Journal of Applied and Computational Mechanics

A Generalized Identification of Joint Structural State and ‎Unknown Inputs Using Data Fusion MKF-UI

Document Type : Special Issue Paper

Authors

1 Department of Civil Engineering, Xiamen University, No.182 Daxue Road, Xiamen, 361005, China

2 Department of Civil Engineering, Xiamen University, No.182 Daxue Road, Xiamen, 361005, China‎

Abstract

The classical Kalman filter (KF) can estimate the structural state online in real time. However, the classical KF presupposes that external excitations are known. The existing methods of Kalman filter with unknown inputs (KF-UI) have limitations that require observing the acceleration response at the excitation point or assuming the unknown force. To surmount the above defects, an innovative modal Kalman filter with unknown inputs (MKF-UI) is proposed in this paper. Modal transformation and modal truncation are used to reduce the dimensionality of the structural state, and the accelerations at the excitation positions do not need to observe. Besides, the proposed MKF-UI does not require the assumption of unknown external excitation. Therefore, the proposed approach is suitable for the generalized identification of dynamic structural states and unknown loadings. The effectiveness and feasibility of the proposed identification approach are ascertained by some numerical simulation examples.

Keywords

Main Subjects

[1] Azam, S.E., Chatzi, E., Papadimitriou, C., A dual Kalman filter approach for state estimation via output-only acceleration measurements, Mechanical Systems and Signal Processing, 60-61, 2015, 866-886.
[2] Liu, L.J., Zhu, J.J., Su, Y., Lei Y., Improved Kalman filter with unknown inputs based on data fusion of partial acceleration and displacement measurements, Smart Structures and Systems, 17(6), 2016, 903-915.
[3] Lei, Y., Lu, J.B., Huang, J.S., Chen, S.Y., A general synthesis of identification and vibration control of building structures under unknown excitations, Mechanical Systems and Signal Processing, 143, 2020, 106803.
[4] Chen, Z., Chan, T.H.T., Yu, L., Comparison of regularization methods for moving force identification with ill-posed problems, Journal of Sound and Vibration, 478, 2020, 115349.
[5] Aucejo, M., De Smet, O., An optimal Bayesian regularization for force reconstruction problems, Mechanical Systems and Signal Processing, 126, 2019, 98-115.
[6] Sanchez, J., Benaroya, H., Review of force reconstruction techniques, Journal of Sound and Vibration, 333, 2014, 2999-3018.
[7] Uhl, T., The inverse identification problem and its technical application, Archive of Applied Mechanics, 77, 2007, 325-337.
[8] Pan, C.D.,  Yu, L., Liu, H.L., Chen, Z.P., Luo, W.F., Moving force identification based on redundant concatenated dictionary and weighted l1-norm regularization, Mechanical Systems and Signal Processing, 98, 2018, 32-49.
[9] Feng, W., Li, Q.F., Lu, Q.H., Force localization and reconstruction based on a novel sparse Kalman filter, Mechanical Systems and Signal Processing, 144, 2020, 106890.
[10] Chan, T.H.T.,  Yu, L., Law, S.S., Yung, T.H., Moving force identification studies, I: Theory, Journal of Sound And Vibration, 247(1), 2001, 59-76.
[11] Majidi, M.A., Hsieh, C.S., Yazdi, H.S., Kalman Filter Reinforced by Least Mean Square for Systems with Unknown Inputs, Circuits Systems and Signal Processing, 37(11), 2018, 4955-4972.  
[12] Wu, A.L., Loh, C.H., Yang, J.N., Weng, J.H., Chen, C.H., Ueng, T.S., Input force identification: application to soil-pile interaction, Structural Control and Health Monitoring, 16, 2009, 223-240.
[13] Pan, S.W., Su, H.Y., Wang, H., Chu J., The study of input and state estimation with Kalman filtering, The Institute of Measurement and Control, 33(8), 2011, 901-918.
[14] Lin, D.C., Input estimation for nonlinear systems, Inverse Problem in Science and Engineering, 18(5), 2010, 673-689.
[15] Zhang, C.D., Xu, Y.L., Structural damage identification via response reconstruction under unknown excitation, Structural Control & Health Monitoring, 24(8), 2017, e1953.
[16] Zhang, C.D., Xu, Y.L., Optimal multi-type sensor placement for response and excitation reconstruction, Journal of Sound and Vibration, 360, 2016, 112-128.
[17] He, J., Zhang, X.X., Dai, N.X., An improved Kalman filter for joint estimation of structural states and unknown loadings, Smart Structures and Systems, ‏24(2), 2019, 209-221.
[18] Lourens, E., Reynders, E., Roeck, G. De, Degrande, G., Lombaert, G., An augmented Kalman filter for force identification in structural dynamics, Mechanical Systems and Signal Processing, 27, 2012, 446-460.
[19] Li, Y., Luo, Y.Z.,  Wan, H.P.,  Yun, C.B., Shen, Y.B., Identification of earthquake ground motion based on limited acceleration measurements of structure using Kalman filtering technique, Structural Control & Health Monitoring, 27, 2020, e2464.
‎[20] Zhi, L.H., Yu, P., Li, Q.S., Chen, B., Fang, M.X., Identification of wind loads on super-tall buildings by Kalman filter, Computers & ‎Structures, 208, 2018, 105-117.‎
[21] Zhi, L.H., Yu, P., Tu, J.W., Chen, B., Li, Y.G., A Kalman filter based algorithm for wind load estimation on high-rise buildings, Structural Engineering and Mechanics, 64(4), 2017, 449-459.
[22] Maes, K., Gillijns, S., Lombaert, G., A smoothing algorithm for joint input-state estimation in structural dynamics, Mechanical Systems and Signal Processing, 98, 2018, 292–309.
[23] Sun, H., Feng, D.M., Liu, Y., Feng, M.Q., Statistical regulari for identification of structural parameters and external loadings using state space model, Computer Aided Civil Infrastructure Engineering, 30(11), 2015, 843-858.
[24] Lei, Y., Chen, F., Zhou H., A two-stage and two-step algorithm for the identification of structural damage and unknown excitations: Numerical and experimental studies, Smart Structures and Systems, 15(1), 2015, 57-80.
[25] Naets F., Cuadrado J., Desmet W., Stable force identification in structural dynamics using Kalman filtering and dummy-measurements, Mechanical Systems and Signal Processing, 50-51, 2015, 235-248.
Journal of Applied and Computational Mechanics
Volume 7, Special Issue
June 2021
Pages 1198-1204