Translation random field with marginal beta distribution in modeling material properties

• Unbiased and consistent estimators for bounds of a beta distribution are proposed.
• The proposed estimators are more efficient than the method of moments.
• Scale of fluctuation in a beta random field can be preserved.
• Non-iterative algorithm to determine the autocorrelation function of an underlying Gaussian field.

For modeling material properties having a bounded range, the beta distribution may be adopted as the marginal distribution of a second-order non-Gaussian random field. Three aspects related to the simulation of such random field are discussed in this study. First, an unbiased and consistent estimator for the lower (and upper) bound of the beta distribution based on sample data is proposed. This estimator is shown to be generally more efficient than that given by the method of moments. Second, a simple explicit function relating the auto-correlation function of the non-Gaussian random field to that of the underlying Gaussian field is proposed. The relationship facilitates control on the scale of fluctuation of the non-Gaussian field. Third, an algorithm is proposed for generating random fields with an approximate marginal beta distribution and a prescribed cross-correlation, where the latter can range from −1 to 1. Numerical examples are given to illustrate the effectiveness and efficiency of each of the three aspects. The estimation of the lower bound of material property is exemplified through field data from a real project.