The estimation of scour depths is extremely important in designing the foundation of piers which ensure the integrity of bridges and other hydraulic structures. Complicated hydrodynamic processes around piers are the main challenge to formulate explicitly empirical equations in providing scour depth estimation. Consequently, the proposed empirical formulae only yield good prediction results for specific conditions. In this study, the particle swarm optimization and Firefly algorithms are proposed to optimize artificial neural network (ANN) models to improve predicting the scour depths around circular piers at the equilibrium stage. The results of the proposed modelling frameworks are compared with an ANN network trained by the Levenberg–Marquardt (LM) algorithm which was widely adopted in the literature for prediction purposes. The predicted results exhibit that the equilibrium maximum scouring depths derived from our proposed models are better compared to the values from empirical models and the single ANN model trained by LM. Our study implicates that the new model frameworks could successfully replace the traditional methods, and more applications of these frameworks on computational fluid mechanics and hydraulic structure designs should be considered.     «

The estimation of scour depths is extremely important in designing the foundation of piers which ensure the integrity of bridges and other hydraulic structures. Complicated hydrodynamic processes around piers are the main challenge to formulate explicitly empirical equations in providing scour depth estimation. Consequently, the proposed empirical formulae only yield good prediction results for specific conditions. In this study, the particle swarm optimization and Firefly algorithms are pro...     »