Direct simulation of two-dimensional isotropic or anisotropic random field from sparse measurement using Bayesian compressive sampling

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

20 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)1477–1496
Journal / PublicationStochastic Environmental Research and Risk Assessment
Volume33
Issue number8-9
Online published24 Aug 2019
Publication statusPublished - Sep 2019

Abstract

Random field theory has been increasingly adopted to simulate spatially varying environmental properties and hydrogeological data in recent years. In a two-dimensional (2D) stochastic analysis, variation of the environmental properties or hydrogeological data along different directions can be similar (i.e., isotropic) or quite different (i.e., anisotropic). To model the spatially isotropic or anisotropic variability in a stochastic analysis, conventional random field generators generally require a vast amount of measurement data to identify the random field parameters (e.g., mean, variance, and correlation structure and correlation length in different directions). However, measurement data available in practice are usually sparse and limited. The random field parameters estimated from sparse measurements might be unreliable, and the subsequent random field modeling or stochastic analysis might be misleading. This underscores the significance and challenge of generating 2D isotropic or anisotropic random fields from sparse measurements. This paper develops a novel 2D random field generator, which does not require a parametric form of correlation function or estimation of correlation length and other random field parameters, and directly generates 2D isotropic or anisotropic random field samples from sparse measurements. The proposed generator is highly efficient because simulation of a 2D random field is achieved by generation of a short 1D random vector. The effectiveness and applicability of the proposed generator are illustrated using isotropic and anisotropic numerical examples.

Research Area(s)

  • Anisotropy, Compressive sensing, Karhunen–Loève expansion, Spatial data

Citation Format(s)

Direct simulation of two-dimensional isotropic or anisotropic random field from sparse measurement using Bayesian compressive sampling. / Hu, Yue; Zhao, Tengyuan; Wang, Yu; Choi, Clarence; Ng, Charles W. W.

In: Stochastic Environmental Research and Risk Assessment, Vol. 33, No. 8-9, 09.2019, p. 1477–1496.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review