The spatial averaging method for non-homogeneous random fields with application to reliability analysis

In probabilistic assessments, inputs with significant spatial variability should be modeled with random fields. Random fields can be non-homogeneous with location-specific marginal distributions, for example, due to site-specific information incorporated through Bayesian analysis or due to spatial trends in the mean or variance of the uncertain quantity. This paper investigates the spatial averaging method for the discretization of non-homogeneous random fields. In this approach, the random field is reduced to a set of random variables representing its local averages over a corresponding set of elemental domains. This is of particular benefit when coupling the random field model with finite elements for structural analysis. We extend the application of the method to non-homogeneous Gaussian and non-Gaussian translation random fields with lognormal, Student's t- and log-Student's t-marginal distribution. The latter two distributions are particularly relevant if spatial data is used in a hierarchical Bayesian random field modeling. Two numerical investigations assess the ability of the method to efficiently represent the response variability and probability of failure of structural systems with spatially variable inputs. The investigations include the effect of different element sizes for the spatial averaging on the system response and applicability of the spatial averaging method to assessing local and global failure modes.