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Risk and Reliability Analysis: Theory and Applications pp 277–302Cite as

FORM Sensitivities to Distribution Parameters with the Nataf Transformation

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Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

Abstract

The Nataf transformation has been proven very useful in reliability assessment when marginal distributions are statistically known and linear correlation is sufficient for modeling the dependence between random inputs. Under the assumption that the use of FORM is appropriate for the problem of interest, it is often of importance to quantify how the FORM solution is sensitive to the distribution parameters of the random inputs. Such information can be exploited in different contexts including optimal design under uncertainty. This chapter describes how sensitivities to marginal distribution parameters and linear correlation can be assessed numerically in the context of FORM based on the Nataf transformation. The emphasis is on the accuracy of such sensitivities with no other approximations than the one due to numerical integration. In the presented examples, the accuracy of these sensitivities is assessed w.r.t. reference solutions. The sensitivity to correlation brings useful information which are complementary to those w.r.t. marginal distribution parameters. High sensitivities may be detected such as illustrated in the context of stochastic crack growth based on the Virkler data set.

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Acknowledgements

I wish to express my deep gratitude to Prof. Armen Der Kiureghian who has played an important role in the course of my career. His high-quality scientific work has been and still is a great source of inspiration in my research.

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Authors and Affiliations

  1. Université Clermont Auvergne, CNRS, SIGMA Clermont, Institut Pascal, F-63000, Clermont Ferrand, France

    Jean-Marc Bourinet

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  1. Jean-Marc Bourinet
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Correspondence to Jean-Marc Bourinet .

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Editors and Affiliations

  1. Civil and Environmental Engineering, 3118 Newmark Civil Engineering Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

    Paolo Gardoni

Appendix: Determination of \(\mathbf{L}_0\) and \({\partial \mathbf{L}_0}/{\partial \rho _{ij}}\)

Appendix: Determination of \(\mathbf{L}_0\) and \({\partial \mathbf{L}_0}/{\partial \rho _{ij}}\)

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Bourinet, JM. (2017). FORM Sensitivities to Distribution Parameters with the Nataf Transformation. In: Gardoni, P. (eds) Risk and Reliability Analysis: Theory and Applications. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-52425-2_12

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  • DOI: https://doi.org/10.1007/978-3-319-52425-2_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52424-5

  • Online ISBN: 978-3-319-52425-2

  • eBook Packages: EngineeringEngineering (R0)

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