Comparison of Magnetorheological Damper Models through Parametric Uncertainty Analysis Using Generalized Likelihood Uncertainty Estimation
Publication: Journal of Engineering Mechanics
Volume 147, Issue 2
Abstract
Magnetorheological (MR) dampers provide a viable alternative for vibration control of structures subjected to external excitations. Realistic modeling of MR dampers is critical for control development and structural design. Many existing phenomenological models of MR dampers are optimized from experimental observations for deterministic parameter values. However, vibration control design based on deterministic values might not provide reliable response prediction due to inherent parameter uncertainties from optimization. Parametric uncertainty analysis of damper models using laboratory experiments enables quantification of potential effect on vibration control design and evaluation. Several existing MR damper models were evaluated for their parametric uncertainties based on characterization tests of a large-scale MR damper. Markov-chain Monte Carlo (MCMC) simulation was integrated with the generalized likelihood uncertainty estimation (GLUE) method to derive the posterior distribution of model parameters. Prediction of MR damper behavior was used to illustrate the influence of model parametric uncertainties. The MR damper models were compared in terms of energy dissipation in the real-time tests with predefined displacements.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The models used herein [the algebraic model, the viscous plus Dhal model, and the simplified MNS model (Table 3)], the data in Figs. 3 and 4, and the code for Figs. 8–10 are available from the corresponding author upon reasonable request.
References
Aguirre, N., F. Ikhouane, J. Rodellar, and R. Christenson. 2012. “Parametric identification of the Dahl model for large scale MR dampers.” Struct. Control Health Monit. 19 (3): 332–347. https://doi.org/10.1002/stc.434.
Ali, S. F., and A. Ramaswamy. 2009. “Testing and modeling of MR damper and its application to SDOF systems using integral backstepping technique.” J. Dyn. Syst. Meas. Contr. 131 (2): 021009. https://doi.org/10.1115/1.3072154.
Beven, K. 1993. “Prophecy, reality and uncertainty in distributed hydrological modelling.” Adv. Water Resour. 16 (1): 41–51. https://doi.org/10.1016/0309-1708(93)90028-E.
Beven, K., and A. Binley. 1992. “The future of distributed models: Model calibration and uncertainty prediction.” Hydrol. Processes 6 (3): 279–298. https://doi.org/10.1002/hyp.3360060305.
Beven, K., J. Freer, B. Hankin, and K. Schulz. 2001. “The use of generalised likelihood measures for uncertainty estimation in high order models of environmental systems.” In Nonlinear and nonstationary signal processing, edited by W. J. Fitzgerald, R. L. Smith, A. T. Walden, and P. C. Young, 115–151. Cambridge, UK: Cambridge University Press.
Caicedo, J. M., Z. Jiang, and S. C. Baxter. 2016. “Including uncertainty in modeling the dynamic response of a large-scale 200 kN magneto-rheological damper.” ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng. 3 (2): G4016002. https://doi.org/10.1061/AJRUA6.0000873.
Camacho, R. A., J. L. Martin, W. McAnally, J. Díaz-Ramirez, H. Rodriguez, P. Sucsy, and S. Zhang. 2015. “A comparison of Bayesian methods for uncertainty analysis in hydraulic and hydrodynamic modeling.” J. Am. Water Resour. Assoc. 51 (5): 1372–1393. https://doi.org/10.1111/1752-1688.12319.
Chae, Y., J. M. Ricles, and R. Sause. 2013a. “Modeling of a large-scale magneto-rheological damper for seismic hazard mitigation. Part I: Passive mode.” Earthquake Eng. Struct. Dyn. 42 (5): 669–685. https://doi.org/10.1002/eqe.2237.
Chae, Y., J. M. Ricles, and R. Sause. 2013b. “Modeling of a large-scale magneto-rheological damper for seismic hazard mitigation. Part II: Semi-active mode.” Earthquake Eng. Struct. Dyn. 42 (5): 687–703. https://doi.org/10.1002/eqe.2236.
