Wyniki wyszukiwania - BazTech

1

Błąd jako podstawa wyznaczania niepewności wyniku pomiaru

Jakubiec J.

Pomiary Automatyka Kontrola

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2014

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R. 60, nr 11

991--993

PL

Podano ogólną definicję błędu pomiaru, a następnie scharakteryzowano dwie jego definicje stosowane dla potrzeb opisu niedokładności wyniku pomiaru. Jedna z nich stosowana jest w symulacyjnym badaniu niedokładności pomiarów, druga stanowi podstawę formalizacji procedur wyznaczania niepewności wyniku pomiaru. Rozważania teoretyczne zilustrowano przykładami.

EN

A general description of a measurement error and two definitions directed to expressing inaccuracy of a measurement result have been presented. The first one (1), called a priori, is useful in simulation experiments while the second one (2), called a posteriori, is the basis of the result uncertainty calculation. Generally, the error is given as a set of values and can be described in deterministic or random ways. The exemplary deterministic equation (4) describes the quantization error of the A/D converter shown in Fig. 1. The graphical form of this error is presented in Fig. 2 and its random representation in Fig. (4) as the histogram which is approximated by the probability density function (5). Values of the a posteriori error can be obtained after realization of a measurement experiment because, in this error definition (2), the reference point needed for the error value calculation is the estimate of the measurement result. Such a property of the error causes that its definition can be the basis of the formal definition (6) of the uncertainty U of a measurement result. Moreover, accordingly with this definition, the uncertainty value can be calculated by using the expression (7) for given value of the confidence level p and, what is more, the measurement result can be written in the interval form (14). Therefore, the a priori definition of the measurement error can be treated as the good formal basis of the procedures used in practice for the measurement uncertainty calculation [7].

2

O formalnych podstawach składania niepewności A i B

Jakubiec W.

Pomiary Automatyka Kontrola

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2012

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R. 58, nr 3

233-235

PL

Przedmiotem rozważań są podstawy formalne procedury składania niepewności typu A i B, zaproponowanej w przewodniku GUM [1]. W artykule poddano analizie podstawy matematyczne tej procedury i wykazano ich niespójność, a następnie omówiono nowy sposób obliczania niepewności, bazujący na modelu wyniku pomiaru.

EN

Considerations presented in the paper deal with the visible absence of formal bases of the A and B type uncertainty composition procedure proposed in GUM [1] and based on partial uncertainty composition described by formula (1). This lack of formality is caused by the fact that the uncertainty of type A is calculated on a basis of the measurement result series and one cannot point any other set of measurements, which may be composed with this series. The first part of the paper is devoted to presentation of a single measurement result model (2) in application to the uncertainty calculation procedure based on the uncertainty definition (3) and determined by functional (4). In the succeeding part, an analysis of formula (1) from the point of view of the random error model given by (6) is realised. By analogy to uncertainties of A and B type, the errors of the same type have been determined, which enabled obtaining equation (10) and comparing it with equation (1). The final part of the paper contains discussion of conclusions which can be drawn from this comparison.

3

Neuronowa korekcja błędów dynamicznych przetwornika II-go rzędu

Roj J.

Pomiary Automatyka Kontrola

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2010

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R. 56, nr 11

1315-1317

PL

W artykule przedstawiono wyniki wstępnych badań dotyczących możliwości wykorzystania jednokierunkowych sieci neuronowych do korekcji błędów dynamicznych wprowadzanych przez przetworniki opisane liniowym równaniem różniczkowym II-go rzędu. Oceniono zasadność stosowania tego rodzaju podejścia do zagadnienia korekcji błędów dynamicznych. Wnioski sformułowano w oparciu o wyniki badań symulacyjnych.

EN

Dynamic properties of second order transducers are usually modelled by the linear differential equation (1) which can be converted to the discrete equation of state (6). Recursive solving of this equation for the input quantity (Eqs. 8 and 9) is a dynamic error correction algorithm. This algorithm can be written in the form of equations (10 and 11) which can be solved by simple, feed-forward neural networks of structures shown in Fig.1. Fig. 2 illustrates the use of neural networks for realisation of the dynamic correction recursive algorithm. The possibility of applying neural networks to dynamic error correction was investigated by simulations in the Matlab Neural Toolbox environment. There were taken the following assumptions concerning the transducer model: , , and the discretization period . The network was learned using a 200 - element learning set generated on a basis of relation (14). The network was tested with a 200 000 - element testing set. The test results of both networks showed error - free implementation of (10) and (11) (errors of 10-15 order). At the next stage the learning sets were quantizied with 12 - bit resolution. The influence of the discretization period on the accuracy of correction realisation was also investigated. Fig. 7 presents the results as a dependency of the output results on the discretization period .