Model predictive control and rainfall Uncertainties: Performance and risk analysis for drainage systems

Abstract

Urban flooding resulting from severe rainstorms is an increasing challenge for cities worldwide due to climate change and rapid urbanization. Model predictive control (MPC) has emerged as a promising approach for real-time management of urban drainage systems to mitigate flooding impacts. However, existing MPC research often relies on idealized rainfall forecasts without adequately accounting for forecast uncertainty, which can compromise the effectiveness of MPC strategies. This study aims to address this critical research gap by developing a framework to evaluate the impacts of forecast uncertainty on MPC performance for urban drainage management. The framework consists of 3 components, (1) martingale model of forecast evolution based on Langevin dynamics for generating rainfall data under different uncertainty conditions (2) MPC, which accepts the rainfall inputs and obtains the real-time control results under different uncertainty conditions and (3) the Scheduling Performance Indicator module, which performs a systematic evaluation of the real-time control system. Using a case study of the Doumen region in Fuzhou City, the results reveal two key findings: First, MPC performance remains close to optimal when forecast uncertainty levels are between 0.1 and 0.3, but deteriorates significantly at uncertainty levels from 0.3 to 0.5. Second, while the MPC error feedback module can occasionally degrade performance for individual events, its overall impact is beneficial in reducing performance deviation risks.