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

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.