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Non-parametric generation of multivariate cross-correlated random fields directly from sparse measurements using Bayesian compressive sensing and Markov chain Monte Carlo simulation

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Abstract

Simulation of multivariate cross-correlated random field samples (RFSs) is often required in reliability analysis of engineering structures. Conventional parametric methods for cross-correlated RFSs simulation generally require extensive measurements to obtain reliable random field parameters (e.g., type of auto-correlation function, correlation length, and cross-correlation matrix), for characterizing both the auto-correlation and cross-correlation structures among various cross-correlated engineering quantities. However, measurement data available in practice is often limited due to time, budget, technical and/or access constraints. Therefore, it is difficult to provide an accurate estimation of random field parameters (e.g., auto-correlation and cross-correlation matrix), rendering a challenging question of how to properly simulate multivariate cross-correlated RFSs from sparse measurements, especially when the number of engineering quantities of interest is large. This study aims to address this difficulty by developing a novel cross-correlated random field generator based on Bayesian compressive sensing (BCS) and Markov chain Monte Carlo (MCMC) simulation. The proposed method is data-driven and non-parametric, and it directly uses sparse measurements as input and provides cross-correlated RFSs as output. More importantly, the proposed method is able to deal with a large number of cross-correlated quantities for big data analytics in a high-dimension domain.

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Funding

The work described in this paper was supported by a grant from the Research Grant Council of Hong Kong Special Administrative Region (Project no. CityU 11203322), a grant from the Innovation and Technology Commission of Hong Kong Special Administrative region (Project no: MHP/099/21), and a grant from Shenzhen Science and Technology Innovation Commission (Shenzhen-Hong Kong-Macau Science and Technology Project (Category C) No: SGDX20210823104002020), China. The financial support is 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

    Peiping Li & Yu Wang

  2. State Key Laboratory of Internet of Things for Smart City, Department of Civil and Environment Engineering, University of Macau, Macau, China

    Zheng Guan

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  1. Peiping Li
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  2. Yu Wang
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Contributions

Peiping Li and Yu Wang wrote the main manuscript text and developed all figures and tables. Zheng Guan contributed the implementation of treating cross-correlation as auto-correlation and data preprocessing.

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Correspondence to Yu Wang.

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Li, P., Wang, Y. & Guan, Z. Non-parametric generation of multivariate cross-correlated random fields directly from sparse measurements using Bayesian compressive sensing and Markov chain Monte Carlo simulation. Stoch Environ Res Risk Assess 37, 4607–4628 (2023). https://doi.org/10.1007/s00477-023-02523-z

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