Simulation of cross-correlated random field samples from sparse measurements using Bayesian compressive sensing

Cross-correlated random field samples (RFSs) of engineering quantities (e.g., mechanical properties of materials) are often needed for stochastic analysis of structures when cross-correlation between engineering quantities and spatial/temporal auto-correlation of each quantity are considered. Theoretically, cross-correlated RFSs may be simulated using a cross-correlated random field generator with prescribed random field parameters and cross-correlation. In engineering practice, random field parameters and cross-correlation are often unknown, and they need to be estimated from extensive measurements. When the number of measurements is sparse and limited, due to sensor failure, budget limit etc., it is challenging to accurately estimate random field parameters or properly simulate cross-correlated RFSs. This paper aims to address this challenge by developing a cross-correlated random field generator based on Bayesian compressive sampling (BCS) and Karhunen-Loève (KL) expansion. The generator proposed only requires sparse measurements as input, and provides cross-correlated RFSs with a high resolution as output. The cross-correlated RFSs are able to simultaneously characterize the cross-correlation between different quantities and the spatial/temporal auto-correlation for each quantity. The generator proposed is illustrated using numerical examples. The results show that proposed generator performs reasonably well.