High Order Pseudo Mac Laurin Feedforward Backpropagation Artificial Neural Networks: Infilling Mean Annual Flows

Masengo Ilunga


MacLaurin, Neural Networks, Modelling


Variants of feedforward backpropagation (BP) artificial neural network (ANNs) such as pseudo Mac Laurin power series order 1 (McL1BP), order 2 (McL2BP), order 3 (McL3BP), order 4 (McL4BP) models are used to fill in mean annual streamflows. The baseline of modeling process is the standard feedforward backpropagation ANN (StandBP). The sigmoid function is used as activation function. Performance comparisons of data infilling models (ANNs) are conducted using the Root Mean Square Error of Predictions (RMSEp) and graphical plots. To test the performance of the data infilling techniques, selected streamflow gauges (i.e. the Diepkloof (control) gauge on the Wonderboomspruit River and the Molteno (target) gauge on Stormbergspruit River) of the Orange drainage river systems of South Africa have been used. The results demonstrated that relatively higher order ANN models; i.e. McL3BP, McL4BP can still outperform the rest of techniques for 7 % (except StandBP), 20 % and 30 % missing data proportions at Molteno gauge. At the same time they have been outperformed by the rest of ANN models at 13 %. Generally higher and low order Pseudo MacLaurin ANNs are acceptable to fill in missing mean annual flows at Molteno gauge. The accuracy of estimated mean annual values at Molteno is substantially negatively affected beyond 20 % gap size for all ANNs. Hence gap size beyond 20 % yields to relatively higher value of RMSEp for both high and low MacLaurin feedforward ANN techniques. A linear relationship could describe accuracy of estimated values and gap size at Molteno. Further work should include other data regimes as well as other South African catchment areas. Other activation functions should also be tested.

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