Continuous score-based optimization of pressure sensor placement for burst detection in water distribution networks

Pipe bursts in water distribution networks (WDNs) can cause substantial water loss and service disruption, making reliable pressure monitoring essential. However, existing event-driven methods for optimal pressure sensor placement (OSP) commonly rely on a single predefined detection threshold to distinguish burst-induced pressure residuals from background noise. This can lead to unstable optimization outcomes, multiple equivalent layouts, and degraded performance under varying noise conditions. To address these limitations, this study proposes a continuous score-based placement optimization (CSPO) method. Compared with commonly used threshold-based binary placement optimization (TBPO), CSPO uses a sigmoid function to map pressure residuals to continuous scores and optimizes the continuous detection score (CDS). This preserves hydraulic response magnitudes and provides a more discriminative objective for sensor placement. Results from the Hanoi and C-Town networks show that CSPO produces more stable and consistent layouts than TBPO while requiring fewer simulated burst events. It also reduces solution multiplicity and yields a single Pareto-optimal layout for each sensor count, providing a clearer basis for deployment decisions. Under cross-evaluation across multiple background noise conditions, CSPO maintains robust performance, with the mean relative performance index generally above 0.98 and the coefficient of variation below 0.02. Further results from L-Town, with pressure data and an expert-guided reference layout, show that CSPO provides a more balanced layout than the TBPO variants across threshold-based detection standards. Overall, CSPO provides a robust and practical method for pressure sensor placement, supporting the design of reliable and effective monitoring systems in WDNs.