INTERVAL APPROACH TO DETERMINATION OF CALIBRATION CHARACTERISTICS OF INFORMATION TRANSFORMERS
Keywords:Measuring instrument, calibration characteristic, measured value, measurement result, interval mathematics
AbstractContext. When designing various measuring instruments, the problem arises of constructing the so-called calibration characteristic
of a measuring device, i.e. the quantitative dependence of the measurement result on the measured value. This characteristic is
inverse to the direct characteristic – the dependence of the measured value on the measurement result. This problem is solved on the
basis of approximate data obtained during the experiment with the measuring instrument. A new method for solving this problem is
proposed, based on the apparatus of interval mathematics.
Objective. The aim of the work is to develop a completely formalized method for constructing the calibration characteristic
of a measuring instrument from approximate data obtained in the experiment with this instrument.
Method. The method proposed in this article consists in presenting the function of direct con-version of a measuring device in the
form of a linear interval function, determining its interval parameters (coefficients) from experimental data and solving the resulting
interval dependence between the measurement result and the measured quantity with respect to the measured value. The method of
solving interval equations is used.
Result. General formulas are obtained that determine interval calibration characteristic of the measuring instrument on the basis of
data obtained in the experiment with the instrument. A detailed analysis of formulas is performed. General laws are established that
obey direct and inverse (calibration) characteristics of measuring instrument, as well as the relationship between direct and inverse
characteristics (if the instrument is linear transformer).
Conclusions. The article proposes a new approach to the construction of calibration characteristics of measuring instruments,
based on use of interval mathematics, for processing data from experiments with instruments. This approach, unlike existing ones,
makes it possible to build calibration characteristics of measuring devices and analyze them purely analytically.
Wiener N. Extrapolation, Interpolation and Smoothing of Stationary Time Series. N.-Y., Technology Press and Wiley, 1949, 180p.
Kolmogorov A.N. Interpolirovanie i Ekstrapolirovanie Stacionarnyh Sluchaynyh Posledovatelnostey, Transactions of Academy
of Sciences of USSR. Mathematics, 1941, No. 5, pp. 3–14.
Morse P. M., Kimbal. G.E. Methods of Operations Research. N.-Y.: J. Wiley, 1951, 158 p.
Ventcel E. S., Lihterev Ya. M., Milgram Yu. G., Hudyakov I. V. Osnovy Teorii Boevoy Effektivnosti i Issledovaniya Operaciy. Мoscow, VVIA, 1961, 524 p.
Nalimov V. V., Chernova N. A. Statisticheskie Metody Planirovaniya Extremalnyh Experimentov. Moscow, Nauka, 1965, 340 p.
Nalimov V. V., Chernova N. A. Teoriya Experimenta. Moscow, Nauka, 1971, 320 p.
Zadeh L.A. The Concept of a Linguistic Variable and its Application to Approximate Reasoning. N-Y, American Elsevier
Publishing Company, 1973, 176 p.
Narinjyani A. S. Nedoopredelennost v Sisteme Predstavleniya i Obrabotki Znaniya, Transactions of Academy of Science of
USSR. Technical Cybernetics, 1986, No. 5, pp. 17–25.
Hyvonen E. Constraint Reasoning Based on Interval Arithmetic:the Tolerance Propagation Approach, Artificial Intelligence,
, Vol. 58, P. 19.
Moore R.E. Interval Analysis. N.-Y., Prentice-Hall, 1966, 230 p.
Kantorovich L. V. O Nekotoryh Novyh Podhodah k Vyhchislitelnym Metodam i Obrabotke Nablyudeniy, Sibirskiy matematicheskiy
zhurnal, 1962, Vol. 3, No. 5, pp. 17–25.
Alefeld G., Herzberger J. Introduction to Interval Computation. N.Y., Academic Press, 1983, 352 p.
Voschinin A. P., Sotirov G. R. Optimizaciya v Usloviyah Neopredelennosti. Moscow, MEI, Sofiya, Tehnika, 1989, 226 p.
Kurzhanskiy A. B. Identification Problem – Theory of Guaranteed Estimates. Part 1, Automation and Remote Control,
, Vol. 52, No. 4, pp. 447–465.
Levin V. I. Discrete Optimization under Interval Uncertainty, Automation and Remote Control, 1992, Vol. 53, No. 7,
Levin V. I. Boolean Linear Programming with Interval Coefficients, Automation and Remote Control, 1994, Vol. 55,
No. 7, pp. 1019–1028.
Levin V. I. Interval Discrete Programming, Cybernetics and Systems Analysis, 1994, Vol. 30, No. 6, pp. 866–874.
Voschinin A. P. Intervalniy Analiz Dannyh: Razvitie i Perspektivy, Zavodskaya Laboratoriya, 2002, Vol. 68, No. 1,
Orlov A. I. Statistika Intervalnyh Dannyh, Zavodskaya Laboratoriya. Diagnostika Materialov, 2015, Vol. 81, No. 3,
Skibickiy N. V. Postroenie Pryamyh i Obratnyh Statisticheskih Harakteristik Objektov po Intervalnym Dannym, Zavodskaya Laboratoriya. Diagnostika Materialov, 2017, Vol. 83, No. 1, pp. 87–98.
Semenov L. A., Siraya T. N. Metody Postroeniya Graduirovochnyh Harakteristik Sredstv Izmereniya. Moscow, Izd-vo
Standartov, 1986, 127 p.
Levin V. I. Intervalnye Uravneniya i Modelirovanie Neopredelennyh Sistem, Sistemy Upravleniya, Svyazi i Bezopasnosti,
, No. 2, pp. 101–112.
Levin V. I. Determination Method and Optimization in the Interval Uncertainty, Proceedings of 10th International conference
“Management of Large-Scale System Development”, MLSD 2017. Moscow, 2017, pp. 214–223.
Levin V.I. Intervalnye Uravneniya v Zadachah Obrabotki Dannyh, Zavodskaya Laboratoriya. Diagnostika Materialov, 2018,
Vol. 84, No. 3, pp. 73–78.
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