Wavelet Filtering in Shock Stochastic Systems with High Availability

Sinitsyn Igor Nikolaevich; Sinitsyn Vladimir Igorevich; Korepanov Edward Rudolfovich; Konashenkova Tatyana Dmitirievna

doi:doi:10.11648/j.ijse.20210501.11

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Wavelet Filtering in Shock Stochastic Systems with High Availability

Sinitsyn Igor Nikolaevich, Sinitsyn Vladimir Igorevich, Korepanov Edward Rudolfovich, Konashenkova Tatyana Dmitirievna

Published in International Journal of Systems Engineering (Volume 5, Issue 1)

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), 2024. 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, 1^st ed; 2007, 2^nd 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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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

Sinitsyn Igor Nikolaevich

Federal Research Centre “Computer Sciences and Control”, Moscow, Russia
Sinitsyn Vladimir Igorevich

Federal Research Centre “Computer Sciences and Control”, Moscow, Russia
Korepanov Edward Rudolfovich

Federal Research Centre “Computer Sciences and Control”, Moscow, Russia
Konashenkova Tatyana Dmitirievna

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

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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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