Skip to main content
SpringerLink
Log in

The Numerical Algorithms for the Measurement of the Deterministic and Stochastic Signals

  • Conference paper
  • First Online:
Book cover Semigroups of Operators -Theory and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 113))

Abstract

Numerical algorithms for the restoration of deterministic and stochastic signals distorted by measuring transducer’s (MT) mechanical inertia and resonances are discussed. The algorithm is based on mathematical model (MM) which consists of the Leontieff type system of equations, the Showalter–Sidorov initial condition, the functional including the difference between the calculated and obtained during the natural experiments observations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Da Prato, G., Zabczyk, J.: Stochastic equations in infinite dimensions. Cambridge University Press, Cambridge. (1992)

    Google Scholar 

  2. Gantmacher, F.R.: The Theory of Matrices. AMS Chelsea Publishing: Reprinted by American Mathematical Society. (2000)

    Google Scholar 

  3. Gliklikh, Yu.E.: Global and Stochastic Analysis with Applications to Mathematical Physics. Springer, London; Dordrecht; Heidelberg; N.-Y. (2011)

    Google Scholar 

  4. Gliklikh, Yu.E.: Izuchenie uravnenij leont’evskogo tipa s belym shumom metodami proizvodnyh v srednem sluchajnyh processov (Investigation of Leontieff Type Equations with White Noise by the Methods of Mean Derivatives of Stochastic Processes). Bulletin of the South Ural State University. Series “Mathematical Modelling, Programming & Computer Software”. 27, 24–34 (2012)

    Google Scholar 

  5. Keller, A.V.: Chislennoe reshenie zadachi optimal’nogo upravlenija vyrozhdennoj linejnoj sistemoj uravnenij s nachal’nymi uslovijami Shouoltera–Sidorova (Numerical Solution of the Optimal Control Problem for Degenerate Linear System of Equations with Showalter-Sidorov Initial Conditions). Bulletin of the South Ural State University. Series “Mathematical Modelling, Programming & Computer Software”. 17(127), 50–56 (2008)

    Google Scholar 

  6. Keller, A.V.: Sistema leont’evskogo tipa: klassy zadach s nachal’nym usloviem Shouoltera–Sidorova i chislennoe reshenie. “The Bulletin of Irkutsk State University” Series “Mathematics”. 3(2), 30–43 (2010)

    Google Scholar 

  7. Keller, A.V.: Chislennoe issledovanie zadach optimal’nogo upravlenija dlja modelej leont’evskogo tipa. - Dissertacija na soiskanie uchenoj stepeni doktora fiziko-matematicheskih nauk. South Ural State University. (2011)

    Google Scholar 

  8. Keller, A.V., Nazarova, E.I.: Svojstvo reguljarizuemosti i chislennoe reshenie zadachi dinamicheskogo izmerenija (The Regularization Property and the Computational Solution of the Dynamic Measure Problem). Bulletin of the South Ural State University. Series “Mathematical Modelling, Programming & Computer Software”. 16(192)(5), 32–38 (2010)

    Google Scholar 

  9. Khudyakov, Yu.V.: Algoritm chislennogo issledovanija modeli Shestakova–Sviridjuka izmeritel’nogo ustrojstva s inercionnost’ju i rezonansami (The Numerical Algorithm to Investigate Shestakov-Sviridyuk’s Model of Measuring Device with Inertia and Resonances). Mat. Zametki YAGU. 20(2), 225–236 (2013)

    Google Scholar 

  10. Kovacs, M., Larsson, S.: Introduction to stochastic partial differential equations. Processing of “New Directions in the Mathematical and Computer Sciences”, National Universities Commission. Abuja. Nigeria. October 8–12. 2007. Publications of the ICMCS. 4, 159–232 (2008)

    Google Scholar 

  11. Melnikova, I.V., Filinkov, A.I., Alshansky, M.A.: Abstract Stochastic Equations II. Solutions in Spaces of Abstract Stochastic Distribotions. Journal of Mathematical Sciences. 116(5), 3620–3656 (2003)

    Google Scholar 

  12. Melnikova, I.V., Filinkov, A.I.: Generalized solutions to abstract stochastic problems. J. Integ. Transf. and Special Funct. 20(3–4), 199–206 (2009)

    Google Scholar 

  13. Nelson, E.: Dynamical Theories of Brownian Motion. Princeton: Princeton University Press. (1967)

    Google Scholar 

  14. Shestakov, A.L.: Dinamicheskaja tochnost’ izmeritel’nogo preobrazovatelja s korrektirujushhim ustrojstvom v vide modeli datchika. Metrology. 2, 26 (1987)

    Google Scholar 

  15. Shestakov, A.L., Keller, A.V., Nazarova E.I.: Numerical solution of the optimal measurement problem. Automation and Remote Control. 1, 107–115 (2012)

