Reliability Analysis In High Dimensions

Adhikari, S.
Ninth ASCE EMD/SEI/GI/AD Joint Speciality Conference on Probabilistic Mechanics and Structural Reliability, Albuquerque, New Mexico, USA, July 26-28, 2004.

In the reliability analysis of a complex engineering structure a very large number of the system parameters can be considered to be random variables. The difficulty in computing the failure probability using the First and Second-Order Reliability Methods (FORM and SORM) increases rapidly with the number of variables or `dimension'. There are mainly two reasons behind this. The first is the increase in computational time with the increase in the number of random variables. In principle this problem can be handled with superior computational tools [see Schuëller et al (2003)]. The second, which is perhaps more fundamental, is that there are some conceptual difficulties associated typically with high dimensions. This means that even one manages to carry out the necessary computations, the application of existing FORM and SORM may still lead to incorrect results in high dimensions. This issue has received little attention in the literature and this paper is aimed at addressing it. An asymptotic approximation for the case when the number of random variables n ® ¥ is provided. The new asymptotic SORM is based on parabolic approximation of the failure surface in the transformed standard Gaussian space. A simple closed-form asymptotic expression is derived. The proposed asymptotic approximation for n ® ¥ case is compared with existing approximations and Monte-Carlo simulations using numerical examples.

References

[1]

G. I. Schuëller, H. J. Pradlwarter, and P. S. Koutsourelakis. A comparative study of reliability estimation procedures for high dimensions using FE analysis. In G. Turkiyyah, editor, Electronic Proceedings of the 16th ASCE Engineering Mechanics Conference, Seattle, USA, 2003.

@INPROCEEDINGS{cp10,
    AUTHOR={S. Adhikari},
    TITLE={Reliability analysis in high dimensions},
    BOOKTITLE={Ninth ASCE EMD/SEI/GI/AD Joint Speciality Conference on Probabilistic Mechanics and Structural Reliability},
    YEAR={2004},
    Address={Albuquerque, New Mexico, USA},
    Month={July},
    Note={}
}