve the problem of setting the values of P, Q, and R, which are important parameters determining the convergence performance of the EKF state vector. By using the AEKF method proposed in this study, the P, Q, and R parameters are updated every k steps. The proposed algorithm is applied for the estimation of stiffness and the damage detection of 3-DOF problem. Based of the verification, it can be found that the selection process for the values of P, Q, and R can improve the convergence performance of EKF.

키워드

참고문헌

  1. Ghorbani, E., Cha, Y.J. (2018), An Iterated Cubature Uncscented Kalman Filter for Large-DoF Systems Identification with Noisy Data, J. Sound & Vib., 420, pp.21-34. https://doi.org/10.1016/j.jsv.2018.01.035
  2. Hoshiya, M., Saito, E. (1984) Structural Identification by Extended Kalman Filtert, J. Eng. Mech., 110(12), pp.1757-1770. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1757)
  3. Hernandez, E.M. (2013) Optimal Model-based State Estimation in Mechanical and Structural Systems, Struct. Control & Health Monit., 20, pp.532-543. https://doi.org/10.1002/stc.513
  4. Jazwinski, A.H. (1970) Stochastic Process and Filtering Theory, Academic Press, New York
  5. Julier, S.J., Uhlmann J.K. (2004) Unsented Filtering and Nonlinear Estimation, Proc. IEEE, 92(3), pp.401-422. https://doi.org/10.1109/JPROC.2003.823141
  6. Kim, D.Y., Oh, B.K., Park, H.S. (2017) Modal Ifentification for High-Rise Building Structures using Orthogonality of Filtered Response Vector, Computer-Aided Civil & Infrastruct. Eng., 32, pp.1064-1084. https://doi.org/10.1111/mice.12310
  7. Lei, Y., Liu., Liu, L.J. (2014), Identification of Multistory Shear Buildings under Unknown Earthquake Excitation using Partial Output Measurements: Numerical and Experimental Studies, Struct. Control & Health Monit., 21, pp.774-784. https://doi.org/10.1002/stc.1600
  8. Lin, J.S., Zhang, Y. (1994) Nonlinear Structural Identification using Extended Kalman Filter, Comput. & Struct., 52(4), pp.757-764. https://doi.org/10.1016/0045-7949(94)90357-3
  9. Ming, G., Kerrigan, E.C. (2017) Noise Covariance Identification for Time-Varing and Nonlinear Systems, Int. J. Control, 90(9), pp.1903-1915. https://doi.org/10.1080/00207179.2016.1228123
  10. Odelson, B.J., Rajamani, M.R., Rawlings, J.B. (2006) A New Autocovariance Least-Squares Method for Estimating Noise Covariances, Automatica, 42(2), pp.303-308. https://doi.org/10.1016/j.automatica.2005.09.006
  11. Oh, B.K., Kim, D.Y., Park, H.S. (2017) Modal Response-Based Visual System Identification and Model Updating Methods for building Structures, Computer-Aided Civil & Infrastruct. Eng., 32, pp.34-56. https://doi.org/10.1111/mice.12229
  12. Oh, B.K., Kim, J.H., Park, H.S. (2019) Model Updating Method for Damage Detection of Building Structures Under Ambient Excitation using Modal Participation Ratio, Measurement, 133, pp.251-261. https://doi.org/10.1016/j.measurement.2018.10.023
  13. Park, H,S., Oh, B.K. (2018) Damage Detection of Building Structures under Ambient Excitation through the Analysis of the Relationship between the Modal Participation Ratio and Story Stiffness, J. Sound & Vib., 418, pp.122-143. https://doi.org/10.1016/j.jsv.2017.12.036
  14. Schneider, R., Georgakis, C. (2013) How to not Make the Rxtended Kalman Filter Fail, Industrial & Eng. Chem. Res., 52, pp.3354-3362. https://doi.org/10.1021/ie300415d
  15. Solonen, A., Hakkarainen, J., Ilin, A. Abbas, M., Bibov, A. (2014), Estimating Model Error Covariance Matrix Parameters in Extended Kalmna Filtering, Nonlinear Proc. Geophys., 21, pp.919-927. https://doi.org/10.5194/npg-21-919-2014
  16. Wang, D., Haldar, A. (1997) System Identification with Limited Observations and Without Input, J. Eng. Mech., 123(5), pp.504-510. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:5(504)
  17. Wang, J., Wang, J., Zhang, D., Shao, X., Chen, G. (2018) Kalman Filtering through the Feedback Adaption of Prior Error Covariance, Signal Proc., 152, pp.47-53. https://doi.org/10.1016/j.sigpro.2018.05.011
  18. Wu, M., Smyth, A.W. (2007) Application of the Unscented Kalman Filter for Real-Time Nonlinear Structural System Identification, Struct. Control & Health Monit., 14, pp.971-990. https://doi.org/10.1002/stc.186
  19. Zhang, C., Huang, J.Z., Song, G.Q., Chen, L. (2017) Structural Damage Identification by Extended Kalman Filter with l1-norm Regularization Scheme Structural System Identification, Struct. Control & Health Monit., 24(11), e1999. https://doi.org/10.1002/stc.1999