International Society for Industrial Process Tomography

Application of Electrical Tomography for Spatial Analysis
of Damp Walls Using Statistical Methods

T. Rymarczyk^1,2*, E. Kozłowski³

¹ Research & Development Centre Netrix S.A., Lublin, Poland

² University of Economics and Innovation, Lublin, Poland

³ Lublin University of Technology, Lublin, Poland

^*Email: tomasz@rymarczyk.com

ABSTRACT

The paper presents a solution for testing the moisture of walls using the statistical methods in electrical tomography. Moisture transfer in the walls of old buildings that are in direct contact with the soil, leads to migration of soluble salts in relation to many wall problems. Moisture can be pulled up under the influence of gravity (capillary effect). The main problem in studies on the moisture concentration in the walls is the lack of a method that ensures spatial distribution without the need to collect samples. The highly correlated predictors with each other’s in linear models do not allow to determine the precisely influences of these predictors on the output variable. Directly application the least square method to estimate the unknown parameters may lead to a poor prediction. The addition of penalty depending on quantities of parameters to the least square criterion allows us to determine the biased estimators but also to reduce the variance of estimators. The statistical method was used to reconstruct the image in electrical impedance tomography. This article proposes a new solution based on the Least Angle Regression method to obtain more accurate and stable reconstruction results in solving the inverse problem in electrical tomography for determining the moisture of the walls. Reconstruction of the image was also carried out using the elastic net, which is connection of two methods: ridge regression and LASSO. The combination of the proposed algorithms is effective in the simulation. This work gives promise results as a new horizon to solve practical problems. The main goal of tomography is to make an image reconstruction. The most common approach depends on reduction of set of the input variables (deleting the same predictors which involve in multicollinearity). Then, the predictor variables are selected, which will be included in the regression model.

Keywords Electrical Impedance Tomography, Inverse Problem, Statistical Methods

Industrial Application General