A Machine Learning-Driven Framework for Risk-Based Sensor Placement in Wastewater Collection Systems

Aging wastewater collection systems face increasing failure rates, yet most utilities lack systematic, data-driven methods for optimizing sensor deployment to monitor infrastructure risk. This study presents a six-stage computational framework that integrates GIS-based network reconstruction, machine learning-based failure probability estimation, composite risk quantification, directed graph-based hydraulic coverage modeling, submodular optimization, and Bayesian adaptive updating to determine optimal sensor placement in large-scale sewer networks. The framework was applied to a large municipal collection system comprising 33,474 nodes (manholes, pump stations, vaults, and virtual junctions) and 33,349 pipe segments (gravity and force mains). In Stage 1, the network graph was constructed from GIS shapefiles using a spatial snapping tolerance of 50 ft under a projected coordinate system (State Plane). The raw GIS data exhibited significant topological fragmentation, with 130 disconnected components and only 29.8% of nodes contained within the largest component. To address this, additional asset layers were integrated, and virtual junction nodes were algorithmically generated at pipe-to-pipe intersections lacking explicit connectivity. Following reconstruction, the largest connected component increased to 89.4% of the network, representing a 59.6 percentage point improvement. Topological validation confirmed full network integrity, including resolution of duplicate nodes and missing identifiers. This step ensures hydraulic consistency and enables reliable graph-based analysis. In Stage 2, pipe-level failure probabilities (P_i) were estimated using a Random Forest classifier (200 trees, maximum depth = 10, class-weight balanced) trained on 12 engineered features derived from asset attributes and historical condition data. These included pipe age, diameter, material encoding, slope, length, force main indicator, and failure proxies from inspection databases, maintenance records, and overflow history. The model achieved an AUC of 0.808 under stratified validation, indicating strong discriminative performance despite class imbalance. Feature importance analysis identified pipe age, inspection frequency, and pipe length as dominant predictors. The trained model generated probabilistic failure estimates for all network edges, providing a continuous risk likelihood surface. In Stage 3, a composite risk metric (R_i = P_i × S_i) was computed, where S_i represents a multi-criteria severity index incorporating asset characteristics and network criticality. For pipes, S_i integrates diameter, material vulnerability, force main status, and structural connectivity. For nodes, S_i reflects asset type, network centrality (degree), and component membership. The resulting risk distribution exhibits significant spatial heterogeneity, with concentrated high-risk corridors aligned with older infrastructure and hydraulically critical segments. This risk surface serves as the objective function for subsequent optimization. In Stage 4, a directed flow graph was constructed using pipe invert elevations to enforce gravity-driven flow directionality. Hydraulic reachability was evaluated using upstream breadth-first search (BFS) constrained by a detection threshold distance (H_d = 50 ft). Candidate sensor locations were defined at physically accessible nodes within the main connected component. Approximately 86.8% of nodes qualified as candidates, collectively providing theoretical coverage of 87.1% of edges and 93.3% of total network risk. This defines the feasible monitoring envelope and highlights structural limits imposed by network topology and elevation gradients. In Stage 5, sensor placement was formulated as a weighted maximum coverage problem and solved using a greedy submodular optimization algorithm with lazy evaluation. The objective was to maximize cumulative uncovered risk captured by K sensors. The resulting risk capture curve demonstrates clear diminishing returns consistent with submodular behavior. Early placements yield high marginal gains, with 20 sensors capturing 18.3% of total risk and 50 sensors capturing 30.2%, while 160 sensors are required to exceed 50% coverage. Even at K = 500, total coverage reaches 72%, indicating that full observability is constrained by network structure and hydraulic detectability. These results provide a quantitative basis for budget-constrained, phased deployment strategies. In Stage 6, an adaptive Bayesian updating module incorporated time-series data from existing sensors to refine failure probability estimates. Sensor anomaly scores were derived from multiple statistical indicators, and multiplicative Bayesian updating was applied to adjust P_i values for hydraulically connected upstream assets. Re-optimization results demonstrated high solution stability, with strong agreement between original and updated sensor placements. This confirms that the framework is robust while remaining responsive to new monitoring information. The proposed framework is scalable, computationally efficient, and transferable to other collection systems using commonly available GIS and asset management data. By explicitly integrating predictive modeling, network topology, and hydraulic detectability within an optimization framework, this approach provides a rigorous foundation for transitioning from reactive maintenance to proactive, risk-informed monitoring. The results further demonstrate that optimal sensor placement is jointly governed by failure likelihood, consequence severity, and network-driven observability constraints, offering utilities a defensible and quantitative strategy for intelligent sensor deployment.