Hybrid Simulation with Improved Operator-Splitting Integration Using Experimental Tangent Stiffness Matrix Estimation
Publication: Journal of Structural Engineering
Volume 134, Issue 12
Abstract
Improved numerical integration procedures are essential for the extension of hybrid numerical and experimental simulation to large and complex structural systems. While implicit integration algorithms are widely used in pure numerical simulations for their superior stability and accuracy, their direct application to hybrid simulation has been partially limited by difficulties in estimating the tangent stiffness matrix of multi-degree-of-freedom experimental substructures. Current applications of hybrid simulation using integrators with improved stability have mostly resorted to methods that are noniterative or utilize the initial stiffness matrix for iterative corrections. To improve the accuracy of integration procedures for hybrid simulation, a new method for online estimation of experimental tangent stiffness is proposed. The stiffness estimation procedure is tailored for fast online applications by transforming the measurements into a coordinate system, which reduces the number of unknown stiffness coefficients that need to be updated during the simulation. The updated experimental stiffness matrix is used in a modified operator-splitting integration scheme to improve the accuracy of hybrid simulations with highly nonlinear experimental substructures. The application and effectiveness of the proposed approach is demonstrated through hybrid simulations with multi-degree-of-freedom experimental substructures.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was partially supported by National Science Foundation Grant No. CMS-0402490 for development of hybrid testing capabilities through NEES maintenance, operations, and management task. Their support is gratefully acknowledged.
References
Ahmadizadeh, M. (2007). “Real-time seismic hybrid simulation procedures for reliable structural performance testing.” Ph.D. dissertation, Dept. of Civil, Structural and Environmental Engineering, Univ. at Buffalo, Buffalo, N.Y.
Ahmadizadeh, M., Mosqueda, G., and Reinhorn, A. M. (2007). “Compensation of actuator delay and dynamics for real-time hybrid structural simulation.” Earthquake Eng. Struct. Dyn., 37(1), 21–42.
Bayer, V., Dorka, U. E., Fullekrug, U., and Gschwilm, J. (2005). “On real-time pseudodynamic substructure testing: Algorithm, numerical, and experimental results.” Aerosp. Sci. Technol., 9(3), 223–232.
Bouc, R. (1967). “Forced vibration of mechanical systems with hysteresis.” Proc., 4th Conf. on Nonlinear Oscillations, Prague, Czechoslovakia.
Broyden, C. G. (1965). “A class of methods for solving nonlinear simultaneous equations.” Math. Comput., 19(92), 577–593.
Carrion, J. E., and Spencer, B. F. (2006). “Real-time hybrid testing using model-based delay compensation.” Proc., 4th Int. Conf. on Earthquake Engineering, Taipei, Taiwan.
Chang, S. Y. (2001). “Application of the momentum equations of motion to pseudo-dynamic testing.” Philos. Trans. R. Soc. London, Ser. A, 359(1786), 1801–1827.
Chang, S. Y., and Sung, Y. C. (2006). “An enhanced explicit pseudodynamic algorithm with unconditional stability.” Proc., 8th National Conf. on Earthquake Engineering, San Francisco.
Chen, C., and Ricles, J. M. (2006). “Effective force testing method using virtual mass for real-time earthquake simulation.” Proc., 8th National Conf. on Earthquake Engineering, San Francisco.
Dimig, J., Shield, C., French, C., Bailey, F., and Clark, A. (1999). “Effective force testing: A method of seismic simulation for structural testing.” J. Struct. Eng., 125(9), 1028–1037.
Filiatrault, A., Leger, P., and Tinawi, R. (1994). “On the computation of seismic energy in inelastic structures.” Eng. Struct., 16(6), 425–436.
Ghaboussi, J., Yun, G. J., and Hashash, Y. M. A. (2006). “A novel predictor–corrector algorithm for substructure pseudodynamic testing.” Earthquake Eng. Struct. Dyn., 35(4), 453–476.
Hilber, H. M., Hughes, T. J. R., and Taylor, R. L. (1977). “Improved numerical dissipation for time integration algorithms in structural dynamics.” Earthquake Eng. Struct. Dyn., 5(3), 283–292.
