Date of Award

2011

Document Type

Thesis

First Advisor

Chang, Dr. Shoou-Yuh

Abstract

Due to the inherent randomness and heterogeneity of the transport process, macrodispersion, non-fickian motion, and ergodicity, general assumptions of linearity and Gaussian distribution do not hold for the real field. Therefore, a state-space transport model for the non-linear and non-Gaussian system is proposed in this study. In this study, the state variable (concentration vector) and parameter (first-order decay) are updated with the available measurements. The probabilistic state-space formulation and updating of information on receipt of new measurements is formulated in the Bayesian framework. particle filter, a sequential Monte Carlo method, provides a rigorous general framework for dynamic state estimation problems in the Bayesian scheme. Here the reactive contaminant transport in subsurface is treated as a dynamic state and parameter estimation problem. A type of particle filter, commonly called Sequential Importance Resampling (SIR) is used for this subsurface transport problem. The model estimation is compared with a reference true random field. A promising improvement of the estimation accuracy is attained with the SIR particle filter while compared with a traditional deterministic approach. The standard deviations of the residuals were calculated for the comparison purpose. The particle filter data assimilation scheme reduces the prediction error by 48% in estimation accuracy. In case of having fixed parameters in the model, a standard technique to perform parameter estimation consists of extending the state with the parameter to transform the problem into optimal filtering problem. This approach requires the use of special particle filtering techniques which suffer from several drawbacks. An alternative statistical approach was adopted here to combine parameter estimation with the particle filter scheme. The concept of Euclidian norm was introduced in order to address the sequential weight assignment to the parameter estimation. The SIR particle filter scheme successfully estimated the parameter (first-order decay). With the use of the updated parameter in the state prediction, prediction error of the SIR particle filter data assimilation scheme became 78% smaller than the error from the deterministic model.

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