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

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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.

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Acknowledgements

The work described in this paper was supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project Nos. CityU 11225216 and T22-603/15N). The financial supports are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China

    Yue Hu & Yu Wang

  2. School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an, China

    Tengyuan Zhao

  3. Department of Civil Engineering, The University of Hong Kong, Pokfulam, Hong Kong SAR, China

    Clarence Choi

  4. Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, China

    Charles W. W. Ng

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  1. Yue Hu
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  2. Tengyuan Zhao
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  5. Charles W. W. Ng
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Correspondence to Yu Wang.

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Hu, Y., Zhao, T., Wang, Y. et al. Direct simulation of two-dimensional isotropic or anisotropic random field from sparse measurement using Bayesian compressive sampling. Stoch Environ Res Risk Assess 33, 1477–1496 (2019). https://doi.org/10.1007/s00477-019-01718-7

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