Optimal Sampling for Parameters Estimation

In the problems concerning prediction and modeling, parameters estimation constitutes one of the main uncertain items that must be taken into account. The easiest way to minimize this uncertainty is to collect great amounts of data. The aim of this work is to build a decision model able to choose the optimal position of the sample point used for the parameters estimation, minimizing the parameters uncertainty. The decision model is applied to the estimation of the dispersivity coefficients, longitudinal and transversal, from soil column experiment. The classical design of experiments 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. Since this assumption does not reflect the real experimental situation, especially when field campaigns are to be performed and the position of the piezometric wells is fixed, an approach based on discrete optimization over a fixed grid of possible sampling is proposed. The soil column representation is discretized in the 2D domain, while the concentration experimental data are generated using a rigorous analytical solution of the advection dispersion model and a Monte Carlo simulator to generate the experimental error at given variance. In order to define the optimal sampling points in the soil column, 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 to be finally minimized is proportional to the calculated covariance of the estimated parameters and to the decision variables.. The formalized constraints regard the possible number of measures, according to the available funds. Finally, the results of the optimisation problem are discussed.