A Decision Analytic Approach for Inspecting Leaking Hydraulic Distribution Systems that Relies on Bayesian Updating of Limited Information

When a liquid distribution system, particularly Hydraulic Distribution Systems, composed of several sections, experiences a leak, limited prior knowledge is available regarding which section is leaking. Longer sections have a higher likelihood of leaking, whereas larger fractures tend to occur in sections with greater diameter and higher pressure. This study proposes a procedure to update this information based on a gross observation of the leak size. The goal is to support strategic planning of leak detection by accounting for the time required to inspect each section.

The procedure employs a Decision Analysis approach to the problem, utilizing simulation and a basic hydraulic model. The available information is classified into “a priori” (available before the leak appears) and “a posteriori” (a Bayesian update of the a priori information after observing the flow rate at the end of the system). The data is used in decision trees that select the inspection sequence, minimizing the expected value of the total volume of lost fluid.

A three-section hydraulic distribution system is analyzed numerically in a case study. When based on a priori information, the recommended review sequences begin with longer and higher-pressure sections. In contrast, when based on updated information, high-pressure sections are reviewed first if the leak is believed to be significant, while low-pressure ones are favored when the leak appears to be minor. Generally, the procedure recommends reviewing the first sections that can be checked swiftly.

As the results are consistent with expectations for the system behavior, the procedure successfully leverages the available information and observations. As the presented approach uses a basic hydraulic model, it can be readily used by engineers without extensive computational resources.

A Decision Analytic perspective can be used to leverage available knowledge and modelling tools, whether the former is scarce or the latter basic, to improve leak detection in a multi-section hydraulic system, accounting for the time required to review each section.