Extended Method of Characteristics for Inverse Hydraulic Transient Modeling Using Sensor Data

Hydraulic transient modeling is a critical tool for analyzing and managing pipeline systems. However, its practical application is often hindered by the need for precise boundary conditions and uncertainties in pipeline properties, initial conditions, and measurements. To address these challenges, this paper proposed the Extended Method of Characteristics (EMOC), an inverse transient modeling that integrates observed pressure or flow data into transient models, enabling accurate reconstruction of hydraulic states without predefined boundary conditions. By leveraging additional sensor data and a marching scheme, EMOC can inversely infer the unknown boundary conditions and efficiently solve transient scenarios. The effectiveness and accuracy of the proposed method in both single pipelines and pipe network systems were validated through numerical simulations and laboratory experiments. The EMOC accurately reconstructed transient pressures and flows under various uncertainties, such as errors in initial conditions, pipe parameters, wave damping, and measurements, indicating its robustness. The successful transient reconstruction in a subnetwork system (separated from a larger pipe network) highlights EMOC’s superiority in such scenarios where conventional methods may struggle due to unknown conditions at boundaries and connections.