Modified linear estimation method for generating multi-dimensional multi-variate Gaussian field in modelling material properties

Abstract

Although a number of methods have been developed to generate random fields, it remains a challenge to efficiently generate a large, multi-dimensional, multi-variate property field. For such problems, the widely used spectral representation method tends to require relatively longer computing time. In this paper, a modified linear estimation method is proposed, which involves mapping the linearly estimated field through a series of randomized translations and rotations from one realization to the next. These randomized translations and rotations enable the simulated property field to be stationary. The autocorrelation function of the simulated fields can be approximately described by a squared exponential function. The algorithms of the proposed method in both the rectangular and cylindrical polar coordinate systems are demonstrated and the results validated by Monte-Carlo simulations. Comparisons between the proposed method and spectral representation method show that the results from both methods are in good agreement, as long as the cut-off wave numbers of the spectral representation method are sufficiently large. However, the proposed method requires much less computational time than the spectral representation method. This makes it potentially useful for generating large multi-dimensional fields in random finite element analysis. Applications of the proposed method are exemplified in both rectangular and cylindrical polar coordinate systems.