Real-time estimation of states and unknown boundary conditions in pressurized pipeline systems

Accurate estimation of boundary conditions in pressurized pipelines is essential for effective monitoring, control, and fault detection. However, boundary variables such as unmeasured demands and unknown pressure heads are often unavailable, introducing uncertainty into hydraulic models. This study presents a real-time observer-based framework for joint estimation of system states and unknown boundary inputs. The approach employs the Elastic Water Column Model (EWCM) to derive a linear time-invariant (LTI) representation compatible with observer design. Because the system does not satisfy the observer matching condition, auxiliary outputs are generated to transform it into a matched form. These outputs are first estimated using a High-Gain Observer (HGO) and then incorporated into a Sliding Mode Observer (SMO) for reconstructing both states and boundary conditions. The framework is validated through two numerical case studies and laboratory experiments involving transient pipeline flows. Results demonstrate accurate real-time estimation of unknown boundary conditions using only internal pressure data. Compared with batch-based methods such as Expectation–Maximization and Weighted Least Squares, the proposed observer-based strategy provides a computationally efficient and real-time alternative for hydraulic system monitoring.