DIRECT APPROXIMATION OF THE EXTREME-VALUE DISTRIBUTION OF NONHOMOGENEOUS GAUSSIAN RANDOM-FIELDS

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 critical ly important. In the case of stationary differentiable Gaussian proces ses, approximations for the distribution of the maxima using upcrossin g rates are well known. In this paper, we consider nonstationary diffe rentiable Gaussian random fields. A new technique first applied by Sun (1993) can be used to derive direct approximations for the tail proba bility. This is an alternative approach based on an expansion of the c ovariance operator and on more or less geometric concepts. The method does not rely on assumptions regarding the point process of upcrossing s. It provides directly, an asymptotic approximation for the distribut ion of the maximum of the random field.