Efficiency improvement of radial basis function meshless method in conjunction with bayesian theorem for electrical tomography of heterogeneous concrete

Abstract

Electric potential measurement technique (tomography) has been presented as a non-destructive method to evaluate concrete's physical properties and durability. In this study, a radial basis function (RBF) meshless method combined with the Bayesian probabilistic theorem was proposed to solve Poisson's differential equation that simulates electric potential distribution for heterogeneous concrete with inclusion in 2D. Thus, prior information about shape coefficient (c) and electrical conductivity could contribute to problem-solving, leading to an accurate high-speed tomography. Two types of concrete mixes with significant differences in electrical conductivity were used to create heterogeneity in concrete. For this purpose, concrete samples with iron block inclusion in various locations were made. Probabilistic tomography was performed using optimized c and Bayes' method. Since c plays a significant role in RBF, different validation patterns were used to optimize it. Results showed that c is highly dependent on the validation pattern, injecting pair electrode, location of inclusions, and degree of uncertainty of concrete. Deterministic and probabilistic tomography was performed to detect the iron block inclusion. The experimental results showed that using various validation patterns, the proposed hybrid method of meshless and Bayesian theorem can eliminate the substantial physical uncertainty, and tomography can be performed with appropriate accuracy.