Assessing the observability of demand pattern multipliers in water distribution systems using algebraic and numerical derivatives

The estimation of user demands in water distribution systems is usually based on flow and pressure measurements in the system. Even when the number of measurements is larger than or equal to the number of unknowns, the system may not be observable; i.e., not all unknown variables can be estimated. Common estimation methods (e.g., the weighted least-square error) do not automatically identify an unobservable system and may provide unreliable results. This paper builds on the algebraic approach recently proposed, where the unknown variables considered were the nodal heads, and modifies the approach in order to estimate the demand multipliers of the demand patterns. A comparison between algebraic and finite difference derivatives is also presented and shows that finite differences cannot be used to assess the observability of the system.