Tunnels are increasingly used worldwide to expand the capacity of urban drainage systems, but they are difficult to monitor with sensors alone. This study enables soft sensing of urban drainage tunnels by assimilating water level observations into an ensemble of hydrodynamic models. Ensemble-based data assimilation is suitable for non-linear models and provides useful uncertainty estimates. To limit the computational cost, our proposed scheme restricts the assimilation and ensemble implementation to the tunnel and represents the surrounding drainage system deterministically. We applied the scheme to a combined sewer overflow tunnel in Copenhagen, Denmark, with two sensors 3.4 km apart. The downstream observations were assimilated, while those upstream were used for validation. The scheme was tuned using a high-intensity event and validated with a low-intensity one. In a third event, the scheme was able to provide soft sensing as well as identify errors in the upstream sensor with high confidence.

隧道在世界范围内越来越多地用于扩大城市排水系统的容量，但仅凭传感器很难对其进行监控。这项研究通过将水位观测值整合为一组水动力模型，从而实现了城市排水隧道的软传感。基于集合的数据同化适用于非线性模型，并提供有用的不确定性估计。为了限制计算成本，我们提出的方案将同化和集成实施限制在隧道内，并确定性地表示周围的排水系统。我们将该方案应用于丹麦哥本哈根的一个下水道联合下水道隧道，两个相距3.4 km的传感器。下游观察被同化，而上游观察被用于验证。该方案使用高强度事件进行了调整，并使用低强度事件进行了验证。在第三事件中，该方案能够提供软感测并以高置信度识别上游传感器中的错误。