Comparison of the MLP and RBF Neural Networks for the Determination of Confined Aquifer Parameters
Subject Areas :
Tahereh
Azari
1
Nozar
Samani
2
Abstract :
In this paper, Multi-Layer Perceptron (MLP) and Radial Basis Function (RBF) Artificial Neural Networks (ANNs) are designed for the determination of confined aquifer parameters: transmissibility and storage coefficient. The networks are trained for the well function of confined aquifers. By applying the principal component analysis (PCA) on the training data sets the topology of the MLP and RBF networks is reduced and fixed to [1×12×1] and [1×14×1], respectively regardless of number of records in the pumping test data. The networks generate the optimal match point coordinates for any individual real pumping test data set. The match point coordinates are then incorporated with Theis analytical solution (1935) and the aquifer parameter values are determined. The generalization ability and performance of the developed networks is evaluated with 100000 sets of synthetic data and their accuracy is compared with that of type curve matching technique by two sets of real pumping test data. The results showed that though both MLP and RBF networks are able to determine the confined aquifers parameters and eliminate graphical error inherent in the type curve matching technique but the MLP network is more accurate than the RBF network. Therefore, the proposed MLP network is recommended as an accurate automatic and fast procedure for the confined aquifer parameters estimation.
ASCE Task Committee on Application of Artificial Neural Networks in Hydrology., 2000a. Artificial Neural Networks in hydrology. I: preliminary concepts. J Hydrol Eng, 5(2), 115-123.
Chang, F.J., Kao, L.S., Kuo, Y.M., and Liu, C.W., 2010. Artificial neural networks for estimating regional arsenic concentrations in a black foot disease area in Taiwan. J Hydrol, (388), 65-76.
Chang, L.Ch., Chu, H.J., and Hsiao, Ch.T., 2012. Integration of optimal dynamic control and neural network for groundwater quality management. Water Resour Manage, (26), 1253–1269.
Chau, K.W., 2007. An ontology-based knowledge management system for flow and water quality modeling. Adv Eng Softw, 38(3), 172-181.
Cheng, Ch., Chau, K., Sun, Y., and Lin, J., 2005. Long-term prediction of discharges in Manwan Reservoir using artificial neural network models. LNCS 3498, 1040-1045.
Coulibaly, P., Anctil, F., Aravena, R., and Bobee, B., 2001. Artificial neural network modeling of water table depth fluctuations. Water Resour Res, 37(4), 885–896.
Daliakopoulos, I.N., Coulibaly, P., and Tsanis, I.K., 2005. Groundwater level forecasting using artificial neural networks. J Hydrol, 309(1–4), 229–240.
Davis, J.C., 2002. Statistics and data analysis in geology. 3rd edn. Wiley, New York.
Fausett, L., 1994. Fundamentals of neural networks. Prentice Hall, Englewood Cliffs, N.J.
Hantush, M.S., Jacob, C.E., 1955. Non-steady radial flow in an infinite leaky aquifer. Trans Am Geophys Union, 36(1), 95–100.
Haykin, S., 1999. Neural networks: a comprehensive foundation. Prentice-Hall: Englewood Cliffs, NJ.
Lin, G.F., and Chen, G.R., 2005. Determination of aquifer parameters using radial basis function network approach. J Chinese Inst Engrs, 28(2), 241-249.
Lin, G.F., and Chen, G.R. 2006. An improved neural network approach to the determination of aquifer parameters. J Hydrol, 316(1–4), 281–289.
Lin, H.T., Ke, K.Y., Chen, Ch.H., Wu, Sh.Ch., and Tan, Y.Ch., 2010. Estimating anisotropic aquifer parameters by artificial neural networks. Hydrol Process, (24), 3237–3250.
Maier, H.R., and Dandy, G.C., 1999. Empirical comparison of various methods for training feed-forward neural networks for salinity forecasting. Water Resour Res, 32(8), 2591–2596.
Maier, H.R., and Dandy, G.C., 2000. Neural networks for the prediction and forecasting of water resources variables: a review of modeling issues and applications. Environ Modell Softw, (15), 101–124.
Maier, H.R., Jain, A., Dandy, G.C., and Sudheer, K.P., 2010. Methods used for the development of neural networks for the prediction of water resource variables in river systems: current status and future directions. Environ Model Softw, 25(8), 891-909.
Ranjithan, S., Eheart, J.W., and Garrett, J.H., 1993. Neural network-based screening for groundwater reclamation under uncertainty. Water Resour Res, 29(3), 563-574.
Ray, C., and Klindworth, K.K., 2000. Neural networks for agrichemical vulnerability assessment of rural private wells. J Hydrol Eng, 5(2), 162-171.
Razavi, S., and Tolson, B.A., 2011. A new formulation for feed forward neural networks. Neural Netw IEEE Trans, 22(10), 1588-1598.
Rumelhart, D.E., Hinton, G.R., and Williams, R.J., 1986. Learning internal representations by error propagation. In: Rumelhart, D.E., David, E., (Eds.), Parallel Distributed Processing. MIT Press, Massachusetts, 318–362.
Samani, N., Gohari-Moghadam, M., and Safavi, A.A., 2007. A simple neural network model for the determination of aquifer parameters. J Hydrol, 340(1–2), 1–11.
Singh, R.M., and Datta, B., 2007. Artificial neural network modeling for identification of unknown pollution sources in groundwater with partially missing concentration observation data. Water Resour Manage, (21), 557–572.
Theis, C.V., 1935. The relationship between the lowering of the piezometric surface and the rate and duration of discharge of a well using ground-water storage. Trans Am Geophys Union, (16), 519–524.
Todd, D.K., and Mays, L.W., 2005. Groundwater Hydrology. Wiley, New York.
Walton, W.C., 1962. Leaky artesian aquifer conditions in Illinois. Illinois State Water Survey, Illinois.
Wu, C.L., Chau, K.W., and Li, Y.S., 2009. Predicting monthly streamflow using data-driven models coupled with data-preprocessing techniques. Water Resour Res, (45), W08432.
Wu, W., Dandy, G.C., and Maier, H.R., 2014. Protocol for developing ANN models and its application to the assessment of the quality of the ANN model development process in drinking water quality modeling. Environ Modell Softw, (54), 108–127.