Two-stage optimization method for the simultaneous calibration of pipe roughness coefficients and nodal demands for water distribution networks

This paper presents a two-stage optimization framework for the simultaneous calibration of pipe roughness coefficients and nodal demands in water distribution networks (WDNs). Traditional calibration methods, such as iterative optimization algorithm and sequential data assimilation have limitations. Iterative optimization algorithm can adjust parameters within prior ranges but ignore historical data, while sequential data assimilation incorporates historical information but doesn’ t restrict parameters to their prior ranges. To address these issues, based on the principle of complementary advantages, we propose combining the Cubature Kalman Filter (CKF) from sequential data assimilation with the Levenberg‒Marquardt (LM) algorithm in iterative optimization. In the first stage, CKF estimates the parameters while accounting for historical data and system uncertainties, and its results are used as both empirical values for the objective function of the LM algorithm and its initial iterative values. In the second stage, the LM algorithm iteratively fine-tunes the CKF results within the prior ranges, improving the calibration accuracy. The proposed method was tested on a complex looped network, demonstrating superior calibration accuracy compared to using either method alone. The results show that this two-stage approach effectively integrates prior knowledge and historical data, leading to more accurate and realistic parameter calibration.