Dealing with nonlattice spatially variable data contaminated by white noise using Kronecker-product formulation
Journal
Computers and Geotechnics
Journal Volume
154
Date Issued
2023-02-01
Author(s)
Abstract
Gaussian random field is often used to model the spatial variability in geotechnical engineering. In order to characterize the spatial variability of a site of interest, it may be necessary to estimate the autocovariance parameters based on the site investigation data. When the site investigation data consist of multiple soundings, the computational cost for the autocovariance parameter estimation can be high. The Kronecker-product (KP) formulation is a useful tool for reducing this computational cost. However, there are two implementation limitations for the KP formulation. One is the consideration of the observation noise, and another is its implementation to nonlattice data. This paper proposes a method to overcome these two limitations while maintaining the KP formulation and the rigor of the solution. Because the proposed method provides analytical solutions, the computed results are in full agreement with those without the KP formula. For the observation noise, the eigen-decomposition of the autocovariance matrix is adopted. For nonlattice data, they are linked to lattice data by subtracting/adding data points from/to lattice data, and the block matrix inversion is used to derive the KP formulation. The reduction of the computational cost due to the use of the KP formulation is confirmed via numerical simulations.
Subjects
Computational cost | Kronecker product | Random field | Spatial variability
Publisher
ELSEVIER SCI LTD
Type
journal article