Performance of back-propagation neural network in chaotic data time series forecasting and evaluation over parametric forecast: a case study for rainfall-runoff modelling over a river basin

Abstract

Back-propagation neural network (BPN) is sufficiently suitable for forecasting of Chaotic data time series by two approaches i.e., parametric forecasting and time-series forecasting. However, conformation of its optimum architecture for a specific case is pre-requisite. Total rainfall-runoff (R–R) from Basantpur station over Mahanadi river basin was in under study. Initially modelling of R–R by parametric forecast approach was done by optimum architecture of BPN. It is found that BPN performs excellent for the months of July, August, and October. For the September performance was drastically unfortunate. Modelling was denied by hypothesis \(MAD\,\left( {\% \,of\,LPA} \right)\,<\,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {2 }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${2 }$}} SD (\% \,of\,LPA)\). By 20,000,000 epochs of training \(MAD\,\left( {\% \,of\,LPA} \right)\) were 23.40 and \(SD\,\left( {\% \,of\,LPA} \right)\) were 33.84. Therefore second approach of modelling i.e., time-series forecasting was applied. In which, ‘n’ years monthly past recorded R–R over the station is used to forecast of \((n + 1)\)th year monthly R–R over the station. This was significantly found appropriate and better evaluated over parametric approach. The model was highly acceptable under the hypothesis wherein \(MAD\,\left( {\% \,of\,LPA} \right)\) was 2.4516164772862348E-6 and \(SD\,\left( {\% \,of\,LPA} \right)\) was 33.45 and corelation coefficient (CC) between actual and predicted R–R is obtained 1.0 in training and 0.82 in testing independently. In this paper detail design of BPN in time-series forecasting, optimization of its architecture, training with 35 years data sets, testing with 7 years data sets, its evaluation over BPN in parametric forecast is discussed.