RECOVERING INPUT SIGNALS OF NON STATIONARY DYNAMICAL SYSTEMS 

Krivulin Nikolay Petrovich, Candidate of engineering sciences, associate professor, sub-department of higher and applied mathematics, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: krivulin@bk.ru 

681.311 

10.21685/2072-3040-2018-3-6 

Background. The development of hardware and software methods for restoring input signals and increasing their accuracy is an actual problem that occurs in many branches of technology. This work is devoted to the development of methods for reconstructing input signals of non stationary dynamical systems. The methods proposed in the work do not depend on the physical nature of the measured value, which makes it possible to apply in many measurement areas and to build computational algorithms for restoring the input signals of measuring converters made on a different element base.
Materials and methods. Methods for restoring input signals are based on numerical algorithms and parametric identification. The proposed ones allow to correct the output signal of dynamic systems, consisting in the hardware or software implementation of the inverse operator to the operator simulating the measuring transducer.
Results. The methods of restoring input signals developed in this work allow us to construct algorithms that perform reduction to an ideal instrument.
Conclusions. The methods allow the correction of distortions by a computing device, which can be a specialized computing device made in the form of a microcontroller or a PC. Computational algorithms that allow to reconstruct the input signals of continuous systems with high accuracy are considered. 

restoration of input signals, reduction to an ideal device, identification of dynamic systems, impulse response function, computational algorithms 

1. Boykov I. V., Krivulin N. P. Analiticheskie i chislennye metody identifikatsii dinamicheskikh sistem: monografiya [Analytical and numerical methods of synamic system identification: monograph]. Penza: Izd-vo PGU, 2016, 398 p.
2. Vasilenko G. I. Teoriya vosstanovleniya signalov [The theory of signal restoration]. Moscow: Sov. radio, 1979, 272 p.
3. Granovskiy V. A. Datchiki i sistemy [Sensors and systems]. 2016, no. 3 (201), pp. 57–72.
4. Sizikov V. S. Ustoychivye metody obrabotki rezul'tatov izmereniy: ucheb. posobie [Stable methods of measurement results processing: tutorial]. Saint-Petersburg: Spetsial'naya literatura, 1999, 240 p.
5. Boykov I. V., Krivulin N. P. Izmeritel'naya tekhnika [Measurement technology]. 2000, no. 9, p. 29.
6. Tikhonov A. H., Arsenin V. Ya. Metody resheniya nekorrektnykh zadach [Methods of incorrect problem solution]. 2nd ed. Moscow: Nauka; Glavnaya redaktsiya fizikomatematicheskoy literatury, 1979, 386 p.
7. Kronrod A. S. Uzly i vesa kvadraturnykh formul. Shestnadtsatiznachnye tablitsy [Nodes and weights of quadrature formulas. Sixteen-digit tables]. Moscow: Nauka, 1964, 144 p.
8. Boykov I. V., Krivulin N. P. Izmeritel'naya tekhnika [Measurement technology]. 2017, no. 11, pp. 3–7.
9. Boykov I. V., Krivulin N. P. Izmeritel'naya tekhnika [Measurement technology]. 2013, no. 4, pp. 6−11.
10. Boykov I. V. Priblizhennye metody vychisleniya singulyarnykh i gipersingulyarnykh integralov. Ch. 2. Gipersingulyarnye integraly [Approximate methods of computing singular and hypersingular integrals. Part 2. Hypersingular integrals]. Penza: Izd-vo PGU,
2009, 252 p.
11. Boykov I. V., Dobrynina H. F., Domnin L. H. Ppiblizhennye metody vychisleniya integpalov Adamapa i peshenie gipepsingulyapnykh integpal'nykh uravneniy [Approximate methods of computing Hadamard integrals and solving hypersingular integral equations]. Penza: Izd-vo PGTU, 1996, 188 p.
12. Boykov I. V., Krivulin N. P. Metrologiya [Metrology]. 2012, no. 8, pp. 3–14.
13. Boykov I. V., Krivulin N. P. Sibirskiy zhurnal industrial'noy matematiki [Siberian journal of industrial mathematics]. 2018, vol. XXI, no. 2 (74), pp. 17−31.
14. Shcherbakov M. A. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki [University proceedings. Volga region. Engineering sciences]. 2011, no. 4 (20), pp. 43–56.
15. Krivulin N. P. Matematicheskoe i komp'yuternoe modelirovanie estestvennonauchnykh i sotsial'nykh problem: sb. st. VIII Mezhdunar. nauch.-tekhn. konf. molodykh spetsialistov, aspirantov i studentov [Mathematical and computer modeling of natural scientific and social problems: proceedings of VIII International scientific and technical conference of young specialists, undergraduate and postgraduate students]. Penza: Izd-vo PGU, 2014, pp. 172–178.
16. Boykov I. V., Krivulin N. P. Metrologiya [Metrology]. 2014, no. 7, pp. 13–23.
17. Boykov I. V., Krivulin N. P. Metrologiya [Metrology]. 2013, no. 9, pp. 3–16.
18. Boykov I. V., Krivulin N. P. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki [University proceedings. Volga region. Engineering sciences]. 2013, no. 2 (26), pp. 120–129.