A new perspective on the simulation of cross-correlated random fields. (May 2022)

• Record Type: Journal Article
• Authors: Dai, Hongzhe; Zhang, Ruijing; Beer, Michael
• Is Part Of: Structural safety. Volume 96(2022)
• Publication Date: 2022-05
• Subjects: Cross-correlation -- Random field simulation -- Finite element discretization -- Dimension reduction -- Non-Gaussian; Structural stability -- Periodicals; Safety factor in engineering -- Periodicals; Reliability (Engineering) -- Periodicals; Constructions -- Stabilité -- Périodiques; Coefficient de sécurité en ingénierie -- Périodiques; Fiabilité -- Périodiques; 620.86
• DOI: 10.1016/j.strusafe.2022.102201
• Languages: English
• ISSNs: 0167-4730

Abstract

Highlights: A unified framework for simulating cross-correlated random fields with arbitrary correlation structure is established. The developed method is conceptually simple and computationally efficient. The method is further generalized to a consistent framework for the simulation of multi-dimensional random fields. Five examples illustrate the effectiveness of the developed method. Abstract: Cross-correlated random fields are widely used to model multiple uncertain parameters and/or phenomena with inherent spatial/temporal variability in numerous engineering systems. The effective representation of such fields is therefore the key element in the stochastic simulation, reliability analysis and safety assessment of engineering problems with mutual correlations. However, the simulation of such fields is generally not straightforward given the complexity of correlation structure. In this paper, we develop a unified framework for simulating non-Gaussian and non-stationary cross-correlated random fields that have been specified by their correlation structure and marginal cumulative distribution functions. Our method firstly represents the cross-correlated random fields by means of a new general stochastic expansion, in which the fields are expanded in terms of a set of deterministic functions with corresponding random variables. A finite element discretization scheme is then developed to further approximate the fields, so that the sets of deterministic functions reflecting the cross-covariance structure can be straightforwardly determined from the spectral decomposition of the resulting discretized fields. For non-Gaussian random fields, an iterative mapping procedure is developed to generate random variables to fit non-Gaussian marginal distribution of the fields. By virtue of the remarkable property of the presented stochastic expansion, i.e., various random fields share an identical set of random variables, the framework we develop is conceptually simple for simulating non-Gaussian cross-correlated fields with arbitrary covariance functions, which need not be stationary. In particular, the developed method is further generalized to a consistent framework for the simulation of multi-dimensional random fields. Five illustrative examples, including a spatially varying non-Gaussian and nonstationary seismic ground motions, are used to demonstrate the application of the developed method.