Detection and Characterization of Multiple Discontinuities in Cables with Time-Domain Reflectometry and Convolutional Neural Networks

In this paper, a convolutional neural network for the detection and characterization of impedance discontinuity points in cables is presented. The neural network analyzes time-domain reflectometry signals and produces a set of estimated discontinuity points, each of them characterized by a class describing the type of discontinuity, a position, and a value quantifying the entity of the impedance discontinuity. The neural network was trained using a great number of simulated signals, obtained with a transmission line simulator. The transmission line model used in simulations was calibrated using data obtained from stepped-frequency waveform reflectometry measurements, following a novel procedure presented in the paper. After the training process, the neural network model was tested on both simulated signals and measured signals, and its detection and accuracy performances were assessed. In experimental tests, where the discontinuity points were capacitive faults, the proposed method was able to correctly identify 100% of the discontinuity points, and to estimate their position and entity with a root-mean-squared error of 13 cm and 14 pF, respectively.

Analytical Solutions for Side-branch Impedance Producing Spatial Localization of Acoustic Waves in Ducts with Varying Cross Sections

Analytical mathematical models and solutions for spatial localization of acoustic waves through an impedance discontinuity produced by an intermediate damped side branch are studied in stationary media in ducts with varying cross sections. Three specific geometries, namely, with polynomial, sinusoidal, and exponential longitudinal variations, are investigated. The sound fields inside the ducts are modeled by Webster's horn equation. Traveling-wave solutions are obtained by appropriate transformations. The side-branch impedances required for spatial localization (confinement) of traveling and standing waves are found analytically and verified numerically using three-dimensional finite element analysis. The impact of the longitudinal variation of the duct's cross-sectional area (CSA) on the side-branch impedance is examined. It was found that the required side-branch resistance changes more than the reactance with the variation of the duct CSA. A measure of a traveling wave is defined to quantitatively examine the spatial localization of acoustic waves. It was found that the CSA corrections on the side-branch impedances are important. The results of this study reveal the quantitative relationships between the side-branch impedance and the CSA variations for zero reflection from the impedance discontinuity. The mathematical approach presented is potentially helpful for a design of a full anechoic termination and energy localization in duct systems.

Separation of Traveling and Standing Waves in a Rigid-Walled Circular Duct Containing an Intermediate Impedance Discontinuity

In this paper, we study the phenomenon of separation of traveling and standing waves in a one-dimensional rigid-walled circular duct. The underlying mechanism for separation, mode complexity, is linear and introduced here by a damped side branch representing an impedance discontinuity. The left end of the duct is driven at a single frequency by a harmonic acoustic source, and the right end is a rigid termination. The position and impedance of the side branch are independent parameters in the analysis. Sufficient conditions for acoustic wave separation in the duct are derived analytically and employed in a three-dimensional finite element analysis to verify the theoretical result. A physical experiment, consisting of a circular duct with a damped side branch, was constructed based on analytical predictions, the physical parameters were measured or identified, and its performance was documented. These experimental parameters were employed in a second three-dimensional finite element analysis to obtain a direct comparison with experimental results. The comparison reveals the extent to which higher-order (unmodeled) effects degrade the separation phenomenon. It is demonstrated that an intermediate damped side branch used as a nonresonant device can be predictively designed to achieve nearly ideal separation of traveling and standing waves in a rigid-walled circular duct in order to direct and control acoustic energy transmission through the duct system.