Uncertainty analysis for artificial neural network applying monte carlo simulation to forecast sodium adsorption ratio: a case study, a few rivers in iran.
1 Departement of Natural Resources Engineering, Faculty of Agricultural Engineering and Natural Resources, University of Hormozgan
2 Civil Engineering Department, Faculty of Engineering, Kharazmi University, Tehran, Iran
3 Departement of Mathematics, School of Mathematical and Statistical Sciences, Southern Illinois University, Carbondale, IL, USA
2 Civil Engineering Department, Faculty of Engineering, Kharazmi University, Tehran, Iran
3 Departement of Mathematics, School of Mathematical and Statistical Sciences, Southern Illinois University, Carbondale, IL, USA
Abstract
Effective water quality management requires a thorough understanding of anticipated changes in the characteristics of surface and groundwater to support decision-making related to drinking water, irrigation, and industrial uses. Various mathematical models, such as time series approaches (including Box-Jenkins and Bayesian methods) and data-driven models, are utilized for forecasting water quality trends. Despite their usefulness, a significant challenge in applying these models is the inherent uncertainty in their predictions. This study evaluates the uncertainty of the Adaptive Neuro-Fuzzy Inference System (ANFIS) based on Fuzzy c-means clustering (FCMC) using the Genfis 3 model. Monte Carlo simulations were employed to predict the Sodium Adsorption Ratio (SAR) for the Aras, Sepid-Rud, and Karun Rivers. The findings reveal that for the Aras River, the combined standard uncertainty and expanded uncertainty for SAR were 0.58 and 1.16, respectively, with a gap of 2.412 1.1622. Similarly, for the Sepid-Rud River, the combined standard uncertainty and expanded uncertainty were 1.11 and 2.22, respectively, with a gap of 2.235 2.22. For the Karun River, the combined standard uncertainty and expanded uncertainty were calculated as 2.063 and 4.126, with a gap of 4.79 4.126. Overall, the lowest uncertainty was observed in the SAR prediction for the Aras River, while the highest uncertainty was associated with the Karun River forecast using the ANFIS-FCMC approach.
Keywords
ANFIS-FCMC; Monte Carlo Simulation; SAR; water quality