Optimal Design Techniques for Distributed Parameter Systems
Harvey Thomas Banks, Diana Rubio, N. Saintier, María Inés Troparevsky · Society for Industrial and Applied Mathematics eBooks · 2013
A wide number of inverse problems consist in selecting best parameter values of a given mathematical model based fits to measured data. These are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data. The problem of collecting data in the “best way” in order to assure a statistically efficient estimate of the parameter is known as Optimal Design. In this work we consider the problem of finding optimal locations for source identification in the 3D unit sphere from data on its boundary. We apply three different optimal design criteria to this 3D problem: the Incremental Generalized Sensitivity Function (IGSF), the classical D-optimal criterion and the SE-criterion recently introduced in [3]. The estimation of the parameters is then obtained by means of the Ordinary Least Square procedure on the resulting optimal observation points and compared to that for a uniform observation mesh‥ In order to analyze the performance of each strategy, the data are numerically simulated and the estimated values are compared with the values used for simulation.