Wiring Diagnostics Via $\ell _1$ -Regularized Least Squares

A new method for detecting and locating wiring damage using time domain reflectometry with arbitrary input interrogation signals is presented. This method employs existing ℓ₁ regularization techniques from convex optimization and compressed sensing to exploit sparsity in the distribution of faults along the length of a wire, while further generalizing and improving commonly used fault detection techniques based on sliding correlation and peak detection. The method´s effectiveness is demonstrated using a simulated example, and it is shown how Monte Carlo techniques are used to tune it to achieve specific detection goals, like a certain false positive error rate. Furthermore, the method is easily implemented by adapting readily available optimization algorithms to quickly solve large, high resolution, versions of this estimation problem. Finally, the technique is applied to a real data set, which reveals its impressive ability to identify a subtle type of chafing damage on real wire.