Numerical Meshless Method in Conjunction with Bayesian Theorem for Electrical Tomography of Concrete

Abstract

Electric potential measurement technique (tomography) was introduced as a nondestructive method to evaluate concrete properties and durability. In this study, numerical meshless method was developed to solve a differential equation which simulates electric potential distribution for concrete with inclusion in two dimensions. Therefore, concrete samples with iron block inclusion in different locations were cast. Then, via a pair of electrodes attached to the samples, DC current was injected into concrete and electric potential was measured through 14 electrodes placed in the perimeter of the samples. In total, 35 different pair electrode configurations were planned for current injection. Bayesian theorem was employed to perform probabilistic tomography as well as to calculate the optimal shape coefficient in the numerical meshless method. Results of this study indicated that shape coefficient in multiquadratic radial-based function (MQ-RBF) model does significantly depend on boundary conditions. Furthermore, when the main current line is long, distribution of random variables <em>c</em> and <strong><em>e</em></strong> fits well with normal distribution, which is in agreement with the study assumption. Also, results reveal that probabilistic tomography is more precise than deterministic tomography even without using <em>prior</em> functions. Experimental results showed that MQ-RBF model has good performance in electrical tomography. This is due to uncertainty of concrete physical properties in real conditions which can be resolved by meshless method using optimization of shape coefficient.<strong><em><br /></em></strong>