Non-parametric construction of site-specific non-Gaussian multivariate joint probability distribution from sparse measurements

Abstract

Construction of a joint probability distribution for correlated geotechnical properties is often needed in geotechnical reliability-based analysis and design. Geotechnical properties vary across sites and follow site-specific and non-Gaussian probability distribution, because of different geological processes that soils and rocks in different sites have undergone. In addition, site-specific measurements on geotechnical properties are usually sparse and correlated in geotechnical practice, leading to the difficulty in estimation of meaningful joint probability distribution when using conventional parametric statistical methods. To address this issue, this paper develops a non-parametric and data-driven approach for characterizing the site-specific non-Gaussian multivariate joint probability distribution without pre-selection of the marginal probability distribution type. Two key components for constructing a multivariate joint probability distribution (i.e., marginal probability distribution for each variable and correlation matrix for all variables) are estimated separately using Bayesian Gaussian mixture and Bayesian compressive sampling (BCS) and Karhunen-Loève (KL) expansion. The proposed method is illustrated using both simulated and real data in geotechnical site investigation. The results show that the proposed method performs well for both examples. The proposed method does not model spatial variability explicitly but is based on the assumption of independent measurement data along depth, and thus measurement records are required to be sufficiently spaced apart in depth (e.g., more than 1 scale of fluctuation) to satisfy this assumption.