Uncertainty Quantification of Random Fields Based on Spatially Sparse Data by Synthesizing Bayesian Compressive Sensing and Stochastic Harmonic Function

Abstract

Spatial variation occurs widely in engineering practice and could be quantified by random fields. For instance, the strength of concrete in a large-sized shear wall might be described by a two-dimensional random field in the framework of probability theory. Therefore, how to quantify the spatial variation based on limited available observation data is of paramount importance. In the present paper, two types of engineering problems with uncertainties, i.e. those due to the incompleteness of observation and those due to hard-to-control, are firstly discussed. The Bayesian Compressive Sensing (BCS) is then introduced to estimate an enriched field based on the sparsely measured data and quantify the statistical uncertainty. Further, the Stochastic Harmonic Function (SHF) is synthesized with BCS (named as the BCS-SHF scheme) to quantify the spatially varying randomness based on very limited data to resolve the problems involving uncertainty due to hard-to-control. By the proposed method new random field samples can be generated. Through numerical examples, it is demonstrated that the proposed method can reproduce the target mean value and the covariance function with high accuracy and efficiency. Finally, the proposed BCS-SHF approach is employed to quantify the uncertainty of the random field of concrete strength, and then further applied to the stochastic response analysis of a reinforced concrete shear wall model under cyclic loading, revealing that the spatial variation will greatly affect the failure modes of the shear wall.