Abstract
Real-time modeling of a water distribution system (WDS) is a critical step for the control and operation of such systems. The nodal water demand, as the most important time-varying parameter, must be estimated in real time. The computational burden of nodal water demand estimation is intensive, leading to inefficiency in the modeling of large-scale networks. The Jacobian matrix computation and Hessian matrix inversion are the main processes that dominate the computation time. To address this problem, an approach for shortening the computation time for real-time demand estimation in large-scale network is proposed. This approach allows the Jacobian matrix to be efficiently computed based on solving a system of linear equations, and a Hessian matrix inversion method based on matrix partitioning and the iterative Woodbury-Matrix-Identity Formula is proposed. The developed approach is applied to a large-scale network, in which the number of nodal water demands is 12523, and the number of measurements ranges from 10 to 2000. The results show that the time consumptions for the Jacobian computation and Hessian matrix inversion are within 465.3 ms and 1219.0 ms, respectively. The time consumption is significantly shortened compared with the existing approach, especially for nodal water demand estimation in large-scale WDSs.
Highlights
The hydraulic models of the water distribution system (WDS) have been widely used in the analysis and operation of such systems (Chu et al 2020;Moasheri and Jalili-Ghazizadeh 2019)
Comparing with the method provided by Chu et al (2021b), the developed method provides a more flexible means to select the appropriate number of measurement groups (NG) to balance time consumptions of inverse operation of matrix S and other matrix operations, and obtains a significant improvement when dealing with sensor-dense networks
The algorithm for the Jacobian matrix needs to allocate a large amount of memory to store matrix W, and CPU is more suitable to process the parallel algorithm for Jacobian matrix computation
Summary
The hydraulic models of the water distribution system (WDS) have been widely used in the analysis and operation of such systems (Chu et al 2020;Moasheri and Jalili-Ghazizadeh 2019). The sensors distributed in the WDS network usually upload measurements at a regular time interval, typically 5-15minutes in China, and these data are used for the nodal water demand estimation. The computational burden of demand estimation is intensive, and the time consumption grows exponentially as the number of network nodes increase (Chu et al 2021b). This leads to the inefficiency of the existing approach when estimating the nodal water demand in the large-scale network. There is an urgent need to address inefficiency problems for real-time nodal water demand estimation in the large-scale network
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