Time domain reflectometry imaging - A new moisture measurement technique for industry and soil science

Abstract

This thesis describes the theoretical and practical aspects of a new technique for quantitative, non-invasive and non-destructive imaging of the near-surface moisture content distribution of composite materials. The technique relies on the alteration by a nearby composite material, of the propagation velocity of an electromagnetic pulse along a parallel transmission line, through distortion of the evanescent field. A set of measurements taken at different relative positions of the transmission line and composite material are, in conjunction with a forward model describing propagation velocity on the line, inverted to provide the image of moisture content distribution. Development of the technique, called 'Time Domain Reflectometry Imaging' (TDRI), involved four steps:

1. Instrumentation to obtain a set of measurements of propagation times; 2. A forward model; 3. An inverse procedure; and 4. Conversion of a calculated permittivity distribution to a moisture distribution.

Critical to the success of the inverse method is a set of measurements of propagation velocity that provide pico-second propagation time accuracy, and are sufficiently linearly independent to enable discrimination of the permittivity of each discretised cell within the composite material. Using commercial time domain reflectometry (TDR) instruments, a switched reference measurement, waveform subtraction and intersecting waveform tangents, sufficient timing accuracy has been achieved.

The forward model was developed using the moment method. The advantage of such an integral equation method is that recalculation is not required when changing the impressed field. Hence for a particular model of the composite material's moisture distribution, just one execution of the forward model provides predicted propagation velocities for all positions of the transmission line. A new pseudo 3-D variant of the volume integral equation approach was developed to suit the 2-D transmission line, and resulted in a 100 fold reduction in memory use, and a greater than 10 fold reduction in execution time. The forward solution uses the telegrapher's equation to predict propagation velocity from an arbitrary permittivity distribution surrounding the line.

Inversion of the measured data was accelerated by the use of three novel tactics: a rapid electric field surrogate for the Jacobian; a dynamic method of determining the conjugate gradient weighting factor; and a new blocking technique that accelerated the convergence of buried cells that have only a small influence on propagation velocity.

The final TDRI step is a numerical model to translate both the a priori moisture distribution data to a permittivity distribution, and conversely the solution permittivity distribution to moisture content. A dielectric model based on an earlier model of Looyenga was adapted to include both the different characteristic of tightly held water, and the Debye relaxation of free water. The intention was a model with applicability to a range of composite materials. It was tested with data for soil, bentonite clay and wood, and except for one free parameter, model parameters were set by measurable physical properties of the host material.