Parameter Estimation for the Tuned Liquid Damper Model Based on Robust Extended Kalman Filter
Article Information
Abstract
The Tuned Liquid Damper (TLD) method offers a practical and cost-effective solution for seismic design. Accurate modeling of the TLD system’s dynamic behavior is crucial for optimizing its performance. In this study, the nonlinear dynamics of the TLD system are characterized using the Housner model, with parameters estimated via a nonlinear state estimation approach. To address challenges associated with model discretization and unknown noise processes, we introduce a Robust Extended Kalman Filter (REKF) that incrementally incorporates uncertainties to more accurately capture system dynamics. The proposed method is evaluated through real-time hybrid simulation, employing seismic input signals from the El Centro and Hachinohe ground motions. Comparative analyses indicate that the robust algorithm achieves superior parameter estimation relative to conventional methods, with estimated parameters closely aligning with reference values and resulting in minimal relative error. This work underscores the efficacy of robust algorithms in TLD vibration response analysis and presents a promising approach for dynamic modeling and seismic performance optimization.
Graphical Abstract
Keywords
Data Availability Statement
Funding
Conflicts of Interest
Ethical Approval and Consent to Participate
References
- Housner, G. W. (1963). The dynamic behavior of water tanks. Bulletin of the seismological society of America, 53(2), 381-387.
[CrossRef] [Google Scholar] - Limin, S. (1991). Semi-analytical modelling of tuned liquid damper (tld) with emphasis on damping of liquid sloshing. University of Tokyo.
[Google Scholar] - Kamgar, R., Gholami, F., Zarif Sanayei, H. R., & Heidarzadeh, H. (2020). Modified tuned liquid dampers for seismic protection of buildings considering soil–structure interaction effects. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 44(1), 339-354.
[CrossRef] [Google Scholar] - Pandit, A. R., & Biswal, K. C. (2020, June). Seismic control of multi degree of freedom structure outfitted with sloped bottom tuned liquid damper. In Structures (Vol. 25, pp. 229-240). Elsevier.
[CrossRef] [Google Scholar] - Zorzi, M. (2017). Convergence analysis of a family of robust Kalman filters based on the contraction principle. SIAM Journal on Control and Optimization, 55(5), 3116-3131.
[CrossRef] [Google Scholar] - Barrau, A., & Bonnabel, S. (2016). The invariant extended Kalman filter as a stable observer. IEEE Transactions on Automatic Control, 62(4), 1797-1812.
[CrossRef] [Google Scholar] - An, Y., Wang, Z., Ou, G., Pan, S., & Ou, J. (2019). Vibration mitigation of suspension bridge suspender cables using a ring-shaped tuned liquid damper. Journal of Bridge Engineering, 24(4), 04019020.
[CrossRef] [Google Scholar] - Wang, X., & Yaz, E. E. (2019). Second-order fault tolerant extended Kalman filter for discrete time nonlinear systems. IEEE Transactions on Automatic Control, 64(12), 5086-5093.
[CrossRef] [Google Scholar] - Zorzi, M. (2016). Robust Kalman filtering under model perturbations. IEEE Transactions on Automatic Control, 62(6), 2902-2907.
[CrossRef] [Google Scholar] - Levy, B. C., & Zorzi, M. (2016). A contraction analysis of the convergence of risk-sensitive filters. SIAM Journal on Control and Optimization, 54(4), 2154-2173.
[CrossRef] [Google Scholar] - Zenere, A., & Zorzi, M. (2018). On the coupling of model predictive control and robust Kalman filtering. IET Control Theory & Applications, 12(13), 1873-1881.
[CrossRef] [Google Scholar] - Emanuele, A., Gasparotto, F., Guerra, G., & Zorzi, M. (2020). Robust distributed Kalman filtering: On the choice of the local tolerance. Sensors, 20(11), 3244. 1873-1881.
[CrossRef] [Google Scholar] - Levy, B. C., & Nikoukhah, R. (2004). Robust least-squares estimation with a relative entropy constraint. IEEE Transactions on Information Theory, 50(1), 89-104.
[CrossRef] [Google Scholar] - Levy, B. C., \& Nikoukhah, R. (2012). Robust state space filtering under incremental model perturbations subject to a relative entropy tolerance. IEEE Transactions on Automatic Control, 58(3), 682-695.
[CrossRef] [Google Scholar] - Kim, S., Deshpande, V. M., & Bhattacharya, R. (2020). Robust Kalman filtering with probabilistic uncertainty in system parameters. IEEE Control Systems Letters, 5(1), 295-300.
