Abstract
Abstract. In this work, results obtained by investigating the application of different neural network backpropagation training algorithms are presented. This was done to assess the performance accuracy of each training algorithm in total electron content (TEC) estimations using identical datasets in models development and verification processes. Investigated training algorithms are standard backpropagation (SBP), backpropagation with weight delay (BPWD), backpropagation with momentum (BPM) term, backpropagation with chunkwise weight update (BPC) and backpropagation for batch (BPB) training. These five algorithms are inbuilt functions within the Stuttgart Neural Network Simulator (SNNS) and the main objective was to find out the training algorithm that generates the minimum error between the TEC derived from Global Positioning System (GPS) observations and the modelled TEC data. Another investigated algorithm is the MatLab based Levenberg-Marquardt backpropagation (L-MBP), which achieves convergence after the least number of iterations during training. In this paper, neural network (NN) models were developed using hourly TEC data (for 8 years: 2000–2007) derived from GPS observations over a receiver station located at Sutherland (SUTH) (32.38° S, 20.81° E), South Africa. Verification of the NN models for all algorithms considered was performed on both "seen" and "unseen" data. Hourly TEC values over SUTH for 2003 formed the "seen" dataset. The "unseen" dataset consisted of hourly TEC data for 2002 and 2008 over Cape Town (CPTN) (33.95° S, 18.47° E) and SUTH, respectively. The models' verification showed that all algorithms investigated provide comparable results statistically, but differ significantly in terms of time required to achieve convergence during input-output data training/learning. This paper therefore provides a guide to neural network users for choosing appropriate algorithms based on the availability of computation capabilities used for research.
Highlights
Total electron content (TEC) estimations using the neural network (NN) technique have been done over many years with relative success (e.g. Hernandez-Pajares et al, 1997; Tulunay et al, 2004, 2006; Leandro and Santos, 2007; Senalp et al, 2008; Yilmaz et al, 2009)
It is known that neural networks interpolate well within the input space, and the network is expected to reproduce the dataset that was used to train it with relatively good accuracy (McKinnell, 2002; Habarulema et al, 2007)
Presented extrapolation results show that backpropagation with momentum (BPM) and backpropagation with weight delay (BPWD) provide better TEC estimates with LevernbergMarquardt backpropagation (L-MBP) giving the least accuracy for January 2008
Summary
Total electron content (TEC) estimations using the neural network (NN) technique have been done over many years with relative success (e.g. Hernandez-Pajares et al, 1997; Tulunay et al, 2004, 2006; Leandro and Santos, 2007; Senalp et al, 2008; Yilmaz et al, 2009). In space weather applications involving predictions that use solar wind data as inputs, recurrent networks have been found to be more desirable (Lundstedt et al, 2002; Weigel et al, 2002, 2003; Vandegriff et al, 2005; Lundestedt, 2006; Habarulema et al, 2009; Heilig et al, 2010) Other ionospheric parameters, such as the critical frequency of the Eregion (foE) and critical frequency of the F2 layer (foF2), have been predicted using feed forward networks (e.g. Cander et al, 1998; Cander, 1998; McKinnell, 2002; McKinnell and Poole, 2004; Oyeyemi et al, 2006). TEC modelled and forecasted results for models, which utilised the L-MBP algorithm, have been presented (Tulunay et al, 2006; Yilmaz et al, 2009) This algorithm is credited for its time savings during NN training/learning processes (Jang et al, 1997). The verification was done on 2003 and 2008 datasets over SUTH, as well as the 2002 dataset over Cape Town (CPTN), South Africa (33.95◦ S, 18.47◦ E)
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