Artificial neural network ensembles and their application in pooled flood frequency analysis

[ 1] Recent theoretical and empirical studies show that the generalization ability of artificial neural networks can be improved by combining several artificial neural networks in redundant ensembles. In this paper, a review is given of popular ensemble methods. Six approaches for creating artificial neural network ensembles are applied in pooled flood frequency analysis for estimating the index flood and the 10-year flood quantile. The results show that artificial neural network ensembles generate improved flood estimates and are less sensitive to the choice of initial parameters when compared with a single artificial neural network. Factors that may affect the generalization of an artificial neural network ensemble are analyzed. In terms of the methods for creating ensemble members, the model diversity introduced by varying the initial conditions of the base artificial neural networks to reduce the prediction error is comparable with more sophisticated methods, such as bagging and boosting. When the same method for creating ensemble members is used, combining member networks using stacking is generally better than using simple averaging. An ensemble size of at least 10 artificial neural networks is suggested to achieve sufficient generalization ability. In comparison with parametric regression methods, properly designed artificial neural network ensembles can significantly reduce the prediction error.