Science Inventory

Modeling of Truncated Normal Distribution for Estimating Hydraulic Parameters in Water Distribution Systems: Taking Nodal Water Demand as an Example

Citation:

Shao, Y., K. Li, T. Zhang, J. Yang, AND S. Chu. Modeling of Truncated Normal Distribution for Estimating Hydraulic Parameters in Water Distribution Systems: Taking Nodal Water Demand as an Example. Journal of Hydroinformatics. IWA Publishing, London, Uk, 25(5):2053–2068, (2023). https://doi.org/10.2166/hydro.2023.250

Impact/Purpose:

The mathematical model presented in this journal article marks meaningful progress in predicting water demand, a difficult problem in the water supply and water management field. A reliable model helps water demand forecasting, and hence lays a technical ground to plan urban adaptation using measures such as green-gray infrastructure integration in nature-based solutions.

Description:

The normal probability density function (PDF) is widely used in parameter estimation in the modeling of dynamic systems. The values of random variables that obey the normal PDF are distributed at assumed infinite intervals. However, in practice, these random variables are usually distributed in a finite region confined by the physical process and engineering practice. In this study, we address this issue through the process-informed application of truncated normal PDF. Our proposed method avoids a non-differentiable problem inherited in the truncated normal PDF at the truncation points, a limitation that can limit the use of analytical methods (e.g. Gaussian approximation). To overcome the non-differentiable problem, a data assimilation method with the derived formula is proposed to describe the probability of parameter and measurement noise in the truncated space. In application to a water distribution system (WDS), the proposed method leads to estimating the nodal water demand and hydraulic pressure key to hydraulic and water quality model simulations. Application results to a hypothetical and a large field WDS clearly show the superiority of the proposed method in parameter estimation for WDS simulations. This improvement is essential for developing real-time hydraulic and water quality simulation and process control in field applications when the parameter and measurement noise are distributed in the finite region.