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Wavelet Filtering in Shock Stochastic Systems with High Availability

Received: 19 January 2021     Accepted: 2 February 2021     Published: 23 February 2021
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Abstract

For filtering problems in StSHA under nonGaussian ShD methodological and algorithmically WL support is developed. 3 types of filters are considered: KBF (WLKBF), LPF (WLLPF) and SOLF (WLSOLF). These filters have the following advantages: on-line regime, high accuracy and possibility of algorithmically description of complex ShD. Wavelet filter modifications are based on Galerkin method and Haar wavelet expansions. WLF unlike KBF, LPF and SOLF do not need to integrate system of ordinary differential Eqs. These filters must solve system of linear algebraic Eqs with constant coefficients. KBF (WLKBF) and SOLF (WLSOLF) are recommended for StSHA with additive ShD whereas LPF (WLLPF) are recommended for StSHA with parametric and additive ShD. Basic applications are: on-line identification and calibration of nonstationary processes in StSHA of ShD. Methods are illustrated by example of 3 dimensional differential linear information control system at complex ShD. Basic algorithms and error analysis for KBF (WLKBF) and LPF (WLLPF) are presented and 15 Figure; illustrate filters peculiarities for small and fin damping. These filters allow to estimate the accumulation effects for systematic and random errors. Results may be generalized for filtration, extrapolation with interpolation problems in StSHA and multiple ShD.

Published in International Journal of Systems Engineering (Volume 5, Issue 1)
DOI 10.11648/j.ijse.20210501.11
Page(s) 1-12
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Kalman-Bucy WLF, Linear Pugachev WLF, Shock Disturbances, Stochastic Systems with High Availability (StSHA), Suboptimal Linear WLF, Wavelet Filtering (WLF)

References
[1] Sinitsyn I. N., Sergeev I. V., Korepanov E. R., Konashenkova T. D. Software tools for analysis and synthesis of stochastic systems with high availability (IV). Highly Available Systems. 2017. V. 13. № 3. P. 55−69.
[2] Sinitsyn I. N., Sergeev I. V., Korepanov E. R., Konashenkova T. D. Software tools for analysis and synthesis of stochastic systems with high availability (V). Highly Available Systems. 2018. V. 14. № 1. P. 59−70.
[3] Sinitsyn I. N., Sergeev I. V., Korepanov E. R., Konashenkova T. D. Software tools for analysis and synthesis of stochastic systems with high availability (VI). Highly Available Systems. 2017. V. 14. № 2. P. 40−56.
[4] Sinitsyn I. N., Zykov D. V., Korepanov E. R., Konashenkova T. D. Software tools for analysis and synthesis of stochastic systems with high availability (VII). Highly Available Systems. 2019. V. 15. № 1. P. 47−61.
[5] Sinitsyn I. N., Zykov D. V., Korepanov E. R., Konashenkova T. D. Software tools for analysis and synthesis of stochastic systems with high availability (VIII). Highly Available Systems. 2019. V. 15. № 1. P. 62−69.
[6] Sinitsyn I. N., Sinitsyn V. I., Korepanov E. R., Konashenkova T. D. Software tools for analysis and synthesis of stochastic systems with high availability (X). Highly Available Systems. 2020. V. 16. № 4. P. 24−39. DOI: 10.18127/j20729472-202004-02 (In Russian).
[7] Pugachev V. S., Sinitsyn I. N. Stochastic Differential Systems. Analysis and Filtering, John Wiley & Sons, Chichester, 1987.
[8] Pugachev V. S., Sinitsyn I. N. Stochastic Systems. Theory and Applications, World Scientific, Singapore, 2001.
[9] Socha L. Linearization Methods for Stochastic Dynamic Systems. Lect. Notes Phys. 730. Springer, Berlin Heidelberg, 2008.
[10] Sinitsyn I. N. Kalman and Pugachev Filtering, Torus Press, Moscow, 2005, 1st ed; 2007, 2nd ed.
[11] Heil C., Walnut D. F. Fundamental Papers om Wavelet Theory. Princeton University Press, Princeton, New-Jersey, 2006.
[12] Percival D. B., Walden A. T. Wavelet Methods for Time Series Analysis. Cambridge University Press, Cambridge, 2000.
[13] Gagnon L., Lina J. M. (1994). Symmetric Daubechies' wavelets and numerical solutions of NLS2 equations. J. Phys. A: Math. Gen. 27: 8207–8230.
[14] Xu J., Shann W. (1992). Galerkin-wavelet methods for two point value problems. Number. Math. 63: 123–144.
[15] Lepik U. (2005). Numerical solution of differential equations using Haar wavelets. Mathematics and Computers in Simulation, 68: 127–143.
[16] Nason G. P. Wavelet Methods in Statistics with R, 2008, Springer Science Business Media, LLC.
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  • APA Style

    Sinitsyn Igor Nikolaevich, Sinitsyn Vladimir Igorevich, Korepanov Edward Rudolfovich, Konashenkova Tatyana Dmitirievna. (2021). Wavelet Filtering in Shock Stochastic Systems with High Availability. International Journal of Systems Engineering, 5(1), 1-12. https://doi.org/10.11648/j.ijse.20210501.11

