A patching algorithm for conditional random fields in modeling material properties

Abstract

The random field theory is often utilized to characterize the inherent spatial variability of material properties. In order to incorporate sampled data from site investigations or experiments into simulations, a patching algorithm is developed to yield a conditional random field in this study. Comparison is conducted between the proposed algorithm and the conventional Kriging algorithm to underscore the former’s advantages in simulating material properties with limited sampled data. Unlike the Kriging algorithm that interpolates the entire spatial domain, the proposed algorithm restricts the influence domain of sampled data within a reasonable range, which is determined as a function of the scale of fluctuation. The simulated conditional random field via the proposed algorithm is stationary in mean and variance; thus, it would be preferable for situations with a few known data. Additionally, a tunnel excavation model is considered to exemplify the effectiveness of the proposed algorithm. By virtue of Monte-Carlo simulations, maximum tunnel convergence modeled by unconditional and conditional random fields is analyzed in a statistical manner. The results indicate that the proposed algorithm can effectively reduce the uncertainty of prediction in responses. Furthermore, the proposed algorithm is also applicable with a sparse sampling pattern.