Time-domain reflectometry based multiple leak detection system using bayesian S-parameters model for pipelines

Abstract

Leaks in water distribution systems cause economic, environmental, and social problems. In order to detect leaks in pipelines, techniques have been developed based on time-domain reflectometry (TDR) combined with Bayesian inference. However, these techniques are not practical for applications involving long-distance pipelines due to the large size and significant time required to build the training sample data set required for Bayesian inference in these settings. To solve these challenges, this study proposes two approaches: (a) an S-parameter based forward model to reduce the size of sample data, and (b) an algorithm to estimate the time required to build an training sample data set. Unlike existing methods that model the voltage from both the TDR instrument and the sensing cable, the proposed S-parameter based model has only to estimate the voltage measured at only the input port of TDR instrument without considering the sensing cable. Thus, the voltage of the sensing cable is not required for modeling the TDR signal in this proposed detection system. In terms of the amount of training data required by each method, therefore, the S-parameter based model is much more efficient than existing models from a computational point of view. In addition, the algorithm proposed here to predict the time required to build the sample data allows the user to determine the feasibility of the TDR-based leak detection technique for a particular setting. To validate the proposed method, lab experiments were conducted using a pipeline, leak detectors, sensing cable, and TDR instrument. Through the experiments, the applicability of the suggested S-parameter based model in a long-distance pipeline was validated.