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1

Distributed scheduling of measurements in a sensor network for parameter estimation of spatio-temporal systems

Patan M., Kowalów D.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 1

39--54

EN

The main aim of the paper is to develop a distributed algorithm for optimal node activation in a sensor network whose measurements are used for parameter estimation of the underlying distributed parameter system. Given a fixed partition of the observation horizon into a finite number of consecutive intervals, the problem under consideration is to optimize the percentage of the total number of observations spent at given sensor nodes in such a way as to maximize the accuracy of system parameter estimates. To achieve this, the determinant of the Fisher information matrix related to the covariance matrix of the parameter estimates is used as the qualitative design criterion (the so-called D-optimality). The proposed approach converts the measurement scheduling problem to a convex optimization one, in which the sensor locations are given a priori and the aim is to determine the associated weights, which quantify the contributions of individual gaged sites to the total measurement plan. Then, adopting a pairwise communication scheme, a fully distributed procedure for calculating the percentage of observations spent at given sensor locations is developed, which is a major novelty here. Another significant contribution of this work consists in derivation of necessary and sufficient conditions for the optimality of solutions. As a result, a simple and effective computational scheme is obtained which can be implemented without resorting to sophisticated numerical software. The delineated approach is illustrated by simulation examples of a sensor network design for a two-dimensional convective diffusion process.

2

Distributed scheduling of sensor networks for identification of spatio-temporal processes

Patan M.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 2

299-311

EN

An approach to determine a scheduling policy for a sensor network monitoring some spatial domain in order to identify unknown parameters of a distributed system is discussed. Given a finite number of possible sites at which sensors are located, the activation schedule for scanning sensors is provided so as to maximize a criterion defined on the Fisher information matrix associated with the estimated parameters. The related combinatorial problem is relaxed through operating on the density of sensors in lieu of individual sensor positions. Then, based on the adaptation of pairwise communication algorithms and the idea of running consensus, a numerical scheme is developed which distributes the computational burden between the network nodes. As a result, a simple exchange algorithm is outlined to solve the design problem in a decentralized fashion.

3

Optimal training strategies for locally recurrent neural networks

Patan K., Patan M.

Journal of Artificial Intelligence and Soft Computing Research

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2011

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Vol. 1, No. 2

103--114

EN

The problem of determining an optimal training schedule for locally recurrent neural network is discussed. Specifically, the proper choice of the most informative measurement data guaranteeing the reliable prediction of neural network response is considered. Based on a scalar measure of performance defined on the Fisher information matrix related to the network parameters, the problem was formulated in terms of optimal experimental design. Then, its solution can be readily achieved via adaptation of effective numerical algorithms based on the convex optimization theory. Finally, some illustrative experiments are provided to verify the presented approach.

4

Sensor network design for the estimation of spatially distributed processes

Uciński D., Patan M.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 3

459-481

EN

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--ikelihood 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.

5

Configuring a sensor network for fault detection in distributed parameter systems

Patan M., Uciński D.

International Journal of Applied Mathematics and Computer Science

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2008

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Vol. 18, no 4

513-524

EN

The problem of fault detection in distributed parameter systems (DPSs) is formulated as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A computational scheme is provided for the design of a network of observation locations in a spatial domain that are supposed to be used while detecting changes in the underlying parameters of a distributed parameter system. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset 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. Then, the solution of a resulting combinatorial problem is determined based on the branch-and-bound method. As its essential part, a relaxed problem is discussed in which the sensor locations are given a priori and the aim is to determine the associated weights, which quantify the contributions of individual gauged sites. The concavity and differentiability properties of the criterion are established and a gradient projection algorithm is proposed to perform the search for the optimal solution. The delineated approach is illustrated by a numerical example on a sensor network design for a two-dimensional convective diffusion process.

6

Optymalne strategie obserwacji w detekcji uszkodzeń układów o parametrach rozłożonych

Patan M., Uciński D., Baranowski P.

Pomiary Automatyka Kontrola

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2005

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R. 51, nr 9 bis

71--73

PL

W pracy przedstawiono problem optymalizacji trajektorii ruchomych czujników pomiarowych w sposób zapewniający maksymalną moc testu weryfikującego prostą hipotezę parametryczną dotyczącą nominalnych wartości parametrów charakteryzujących normalny stan pracy układu o parametrach rozłożonych zdefiniowany w zadanym obszarze przestrzennym. Opracowane podejście polega na sformułowaniu problemu optymalizacji trajektorii ruchu czujników w kategoriach zadania sterowania optymalnego, a następnie jego efektywnym rozwiązaniu w oparciu o istniejące pakiety numeryczne. Zaprezentowano ogólny schemat takiego podejścia prowadzącego do maksymalizacji wiarygodności detekcji oraz dokonano jego weryfikacji w oparciu o przykład numeryczny dotyczący problemu adwekeji-dyfuzji.

EN

The problem under consideration is to determine the optimal strategics of observation taken with movable sensors in such a way as to maximize the power of a simple parametric hypothesis test, which verifies the nominal state of the considered distributed system specified on a given multi-dimensional spatial domain. The optimal trajectiores of sensors movements are determined based on the Ds-optimality criterion defined on the respective Fisher Information Matrix. The proposed approach consists in reformulating the problem of sensor trajectory design as an optimal control one and its effective solution with the use of some existing numerical packages. In this work, a general scheme of such an approach leading to Maximization of the fault detection efficiency in distributed-parameter systems is delineated and tested via computer simulations regarding an advection-diffusion problem.