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1

Zastosowanie cyfrowych filtrów rzędu ułamkowego typu wykładniczego do analizy układów o parametrach rozłożonych

100%

Siwczyński M. , Drwal A. , Żaba S.

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tom R. 88, nr 2

184-190

PL

Niektóre zjawiska fizyczne opisywane są równaniami różniczkowymi z pochodnymi rzędu ułamkowego. W artykule zaprezentowano sposób modelowania takich zjawisk przy użyciu filtru cyfrowego rzędu ułamkowego typu wykładniczego. Przedstawiono sposób projektowania filtru cyfrowego rzędu ułamkowego w oparciu o metodę pierwiastka splotowego. Współczynniki filtru typu wykładniczego wyznaczono w oparciu o metodę splotową oraz metodę szeregu potęgowego. Jako przykład zastosowania zaprojektowanego filtru przedstawiono sposób modelowania procesów falowych w linii długiej. Parametry filtru dobrano dla różnych modeli linii: stratnej, niezniekształcającej, bezindukcyjnej i bezpojemnościowej.

EN

Some physical phenomena are described by differential equations with fractional order derivatives. The article demonstrates how to model these phenomena using the fractional order digital filter of an exponential type. There is a design method of the fractional order digital filter presented, which is based on a fractional convolution method. The coefficients of the exponential filter type were determined on the basis of the convolution and the power series method. As an example of usage of the designed filter, there is the way of modeling of wave processes in a long line demonstrated. The filter parameters were chosen for various models of the lines – a lossy, a non-distortion, a non-inductive and a noncapacitive.

2

Feedback design of differential equations of reconstruction for second-order distributed parameter systems

100%

Maksimov V. I. , Mordukhovich B. S.

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tom Vol. 27, no. 3

467--475

EN

The paper aims at studying a class of second-order partial differential equations subject to uncertainty involving unknown inputs for which no probabilistic information is available. Developing an approach of feedback control with a model, we derive an efficient reconstruction procedure and thereby design differential equations of reconstruction. A characteristic feature of the obtained equations is that their inputs formed by the feedback control principle constructively approximate unknown inputs of the given second-order distributed parameter system.

3

Regional observation and sensors

84%

El Jai A. , Hamzaoui H.

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tom Vol. 19, no 1

5-14

EN

The purpose of this short paper is to provide original results related to the choice of the number of sensors and their supports for general distributed parameter systems. We introduce the notion of extended sensors and we show that the observation error decreases when the support of a sensor is widened. We also show that the observation error decreases when the number of sensors increases.

4

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

84%

Patan M. , Kowalów D.

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tom 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.

5

Configuring a sensor network for fault detection in distributed parameter systems

67%

Patan M. , Uciński D.

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tom 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.