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

• Published in: Mechanical systems and signal processing Vol. 153; p. 107377
• Main Authors: He, Jingran, Chen, Jianbing, Ren, Xiaodan, Li, Jie
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 15.05.2021; Elsevier BV
• Subjects: Bayesian analysis; Bayesian compressive sensing; Concrete; Concrete properties; Concrete structures; Covariance; Cyclic loads; Failure modes; Fields (mathematics); Harmonic functions; Nonlinear analysis; Probability theory; Random field; Randomness; Reinforced concrete; Shear walls; Statistical analysis; Statistical methods; Stochastic harmonic function; Stochastic processes; Superhigh frequencies; Synthesis; Uncertainty; Random field; Bayesian compressive sensing; Concrete structures; Nonlinear analysis; Stochastic harmonic function
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2020.107377

•A new two-term stochastic harmonic function representation of random fields;•A novel Bayesian compressive sensing – stochastic harmonic function approach;•The approach capable of random field quantification based on spatially sparse data;•Effectiveness verified by both theoretically generated and field observed data;•Spatial variation affects greatly the failure modes of concrete shear wall. 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.