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In this paper, a two-dimensional time-domain numerical flume has been established to model and investigate nonlinear interactions between nonlinear surface waves and a submerged inclined thin plate. The model solves the Laplace equation and the fully nonlinear free surface boundary conditions within the framework of potential flow theory based on the high-order boundary element method. The mixed Euler–Lagrangian method is applied to update the water surface at each time step, and the fourth-order Runge–Kutta method for time stepping. A so-called four-point method was employed to separate the second-order harmonic free and bounded wave that has the same wave frequency but different wave celerity in front of and behind the submerged plate. It is found that the amplitude of the second-order harmonic free wave increases with the inclination angle of the submerged plate, and the level/amount of the increase is larger for a larger wave steepness. In addition, the amplitudes of both the second-order reflected and transmitted waves are found to increase with the wave steepness, and their empirical relationships are derived for potential use in practical engineering.

In this study, multi-tracker optimization algorithm (MTOA), particle swarm optimization (PSO), and differential evolution (DE) algorithms were integrated with support vector regression (SVR) to predict energy dissipation downstream of labyrinth weirs (Δ E). In order to evaluate the performance of these methods, the results are compared with corresponding outcome obtained by applying two other methods, namely, multilayer perceptron neural network (MLPNN) and multiple linear regressions methods (MLR). The input parameters comprise the discharge, the upstream flow depth, the crest length of a single cycle of the labyrinth weir, the width of a single cycle of the labyrinth weir, the apex width, the number of labyrinth weir cycles, the sidewall angle, and the height of weir. The results indicate that the meta-heuristic algorithms substantially improve the performance of SVR. The results show that the integrative methods, SVR-MTOA, SVR-PSO, and SVR-DE, are more accurate than the MLPNN and the MLR. In average, the integrative methods provide 39.63% more accurate results than the MLPNN and 79.34% more accurate results than the MLR. The average RMSE and R2 for the integrative methods are 0.0054 m and 0.977, respectively. Among all integrative methods, the SVR-MTOA yields the best results, with RMSE = 0.0044 m and R2 = 0.986. [ABSTRACT FROM AUTHOR]