Chen, C., J. M. Ricles, T. L. Karavasilis, Y. Chae, and R. Sause. 2012. “Evaluation of a real-time hybrid simulation system for performance evaluation of structures with rate dependent devices subjected to seismic loading.” Eng. Struct. 35 (Feb): 71–82. https://doi.org/10.1016/j.engstruct.2011.10.006.
Choi, S.-B., S.-K. Lee, and Y.-P. Park. 2001. “A hysteresis model for the field-dependent damping force of a magnetorheological damper.” J. Sound Vib. 245 (2): 375–383. https://doi.org/10.1006/jsvi.2000.3539.
Christenson, R., Y. Zhonglin, A. Emmons, and B. Bass. 2008. “Large-scale experimental verification of semiactive control through real-time hybrid simulation.” J. Struct. Eng. 134 (4): 522–534. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:4(522).
Constantinou, M. C., T. T. Soong, and G. F. Dargush. 2001. Passive energy dissipation systems for structural design and retrofit. Buffalo, NY: Multidisciplinary Center for Earthquake Engineering Research, State University of New York.
Dahl, P. R. 1976. “Solid friction damping of mechanical vibrations.” AIAA J. 14 (12): 1675–1682. https://doi.org/10.2514/3.61511.
Dominguez, A., R. Sedaghati, and I. Stiharu. 2006. “A new dynamic hysteresis model for magnetorheological dampers.” Smart Mater. Struct. 15 (5): 1179–1189. https://doi.org/10.1088/0964-1726/15/5/004.
Dyke, S. J., B. F. Spencer, M. K. Sain, and J. D. Carlson. 2015. “Modeling and control of magnetorheological dampers for seismic response reduction.” Smart Mater. Struct. 5 (5): 565. https://doi.org/10.1088/0964-1726/5/5/006.
Gavin, H. P. 2001. “Multi-duct ER dampers.” J. Intell. Mater. Syst. Struct. 12 (5): 353–366. https://doi.org/10.1106/8398-U3X9-DHK9-K304.
He, J., J. W. Jones, W. D. Graham, and M. D. Dukes. 2010. “Influence of likelihood function choice for estimating crop model parameters using the generalized likelihood uncertainty estimation method.” Agric. Syst. 103 (5): 256–264. https://doi.org/10.1016/j.agsy.2010.01.006.
Housner, G., L. A. Bergman, T. K. Caughey, A. G. Chassiakos, R. O. Claus, S. F. Masri, R. E. Skelton, T. T. Soong, B. F. Spencer, and J. T. Yao. 1997. “Structural control: Past, present, and future.” J. Eng. Mech. 123 (9): 897–971. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:9(897).
Ikhouane, F., and S. J. Dyke. 2007. “Modeling and identification of a shear mode magnetorheological damper.” Smart Mater. Struct. 16 (3): 605–616. https://doi.org/10.1088/0964-1726/16/3/007.
Jang, J., and A. Smyth. 2017. “Bayesian model updating of a full-scale finite element model with sensitivity-based clustering.” Struct. Control Health Monit. 24 (11): e2004. https://doi.org/10.1002/stc.2004.
Jiang, Z., and R. E. Christenson. 2012. “A fully dynamic magneto-rheological fluid damper model.” Smart Mater. Struct. 21 (6): 065002. https://doi.org/10.1088/0964-1726/21/6/065002.
Jolly, M. R., J. W. Bender, and J. D. Carlson. 1999. “Properties and applications of commercial magnetorheological fluids.” J. Intell. Mater. Syst. Struct. 10 (1): 5–13. https://doi.org/10.1177/1045389X9901000102.
Jung, H.-J., K.-M. Choi, B. F. Spencer, Jr., and I.-W. Lee. 2006. “Application of some semi-active control algorithms to a smart base-isolated building employing MR dampers.” Struct. Control Health Monit. 13 (2–3): 693–704. https://doi.org/10.1002/stc.106.
Kwok, N. M., Q. P. Ha, M. T. Nguyen, J. Li, and B. Samali. 2007. “Bouc–Wen model parameter identification for a MR fluid damper using computationally efficient GA.” ISA Trans. 46 (2): 167–179. https://doi.org/10.1016/j.isatra.2006.08.005.
