Prediction Intervals for the Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) via the LUBE Method

Abstract

AbstractIn this study, the uncertainty associated with Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) was investigated. The uncertainty of rainfall-runoff modeling on daily and monthly scales was evaluated by Prediction Intervals (PIs) for two watersheds, West Nishnabotna River basin in the United States and Lighvanchai River basin in Iran. Upper Lower Bound Estimation (LUBE) method was applied to construct the PIs. In the LUBE method, the ANN and ANFIS were trained by minimizing the objective function via the genetic algorithm optimization method, and the objective function contains the width and coverage criteria of PIs evaluation. PIs coverage probability and PIs width values, respectively were up to 10% higher and 39% lower for the PIs of the ANFIS compared to the those of ANN. Moreover, the CWC measure was lower for ANFIS PIs than that for the ANN. Also, the Lighvanchai basin modeling showed more accurate results than the West Nishnabotna River basin, which is due to four well defined regular seasons of the Lighvanchai basin.KeywordsRainfall-runoffPrediction intervalArtificial Neural NetworkAdaptive Neuro-Fuzzy Inference SystemUpper Lower Bound Estimation