<p>Optimized sensor placement in Water Distribution Networks (WDNs) is fundamental for effective risk assessment and leakage management. However, identifying the minimal sensor subset capable of reconstructing the system’s state under stochastic demand variability presents a complex combinatorial challenge. Specifically, selecting graph nodes that maximize spectral orthogonality (Maximum Orthogonality Subset Selection Problem) is NP-hard, while standard Principal Component Analysis heuristics suffer from bias toward densely clustered variance in the signal space. To address these limitations, a novel stochastic signal processing framework is proposed: Iterative Principal Component Analysis and HyperCone Exclusion (IPHCE). This method integrates Graph Fourier Transform with a geometric pruning heuristic to robustly select sensors that capture the maximum spectral energy of the pressure field. The WDN interactions are modeled by using a weighted graph based on Mutual Information, allowing the algorithm to capture nonlinear stochastic dependencies beyond physical topology. The approach was validated on a benchmark dataset comprising 500 publicly available stochastic scenarios of the Hanoi WDN, incorporating significant parametric uncertainty and Gaussian noise. Results demonstrate that the IPHCE method is highly robust: utilizing a nominal hydraulic model and only two optimized sensors, the system achieved a leaky and non-leaky scenario detection accuracy of 88.40%, comparable to the 92.80% obtained with full observability. This methodology offers a rigorous, mathematically grounded solution for reducing monitoring costs while maintaining high reliability in uncertain environmental systems.</p>