Measurement optimization with minimax criteria for parameter estimation in distributed systems

Uciński, Dariusz; Korbicz, Józef

doi:10.23919/ecc.1997.7082284

Cited by 21 publications

(24 citation statements)

References 9 publications

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“…The refinement means the placement of additional sensors in zones of the large error density. Generally speaking, the redistribution has a greater potential from the viewpoint of optimal sensor configuration and is close to an optimum experiment design [16]. However, it is connected with a great number of algorithmic problems and require high computational resources.…”

Section: Problem Statementmentioning

confidence: 99%

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Criteria of optimality for sensors' location based on adjoint transformation of observation data interpolation error

Alekseev

Navon

2009

Numerical Methods in Fluids

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SUMMARYCriteria of optimality for sensors' location are addressed using an interpolation error transformed by especial adjoint problems. The considered criteria correspond to the analysis error in certain Hessian-based metrics and to the error of some forecast aspect. Both criteria are obtained using adjoint problems that provide computation without the direct use of the Hessian. For a linear inverse heat conduction problem, these criteria are compared and demonstrated promising results when compared with a criterion based on the norm of the interpolation error of observation data. Approaches to sensor set modification using either redistribution of sensors' or refinement of the sensors grid (insertion of additional sensors) are also compared.

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Section: Problem Statementmentioning

confidence: 99%

“…In a significant number of works on the optimum experiment design [16][17][18][19], certain measures of the FIM (determinant, maximum or minimum eigenvalues, traces) are used as criteria for an optimal sensor placement. These approaches are rather computationally extensive due to the need to directly operate with FIM or the Hessian.…”

Section: Introductionmentioning

confidence: 99%

Criteria of optimality for sensors' location based on adjoint transformation of observation data interpolation error

Alekseev

Navon

2009

Numerical Methods in Fluids

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“…where ω(dx) signifies the maximal possible 'number' of sensors per dx (Fedorov and Hackl, 1997;Uciński, 1999;. Logically, this bounding measure must satisfy the condition…”

Section: Reformulation In Terms Of D S -Optimal Sensor Densitiesmentioning

confidence: 99%

Sensor network scheduling for identification of spatially distributed processes

Uciński

2010

2010 Conference on Control and Fault-Tolerant Systems (SysTol)

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The work treats the problem of fault detection for processes described by partial differential equations as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A simple node activation strategy is discussed for the design of a sensor network deployed in a spatial domain that is supposed to be used while detecting changes in the underlying parameters which govern the process evolution. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset of them can be selected because of the cost constraints. As a suitable performance measure, the Ds-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. The problem is then formulated as the determination of the density of gauged sites so as to maximize the adopted design criterion, subject to inequality constraints incorporating a maximum allowable sensor density in a given spatial domain. The search for the optimal solution is performed using a simplicial decomposition algorithm. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional diffusion process.

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“…The operation and control of such systems usually require precise information on the parameters which condition the accuracy of the underlying mathematical model, but that information is only available through a limited number of possibly expensive sensors. Over the past years, this limitation has stimulated laborious research on the development of strategies for efficient sensor placement (for reviews, see the papers by Kubrusly and Malebranche (1985), van de Wal and de Jager (2001), and the comprehensive monographs by Uciński (1999;). Nevertheless, although the need for systematic methods was widely recognized, most techniques communicated by various authors usually are limited to sensor network nodes with no mobility, and rely on exhaustive search over a predefined set of candidates.…”

Section: Problem Formulation In Terms Ofmentioning

confidence: 99%

Sensor network design for the estimation of spatially distributed processes

Uciński¹,

Patan²

2010

International Journal of Applied Mathematics and Computer Science

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In a typical moving contaminating source identification problem, after some type of biological or chemical contamination has occurred, there is a developing cloud of dangerous or toxic material. In order to detect and localize the contamination source, a sensor network can be used. Up to now, however, approaches aiming at guaranteeing a dense region coverage or satisfactory network connectivity have dominated this line of research and abstracted away from the mathematical description of the physical processes underlying the observed phenomena. The present work aims at bridging this gap and meeting the needs created in the context of the source identification problem. We assume that the paths of the moving sources are unknown, but they are sufficiently smooth to be approximated by combinations of given basis functions. This parametrization makes it possible to reduce the source detection and estimation problem to that of parameter identification. In order to estimate the source and medium parameters, the maximum-likelihood estimator is used. Based on a scalar measure of performance defined on the Fisher information matrix related to the unknown parameters, which is commonly used in optimum experimental design theory, the problem is formulated as an optimal control one. From a practical point of view, it is desirable to have the computations dynamic data driven, i.e., the current measurements from the mobile sensors must serve as a basis for the update of parameter estimates and these, in turn, can be used to correct the sensor movements. In the proposed research, an attempt will also be made at applying a nonlinear model-predictive-control-like approach to attack this issue.

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Measurement optimization with minimax criteria for parameter estimation in distributed systems

Cited by 21 publications

References 9 publications

Criteria of optimality for sensors' location based on adjoint transformation of observation data interpolation error

Criteria of optimality for sensors' location based on adjoint transformation of observation data interpolation error

Sensor network scheduling for identification of spatially distributed processes

Sensor network design for the estimation of spatially distributed processes

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