Smart Structures and Systems

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A two-stage Kalman filter for the identification of structural parameters with unknown loads

  • He, Jia (College of Civil Engineering, Key laboratory of wind and bridge engineering of Hunan Province, Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education, Hunan University) ;
  • Zhang, Xiaoxiong (College of Civil Engineering, Key laboratory of wind and bridge engineering of Hunan Province, Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education, Hunan University) ;
  • Feng, Zhouquan (College of Civil Engineering, Key laboratory of wind and bridge engineering of Hunan Province, Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education, Hunan University) ;
  • Chen, Zhengqing (College of Civil Engineering, Key laboratory of wind and bridge engineering of Hunan Province, Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education, Hunan University) ;
  • Cao, Zhang (College of Civil Engineering, Key laboratory of wind and bridge engineering of Hunan Province, Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education, Hunan University)
  • Received : 2019.10.21
  • Accepted : 2020.10.20
  • Published : 2020.12.25
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Abstract

The conventional Kalman Filter (KF) provides a promising way for structural state estimation. However, the physical parameters of structural systems or models should be available for the estimation. Moreover, it is not applicable when the loadings applied to the structures are unknown. To circumvent the aforementioned limitations, a two-stage KF with unknown input approach is proposed for the simultaneous identification of structural parameters and unknown loadings. In stage 1, a modified observation equation is employed. The structural state vector is estimated by KF on the basis of structural parameters identified at the previous time-step. Then, the unknown input is identified by Least Squares Estimation (LSE). In stage 2, based on the concept of sensitivity matrix, the structural parameters are updated at the current time-step by using the estimated structural states obtained from stage 1. The effectiveness of the proposed approach is numerically validated via a five-story shearing model under random and earthquake excitations. Shaking table tests on a five-story structure are also employed to demonstrate the performance of the proposed approach. It is demonstrated from numerical and experimental results that the proposed approach can be used for the identification of parameters of structure and the external force applied to it with acceptable accuracy.

Keywords

Acknowledgement

A great appreciation would be given to Prof. You-Lin Xu and Mr. Sheng Zhan for their kind direction and help for the shaking table tests in The Hong Kong Polytechnic University. The authors also would like to thank for the financial supports from National Natural Science Foundation of China (No. 51708198) and Natural Science Foundation of Hunan Province (No. 2018JJ3054).

