Predictors Generation by Partial Least Square Regression for microwave characterization of dielectric materials
Sadou, H. and Hacib, T. and Le Bihan, Y. and Meyer, O. and Acikgoz, H.
In this paper, the microwave characterization of dielectric materials using open-ended coaxial line probe is proposed. The measuring cell is a coaxial waveguide terminated by a dielectric sample. The study consists in extracting the real and imaginary part of the relative dielectric permittivity (epsilon = epsilon'-j `') of the material under test from the measurements of the probe admittance (Y-mes(f) = G(mes)(f) + jB(mes)(f)) on a broad band frequency If between 1 MHz and 1.8 GHz), hence a dirrect and inverse problems have to be solved. In order to build a database, the direct problem is solved using Finite Elements Method (FEM) for the probe admittance (Y(f) = G(f) + jB(f)). Concerning the inverse problem, Partial Least Square (PLS) Regression (PLSR) is investigated as a fast, simple and accurate inversion tool. It is a dimensionality reduction method which aims to model the relationship between the matrix of independent variables (predictors) X and the matrix of dependant variables (response) Y. The purpose of PLS is to find the Latent Variables (LV) having the higher ability of prediction by projecting original predictors into a new space of reduced dimension. The original inverse model has only three predictors (f, G and B) but is nonlinear, so inspired by the extended X bloc method, more predictors have been created mathematically from the original ones (for example: 1/f(2), B/f(2), GB, 1/B, G/f, f(2)G, fG(2)B, f(2)G(2)B(2), ... etc) in order to take into account the nonlinearity, whence the appellation Predictors Generation Partial Least Square Regression (PG-PLSR). Inversion results of experimental measurements for liquid (ethanol, water) and solid (PEEK (Polyether-ether-ketone)) samples have proved the applicability and efficiency of PG-PLSR in microwave characterization. Moreover, the comparison study in the last section has proved the superiority of PG-PLSR on Multi-Layer Perceptron Neural Network (MTP-NN) in terms of rapidity, simplicity and accuracy.... Show more Show less