Knowledge extraction from trained neural network scour model at culvert outlets

Artificial neural networks (ANNs), due to their outstanding capabilities for modeling complex processes, have been successfully applied to a variety of problems in hydraulics. However, one of the major criticisms of ANNs is that they are just black-box models, since a satisfactory explanation of their behavior has not been offered. They, in particular, do not explain easily how the inputs are related to the output and also whether the selected inputs have any significant relationship with an output. In this paper, a perturbation analysis for determining the order of influence of the elements in the input vector on the output vector is discussed. The analyses of the results suggest that each variable in the input vector (d (50)/d (0), F (0), H/d (0), sigma(g), and W (0)/d (0)) influences the depth of scour in different ways. However, the magnitude of the influence cannot be clearly quantified by this approach. Further it adds that the selection of input vector based on linear measures between the variables of interest, which is commonly employed, may still include certain spurious elements that only increase the model complexity.