Pressure sensor placement in water distribution networks for leak detection using a hybrid information-entropy approach

Highlights

• Optimal pressure sensor placement in water distribution system ensures secure provision.

• Value of Information (VOI) can be used for accurate and robust placement of sensors.

• VOI enhances the decision space and enables exploring the entire feasible space.

• Transinformation Entropy (TE) minimizes redundant information from multiple sensors.

• VOI and TE together ensure optimal, effective and efficient search of decision spectra.

Abstract

This study proposes an optimization framework based on a hybrid information-entropy approach to identify leakage events in water distribution networks (WDN). Optimization-based methods are widely employed in the literature for such purposes; however, they are constrained by time-consuming procedures. Hence, researchers eliminate parts of the decision space to curtail the computational burden. Here, we propose an information theory-based approach, using Value of Information (VOI) and Transinformation Entropy (TE) methods, in conjunction with an optimization model to explore the entire decision space. VOI allows for the entire feasible space search through intelligent sampling, which in turn ensures robust solutions. TE minimizes redundant information and helps maximize the spatial distribution of sensors. The herein proposed model is developed within a multi-objective optimization framework that renders a set of Pareto-optimal solutions. ELimination and Choice Expressing the REality (ELECTRE) multi-criteria decision-making model is then used to select the best compromise solution given several weighting scenarios. The results of this study show that the information-entropy based scheme can improve the precision of leak detection by enhancing the decision space, and can reduce the computational burden.

Introduction

Increasing water demand and warming of the climate collectively reduced available water resources [5] and put an unprecedented toll on the water supply systems around the globe. Reduction of water loss in water distribution networks (WDNs) is, hence, of particular importance among water managers in this era of water shortage [32]. Leakage is the main cause of water loss in WDNs [10], which prompts pressure drop in the pipelines and in turn provokes consumer discontent. Leak detection is, therefore, of particular significance in any WDN. Accurate and well-timed leakage monitoring and detection prevent infrastructure failure, reduce lost revenue and avert excessive energy waste, and help maintain the provision of clean water to consumers.

The exact identification of the quantity and location of leakage in WDNs requires costly detection instruments, such as Permalog acoustic devices [32]. While such highly accurate leak detection instruments are available in the market, the lower cost of installation and maintenance of pressure sensors and their acceptable measurement accuracy made them the most widely selected choice. Electronic pressure sensor devices usually use a silicon strain gauge whose resistance changes as pressure is applied to its surface. They use an integrated circuit to modify a reference signal based on the changes in the resistance of the strain gauge [6]. They are designed to measure pressure in different mediums such as liquids and gases, while providing high accuracy at a few decipascals level. The difference between pressure sensors’ measurements and expected pressure values – obtained from simulation – can be attributed to leakage [31], [32]. It is obviously ideal to install sensors at each joint of WDNs; however, the WDN sizes make deployment and maintenance of sensors at all joints unfeasible. Hence, computational frameworks are used to optimize the deployment of sensors in WDNs.

Researchers have developed various computational frameworks to detect leakage in WDNs and provide an optimum sensor deployment layout when only a limited number of sensors is feasible (e.g., [28], [31]). Recent approaches use multi-objective optimization methods coupled with numerical models [31], [32], which are focused on minimization of leak detection time and number of sensors [12], [31], [32]. Spatial coverage and mutual information are two important factors to consider when placing sensors, as they collectively play a key role in reducing time to leak detection and detection costs in WDNs. These aspects, however, were not fully explored in previous studies. Determining a set of representative pressure sensors that provide maximum information with minimum number of sensors is an effective strategy to reduce costs, as it warrants sufficient spatial coverage and maximum information [16], [17], [30]. The concept of Value of Information (VOI) is applied herein to identify a set of pressure sensor placements (nodes) that renders maximum information, as the first step for leak detection. The VOI concept has been applied in several areas of water science, including design of pollution warning systems in agricultural routine and WDNs [16], [34], design of groundwater quality monitoring systems (e. g. [15]), flood monitoring (e. g. [1], [2]), and reservoir water quality assessment [21]. However, to the best of the authors knowledge, VOI has not been explored for leak detection and pressure sensor placement in WDNs.

Different sensor layouts, even with a similar number of sensors and VOI, may yield different levels of redundancy (i.e. non-unique information). Hence, redundant information from monitoring stations should be minimized for optimal design to ensure maximum spatial coverage is provided by minimum number of sensors. Information redundancy of a given pair of sensors has a negative correlation with their spatial distance in a WDN. Therefore, minimizing information redundancy maximizes spatial distribution, and consequently, coverage of monitoring stations. Transinformation Entropy (TE) is one of the most potent methods to decrease mutual information between each pair of potential stations [30]. This method has been used in various branches of water science such as designing quality monitoring networks in reservoirs [29], rivers (e. g. [19], [22]), and groundwater [20], [23], [24]; however, TE has not been used for leakage identification and placement of pressure sensors in a WDN.

Recently, a hybrid VOI-TE methodology has been proposed to maximize the reliability of sensor-provided information and minimize their redundancy in contamination warning systems for WDNs. This approach was also used to design monitoring networks of reservoir water quality [16], [30]. The superior results of this methodology proved its efficacy and efficiency in the setting employed. However, the coupled VOI-TE approach has not been explored in the literature for leak detection in WDNs. In this study, an information-entropy based framework using VOI and TE approaches is developed to for optimal and effective sensor placement in WDNs. The literature has been mainly focused on optimization approaches, which – although being efficient – are associated with some weaknesses and shortcomings. Optimization approaches use multiple scenarios of simulated leakage events in an optimization framework to achieve the optimal layout of sensors for various objectives. However, due to the large size of simulations, exploring the entire decision spectra, i.e., all possible locations for installing pressure sensors, is associated with a prohibitive computational cost. Hence, eliminating parts of the decision space (i.e., all nodes proper for sensor placement) and determining pre-selected nodes as potential locations for placement of sensors is inevitable in these methods (e.g., [12], [31], [32]). This undermines the robustness of the obtained results.

Through the hybrid VOI-TE method proposed in this study, the simulation scenarios of leakage events are translated into a set of informatic curves. The optimum layout of sensors is accordingly determined by the set of curves with maximum union area AND minimum intersection area. Here, the term “optimum” refers to the objectives used as information metrics for defining the informatic curves. This approach significantly reduces the computational cost of the optimization framework and consequently allows for searching the entire decision spectra. The novelty of the proposed approach not only lies in the application of information theory in leak detection, but also in how it reduces the computational cost and improves the accuracy of leak detection of optimization-based methods. In this framework, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was used to maximize VOI and minimize TE, which collectively maximize coverage of sensors and minimize the number of pressure sensors. Efficacy of the proposed methodology was examined in the C-Town WDN.