Low-cost, data-efficient, on-device soft sensors for sewer flow monitoring - learning from adjacent water level sensors

Flow measurements are critical for sewer monitoring, but direct measurements with flow meters are often expensive due to high sensor costs and frequent sensor maintenance. Soft sensors that derive flow rates from water depth measurements are a more cost-effective approach; however, the training of such sensors still requires extensive direct flow measurements. In this paper, we propose on-device soft flow sensors based on water depth measurements at two adjacent manholes, rather than a single manhole, to reduce the demand for flow data for training. Three model structures, namely the Saint-Venant equations (SVE), a multilayer perceptron (MLP), and a physics-informed neural network (PINN), are used to implement soft sensors for two real-life pipes and one simulated pipe. In all cases, the SVE- and MLP-based soft sensors reliably estimate flow rates with a low computational load that can be implemented on a Raspberry Pi 5 that powers a water level sensor. In contrast, the PINN-based soft sensor failed due to its high computational demand. The SVE-based sensor requires much less flow data for training, while the MLP-based soft sensor delivers more accurate flow estimates but requires more flow data. Both sensors are robust against noise and bias associated with the water depth and flow rate measurements, suitable for real-life applications. The SVE-based sensor is preferrable when scarce flow data are available. © 2025 The Author(s)