Direct Simulation Methods for a Class of Normal and Lognormal Random Fields with Applications in Modeling Material Properties

Abstract

Normal and lognormal random fields are commonly used in modeling material properties. Many series expansion approaches are available to generate a normal random field, whereby a lognormal random field can be transformed. However, those approaches often utilize the central limit theorem that theoretically requires a sum of infinite random terms to ensure Gaussianity and stationarity. A sum of infinite random terms is unattainable in practice. In order to circumvent a sum of infinite random terms, this study proposes straightforward and direct simulation methods for generating normal and lognormal random fields. The proposed methods utilize the additive property of normal random variables and the multiplicative property of lognormal random variables. The methods only involve generating independent and identically distributed random numbers and then conducting simple summation or multiplication operations. The autocorrelation structure of the simulated random field is derived and has conceptually simple geometric significance. The simulated random field has a monotonically decreasing autocorrelation function whose upper bound is one and lower bound is zero, which is capable of simulating the spatial variability of material properties whose autocorrelation decreases with distance. The proposed methods are computationally competitive for generating large-scale random fields, and Monte Carlo simulation can be readily implemented.