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    ACS Style

    Sinitsyn Igor Nikolaevich; Sinitsyn Vladimir Igorevich; Korepanov Edward Rudolfovich; Konashenkova Tatyana Dmitirievna. Wavelet Filtering in Shock Stochastic Systems with High Availability. Int. J. Syst. Eng. 2021, 5(1), 1-12. doi: 10.11648/j.ijse.20210501.11

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    AMA Style

    Sinitsyn Igor Nikolaevich, Sinitsyn Vladimir Igorevich, Korepanov Edward Rudolfovich, Konashenkova Tatyana Dmitirievna. Wavelet Filtering in Shock Stochastic Systems with High Availability. Int J Syst Eng. 2021;5(1):1-12. doi: 10.11648/j.ijse.20210501.11

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  • @article{10.11648/j.ijse.20210501.11,
      author = {Sinitsyn Igor Nikolaevich and Sinitsyn Vladimir Igorevich and Korepanov Edward Rudolfovich and Konashenkova Tatyana Dmitirievna},
      title = {Wavelet Filtering in Shock Stochastic Systems with High Availability},
      journal = {International Journal of Systems Engineering},
      volume = {5},
      number = {1},
      pages = {1-12},
      doi = {10.11648/j.ijse.20210501.11},
      url = {https://doi.org/10.11648/j.ijse.20210501.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijse.20210501.11},
      abstract = {For filtering problems in StSHA under nonGaussian ShD methodological and algorithmically WL support is developed. 3 types of filters are considered: KBF (WLKBF), LPF (WLLPF) and SOLF (WLSOLF). These filters have the following advantages: on-line regime, high accuracy and possibility of algorithmically description of complex ShD. Wavelet filter modifications are based on Galerkin method and Haar wavelet expansions. WLF unlike KBF, LPF and SOLF do not need to integrate system of ordinary differential Eqs. These filters must solve system of linear algebraic Eqs with constant coefficients. KBF (WLKBF) and SOLF (WLSOLF) are recommended for StSHA with additive ShD whereas LPF (WLLPF) are recommended for StSHA with parametric and additive ShD. Basic applications are: on-line identification and calibration of nonstationary processes in StSHA of ShD. Methods are illustrated by example of 3 dimensional differential linear information control system at complex ShD. Basic algorithms and error analysis for KBF (WLKBF) and LPF (WLLPF) are presented and 15 Figure; illustrate filters peculiarities for small and fin damping. These filters allow to estimate the accumulation effects for systematic and random errors. Results may be generalized for filtration, extrapolation with interpolation problems in StSHA and multiple ShD.},
     year = {2021}
    }
    

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  • TY  - JOUR
    T1  - Wavelet Filtering in Shock Stochastic Systems with High Availability
    AU  - Sinitsyn Igor Nikolaevich
    AU  - Sinitsyn Vladimir Igorevich
    AU  - Korepanov Edward Rudolfovich
    AU  - Konashenkova Tatyana Dmitirievna
    Y1  - 2021/02/23
    PY  - 2021
    N1  - https://doi.org/10.11648/j.ijse.20210501.11
    DO  - 10.11648/j.ijse.20210501.11
    T2  - International Journal of Systems Engineering
    JF  - International Journal of Systems Engineering
    JO  - International Journal of Systems Engineering
    SP  - 1
    EP  - 12
    PB  - Science Publishing Group
    SN  - 2640-4230
    UR  - https://doi.org/10.11648/j.ijse.20210501.11
    AB  - For filtering problems in StSHA under nonGaussian ShD methodological and algorithmically WL support is developed. 3 types of filters are considered: KBF (WLKBF), LPF (WLLPF) and SOLF (WLSOLF). These filters have the following advantages: on-line regime, high accuracy and possibility of algorithmically description of complex ShD. Wavelet filter modifications are based on Galerkin method and Haar wavelet expansions. WLF unlike KBF, LPF and SOLF do not need to integrate system of ordinary differential Eqs. These filters must solve system of linear algebraic Eqs with constant coefficients. KBF (WLKBF) and SOLF (WLSOLF) are recommended for StSHA with additive ShD whereas LPF (WLLPF) are recommended for StSHA with parametric and additive ShD. Basic applications are: on-line identification and calibration of nonstationary processes in StSHA of ShD. Methods are illustrated by example of 3 dimensional differential linear information control system at complex ShD. Basic algorithms and error analysis for KBF (WLKBF) and LPF (WLLPF) are presented and 15 Figure; illustrate filters peculiarities for small and fin damping. These filters allow to estimate the accumulation effects for systematic and random errors. Results may be generalized for filtration, extrapolation with interpolation problems in StSHA and multiple ShD.
    VL  - 5
    IS  - 1
    ER  - 

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Author Information
  • Federal Research Centre “Computer Sciences and Control”, Moscow, Russia

  • Federal Research Centre “Computer Sciences and Control”, Moscow, Russia

  • Federal Research Centre “Computer Sciences and Control”, Moscow, Russia

  • Federal Research Centre “Computer Sciences and Control”, Moscow, Russia

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