DOI: https://doi.org/10.15588/1607-3274-2020-2-8

### OPERATIVE RECOGNITION OF STANDARD SIGNAL TYPES

V. V. Avramenko, V. M. Demianenko

#### Abstract

Context. Recognizing the type of function regardless of its parameters is an urgent task.

Objective. To develop methods for the operational quantitative measurement of deviations of the type of the analyzed function, representing the analyzed process, from the standard types of functions: power, polynomial, exponential and sinusoidal according to the data obtained at the current time.

Method. To solve the problem, methods based on disproportion functions have been developed. The existing disproportion functions and their application for the recognition of power and polynomial functions are given. To recognize the exponential and sinusoidal functions at the current time, the disproportion over the first-order derivative with respect to its derivatives is used. With the parametric specification of functions, it is the difference between the ratios of the values of two functions and the ratio of their first derivatives for a given parameter value. In the case of a proportional relationship between two functions, this disproportion function is equal to zero for any value of the proportionality coefficient. It is shown that if for a given value of the argument the disproportion over the first-order derivative of the analyzed function with respect to its first derivative is zero, this is a sign that the function is exponential at this point regardless if it’s parameters. To control the sinusoidality at the current time, the disproportion over the first-order derivative of the analyzed function with respect to its second derivative is calculated. If it is zero, this is a sign that the function is sinusoidal at a given point regardless of its amplitude, frequency and phase of the oscillations. It is shown that in this way it is also possible to control the sum of sinusoids with different amplitudes and phases, but with the same frequency. You can also control second-degree sine waves.

Results. The effectiveness of the proposed methods is shown by computer simulation of the decay of radioactive isotopes, as well as simulation in violation of the sinusoidal nature of the controlled process.

Conclusions. Based on the disproportion functions, methods have been developed for the operative recognition of the type of function that describes the analyzed process. These methods can be used to analyze chemical-technological processes, control the purity of radioactive isotopes, and also to control the sinusoidality of processes in electrical networks.

#### Keywords

Disproportion functions, type of numerical function, sinusoid distortion, exponential function, polynomial function, power function.

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#### References

Holin B. G. Centrobezhnye i vibracionnye granuljatory plavov i raspyliteli zhidkosti. Moscow, Mashinostroenie, 1977, 182 p.

Varetskiy Yu. E., Nakonechnyiy T. I. , N. D. Fedonyuk, V. A. Komar Arhitektura intellektualnoy sistemyi monitoringa nesinusoidalnyih rezhimov raboty elektricheskoy seti, Energetika i electronika, 2010, No. 1, pp. 1–11.

Ahammodullah H., Mohammad A. M., Mohammad O. M. Applications of Fourier Series in Electric Circuit and Digital Multimedia Visualization Signal Process of Communication System, American Journal of Circuits, Systems and Signal Processing, 2018, Vol. 4, No. 4, pp. 72–80.

Marques C. A. G., Ribeiro M. V., Duque C. A. et al. Parameters Estimation of Time-Varying Harmonics / // Power Quality Issues eds.: A. F. Zobaa. London, 2013, Chapter 9, pp. 231–248. DOI: 10.5772/53816

Miroshnik A. A. Raspoznavanie tipa nesinusoidalnyh iskazhenij s pomoshyu nejronnoj seti, Energetika i avtomatika, 2014, No. 3, pp. 86–95.

Popov S. V., Gapon D. A., Cheremisin N. M., Miroshnik A. A. Raspoznavanie obraza iskazhennogo elektricheskogo signala v raspredelitelnyh setyah s ispolzovanie vejvlet-analiza i nejrosetevogo modelirovaniya, Energetika ta komp’yuterno-integrovani tehnologiyi v APK, 2014, No. 2, pp. 69–75.

Wei Yi, Yang Chenhui, Yangand Hang, Xu Yaming A Novel Signal Similarity Evaluation Algorithm and its Application in Irregular Shape Recognition, Journal of Physics: Conf. Series, 2017, Vol. 910, Article number: 012033. DOI: 10.1088/1742-6596/910/1/012033

Rix H. Detection of small variations in shape between two chromatographic peaks, Journal of Chromatogrraphy, 1981, Vol. 204, pp. 163–165.

Rix H. Signal shape recognition in a sum of two signals : project report : ISRN I3S/RR–2010-12-FR / UNSA-CNRS ; Informatique, signaux et systemes de Sophia Antipolis, 2010, 16 p.

Rix H. Offset removing in the domain of signal shapes, Colloque National Recherche en Imagerieet Technologies pour la Santé, Rennes, France, 6–8 April 2011, pp. 10–13.

Avramenko V. V. Ispol’zovanie harakteristik neproporcional’nosti dlja raspoznavanija vida chislovyh funkcij, Vіsnik SumDU, 2002, No. 12, P. 15.

Avramenko V. V. Harakteristiki neproporcional’nosti i ih primenenie pri reshenii zadach diagnostiki, Vіsnik SumDU. 2000, No. 16, pp. 12–20.

Kalashnikov V. V., Avramenko V. V., Slipushko N. Y. , et al.]. Identification of quasi-stationary dynamic objects with the use of derivative disproportion functions, Procedia Comput Sci, 2017, Vol. 108, pp. 2100–2109.

