Assessment of Uncertainty Propagation in the Dynamic Response of Single-Degree-of-Freedom Structures Using Reachability Analysis
Publication: Journal of Engineering Mechanics
Volume 140, Issue 6
Abstract
A novel method to compute the bounds of the response of structures to dynamic loads, including earthquakes, is presented. This method, based on reachability analysis, deterministically predicts the sets of states an elastic structural system can reach under uncertain dynamic excitation starting from uncertain initial conditions, where deterministic uncertainty ranges describe uncertainties. Ellipsoidal approximations of these reachable sets for three canonical dynamic problems are presented to demonstrate the applicability of this method to single-degree-of-freedom (SDOF) systems. The principle of superposition is formulated as a concatenation of ellipsoidal reachable sets using their semigroup properties. Using this extension, computation of the external (worst-case) ellipsoidal approximation of reachable sets for a SDOF system under earthquake excitation is presented. Possible applications of this method for software validation and hybrid simulation are discussed.
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Acknowledgments
The authors thank Dr. Alexander A. Kurzhanskiy for his useful conversations about ellipsoidal techniques for reachability analysis. They are also grateful to the anonymous reviewers of this article for their valuable comments. Funding for this work was provided in part by the National Science Foundation (NSF) through the George E. Brown Jr. Network for Earthquake Engineering Simulation (NEES) nees@berkeley Equipment Site capability enhancement project and by the Pacific Earthquake Engineering Research (PEER) Center. Any opinions, findings, and conclusions or recommendations expressed in this article are those of the authors and do not necessarily reflect those of the funding agencies.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 6 • June 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Feb 28, 2012
Accepted: May 29, 2013
Published online: Jun 1, 2013
Published in print: Jun 1, 2014
Discussion open until: Jul 3, 2014
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