A direct simulation algorithm for a class of beta random fields in modelling material properties

Abstract

Numerous translation approaches have been developed to generate non-Gaussian random fields; however, non-translation or direct simulation methods are much rare. The translation approaches invoke the memoryless transformation from an underlying Gaussian random field to a target non-Gaussian random field. The correlation structure is changed by the memoryless transformation from a Gaussian to a non-Gaussian field and as a result the non-Gaussian correlation structure is obtained after amending the Gaussian correlation structure. In addition, the underlying Gaussian random field is often generated by series expansion approaches (e.g. spectral representation method), which require a sum of infinite terms. Consequently, the computational efforts involved in generating the Gaussian random fields can be significant. After considering the difficulties in simulating a translation random field, a direct approach without utilizing the memoryless transformation is proposed to generate a beta random field. Though the marginal distribution is restricted to the beta distribution, the proposed approach is simple and efficient. This would make it attractive in simulating large-scale random fields for material properties. This is exemplified with an engineering application.