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This paper describes a non-invasive method for detecting leaks in buried pipes, which uses a surface linear electrode array perpendicular to the axis of the pipe. Two electrodes inject current and the remaining electrodes detect the drop in voltage on the ground surface using both the dipole-dipole array and a modified Schlumberger array. A single-step reconstruction algorithm based on the sensitivity theorem yields two-dimensional images of the cross section. A personal computer controls current injection, electrode switching and voltage detection, which allows us to easily test various arrays of electrodes and speed up the process of measurement. The system was first tested in the laboratory using a stainless steel tube immersed in water and covered by a rubber sleeve to simulate a non-conductive leak. By taking reference measurements with the immersed bare pipe, it is possible to reconstruct images showing the simulated leak using only 16 electrodes and even as few as eight electrodes, albeit with reduced resolution. Field measurements have involved simulated leaks of water from a plastic tube 1 m long and 8 cm in radius buried at a depth of about 24 cm in a farm field. The hardware system injected 1 kHz, 20 V peak-to-valley square waveforms, thus avoiding electrode polarization effects. The simulated leak was unmistakably distinguished.

Abstract-This paper proposes and analyses a microcontroller-based interface circuit for inductive sensors with a variable self-inductance. Besides the microcontroller (µC) and the sensor, the circuit just requires an external resistor and a reference inductor so that two RL circuits are formed. The µC appropriately excites such RL circuits in order to measure the discharging time of the voltage across each inductor (i.e. sensing and reference) and then it uses such discharging times to estimate the sensor inductance. Experimental tests using different commercial µCs at different clock frequencies show the limitations (especially, due to parasitic resistances and quantisation) and the performance of the proposed circuit when measuring inductances in the millihenry range. A non-linearity error lower than 0.3% FullScale Span (FSS) and a resolution of 10 bits are achieved, which are remarkable values considering the simplicity of the circuit.

Measurement devices and instruments must be calibrated after manufacture to correct for component and assembly tolerances, and periodically to correct for drift and aging effects. The number of reference inputs needed for calibration depends on the actual transfer characteristic and the desired accuracy. Often, a linear characteristic is assumed for simplicity, either for the overall input range (global linearization) or for successive input subranges (piecewise linearization). Thus, only two reference inputs are needed for each straight line. This two-point static calibration can be easily implemented in any system having some basic computation capability and allows for the correction of zero and gain errors, and of their drifts if the system is periodically calibrated. Often, the reference inputs for that calibration are the end values of the measurement range (or subrange). However, this is not always the optimal selection because the calibration error is minimal for those reference inputs only, which are not necessarily the most relevant inputs for the system being considered. This article proposes three optimization criteria for the selection of calibration points: limiting the maximal error (LME), minimizing the integral square error (ISE), and minimizing the integral absolute error (IAE). Each of these criteria needs reference inputs whose values are symmetrical with respect to the midrange input (xc), have the form xc±Δx/(2√n) when the measurand has a uniform probability distribution function, Δx being the measurement span, and do not depend on the nonlinearity of the actual response, provided this is quadratic. The factor n depends on the particular criterion selected: n=2 for LME, n=3 for ISE, and n=4 for IAE. These three criteria give parallel calibration lines and can also be applied to other nonlinear responses by dividing the measurement span into convenient intervals. The application of those criteria to the linearization of a type-J thermocouple illustrate their performance and advantages with respect to the customary end-point linearization (n=1) even for nonquadratic responses. For quadratic responses, n=1 yields the maximal error at the center of the input measurement range.

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