Scour depth modelling by a multi-objective evolutionary paradigm

Local scour modelling is an important issue in environmental engineering in order to prevent degradation of river bed and safeguard the stability of grade-control structures. Many empirical formulations can be retrieved from literature to predict the equilibrium scour depth, which is usually assumed as representative of the phenomenon. These empirical equations have been mostly constructed in some ways by leveraging regression procedures on experimental data, usually laboratory observations (thus from small/medium scale experiments). Laboratory data are more accurate measurements but generally not completely representative of the actual conditions in real-world cases, that are often much more complex than those schematized by the laboratory equipment. This is the main reason why some of the literature expressions were not adequate when used for practical applications in large-scale examples. This work deals with the application of an evolutionary modelling paradigm, named Evolutionary Polynomial Regression (EPR), to such problem. Such a technique was originally presented as a classical approach, used to achieve a single model for each analysis, and has been recently updated by implementing a multi-modelling approach (i.e., to obtain a set of optimal candidate solutions/models) where a multi-objective genetic algorithm is used to get optimal models in terms of parsimony of mathematical expressions vs. fitting to data. A wide database of field and laboratory observations is used for predicting the equilibrium scour depth as a function of a set of variables characterizing the flow, the sediments and the dimension of the grade-control structure. Results are discussed considering two regressive models available in literature that have been trained on the same data used for EPR. The proposed modelling paradigm proved to be a useful tool for data analysis and, in the particular case study, able to find feasible explicit models featured by an appreciable generalization performance.