TDR Inversion for Water Localization and Uncertainty Evaluation

This work presents the application of a Time-Domain Reflectometry (TDR) inversion algorithm for localizing water along a bi-wire cable acting as a distributed sensing element (SE), and for evaluating the uncertainty of the water position measurement. The TDR inversion relies on a simplified yet effective gray-box circuital model of the measurement system that, without attempting a full-wave electromagnetic (EM) simulation, reproduces with good accuracy any actually observed reflectograms. The model parameters are estimated from a single acquired reflectogram so as to reproduce the measured signal, without a prior EM characterization of the system components. The model provides the water localization and enables extensive simulation campaigns under realistic variations in water position, stimulus pulse duration, and disturbance effects. A specific measurement setup, designed to perform repeated measurements in controlled laboratory conditions, is analyzed in detail as a case study. The water localization error of the measurement system is statistically evaluated in terms of confidence intervals, bias, and standard deviation, by means of simulated measurements of the model, with different water positions and TDR pulse durations. Then, the uncertainty evaluation is validated through 45 actual measurements, using multiple SEs, and the same water positions and pulse durations. The work proves the viability and the performance of the presented TDR inversion method for both localization measurements and for their uncertainty evaluation under different experimental conditions. More generally, it establishes a general framework for TDR measurements and uncertainty evaluation combining physical modeling, simulation-based uncertainty evaluation, and experimental verification.