Application of Kalman Filter Embedded with Neural Network in 3-Dimensional Subsurface Contaminant Transport Modeling

Abstract

Predictive tools in the form of mathematical models have been used to simulate the movement and behavior of contaminants in groundwater. Conventionally, numerical models have been used to simulate these contaminants in the porous subsurface environment. A 3-D subsurface contaminant transport model numerically solved by approximation plagued the model with truncation and round-off errors and; assumes constant hydrologic parameters. In this research, to improve the accuracy of subsurface contaminant prediction spatially and temporally and to assess the impact of first-order decay rate parameter estimation, Kalman filter (KF) embedded with Neural Network (NN) was used in a specified 3-D domain space. The filter is perturbed with random Gaussian noise to reflect real life case of contaminant movement. Set of sparse observation points selected at specific locations are used to guide the filter at every time step to improve the accuracy of the prediction. The algorithms to generate the simulation results were run on Matlab 7.1. The accuracy of the KF embedded with NN, KF without Parameter Estimation and the numerical method were tested using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) equations. The KF embedded with NN performs better than both the discrete Kalman filter and the numerical method. Also, the KF embedded with NN is capable of reducing the error in the numerical solution by approximately 75 %.