Flexible modeling of the trend for geotechnical spatial variability by Gaussian process regression

Abstract

The spatial variation of a soil parameter is usually modeled as the summation of spatial trend and spatial variability. Traditional, the trend is assumed deterministic and is fitted by spatial data. However, previous studies showed that it is more reasonable to model the trend as uncertain rather than deterministic. This paper proposes a probabilistic model that is based on the Gaussian process regression (GPR). In this model, the spatial trend is represented as a stationary normal random field with an auto-correlation function modeled by the squared exponential (QExp) model, which produces smooth random field realizations in order to mimic the trend. In contrast, the spatial variability is modeled as a stationary normal random field modeled by the Whittle-Matern (WM) model. Numerical and real examples are adopted to illustrate the effectiveness of this GPR model.