![]() ![]() ![]() 2014) mainly derived from the CLASH database. (2016) developed an improved neural network for a broad range of coastal structures, released in EurOtop (2018) and EurOtop (2018)-ANN, using dimensionless input parameters based on an extended database ( Zanuttigh et al. In the training of this model, dimensional input parameters have been used which may not be appropriate for all cases with different scales. Among them all, initially developed within the CLASH ( De Rouck & Geeraerts 2005) project and presented by EurOtop (2007), the ANN model is the most well-known soft computing tool applicable for a wide range of structures. Due to the complex nature of the overtopping process and the existing limitations of empirical formulae, some soft computing approaches, as alternative tools, have been implemented to predict the mean overtopping rate for a broad range of coastal structures. These techniques provide a quick and cost-effective solution that can be useful for complicated problems. artificial neural network (ANN)) for water engineering problems can be found (e.g. In recent decades, several applications of soft computing techniques (e.g. The ET formula remarkably underestimates overtopping rates, which could be misleading for the design procedure. As seen, some predictions lie out of 10 times over/under estimation lines (dashed). More details of the dataset used are given in the section of the used dataset. In this figure, the data of rubble mound structures with permeable core and simple slope without crown wall, including both head-on and oblique waves, have been selected from the EurOtop (2018) database. Here, q (m 3/s/m) is the dimensional mean overtopping rate per unit width, g (m/s 2) represents the gravitational acceleration, and (m) refers to the significant wave height at the toe of the structure. The dimensionless measured and predicted mean overtopping rates defined as are shown in this figure. Figure 1 displays the performances of Jafari & Etemad-Shahidi (2011) (hereafter JE), and EurOtop (2018) (mean approach: Equation (6.5)) (hereafter ET), formulae for simple sloped breakwaters. However, poor predictions of mean overtopping rate at armoured structures using empirical formulae have been reported in the literature (e.g. The mentioned formulae correlate the dimensionless mean overtopping rate to dimensionless wave and structural parameters through physical arguments. Owen 1980 van der Meer & Janssen 1995 EurOtop 2007 EurOtop 2018 Shaeri & Etemad-Shahidi 2021) have mostly been derived by regression analysis of small-scale experiments. The existing empirical formulae to predict mean overtopping rate (e.g. Finally, the physical consistencies of developed models were investigated, the results of which demonstrated the reliability of kernel-based models in terms of delivering physics of overtopping phenomenon. In addition, the optimal input combination was introduced based on accuracy and the number of input parameters criteria. The results showed the superiority of kernel-based models, especially the GPR model over the ANN model and empirical formulae. The modified Taylor diagram was used to compare the models graphically. The obtained results were compared with those of the ANN model and the existing empirical formulae. Different combinations of the important dimensionless parameters representing structural features and wave conditions were tested based on the sensitivity analysis for developing the models. An extensive dataset taken from the EurOtop database, including rubble mound structures with permeable core, straight slopes, without berm, and crown wall, was employed to develop the models. The goal of this paper is to assess the capabilities of two kernel-based methods, namely Gaussian process regression (GPR) and support vector regression for the prediction of mean wave overtopping rate at sloped breakwaters. Recently, soft computing tools such as artificial neural networks (ANN) have been developed as alternatives to traditional overtopping formulae. Hence, providing a robust tool as a preliminary estimator can be useful for practitioners. The accurate prediction of the mean wave overtopping rate at breakwaters is vital for a safe design. ![]()
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