Integration of Artificial Neural Networks with Radial Basis Function Interpolation in Earthfill Dam Seepage Modeling

In this study, the radial basis function (RBF) spatial interpolation method was used to estimate the potential water heads through an earthen dam. The multiquadric (MQ) function was used to discretize the seepage governing partial differential equation and related boundary conditions. The function contains a shape coefficient of c, which plays an important role in model calibration. Therefore, the coefficient of c was first optimized via Hardy and cross validation methods, and then, by employing the optimal c (copt), two scenarios of modeling with and without considering the internal conditions were provided and the results were compared with the results of the finite difference method (FDM). In the next step, an artificial neural network was used for handling the nonlinear time variability of the phenomenon to cope with the limitations of the FDM and RBF methods in temporal modeling. Thus, by training neural networks for the piezometers located in the core, the potential time series of water were predicted and their results were imposed upon the RBF method as the internal conditions, along with the boundary conditions for spatial-temporal modeling of the water heads. Finally, the assumed time-invariant inherency of c was confirmed by the cross-validation method. The results show no notable time variation in time series of copt, and therefore, it can be concluded that the value of the shape coefficient in MQ formulations generally depends on the geometry of the problem rather than the temporal variation of the boundary conditions.