Optimal design techniques for distributed parameter systems

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 d...

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Detalles Bibliográficos
Publicado:	2013
Materias:	Estimation Optimal systems Optimization Distributed parameter systems Optimal locations Optimal observation Optimization problems Optimization scheme Ordinary least squares Sensitivity functions Source identification Inverse problems
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97815108_v_n_p83_Banks http://hdl.handle.net/20.500.12110/paper_97815108_v_n_p83_Banks
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_97815108_v_n_p83_Banks
record_format	dspace
spelling	paper:paper_97815108_v_n_p83_Banks2023-06-08T16:37:55Z Optimal design techniques for distributed parameter systems Estimation Optimal systems Optimization Distributed parameter systems Optimal locations Optimal observation Optimization problems Optimization scheme Ordinary least squares Sensitivity functions Source identification Inverse problems 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. © Copyright SIAM. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97815108_v_n_p83_Banks http://hdl.handle.net/20.500.12110/paper_97815108_v_n_p83_Banks
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Estimation Optimal systems Optimization Distributed parameter systems Optimal locations Optimal observation Optimization problems Optimization scheme Ordinary least squares Sensitivity functions Source identification Inverse problems
spellingShingle	Estimation Optimal systems Optimization Distributed parameter systems Optimal locations Optimal observation Optimization problems Optimization scheme Ordinary least squares Sensitivity functions Source identification Inverse problems Optimal design techniques for distributed parameter systems
topic_facet	Estimation Optimal systems Optimization Distributed parameter systems Optimal locations Optimal observation Optimization problems Optimization scheme Ordinary least squares Sensitivity functions Source identification Inverse problems
description	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. © Copyright SIAM.
title	Optimal design techniques for distributed parameter systems
title_short	Optimal design techniques for distributed parameter systems
title_full	Optimal design techniques for distributed parameter systems
title_fullStr	Optimal design techniques for distributed parameter systems
title_full_unstemmed	Optimal design techniques for distributed parameter systems
title_sort	optimal design techniques for distributed parameter systems
publishDate	2013
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97815108_v_n_p83_Banks http://hdl.handle.net/20.500.12110/paper_97815108_v_n_p83_Banks
_version_	1768542763374084096

Optimal design techniques for distributed parameter systems

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