[CrossRef] [Google Scholar] - Tang, Z., Dietz, M., Hong, Y., & Li, Z. (2020). Performance extension of shaking table‐based real‐time dynamic hybrid testing through full state control via simulation. Structural Control and Health Monitoring, 27(10), e2611.
[CrossRef] [Google Scholar]
Cited By (3)
-
Zhongwei Hou, Jin Han, Wenbing Yu, Fenglei Han, Xuefu Zhang. Research on spatial coordinate perception technology for water-rich underground channels based on inertial signal representation analysis.
Measurement, 2026 , 280 .
[CrossRef] -
Feng Ding, Yongsong Xiao, Ling Xu, Zhiming Fang. Hierarchical Stochastic Gradient and Hierarchical Multi‐Innovation Stochastic Gradient Identification for Multivariable ARX Models.
International Journal of Adaptive Control and Signal Processing, 2026 , 40 (1).
[CrossRef] -
Kenan Can Taşan, Ahmet Akbulut. A Learning-Based Measurement Validation Approach for Cooperative Multi-UAV Navigation Using Kalman Filtering.
Drones, 2025 , 9 (12).
[CrossRef]
Cite This Article
TY - JOUR AU - Su, Tingli AU - Zhang, Yao AU - Tang, Zhenyun PY - 2025 DA - 2025/04/30 TI - Parameter Estimation for the Tuned Liquid Damper Model Based on Robust Extended Kalman Filter JO - ICCK Transactions on Sensing, Communication, and Control T2 - ICCK Transactions on Sensing, Communication, and Control JF - ICCK Transactions on Sensing, Communication, and Control VL - 2 IS - 2 SP - 75 EP - 84 DO - 10.62762/TSCC.2025.663633 UR - https://www.icck.org/article/abs/TSCC.2025.663633 KW - nonlinear state estimation KW - robust kalman filter KW - TLD AB - The Tuned Liquid Damper (TLD) method offers a practical and cost-effective solution for seismic design. Accurate modeling of the TLD system’s dynamic behavior is crucial for optimizing its performance. In this study, the nonlinear dynamics of the TLD system are characterized using the Housner model, with parameters estimated via a nonlinear state estimation approach. To address challenges associated with model discretization and unknown noise processes, we introduce a Robust Extended Kalman Filter (REKF) that incrementally incorporates uncertainties to more accurately capture system dynamics. The proposed method is evaluated through real-time hybrid simulation, employing seismic input signals from the El Centro and Hachinohe ground motions. Comparative analyses indicate that the robust algorithm achieves superior parameter estimation relative to conventional methods, with estimated parameters closely aligning with reference values and resulting in minimal relative error. This work underscores the efficacy of robust algorithms in TLD vibration response analysis and presents a promising approach for dynamic modeling and seismic performance optimization. SN - 3068-9287 PB - Institute of Central Computation and Knowledge LA - English ER -
@article{Su2025Parameter,
author = {Tingli Su and Yao Zhang and Zhenyun Tang},
title = {Parameter Estimation for the Tuned Liquid Damper Model Based on Robust Extended Kalman Filter},
journal = {ICCK Transactions on Sensing, Communication, and Control},
year = {2025},
volume = {2},
number = {2},
pages = {75-84},
doi = {10.62762/TSCC.2025.663633},
url = {https://www.icck.org/article/abs/TSCC.2025.663633},
abstract = {The Tuned Liquid Damper (TLD) method offers a practical and cost-effective solution for seismic design. Accurate modeling of the TLD system’s dynamic behavior is crucial for optimizing its performance. In this study, the nonlinear dynamics of the TLD system are characterized using the Housner model, with parameters estimated via a nonlinear state estimation approach. To address challenges associated with model discretization and unknown noise processes, we introduce a Robust Extended Kalman Filter (REKF) that incrementally incorporates uncertainties to more accurately capture system dynamics. The proposed method is evaluated through real-time hybrid simulation, employing seismic input signals from the El Centro and Hachinohe ground motions. Comparative analyses indicate that the robust algorithm achieves superior parameter estimation relative to conventional methods, with estimated parameters closely aligning with reference values and resulting in minimal relative error. This work underscores the efficacy of robust algorithms in TLD vibration response analysis and presents a promising approach for dynamic modeling and seismic performance optimization.},
keywords = {nonlinear state estimation, robust kalman filter, TLD},
issn = {3068-9287},
publisher = {Institute of Central Computation and Knowledge}
}
Publisher's Note
ICCK stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and Permissions
Portico