Reliability-Based Performance Objectives and Probabilistic Robustness in Structural Control Applications
Publication: Journal of Engineering Mechanics
Volume 134, Issue 4
Abstract
A reliability-based structural control design approach is presented that optimizes a control system explicitly to minimize the probability of structural failure. Failure is interpreted as the system’s state trajectory exiting a safe region within a given time duration. This safe region is bounded by hyperplanes in the system state space, each of them corresponding to an important response quantity. An efficient approximation is discussed for the analytical evaluation of this probability, and for its optimization through feedback control. This analytical approximation facilitates theoretical discussions regarding the characteristics of reliability-optimal controllers. Versions of the controller design are described for the case using a nominal model of the system, as well as for the case with uncertain model parameters. For the latter case, knowledge about the relative plausibility of the different possible values of the uncertain parameters is quantified through the use of probability distributions on the uncertain parameter space. The influence of the excitation time duration on feedback control design is discussed and a probabilistic treatment of this time duration is suggested. The relationship to (i.e., minimum variance) controller synthesis is also examined.
Get full access to this article
View all available purchase options and get full access to this article.
References
Au, S. K., and Beck, J. L. (2001). “First-excursion probabilities for linear systems by very efficient importance sampling.” Probab. Eng. Mech., 16, 193–207.
Au, S. K., Papadimitriou, C., and Beck, J. L. (1999). “Reliability of uncertain dynamical systems with multiple design points.” Struct. Safety, 21, 113–133.
Dullerud, G. E., and Paganini, F. (1999). A course in robust control theory, Springer, New York.
Field, R. V., and Bergman, L. A. (1998). “Reliability-based approach to linear covariance control design.” J. Eng. Mech., 124(2), 193–199.
Genz, A. (1992). “Numerical computation of multivariate normal probabilities.” J. Comput. Graph. Stat., 1, 141–149.
Johnson, R. A., and Wichern, D. W. (2002). Applied multivariate statistical analysis, Prentice-Hall, Upper Saddle River, N.J.
Lutes, L. D., and Sarkani, S. (1997). Stochastic analysis of structural and mechanical vibrations, Prentice-Hall, Upper Saddle River, N.J.
May, B., and Beck, J. L. (1998). “Probabilistic control for the active mass driver benchmark structural model.” Earthquake Eng. Struct. Dyn., 27(11), 1331–1346.
Papadimitriou, C., Beck, J. L., and Katafygiotis, L. S. (1997a). “Asymptotic expansions for reliabilities and moments of uncertain dynamic systems.” J. Eng. Mech., 123(12), 1219–1229.
Papadimitriou, C., Beck, J. L., and Katafygiotis, L. S. (2001). “Updating robust reliability using structural test data.” Probab. Eng. Mech., 16, 103–113.
Papadimitriou, C., Katafygiotis, L. S., and Au, S. K. (1997b). “Effects of structural uncertainties on TMD design: A reliability based approach.” J. Struct. Control, 4(1), 65–88.
Scruggs, J. T., Taflanidis, A. A., and Beck, J. L. (2006). “Reliability-based control optimization for active base isolation systems.” J. Struct. Control and Health Monitoring, 13, 705–723.
Skelton, R. E., Iwasaki, T., and Grigoriadis, K. (1997). A unified algebraic approach to control design, Taylor & Francis Inc., Bristol, Pa.
Spall, J. C. (2003). Introduction to stochastic search and optimization, Wiley-Interscience, New York.
Spencer, B. F., Jr., Sain, M. K., Won, C.-H., Kaspari, D. C., and Sain, P. M. (1994). “Reliability-based measures of structural control robustness.” Struct. Safety, 15, 111–129.
Stengel, R., Ray, L., and Marrison, C. (1995). “Probabilistic evaluation of control-system robustness.” Int. J. Syst. Sci., 26(7), 1363–1382.
Syrmos, V. L., Abdallah, C. T., and Dorato, P. (1997). “Static output feedback—A survey.” Automatica, 33(2), 125–137.
Taflanidis, A. A., and Beck, J. L. (2005). “Analytical approximation for stationary reliability calculation of linear dynamic systems.” EERL Rep. No. 2005-3, California Institute of Technology, Pasadena, Calif.
Taflanidis, A. A., and Beck, J. L. (2006). “Analytical approximation for stationary reliability of certain and uncertain linear dynamic systems with higher dimensional output.” Earthquake Eng. Struct. Dyn., 35, 1247–1267.
Taflanidis, A. A., Beck, J. L., and Angelides, D. C. (2007). “Robust reliability-based design of liquid column mass dampers under earthquake excitation using an analytical reliability approximation.” Eng. Struct., 29(12), 3525–3529.
Yuen, K., and Beck, J. (2003). “Reliability-based robust control for uncertain dynamical systems using feedback of incomplete noisy response measurements.” Earthquake Eng. Struct. Dyn., 32(5), 751–770.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 134 • Issue 4 • April 2008
Pages: 291 - 301
Copyright
© 2008 ASCE.
History
Received: Sep 27, 2006
Accepted: Jun 18, 2007
Published online: Apr 1, 2008
Published in print: Apr 2008
Notes
Note. Associate Editor: Erik A. Johnson
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.