Hybrid CNN-LSTM Model with Distance-Based Loss Function for Leak Localization in Water Distribution Networks

Water loss in distribution networks represents a critical challenge in urban water management, with significant environmental, economic, and public health implications. Although previous studies developed both leak detection and localization approaches, detection has been prioritized. This paper presents a hybrid deep-learning approach for leakage localization with a proposed loss function that minimizes the distance between predicted and actual leak locations in water distribution networks. A hybrid CNN-LSTM model was developed, combining a Convolutional Neural Network (CNN) for spatial feature extraction across the sensor array and a Long Short-Term Memory (LSTM) network for sequence modeling. In addition, a distance-based loss function was designed to optimize both classification accuracy and the physical distance between predicted and actual leak localizations. The algorithm was validated using the L-Town water distribution network benchmark. Results demonstrate that incorporating network distance into training improves localization accuracy compared to a standard cross-entropy loss. Average localization errors of 181 m for background leakages and 58 m for bursts were achieved with the distance-based loss function approach. These results represent an improvement of about 32% for both leak types relative to the standard loss function. The contribution of this paper is two-fold: first, the accuracy of leakage localization is improved through a hybrid CNN-LSTM model trained with a distance-based loss function; second, the search area for leak localization is reduced, as incorporating network distance into training minimizes the physical distance between predicted and actual leak locations. This reduction in search area translates directly to decreased inspection time and costs for water utilities.