Poisson rectangular pulse (PRP) model establishment based on uncertainty analysis of urban residential water consumption patterns

Jiaxin Zhang; Dragan Savic; Qiang Xu; Kuo Liu; Zhimin Qiang

doi:10.1016/j.ese.2023.100317

Poisson rectangular pulse (PRP) model establishment based on uncertainty analysis of urban residential water consumption patterns

Environ Sci Ecotechnol. 2023 Sep 15:18:100317. doi: 10.1016/j.ese.2023.100317. eCollection 2024 Mar.

Authors

Jiaxin Zhang^{1

2}, Dragan Savic^{3

4

5}, Qiang Xu¹, Kuo Liu⁶, Zhimin Qiang^{1

2}

Affiliations

¹ Key Laboratory of Drinking Water Science and Technology, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, Beijing, 100085, China.
² University of Chinese Academy of Sciences, Beijing, 100049, China.
³ KWR Water Research Institute, Nieuwegein, 3430, BB, the Netherlands.
⁴ Centre for Water Systems, University of Exeter, Exeter, EX44QF, United Kingdom.
⁵ Faculty of Civil Engineering, University of Belgrade, 11000, Belgrade, Serbia.
⁶ Beijing Waterworks Group Co. Ltd, Beijing, 100031, China.

Abstract

The commonly used Poisson rectangular pulse (PRP) model, employed for simulating high-resolution residential water consumption patterns (RWCPs), relies on calibration via medium-resolution RWCPs obtained from practical measurements. This introduces inevitable uncertainty stemming from the measured RWCPs, which consequently impacts the precision of model simulations. Here we enhance the accuracy of the PRP model by addressing the uncertainty of RWCPs. We established a critical sampling size of 2000 household water consumption patterns (HWCPs) with a data logging interval (DLI) of 15 min to attain dependable RWCPs. Through Genetic Algorithm calibration, the optimal values of the PRP model's parameters were determined: pulse frequency λ = 91 d^-1, mean of pulse intensity E(I) = 0.346 m³ h^-1, standard deviation of pulse intensity STD(I) = 0.292 m³ h^-1, mean of pulse duration E(D) = 40 s, and standard deviation of pulse duration STD(D) = 55 s. Furthermore, validation was conducted at both HWCP and RWCP levels. We recommend a sampling size of ≥2000 HWCPs and a DLI of ≤30 min for PRP model calibration to balance simulation precision and practical implementation. This study significantly advances the theoretical foundation and real-world application of the PRP model, enhancing its role in urban water supply system management.

Keywords: Model establishment; Poisson rectangular pulse model; Residential water consumption pattern; Uncertainty analysis.