    Google Scholar 

  16. Shestakov, A.L., Sviridyuk, G.A.: Novyj podhod k izmereniju dinamicheski iskazhennyh signalov (A New Approach to Measurement of Dynamically Perturbed Signal). Bulletin of the South Ural State University. Series “Mathematical Modelling, Programming & Computer Software”. 16(192)(5), 116–120 (2010)

    Google Scholar 

  17. Shestakov, A.L., Sviridyuk, G.A.: Optimal Measurement of Dynamically Distorted Signals. Bulletin of the South Ural State University. Series “Mathematical Modelling, Programming & Computer Software”. 17(234)(8), 70–75 (2011)

    Google Scholar 

  18. Shestakov, A.L., Sviridyuk, G.A.: O novoj koncepcii belogo shuma. Obozrenie prikladnoy i promyshlennoy matematiki. 19(2), 287–288 (2012)

    Google Scholar 

  19. Shestakov, A.L., Sviridyuk, G.A.: On the Measurement of the “White Noise”. Bulletin of the South Ural State University. Series “Mathematical Modelling, Programming & Computer Software”. 27(286)(13), 99–108 (2012)

    Google Scholar 

  20. Shestakov, A.L., Sviridyuk, G.A., Khudyakov, Yu.V.: Dinamicheskie izmerenija v prostranstvah “shumov” (Dynamic Measurements in Spaces of “Noise”). Bulletin of the South Ural State University. Series “Mathematical Modelling, Programming & Computer Software”. 2(13), 4–11 (2013)

    Google Scholar 

  21. Sviridyuk, G.A., Fedorov, V.E.: Linear Sobolev Type Equations and Degenerate Semigroups of Operators. VSP, Utrecht;Boston;Tokio (2003)

    Google Scholar 

  22. Sviridyuk, G.A., Manakova, N.A.: Dinamicheskie modeli sobolevskogo tipa s usloviem Shouoltera–Sidorova i aditivnymi “shumami” (The Dynamical Models of Sobolev Type with Showalter–Sidorov Condition and Additive “Noise”). Bulletin of the South Ural State University. Series “Mathematical Modelling, Programming & Computer Software”. 7(1), 90–103 (2014)

    Google Scholar 

  23. Sviridyuk, G.A., Zagrebina, S.A.: Zadacha Shouoltera–Sidorova kak fenomen uravnenij sobolevskogo tipa. “The Bulletin of Irkutsk State University” Series “Mathematics”. 3(1), 104–125 (2010)

    Google Scholar 

  24. Zagrebina, S.A., Soldatova, E.A.: Linejnye uravnenija sobolevskogo tipa s otnositel’no \(p\)-ogranichennymi operatorami i additivnym belym shumom. “The Bulletin of Irkutsk State University” Series “Mathematics”. 1, 20–34 (2013)

    Google Scholar 

  25. Zamyshlyaeva, A.A.: Stohasticheskie nepolnye linejnye uravnenija sobolevskogo tipa vysokogo porjadka s additivnym belym shumom (Stochastic Incomplete Linear Sobolev Type High-Ordered Equations with Additive White Noise). Bulletin of the South Ural State University. Series “Mathematical Modelling, Programming & Computer Software”. 40(14), 73–82 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Modelling, South Ural State University (National Research University), 76, Lenina ave, 454080, Chelyabinsk, Russian Federation

    Alevtina V. Keller

  2. Department of Information-Measuring Technique, South Ural State University (National Research University), 76, Lenina ave, 454080, Chelyabinsk, Russian Federation

    Alexander L. Shestakov

  3. Department of Mathematical Physics Equations, South Ural State University (National Research University), 76, Lenina ave, 454080, Chelyabinsk, Russian Federation

    Georgy A. Sviridyuk & Yurii V. Khudyakov

Authors
  1. Alevtina V. Keller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander L. Shestakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Georgy A. Sviridyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yurii V. Khudyakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yurii V. Khudyakov .

Editor information

Editors and Affiliations

  1. School of Mathematics,Statistics and Computer Science, Institute of Mathematics,Technical University of Łódź, University of KwaZulu-Natal, Durban, Poland

    Jacek Banasiak

  2. Lublin University of Technology, Lublin, Poland

    Adam Bobrowski

  3. University of Warsaw, Institute of Applied Mathematics and Mechanics, Warsaw, Poland

    Mirosław Lachowicz

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Keller, A.V., Shestakov, A.L., Sviridyuk, G.A., Khudyakov, Y.V. (2015). The Numerical Algorithms for the Measurement of the Deterministic and Stochastic Signals. In: Banasiak, J., Bobrowski, A., Lachowicz, M. (eds) Semigroups of Operators -Theory and Applications. Springer Proceedings in Mathematics & Statistics, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-12145-1_11

Download citation

Publish with us

Policies and ethics

Search

Navigation