Parameter Sensitivity and Importance Measures in Nonlinear Finite Element Reliability Analysis
Publication: Journal of Engineering Mechanics
Volume 131, Issue 10
Abstract
Finite element reliability methods allow the analyst to define material, load, and geometry parameters as random variables to represent uncertainties in these model parameters. Approximate probabilistic analysis methods produce estimates of the response variance/covariances, probabilities of exceeding specified structural performance thresholds, and parameter importance measures. A necessary ingredient for such analysis is consistent, efficient, and accurate algorithms for computing finite element response sensitivities. In this paper, unified response sensitivity equations with respect to material, load, and geometry parameters are developed for the time- and space-discretized finite element model. The sensitivities with respect to nodal coordinates and global shape parameters in the presence of material and geometric nonlinearities represent an extension of previous work. Practical computer implementation issues are emphasized. The equations are implemented in the comprehensive, open-source, object-oriented finite element software OpenSees. Importance measures from reliability analysis, employing the sensitivity results, are presented to enable the investigation of the relative importance of uncertainty in the parameters of a finite element model. Two example applications demonstrate that the variability in nodal coordinates of a structure can be a significant source of uncertainty along with that in key material and load parameters.
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Acknowledgments
This work is primarily supported by the Pacific Earthquake Engineering Research (PEER) Center through the Earthquake Engineering Research Centers Program of the National Science Foundation under Award No. NSFEEC-9701568. This support is gratefully acknowledged. The first writer would also like to thank The Research Council of Norway for a 3 year doctoral fellowship.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 131 • Issue 10 • October 2005
Pages: 1013 - 1026
Copyright
© 2005 ASCE.
History
Received: Jan 29, 2004
Accepted: Nov 22, 2004
Published online: Oct 1, 2005
Published in print: Oct 2005
Notes
Note. Associate Editor: Gerhart I. Schueller
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