Kalashnikov V.V. Avramenko V. V. ., Kalashnykova N. I. eds.: Watada J, Tan SC, Vasant P, et al. Derivative disproportion functions for pattern recognition, Unconventional modelling, simulation, and optimization of geoscience and petroleum engineering. Berlin-Heidelberg, Springer-Verlag, 2018, pp. 95–104.

Kalashnikov V. V., Avramenko V. V., Kalashnykova N. I. eds.: J. Rodrigues, P. J. S. Cardoso, J. Monteiro et al.Sums of key functions generating cryptosystems, Lecture Notes in Computer Science. Cham, Springer; 2019, Vol. 11540, pp. 293–302. https://doi.org/10.1007/978-3-030-22750-0_23

L’Annunziata M. F. Radioactivity: Introduction and History, From the Quantum to Quarks. Amsterdam, Elsevier, 2017, 932 p.

Rao S. B., Shanta C. K. Numerical Methods: With Program in Basic, Fortran, Pascal & C++. Hyderabad, Universities Press, 2004, 504 p.

#### GOST Style Citations

1. Холин Б. Г. Центробежные и вибрационные грануляторы плавов и распылители жидкости / Б. Г. Холин. – М. : Машиностроение, 1977. – 182 с.

2. Архитектура интеллектуальной системы мониторинга несинусоидальных режимов работы электрической сети / [Ю. Е. Варецкий, Т. И. Наконечный, Н. Д. Федонюк,
В. А. Комар]. // Энергетика и электротехника. – 2010. – № 1. – С. 1–11.

3. Ahammodullah H. Applications of Fourier Series in Electric Circuit and Digital Multimedia Visualization Signal Process of Communication System / H. Ahammodullah, A. M. Mohammad, O.M. Mohammad // American Journal of Circuits, Systems and Signal Processing. – 2018. – Vol. 4, No. 4. – P. 72–80.

4. Parameters Estimation of Time-Varying Harmonics / [C. A. G. Marques, M. V. Ribeiro, C. A. Duque et al.] // Power Quality Issues / eds.: A. F. Zobaa. – London, 2013. – Chapter 9. – P. 231–248. DOI: 10.5772/53816

5. Мирошник А. А. Распознавание типа несинусоидальных искажений с помощью нейронной сети / А. А. Мирошник // Енергетика і автоматика. – 2014. – № 3. – С. 86–95.

6. Распознавание образа искаженного электрического сигнала в распределительных сетях с использование вейвлет-анализа и нейросетевого моделирования / [С. В. Попов, Д. А. Гапон, Н. М. Черемисин, А. А. Мирошник] // Енергетика та комп’ютерноінтегровані технології в АПК. – 2014. – № 2. – С. 69–75.

7. A Novel Signal Similarity Evaluation Algorithm and its Application in Irregular Shape Recognition / [Yi Wei, Chenhui Yang, Hang Yangand, Yaming Xu] // Journal of Physics: Conf. Series. – 2017. – Vol. 910. – Article number: 012033. DOI: 10.1088/1742-6596/910/1/012033

8. Rix H. Detection of small variations in shape between two chromatographic peaks / H. Rix // Journal of Chromatogrraphy. – 1981. – Vol. 204. – P. 163–165.

9. Signal shape recognition in a sum of two signals : project report : ISRN I3S/RR–2010-12-FR / UNSA-CNRS ; H. Rix. – Informatique, signaux et systemes de Sophia Antipolis, 2010. – 16 p.

10. Rix H. Offset removing in the domain of signal shapes / H. Rix // Colloque National Recherche en Imagerieet Technologies pour la Santé, Rennes, France, 6–8 April 2011. – P. 10–13.

11. Авраменко В. В. Использование характеристик непропорциональности для распознавания вида числовой функции / В. В. Авраменко // Вісник СумДУ. – 2002. – № 12. – С. 15.

12. Авраменко В. В. Характеристики непропорциональности и их применение при решении задач диагностики / В. В. Авраменко // Вісник СумДУ. – 2000. – № 16. – С. 12–20.

13. Identification of quasi-stationary dynamic objects with the use of derivative disproportion functions / [V. V. Kalashnikov, V. V. Avramenko, N. Y. Slipushko , et al.]. // Procedia Comput Sci. – 2017. – Vol. 108. – P. 2100– 2109.

14. Kalashnikov V.V. Derivative disproportion functions for pattern recognition / V. V. Kalashnikov, V. V. Avramenko., N. I. Kalashnykova // Unconventional modelling, simulation, and optimization of geoscience and petroleum engineering / eds.: Watada J, Tan SC, Vasant P, et al. – Berlin-Heidelberg : Springer-Verlag, 2018. – P. 95–104.

15. Kalashnikova N. I. Sums of key functions generating cryptosystems / V. V. Kalashnikov, V. V. Avramenko, N. I. Kalashnykova // Lecture Notes in Computer Science / eds.: J. Rodrigues, P. J. S. Cardoso, J. Monteiro et al. – Cham: Springer; 2019. – Vol. 11540. – P. 293–302. – https://doi.org/10.1007/978-3-030-22750-0_23

16. L’Annunziata M. F. Radioactivity: Introduction and History, From the Quantum to Quarks / M. F. L’Annunziata. – Amsterdam : Elsevier, 2017. – 932 p.

17. Rao S. B. Numerical Methods: With Program in Basic, Fortran, Pascal & C++ / S. B. Rao, C. K. Shanta. – Hyderabad : Universities Press, 2004. – 504 p.

Copyright (c) 2020 V. V. Avramenko, V. M. Demianenko