Igarashi, A., Seible, F., and Hegemeier, G. A. (1993). “Development of a pseudodynamic technique for testing a full-scale five-story shear wall structure.” Proc., Japan Seminar on the Development and Future Directions of Structural Testing Techniques, Japan.
Jung, R. Y., Shing, P. S. B., Stauffer, E., and Thoen, B. K. (2007). “Performance of a real-time pseudodynamic test system considering nonlinear structural response.” Earthquake Eng. Struct. Dyn., 36(2), 1785–1809.
Mahin, S. A., and Shing, P. S. B. (1985). “Pseudodynamic method for seismic testing.” J. Struct. Eng., 111(7), 1482–1503.
Mahin, S. A., Shing, P. S. B., Thewalt, C. R., and Hanson, R. D. (1989). “Pseudodynamic test method—Current status and future directions.” J. Struct. Eng., 115(8), 2113–2128.
The MathWorks (MathWorks). (2007). Simulink—Simulation and model-based design, The MathWorks, Natick, Mass.
McGuire, W., Gallagher, R. H., and Ziemian, R. D. (2000). Matrix structural analysis, Wiley, New York.
Mosqueda, G., and Ahmadizadeh, M. (2007). “Combined implicit or explicit integration steps for hybrid simulation.” Earthquake Eng. Struct. Dyn., 36(15), 2325–2343.
Mosqueda, G., Stojadinovic, B., and Mahin, S. A. (2007). “Real-time error monitoring for hybrid simulation. II: Structural response modification with error.” J. Struct. Eng., 133(8), 1109–1117.
Nakashima, M. (2001). “Development, potential, and limitations of real-time online (pseudodynamic) testing.” Philos. Trans. R. Soc. London, Ser. A, 359(1786), 1851–1867.
Nakashima, M., Kaminoso, T., Ishida, M., and Kazuhiro, A. (1990). “Integration techniques for substructure online test.” Proc., 4th U.S. National Conf. of Earthquake Engineering, Palm Springs, Calif., Earthquake Engineering Research Institute, Oakland, Calif.
Pan, P., Tada, M., and Nakashima, M. (2005). “Online hybrid test by internet linkage of distributed test-analysis domains.” Earthquake Eng. Struct. Dyn., 34(11), 1407–1425.
Schneider, S. P., and Roeder, C. W. (1994). “An inelastic substructure technique for the pseudodynamic test method.” Earthquake Eng. Struct. Dyn., 23(7), 761–775.
Shao, X. (2006). “Unified control platform for real-time dynamic hybrid simulation.” Ph.D. dissertation, Dept. of Civil, Structural, and Environmental Engineering, Univ. at Buffalo, Buffalo, N.Y.
Shao, X., Reinhorn, A. M., and Sivaselvan, M. (2006). “Real-time dynamic hybrid testing using force-based substructuring.” Proc., 8th National Conf. on Earthquake Engineering, San Francisco.
Shing, P. S. B., Vannan, M. T., and Cater, E. (1991). “Implicit time integration for pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 20(6), 551–576.
Thewalt, C. R., and Mahin, S. A. (1987). “Hybrid solution techniques for generalized pseudodynamic testing.” Rep. No. UCB/EERC-87/09, Univ. of California at Berkeley, Berkeley, Calif.
Thewalt, C. R., and Roman, M. (1994). “Performance parameters for pseudodynamic tests.” J. Struct. Eng., 120(9), 2768–2781.
Wen, Y. (1976). “Method for random vibration of hysteretic systems.” J. Engrg. Mech. Div., 102(2), 249–263.
Wu, B., Xu, G., Wang, Q., and Williams, M. S. (2006). “Operator-splitting method for real-time substructure testing.” Earthquake Eng. Struct. Dyn., 35(3), 293–314.
Zhang, Y. F., Sause, R., Ricles, J. M., and Naito, C. J. (2005). “Modified predictor–corrector numerical scheme for real-time pseudodynamic tests using state–space formulation.” Earthquake Eng. Struct. Dyn., 34(3), 271–288.
Information & Authors
Information
Published In
Copyright
© 2008 ASCE.
History
Received: May 10, 2007
Accepted: Nov 1, 2007
Published online: Dec 1, 2008
Published in print: Dec 2008
Notes
Note. Associate Editor: Marvin W. Halling
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.