Kwok, N. M., Q. P. Ha, T. H. Nguyen, J. Li, and B. Samali. 2006. “A novel hysteretic model for magnetorheological fluid dampers and parameter identification using particle swarm optimization.” Sens. Actuators, A 132 (2): 441–451. https://doi.org/10.1016/j.sna.2006.03.015.
Li, L., J. Xia, C.-Y. Xu, and V. P. Singh. 2010. “Evaluation of the subjective factors of the GLUE method and comparison with the formal Bayesian method in uncertainty assessment of hydrological models.” J. Hydrol. 390 (3–4): 210–221. https://doi.org/10.1016/j.jhydrol.2010.06.044.
Luu, M., M. D. Martinez-Rodrigo, V. Zabel, and C. Könke. 2014. “Semi-active magnetorheological dampers for reducing response of high-speed railway bridges.” Control Eng. Pract. 32 (Nov): 147–160. https://doi.org/10.1016/j.conengprac.2014.08.006.
Ma, X. Q., S. Rakheja, and C. Y. Su. 2007. “Development and relative assessments of models for characterizing the current dependent hysteresis properties of magnetorheological fluid dampers.” J. Intell. Mater. Syst. Struct. 18 (5): 487–502. https://doi.org/10.1177%2F1045389X06067118.
Muto, M., and J. L. Beck. 2008. “Bayesian updating and model class selection for hysteretic structural models using stochastic simulation.” J. Vib. Control 14 (1–2): 7–34. https://doi.org/10.1177/1077546307079400.
Peng, Y., and Z. Zhang. 2020. “Optimal MR damper–based semiactive control scheme for strengthening seismic capacity and structural reliability.” J. Eng. Mech. 146 (6): 04020045. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001768.
Preumont, A., and K. Seto. 2008. Active control of structures. New York: Wiley.
Rodríguez, A., N. Iwata, F. Ikhouane, and J. Rodellar. 2009. “Model identification of a large-scale magnetorheological fluid damper.” Smart Mater. Struct. 18 (1): 015010. https://doi.org/10.1088/0964-1726/18/1/015010.
Ruangrassamee, A., W. Srisamai, and P. Lukkunaprasit. 2006. “Response mitigation of the base isolated benchmark building by semi-active control with the viscous-plus-variable-friction damping force algorithm.” Struct. Control Health Monit. 13 (2–3): 809–822. https://doi.org/10.1002/stc.113.
Sahin, İ., T. Engin, and Ş. Çeşmeci. 2010. “Comparison of some existing parametric models for magnetorheological fluid dampers.” Smart Mater. Struct. 19 (3): 035012. https://doi.org/10.1088/0964-1726/19/3/035012.
Schoups, G., and J. A. Vrugt. 2010. “A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non-Gaussian errors.” Water Resour. Res. 46 (10): W10531. https://doi.org/10.1029/2009WR008933.
Shi, Y. 1998. “A modified particle swarm optimizer.” In Proc., IEEE ICEC Conf., 69–73. New York: IEEE.
Simoen, E., G. D. Roeck, and G. Lombaert. 2015. “Dealing with uncertainty in model updating for damage assessment: A review.” Mech. Syst. Sig. Process. 56–57 (May): 123–149. https://doi.org/10.1016/j.ymssp.2014.11.001.
Somerville, P. G., and H. K. Thio. 2011. Development of ground motion time histories for phase 2 of the FEMA/SAC steel project. Sacramento, CA: SAC Joint Venture.
Song, X., M. Ahmadian, and S. C. Ahmadian. 2005. “Modeling magnetorheological dampers with application of nonparametric approach.” J. Intell. Mater. Syst. Struct. 16 (5): 421–432. https://doi.org/10.1177/1045389X05051071.
Spencer, B. F., S. J. Dyke, M. K. Sain, and J. D. Carlson. 1997. “Phenomenological model of a magnetorheological damper.” J. Eng. Mech. 123 (3): 230–238. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:3(230).
Stanway, R., J. L. Sproston, and N. G. Stevens. 1987. “Non-linear modelling of an electro-rheological vibration damper.” J. Electrostat. 20 (2): 167–184. https://doi.org/10.1016/0304-3886(87)90056-8.