References

  1. Chatzi, E.N. and Fuggini, C. (2015), "Online correction of drift in structural identification using artificial white noise observations and an unscented Kalman Filter", Smart Struct. Syst., Int. J., 16(2), 295-328. https://doi.org/10.12989/sss.2015.16.2.295.
  2. Cumbo, R., Tamarozzi, T., Janssens, K. and Desmet, W. (2019), "Kalman-based load identification and full-field estimation analysis on industrial test case", Mech. Syst. Signal Proc., 117, 771-785. https://doi.org/10.1016/j.ymssp.2018.08.045.
  3. Ding, Z., Li, J. and Hao, H. (2019), "Structural damage identification using improved Jaya algorithm based on sparse regularization and Bayesian inference", Mech. Syst. Signal Proc., 132, 211-231. https://doi.org/10.1016/j.ymssp.2019.06.029.
  4. He, J., Xu, Y.L., Zhang, C.D. and Zhang, X.H. (2015), "Optimum control system for earthquake-excited building structures with minimal number of actuators and sensors", Smart Struct. Syst., Int. J., 16(6), 981-1002. https://doi.org/10.12989/sss.2015.16.6.981.
  5. He, J., Zhang, X.X. and Xu, B. (2019a), "Identification of structural parameters and unknown inputs based on revised observation equation: approach and validation", Int. J. Struct. Stab. Dyn., 19(12), 1950156. https://doi.org/. https://doi.org/10.1142/S0219455419501566
  6. He, J., Zhang, X. and Dai, N. (2019b), "An improved Kalman filter for joint estimation of structural states and unknown loadings", Smart Struct. Syst., Int. J., 24(2), 209-221. https://doi.org/10.12989/sss.2019.24.2.209.
  7. Hu, R.P., Xu, Y.L. and Zhan, S. (2018), "Multi-type sensor placement and response reconstruction for building structures: Experimental investigations", Earthq. Eng. Eng. Vib., 17(1), 29-46. https://doi.org/CNKI:SUN:EEEV.0.2018-01-005. https://doi.org/10.1007/s11803-018-0423-3
  8. Hui, Y., Law, S.S., Liu, M. and Li, S. (2019), "Parameter and aerodynamic force identification of single-degree-of-freedom system in wind tunnel test", J. Eng. Mech., 145(1), 04018120. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001542.
  9. Kim, K., Choi, J., Koo, G. and Sohn, H. (2016), "Dynamic displacement estimation by fusing biased high-sampling rate acceleration and low-sampling rate displacement measurements using two-stage Kalman estimator", Smart Struct. Syst., Int. J., 17(4), 647-667. https://doi.org/10.12989/sss.2016.17.4.647.
  10. Kim, K., Choi, J., Chung, J., Koo, G., Bae, I. and Sohn, H. (2018), "Structural displacement estimation through multi-rate fusion of accelerometer and RTK-GPS displacement and velocity measurements", Measurement, 130, 223-235. https://doi.org/10.1016/j.measurement.2018.07.090.
  11. Lee, H., Kang, S. and Han, S. (2018), "Real-time optimal state estimation scheme with delayed and periodic measurements", IEEE Trans. Ind. Electron., 65(7), 5970-5978. https://doi.org/10.1109/TIE.2017.2774731.
  12. Lei, Y., Jiang, Y. and Xu, Z. (2012a), "Structural damage detection with limited input and output measurement signals", Mech. Syst. Signal Proc., 28, 229-243. https://doi.org/10.1016/j.ymssp.2011.07.026.
  13. Lei, Y., Wu, Y. and Li, T. (2012b), "Identification of non-linear structural parameters under limited input and output measurements", Int. J. Non Linear Mech., 47, 1141-1146. https://doi.org/10.1016/j.ijnonlinmec.2011.09.004.
  14. Lei, Y., Lai, Z., Zhu, S. and Zhang, X. (2014), "Experimental study on impact-induced damage detection using an improved extended Kalman filter", Int. J. Struct. Stab. Dyn., 14(5), 1440007. https://doi.org/10.1142/S0219455414400070.
  15. Lei, Y., Chen, F. and Zhou, H. (2015), "An algorithm based on two-step Kalman filter for intelligent structural damage detection", Struct. Control Health Monit., 22, 694-706. https://doi.org/10.1002/stc.1712.
  16. Li, J. and Hao, H. (2016), "A review of recent research advances on structural health monitoring in western Australia", Struct. Monit. Maint., Int. J., 3(1), 33-49. https://doi.org/10.12989/smm.2016.3.1.033.
  17. Liu, L., Su, Y., Zhu, J. and Lei, Y. (2016), "Data fusion based EKF-UI for real-time simultaneous identification of structural systems and unknown external inputs", Measurement, 88, 456-467. https://doi.org/10.12783/shm2017/13971.
  18. Liu, L., Hua, W. and Lei. Y. (2017), "Real-time simultaneous identification of structural systems and unknown inputs without collocated acceleration measurements based on MEKF-UI", Measurement, 122, 545-553. https://doi.org/10.1016/j.measurement.2017.07.001.
  19. Lourens, E., Reynders, E., De Roeck, G., Degrande, G. and Lombaert, G. (2012), "An augmented Kalman filter for force identification in structural dynamics", Mech. Syst. Signal Proc., 27, 446-460. https://doi.org/10.1016/j.ymssp.2011.09.025.
  20. Naets, F., Cuadrado, J. and Desmet, W. (2015), "Stable force identification in structural dynamics using Kalman filtering and dummy-measurements", Mech. Syst. Signal Proc., 50-51, 235-248. https://doi.org/10.1016/j.ymssp.2014.05.042.
  21. Pan, S., Xiao, D., Xing, S., Law, S.S., Du, P. and Li, Y. (2016), "A general extended Kalman filter for simultaneous estimation of system and unknown inputs", Eng. Struct., 109, 85-98. https://doi.org/10.1016/j.engstruct.2015.11.014.
  22. Ren, P. and Zhou, Z. (2017), "Strain estimation of truss structures based on augmented Kalman filtering and modal expansion", Adv. Mech. Eng., 9(11), 1687814017735788. https://doi.org/10.1177/1687814017735788.
  23. Saleem, M.M. and Jo, H. (2019), "Impact force localization for civil infrastructure using augmented Kalman filter optimization", Smart Struct. Syst., Int. J., 23(2), 123-139. https://doi.org/10.12989/sss.2019.23.2.123.
  24. 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 Proc., 21(2), 706-723. https://doi.org/10.1016/j.ymssp.2006.03.005.
  25. Xiao, M., Zhang, Y., Wang, Z. and Fu, H. (2018), "An adaptive three-stage extended Kalman filter for nonlinear discrete-time system in presence of unknown inputs", ISA Trans., 75, 101-117. https://doi.org/10.1016/j.isatra.2018.02.007.
  26. Xin, Y., Hao, H. and Li, J. (2019), "Time-varying system identification by enhanced empirical wavelet transform based on synchroextracting transform", Eng. Struct., 196, 109313. https://doi.org/10.1016/j.engstruct.2019.109313.
  27. Xu, B. and He, J. (2015), "Substructural parameters and dynamic loading identification with limited observations", Smart Struct. Syst., Int. J., 15(1), 169-189. https://doi.org/10.12989/sss.2015.15.1.169.
  28. Xu, Y.L. and He, J. (2017), Smart Civil Structures, CRC Press, Boca Raton, FL, USA.
  29. Xu, Y.L., Zhang, X.H., Zhu, S.Y. and Zhan, S. (2016), "Multitype sensor placement and response reconstruction for structural health monitoring of long-span suspension bridges", Sci. Bull., 61(4), 313-329. https://doi.org/10.1007/s11434-016-1000-7.
  30. Yang, J.N., Lin, S., Huang, H. and Zhou, L. (2006), "An adaptive extended Kalman filter for structural damage identification", Struct. Control Health Monit., 13, 849-867. https://doi.org/10.1002/stc.84.
  31. Yang, J.N., Huang, H. and Pan, S. (2009), "Adaptive quadratic sum-squares error for structural damage identification", J. Eng. Mech., 135(2), 67-77. https://doi.org/10.1061/(ASCE)0733-9399(2009)135:2(67).
  32. Zhang, C., Huang, J.Z., Song, G.Q. and Chen, L. (2017), "Structural damage identification by extended Kalman filter with 11‐norm regularization scheme", Struct. Control Health Monit., 24(11) e1999. https://doi.org/10.1002/stc.1999.
  33. Zheng, Z., Qiu, H., Wang, Z., Luo, S. and Lei, Y. (2019), "Data fusion based multi-rate Kalman filtering with unknown input for on-line estimation of dynamic displacements", Measurement, 131, 211-218. https://doi.org/10.1016/j.measurement.2018.08.057.
  34. Zhu, S., Zhang, X.H., Xu, Y.L. and Zhan, S. (2013), "Multi-type sensor placement for multi-scale response reconstruction", Adv. Struct. Eng., 16(10), 1779-1797. https://doi.org/10.1260/1369-4332.16.10.1779.