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Analytical reliability calculation of linear dynamical systems in higher dimensions

Taflanidis, A. A. and Beck, J. L. (2005) Analytical reliability calculation of linear dynamical systems in higher dimensions. In: Structural Dynamics: EURODYN 2005. Millpress , Rotterdam, Netherlands, pp. 723-728. ISBN 90-5966-033-1 http://resolver.caltech.edu/CaltechAUTHORS:20110815-134109019

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Abstract

The recent application of reliability analysis to controller synthesis has created the need for a computationally efficient method for the estimation of the first excursion probabilities for linear dynamical systems in higher dimensions. Simulation methods cannot provide an adequate solution to this specific application, which involves numerical optimization of the system reliability with respect to the controller parameters, because the total computational time needed is still prohibitive. Instead, an analytical approach is presented in this paper. The problem reduces to the calculation of the conditional upcrossing rate at each surface of the failure boundary. The correlation between upcrossings of the failure surface for the different failure events may be addressed by the introduction of a multi-dimensional integral. An efficient algorithm is adopted for the numerical calculation of this integral. Also, the problem of approximation of the conditional upcrossing rate is discussed. For the latter there is no known theoretical solution. Three of the semi-empirical corrections that have been proposed previously for scalar processes are compared and it is shown that the correction should be based on the bandwidth characteristics of the system. Finally, examples that verify the validity of the analytical approximations for systems in higher dimensions are discussed.


Item Type:Book Section
Additional Information:© 2005 Millpress. The authors would like to thank Dr Jeffrey Scruggs and Judith Mitrani-Reiser, both at Caltech, for helpful comments on the manuscript.
Record Number:CaltechAUTHORS:20110815-134109019
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20110815-134109019
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24861
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Sep 2011 14:55
Last Modified:26 Dec 2012 13:28

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