Machine learning-based surrogate model assisting stochastic model predictive control of urban drainage systems

Quantifying the uncertainty of stormwater inflow is critical for improving the resilience of urban drainage systems (UDSs). However, the high computational complexity and time consumption obstruct the implementation of uncertainty-addressing methods for real-time control of UDSs. To address this issue, this study developed a machine learning-based surrogate model (MLSM) that maintains high-fidelity descriptions of drainage dynamics and meanwhile diminishes the computational complexity. With stormwater inflow and controls as inputs and system overflow as the output, MLSM is able to fast evaluate system performance, and therefore stochastic optimization becomes feasible. Thus, a real-time control strategy was built by combining MLSM with the stochastic model predictive control. This strategy used stochastic stormwater inflow scenarios as input and aimed to minimize the expected overflow under all scenarios. An ensemble of stormwater inflow scenarios was generated by assuming the forecast errors follow normal distributions. To downsize the ensemble, representative scenarios with their probabilities were selected using the simultaneous backward reduction method. The proposed control strategy was applied to a combined UDS of China. Results are as follows. (1) MLSM fit well with the original high-fidelity urban drainage model, while the computational time was reduced by 99.1%. (2) The proposed strategy consistently outperformed the classical deterministic model predictive control in both magnitude and duration dimensions of system resilience, when the consumed time compatible is with the real-time operation. It is indicated that the proposed control strategy could be used to inform the real-time operation of complex UDSs and thus enhance system resilience to uncertainty.