Bayesian Artificial Intelligence Model Averaging for Hydraulic Conductivity Estimation
Publication: Journal of Hydrologic Engineering
Volume 19, Issue 3
Abstract
This research presents a Bayesian artificial intelligence model averaging (BAIMA) method that incorporates multiple artificial intelligence (AI) models to estimate hydraulic conductivity and evaluate estimation uncertainties. Uncertainty in AI model outputs stems from errors in model input and nonuniqueness in selecting different AI methods. Using one single AI model tends to bias the estimation and underestimate uncertainty. The BAIMA employs a Bayesian model averaging (BMA) technique to address the issue of using one single AI model for estimation. The BAIMA estimates hydraulic conductivity by averaging the outputs of AI models according to their model weights. In this study, the model weights are determined using the Bayesian information criterion (BIC) that follows the parsimony principle. The BAIMA calculates the within-model variances to account for uncertainty propagation from input data to AI model output. Between-model variances are evaluated to account for uncertainty because of model nonuniqueness. The authors employ Takagi-Sugeno fuzzy logic (TS-FL), an artificial neural network (ANN), and neuro-fuzzy (NF) to estimate hydraulic conductivity for the Tasuj plain aquifer, Iran. The BAIMA combines three AI models and produces better fitting than individual models. Although NF was expected to be the best AI model owing to its utilization of both the TS-FL and ANN models, the NF model is nearly discarded by the parsimony principle. The TS-FL model and the ANN model show equal importance, although their hydraulic conductivity estimates are quite different. This results in significant between-model variances that are normally ignored by using one AI model.
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Acknowledgments
This study was supported in part by the Research Office at the University of Tabriz and Iran’s national Elites foundation. The Iran Ministry of Science, Research, and Technology provided a scholarship to A. A. Nadiri to conduct research at Louisiana State University. The study was also supported in part by Grant/Cooperative Agreement No. G10AP00136 from the United States Geological Survey for N. Chitsazan to conduct the BMA study. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the USGS. The authors acknowledge the East Azerbaijan Regional Water Authority for providing pertinent data.
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Published In
Journal of Hydrologic Engineering
Volume 19 • Issue 3 • March 2014
Pages: 520 - 532
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© 2014 American Society of Civil Engineers.
History
Received: Aug 1, 2012
Accepted: Apr 4, 2013
Published online: Apr 5, 2013
Discussion open until: Sep 5, 2013
Published in print: Mar 1, 2014
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