An adaptive scheme for random field discretization using KL expansion

With the increase in computational facilities, interest in probabilistic analysis of engineering structures are observed to grow for a realistic assessment of physical systems. While the probabilistic analyses are generally carried out considering random variable models of physical parameters, a spatially varying random field model is more realistic. A discretization method converts the continuous parameter random field to a set of random variables. Truncated Karhunen–Loève (KL) expansion is one of the popular methods for the discretization of a random field. An accurate discretization can be achieved by considering a fine mesh along with a large number of terms. However, an increase in the number of elements and/or inclusion of more terms leads to an increase in computational cost. It is also found that only an increase in the number of terms in the expansion or number of elements alone does not provide an accurate representation of the random field. An adaptive discretization strategy is presented, which will suitably discretize the concerned domain while ensuring that both global and local level errors are kept within the prescribed limit.