Parameter Estimation in Water‐Distribution Systems by Least Squares

Abstract
The weighted‐least‐squares method using sensitivity‐analysis technique is proposed for the estimation of parameters in water‐distribution systems. The parameters considered are the Hazen‐Williams coefficients for the pipes. The objective function used is the sum of the weighted squares of the differences between the computed and the observed values of the variables. The weighted‐least‐squares method can elegantly handle multiple loading conditions with mixed types of measurements such as heads and consumptions, different sets and number of measurements for each loading condition, and modifications in the network configuration due to inclusion or exclusion of some pipes affected by valve operations in each loading condition. Uncertainty in parameter estimates can also be obtained. The method is applied for the estimation of parameters in a metropolitan urban water‐distribution system in India.