Stedinger, J. R., R. M. Vogel, S. U. Lee, and R. Batchelder. 2008. “Appraisal of the generalized likelihood uncertainty estimation (GLUE) method.” Water Resour. Res. 44 (12): W00B06. https://doi.org/10.1029/2008WR006822.
Straub, D., and I. Papaioannou. 2015. “Bayesian updating with structural reliability methods.” J. Eng. Mech. 141 (3): 04014134. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000839.
Texeira, P. C. F., N. d. S. Saad, F. A. Lara-Molina, A. A. Cavalini, Jr., and V. Steffen, Jr. 2019. “Evaluation of parametric models dedicated to a magnetorheological actuator including uncertainty and sensitivity analyses.” ASCE-ASME J. Risk Uncertainty Eng. Syst., Part B: Mech. Eng. 5 (4): 041003. https://doi.org/10.1115/1.4044039.
Tsouroukdissian, A. R., F. Ikhouane, J. Rodellar, and N. Luo. 2009. “Modelling and identification of a small-scale magnetorheological damper.” J. Intell. Mater. Syst. Struct. 20 (7): 825–835. https://doi.org/10.1177/1045389X08098440.
Vadtala, I. H., D. P. Soni, and D. G. Panchal. 2013. “Semi-active control of a benchmark building using neuro-inverse dynamics of MR damper.” Procedia Eng. 51: 45–54. https://doi.org/10.1016/j.proeng.2013.01.010.
Vrugt, J. A. 2016. “Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation.” Environ. Modell. Software 75 (Jan): 273–316. https://doi.org/10.1016/j.envsoft.2015.08.013.
Vrugt, J. A., and K. J. Beven. 2018. “Embracing equifinality with efficiency: Limits of acceptability sampling using the DREAM(LOA) algorithm.” J. Hydrol. 559 (Apr): 954–971. https://doi.org/10.1016/j.jhydrol.2018.02.026.
Wang, D. H., and W. H. Liao. 2011. “Magnetorheological fluid dampers: A review of parametric modelling.” Smart Mater. Struct. 20 (2): 023001. https://doi.org/10.1088/0964-1726/20/2/023001.
Wang, L. X., and H. Kamath. 2006. “Modelling hysteretic behaviour in magnetorheological fluids and dampers using phase-transition theory.” Smart Mater. Struct. 15 (6): 1725–1733. https://doi.org/10.1088/0964-1726/15/6/027.
Yang, G., B. F. Spencer, J. D. Carlson, and M. Sain. 2002. “Large-scale MR fluid dampers: Modeling and dynamic performance considerations.” Eng. Struct. 24 (3): 309–323. https://doi.org/10.1016/S0141-0296(01)00097-9.
Ye, L., J. Zhou, X. Zeng, J. Guo, and X. Zhang. 2014. “Multi-objective optimization for construction of prediction interval of hydrological models based on ensemble simulations.” J. Hydrol. 519 (Part A): 925–933. https://doi.org/10.1016/j.jhydrol.2014.08.026.
Ye, M., and X. Wang. 2007. “Parameter estimation of the Bouc–Wen hysteresis model using particle swarm optimization.” Smart Mater. Struct. 16 (6): 2341–2349. https://doi.org/10.1088/0964-1726/16/6/038.
Zheng, Y., and A. A. Keller. 2007. “Uncertainty assessment in watershed-scale water quality modeling and management: 1. Framework and application of generalized likelihood uncertainty estimation (GLUE) approach.” Water Resour. Res. 43 (8): W08407. https://doi.org/10.1029/2006WR005345.
Zhou, Q., S. R. K. Nielsen, and W. L. Qu. 2006. “Semi-active control of three-dimensional vibrations of an inclined sag cable with magnetorheological dampers.” J. Sound Vib. 296 (1–2): 1–22. https://doi.org/10.1016/j.jsv.2005.10.028.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 147 • Issue 2 • February 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Apr 5, 2020
Accepted: Sep 23, 2020
Published online: Nov 27, 2020
Published in print: Feb 1, 2021
Discussion open until: Apr 27, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.