Safety-oriented adaptive slow-closing design of check valves: An intelligent multi-objective optimization paradigm

ABSTRACT This study addresses the coordinated control of pump reverse rotation and water-hammer pressure bounds in water-conveyance systems by proposing an intelligent, multi-objective framework for two-stage slow-closing check valves. First, a transient numerical model is validated against experiments and used to select an appropriate slow-closing scheme for sensitivity analysis. A backpropagation neural network (BPNN) is then trained as a surrogate to predict multivariable, two-stage transient responses under pump-trip conditions. Finally, the NSGA-II algorithm optimizes key decision variables (closing times and relative openings) to obtain balanced Pareto solutions that trade off maximum and minimum transient pressures, reverse-rotation speed, and recovery time. The approach is verified on a single-pipe system and applied to a branched pipeline with complex wave-propagation paths, overcoming long-standing difficulties in coordinating two-stage parameters. Results show that the proposed method markedly reduces tuning time and reliably meets surge-protection criteria, yielding solutions with lower pressure peaks, avoidance of negative pressures, limited reverse-rotation, and faster stabilization. The framework offers a practical pathway for efficient design and robust operation in complex conveyance networks.