Multi-objective reliability-based optimization for design of trapezoidal labyrinth weirs

In the present research, the reliability-based design optimization (RBDO) of labyrinth weirs has been investigated. The optimization problem is formulated such that the optimal shape of trapezoidal labyrinth weir described by a number of variables is found by minimizing the volume of the trapezoidal labyrinth weir and maximizing the reliability index. The constraint conditions are the weir geometric shape and its different ratios. In order to achieve this purpose, a framework is presented whereby non-dominated sorting genetic algorithm (NSGA-II) is integrated with monte carlo simulation (MCS) method to solve the RBDO approach of trapezoidal labyrinth weirs. The proposed method is applied to UTE Dam labyrinth weir, and the results are compared with the real one. The results show the need for design based on reliability in the labyrinth weirs that propose using RBDO for weir design. The results showed that RBDO approach can achieve a more reliable design in addition to reducing the volume of the trapezoidal labyrinth weir. Finally, the sensitivity analysis of the parameters effective on the reliability index revealed that three design variables of weir width, total upstream head and discharge coefficient are the main parameters affecting weir RBDO solution.