Asymmetric Error Functions for Reducing the Underestimation of Local Scour around Bridge Piers: Application to Neural Networks Models

Artificial Neural Networks (ANN) have been recently proposed for predicting the maximum expected scour depth at piers: they generally provide accurate predictions but tend to issue high percentages of underpredictions, due to the use of a symmetric error function in the procedure used for their parameterization. A novel error function is here proposed for optimizing neural networks, giving more weight to underestimation than to overestimation discrepancies, in order to obtain safer design predictions. The performances of the proposed model on an independent set of field records are compared with those of a conventionally trained neural network and with those of a set of widely used formulae. The asymmetric error function – that might be applied to optimize any other model or equation, as a proficient alternative to the use of envelope curves – allows to obtain predictions that are closer to the measurements than those issued by the traditional formulae, substantially reducing the extent of unnecessary over-design and, at the same time, the percentage of severe underestimations is comparable with those of the safest formulae.