66-Estimation of Hydraulic Conductivity by Neural Network-Ridge Function.

Abstract

Aquifer properties exhibit significant spatial variation and assigning hydraulic conductivity values to a distributed parameter model based on the available scanty field data is an important problem in modeling of groundwater systems. An estimate of hydraulic conductivity for a two-dimension inverse model based on ridge functions and neural network for a phreatic leaky-aquifer is developed in this study. An objective function is minimized by combining a forward transient groundwater flow model with a proper optimization algorithm to obtain the best set of hydraulic conductivity values. The forward transient groundwater flow model is developed using the finite element method to obtain values of hydraulic conductivity from hydraulic head measurements. An artificial neural network that ensures correspondence between the integral representation of ridge function and neural network algorithm is then incorporated. To account for the high frequency fl uctuations of the estimated hydraulic conductivity values in the model, the input weights are related to the spatial frequency. Later, using an inverse modeling the hydraulic conductivity values are estimated so that the mean square error between the measurements and the model prediction in terms of piezometric head is minimized. The results indicate that complex hydraulic conductivity values can be estimated from the piezometric head measurements taking only few parameters. This is sound to be suitable when hydraulic conductivity field map exhibits heterogeneity with large anisotropy in the aquifer. The procedure also helps to dampen erratic high frequency terms in the estimated parameters and hence is stable and attains fast converge.