ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)

vol 67 / May, 2024

DOI 10.17586/0021-3454-2016-59-7-547-557

UDC 681.326


V. I. Senchenkov
Professor; A. F. Mozhaysky Military Space Academy, Department of Special Technological Systems of Space Complexes; Professor

Read the full article 

Abstract. A new approach to the formation of the set of controlled parameters of the complex technical systems is proposed. The essence of the method is the processing of the trajectories of the output processes of the system on the base of the theory of the spaces of the measurable Lebesgue square-integrable functions. The approach allows for the trajectories with an arbitrary set of the finite discontinuities to be approximated by partial sums of the Fourier series, thereby to take into account the complexity of the structure and algorithms of the systems operation. It is shown that coefficients of the trajectory expansion into a finite Fourier series on the base of orthonormal Legendre polynomials may be employed as control indicators. Dependences used for calculation of values of the controlled indicators and for the definition of their number are improved as compared to those proposed in previous works by the author based on other bases. 
Keywords: technical condition, diagnosis, observed condition, controlled indicator, trajectory, Lebesgue measurability, technical condition image, Legendre basis, orthogonal trigonometric basis

  1. Dmitriev A.K., Mal'tsev P.A. Osnovy teorii postroeniya i kontrolya slozhnykh sistem (Bases of the Theory of Construction and Control of Complex Systems), Leningrad, 1988, 192 р. (in Russ.)
  2. Acar Y., Kadipasaoglu S., Schipperijn P. Intern. J. of Production Research, 2010, no. 11(48), pp. 3245–3268.
  3. Sokolov B., Ivanov D. IFAC – Papers Online, 2015, no. 3(48), pp. 1533–1538. 
  4. Statnikov I.N., Firsov G.I. Transactions of TSTU, 2015, no. 1(21), pp. 36–41. DOI:10.17277/vestnik.2015.01.pp.036-041. (in Russ.)
  5. Sen'chenkov V.I., Motorin V.M., Grushkovskiy P.A. Izv. vuzov. Priborostroenie, 2015, no. 10(58), pp. 783–791. (in Russ.)
  6. Sen'chenkov V.I. Modeli, metody i algoritmy analiza tekhnicheskogo sostoyaniya (Models, Methods and Analysis Algorithms of Technical Condition), Saarbrücken, 2013, 377 р. (in Russ.)
  7. Sen'chenkov V.I. Aerospace Instrument-Making, 2005, no. 10, pp. 27–32. (in Russ.)
  8. Kolmogorov A.N., Fomin S.V. Elementy teorii funktsiy i funktsional'nogo analiza (Elements of the Theory of Functions and Functional Analysis), Moscow, 2009, 572 р. (in Russ.)
  9. Zorich V.A. Matematicheskiy analiz (Mathematical Analysis), pt. 1, Moscow, 2002, 674 р. (in Russ.)
  10. Halmos P.R. Measure Theory, Springer Verlag, 1950.
  11. Tenenev V.A., Rusyak I.G., Sufiyanov V.G., Ermolaev M.A., Nefedov D.G. Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming & Computer Software, 2015, no. 1(8), pp. 76–87. DOI:10.14529/mmp150106. (in Russ.)
  12. Volovich G. I., Solomin E. V., Topolskaya I. G., Topolsky D. V. Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming & Computer Software, 2014, no. 4(7), pp. 120–125. (in Russ.)
  13. Suetin P.K. Klassicheskie ortogonal'nye polinomy (Classical Orthogonal Polynomials), Moscow, 1979, 416 р. (in Russ.)
  14. Sen'chenkov V.I., Absalyamov D.R. Aerospace Instrument-Making, 2011, no. 3, pp. 36–41. (in Russ.)
  15. Sen'chenkov V.I. Izv. vuzov. Priborostroenie, 2010, no. 1(53), pp. 3–8. (in Russ.)
  16. Kan Yu.S. Automation and Remote Control, 2011, no. 2, pp. 71–76. (in Russ.)
  17. Granichin O.N. Automation and Remote Control, 2015, no. 5, pp. 43–59. (in Russ.)
  18. Birger I.A. Tekhnicheskaya diagnostika (Technical Diagnostics), Moscow, 1978, 240 р. (in Russ.)
  19. Tou J.T. and Gonzalez R. Pattern Recognition Principles, Addison-Wesley, Reading, MA, 1974.