Optimal Sampling Strategy for Parameters Estimation
Abstract
In groundwater modeling problems, parameter estimation constitutes one of the main uncertain items that must be taken into account, as inverse solution techniques are blocked by several inherent difficulties (i. e. ill-posedness and insufficient quantity and quality of observation data). The easiest way to minimize this uncertainty is to collect great amounts of data. The aim of this work is to build and test a decision model able to locate the position of a fixed number of sample points in order to obtain the "optimal" parameters estimation minimizing the parameters uncertainty and the overall cost of the experimental campaign. This decision model is applied to the estimation of the longitudinal and transversal dispersivity coefficients from simulated field experiments. The classical design of experiment techniques are based on the optimization of the amount of information obtained from experimental data with the hypothesis that the sample domain is defined on a continuous space over time and position (Altmann-Dieses et al. (2002), Carrera, J. at al. (1984), Jacquez, J.A. (1998)). Since this assumption does not always reflect the real situation, especially when field campaigns are to be performed or when the piezometric wells are already present on the site, an approach based on discrete and iterative optimization over a fixed grid of possible sampling points is proposed. The estimates are updated with a Bayesian approach and the iterative process is stopped when the imposed convergence criterium based on the analysis of the variance is reached. The decision model is tested on a bidimensional transport problem considering a bunch of different boundary conditions often found in reality. The concentration experimental data are generated perturbing some rigorous analytical solutions of the advection-dispersion model with a normally distributed experimental error with given variance (a Monte Carlo based technique is used to generate normally distributed random variables). In order to define the optimal sampling points in the porous medium, binary decision variables are introduced: they assume value one when the concentration is measured at a specific point and time, zero otherwise. The objective function is iteratively minimized with a genetic algorithm and it is proportional to the calculated covariance of the estimated parameters and the decision variables. The formalized constraints regard the possible number of measures, according to the available budget.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2004
- Bibcode:
- 2004AGUFM.H21E1073C
- Keywords:
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- 1829 Groundwater hydrology;
- 1832 Groundwater transport;
- 1869 Stochastic processes