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

Abstract

Many of the empirical formulas used for the prediction of the expected scour depth at piers are excessively conservative, providing substantial overestimations. On the other hand, the recently proposed neural networks methods generally issue accurate predictions but also high percentages of underpredictions, due to the use of a symmetric error function for their parameterization. A novel error function is proposed in this paper 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 independent field records are compared with those of a conventionally trained neural network and with those of a set of widely used formulas. The asymmetric error function (that might be applied to parameterize any other model or equation, as a proficient alternative to least-square errors or envelope curves) allows researchers to obtain predictions closer to the measurements than those issued by traditional formulas, substantially reducing the extent of unnecessary overdesign and at the same time the percentage of severe underestimations is comparable with those of the safest formulas.