Simple and explicit neural network-derived formula to estimate wave reflection on mound breakwaters

The main objective of this study was to develop a new one-parameter explicit formula to estimate wave reflection on mound breakwaters under regular and irregular waves in non-overtopping and non-breaking wave conditions. The Artificial Neural Network (ANN) methodology was used to rank a list of possible explanatory variables and to identify relationships between the key explanatory variables and wave reflection. Data corresponding to 494 small-scale two-dimensional physical tests from University of Granada (UGR) and Aalborg University (AAU) were collected to apply the ANN methodology in developing the new formula. The relative water depth, h/L, being h the water depth and L the wavelength, and the seaward slope angle, cotα, were found to be the two main explanatory variables for the measured squared wave reflection coefficient, KR2. An exponential relationship between KR2 and (h/L) /tanα with only one fitting identified parameter was sufficient to explain 88% of the variance for observed KR2 corresponding to 265 tests using regular waves from the UGR laboratory. A relationship between regular and irregular wave parameters using ANN modelling and the results of 16 tests with irregular waves from UGR was also: HI = 1.416 Hrms,I and T = 1.050 T01; being HI and T the incident wave height and wave period for regular waves, and Hrms,I and T01 the incident root mean square wave height and spectral mean wave period for irregular waves. The new empirical formula depending only on (h/L) /tanα explained 91% of the variance for measured KR2 of 213 additional tests with irregular waves from the AAU laboratory. The new formula was calibrated and validated using physical models with rock and concrete armor units, several seaward slope angles, water depths, and core permeability. The new one-parameter empirical formula showed a better agreement than other simple empirical formulas given in the literature and explained more than 65% of the variance for KR2 observations from a general database used for comparison.