Wavelet Filtering in Shock Stochastic Systems with High Availability

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

doi:10.11648/j.ijse.20210501.11

Korepanov Edward Rudolfovich, Konashenkova Tatyana Dmitirievna + Show 2 more

Open Access

https://doi.org/10.11648/j.ijse.20210501.11

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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.

Highlights

In series [1,2,3,4,5,6] methodological support for on-line express analysis of stochastic systems with high availability (StSHA) functioning at shock disturbances (ShD) was presented
Kalman-Bucy Filter (KBF) for linear nonstationary StSHA is widely used for on-line analysis and synthesis problems
Let nonstationary differential StSHA being described by the following Eqs: Sinitsyn Igor Nikolaevich et al.: Wavelet Filtering in Shock Stochastic Systems with High Availability

Summary

Introduction

In series [1,2,3,4,5,6] methodological support for on-line express analysis of stochastic systems with high availability (StSHA) functioning at shock disturbances (ShD) was presented. Wavelet modifications of Kalan-Bucy filters (WLKBF) for nonstationary linear StSHA at complex ShD were given and illustrated. Wavelet modifications of linear mean square (m.s.) conditionally optimal (Pugachev) filter (WLLPF) for StSHA with parametric ShD are presented and illustrated. Instrumental accuracy of WLKBF and WLLPF was considered. Let generalize [1] for KBF, LPF and suboptimal linearized filters (SOLF) in case of non Gaussian ShD. Basic Propositions 1-5 are illustrated by 3 dimensional information control system at deterministic and stochastic ShD

Kalman-Bucy Filters at Shock Disturbances

Linear Pugachev Filter at Shock Disturbances

Suboptimal Linearized Filters at Shock Disturbances

Example

Conclusion