Non-parametric simulation of non-stationary non-gaussian 3D random field samples directly from sparse measurements using signal decomposition and Markov Chain Monte Carlo (MCMC) simulation

Abstract

With the ever-growing computational power of personal computers over the past few decades, stochastic simulation of spatially varying three-dimensional (3D) quantities has been coupled with numerical analysis models (e.g., 3D finite element model) to consider explicitly the influence of spatial variability of engineering quantities when carrying out design or analysis for mechanical systems and civil- or geo-structures. Random field theory is often adopted in stochastic simulations, where random field samples (RFSs) are generated for representing the spatially varying engineering quantities encountered in practice. Nevertheless, simulation of 3D RFSs is not trivial, especially when measurements are sparse and limited, a case often encountered in engineering practice of a specific project. This is because random field parameters (e.g., the type of auto-correlation structure, correlation length, marginal probability distribution) are difficult to determine when measurements from a project are sparse and limited. The problem becomes more challenging when the quantity of interest is non-stationary and/or non-Gaussian. This renders a great challenge for proper simulation of non-stationary non-Gaussian 3D RFSs from sparse measurements. To address this challenge, this paper proposes a method which integrates the concept of signal decomposition in digital signal processing with Markov Chain Monte Carlo (MCMC) simulation. The proposed method is non-parametric and data-driven. It takes sparse measurements and their corresponding 3D spatial coordinates as input and returns many high-resolution non-stationary non-Gaussian 3D RFSs as output. The method is illustrated using a series of numerical examples. The results show that the proposed method performs reasonably well.