Genetic Programming to Predict Scour Depth at Coastal Structures

1. Scour could cause significant structural instability in front of the coastal structures, which can lead to their failure [1]; hence, prediction of scour depth at coastal structures is of great importance in coastal engineering discipline. Extensive experimental studies carried out to predict the maximum scour depth and resulted in some empirical formulas [2-4]. However, these empirical formulas have not been capable of predicting the maximum scour depth. Another drawback of the empirical formulas is their shortage in considering all of the effective parameters in scour processes; therefore, a comprehensible model for scour depth prediction at the coastal structures is very essential. The main objective of the current study is to present an alternative model in the form of genetic programming (GP) to the present empirical formulas. We utilized around forty eight data set to train and test the evolved GP models. To evaluate the accuracy of developed GP model the statistical parameters were determined, e.g. root mean square error (RMSE) and correlation coefficient (R2) and scatter index (SI). To verify the developed models, the predicted results were compared with those of the measurements and empirical relations. Moreover, a simplified analytic form of the GP proposed model also presented in this study.2. GP (genetic programming) is a branch of the genetic algorithm belonging to the family of evolutionary algorithms used to evolve models. In the first place, the capability of GP in developing accuarate equations compared with those of empirical investigations. In order to have a logical comparison, firstly the same input and output parameters and also the same data set were utilized to evolve models with GP. To develop the best model, GP employs some operations that can affect strongly on the accurate of developed model. These operations depending on the weights relate the input parameters to each other and evolve the GP model. Since with the variation of operations, the evolved model and its accuracy changes, four types of operations considered to evolve GP models. Table. 1 shows these different operation sets.3. Results of different models including GP and empirical ones showed that the trend of prediction is similar in both GP and empirical models. However, the discrepancy of the measured and predicted scour depth in empirical formulas are very larger in comparison with those of GP. Furthermore, the empirical formulas are not able to have an acceptable prediction for the other experiments’ data set and this can be one of the most important shortage of these formulas. In most cases, the experimental investigations studied the effect of one or two important parameters on the scour at coastal structures. However, considering all of the experimental studies, various parameters can affect mainly on the scour process.4. Results of the evolved models with GP showed that in almost all of the models, GP evolved equation significantly perform better than the empirical ones with the same input and output parameters and same data set. Furthermore, GP is capable to develop a comprehensive model includes all of the effective parameters on the scour at the coastal structures. The comprehensive model of GP showed acceptable accuracy and can be utilized for predicting the maximum scour depth.