Design of rubble-mound breakwaters using M5 ′ machine learning method

Predicting the stability of armor blocks of breakwaters and revetments is a very important issue in coastal and ocean engineering. Recently, soft computing tools such as artificial neural networks and fuzzy logic have been used to predict the stability number of armor blocks. However, these tools are not as transparent as empirical formulas. This study presents another soft computing approach, i.e. model trees for predicting the stability number of armor blocks. The main advantage of model trees is that, unlike the other data learning tools, they are easier to use and more importantly they represent understandable mathematical rules. A total of 579 experimental test data from Van der Meer 1988 are used for developing the model. The conventional governing parameters were selected as the input variables and the obtained results were compared with those of measurements, empirical and soft computing models. Using statistical measures, it was shown that the developed models are more accurate than previous empirical and soft computing models. Furthermore, some simple rules are given for armor blocks’ design.     

Predicting wave run-up on rubble-mound structures using M5 model tree

Prediction of run-up level is a key task in design of the coastal structures. For the design of the crest level of coastal structures, the wave run-up level with a 2% exceedance probability, R_u2%, is most commonly used. In this study, the performance of M5 model tree for prediction of the wave run-up on rubble-mound structures was investigated. The main advantage of model trees, unlike the other soft computing tools, is their easier use and more importantly their understandable mathematical rules. Experimental data set of Van der Meer and Stam was used for developing model trees. The conventional governing parameters were selected as the input variables and the obtained results were compared with Van der Meer and Stam’s formula, recommended by the Coastal Engineering Manual (CEM, 2006). The predictive accuracy of the model tree approach was found to be superior to that of Van der Meer and Stam’s empirical formula. Furthermore, to judge the generalization capability of the model tree method, the model developed based on laboratory data set was validated with the prototype run-up measurements on the Zeebrugge breakwater, Belgium. Results show that the model tree is more accurate than empirical formulas and TS Fuzzy approach in estimating the full-scale run-up.