Hypothesis Test for Leakage Detection in Water Pipelines with High-Dimensional Sensor Signals

We design a statistical hypothesis test for performing leak detection in water pipeline channels. By applying an appropriate model for signal propagation, we show that the detection problem becomes one of distinguishing signal from noise, with the noise being described by a multivariate Gaussian distribution with unknown covariance matrix. We present a detection method for high dimensional settings, which employs a regularized covariance matrix estimate. The regularization parameter is optimized for the leak detection application by applying results from large dimensional random matrix theory. The proposed approach is shown to yield improved performance in leak detection under high dimensional settings.