Direct Approximation of the Extreme Value Distribution of Nonhomogeneous Gaussian Random Fields

[+] Author and Article Information
M. A. Maes

Department of Civil Engineering, The University of Calgary, Calgary, Alberta T2N 1N4, Canada

K. W. Breitung

Department of Structural Mechanics, University of Pavia, Pavia, Italy

J. Offshore Mech. Arct. Eng 119(4), 252-256 (Nov 01, 1997) (5 pages) doi:10.1115/1.2829104 History: Received July 01, 1996; Revised May 12, 1997; Online December 17, 2007


In many reliability problems, particularly in the area of offshore and marine safety analysis, the maxima of stochastic processes and random fields, describing random load responses and resistances, are critically important. In the case of stationary differentiable Gaussian processes, approximations for the distribution of the maxima using upcrossing rates are well known. In this paper, we consider nonstationary differentiable Gaussian random fields. A new technique first applied by Sun (1993) can be used to derive direct approximations for the tail probability. This is an alternative approach based on an expansion of the covariance operator and on more or less geometric concepts. The method does not rely on assumptions regarding the point process of upcrossings. It provides, directly, an asymptotic approximation for the distribution of the maximum of the random field.

Copyright © 1997 by The American Society of Mechanical Engineers
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