Using machine learning algorithms to link volumetric water content to complex dielectric permittivity in a wide (33-2000 MHz) frequency band for hydraulic concretes

This paper focuses on the development and validation of an innovative method for estimating volumetric water content in concrete mixtures. A supervised learning method (support vector machine) has been used to resolve the inverse problem, i.e., generate in-laboratory calibration curves correlating the controlled water content in various concrete mixtures with the frequency-dependent complex dielectric permittivity originating from the coaxial electromagnetic transition line. An extrapolation procedure using a frequency-power-law model has been developed and validated for estimating the complex permittivity over a broad frequency bandwidth. Implementation of this extrapolation method allows considering various physical phenomena (i.e., polarisation versus water content) that typically affect the dielectric behaviour of concrete as a function of frequency. The two-step estimation procedure (involving extrapolation and support vector regression methods) proposed in this paper has been validated on a wide array of moisture-controlled concrete specimens in the laboratory. The procedure helps building calibration curves that rely on both complex effective permittivity and volumetric water content, taking into consideration the frequency dependence.