Nonparametric frequency response function estimates for switching piecewise linear systems

Tao Song; Fubiao Zhang; Defu Lin

doi:10.1016/j.sigpro.2016.05.012

Nonparametric frequency response function estimates for switching piecewise linear systems

Tao Song, Fubiao Zhang^*, Defu Lin

^*Corresponding author for this work

School of Aerospace Engineering

Technical University of Munich

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

This paper proposes two algorithms (ATIRMM and ALPM) for estimating the time-varying behavior of single input single output (SISO) switching piecewise linear systems. Walsh basis functions are used to capture the non-smooth fast varying dynamics. The piecewise time-varying frequency response function (TV-FRF) is approximated by the sum of a series of LTI FRFs multiplied with a set of Walsh functions. The best linear time invariant approximation (BLTIA) of the TV-FRF is estimated with small uncertainty. Besides the BLTIA, the two methods are capable of estimating the noise power spectrum and the TV-FRF. The error analysis shows that ATIRMM delivers more accurate TV-FRF and BLTIA estimations, while ALPM has better performance in noise power spectrum estimation. The conclusions are illustrated by simulations.

Original language	English
Pages (from-to)	150-165
Number of pages	16
Journal	Signal Processing
Volume	129
DOIs	https://doi.org/10.1016/j.sigpro.2016.05.012
Publication status	Published - 1 Dec 2016

Keywords

Estimation uncertainty
Frequency response function
Nonparametric identification
Switching piecewise time-varying system

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10.1016/j.sigpro.2016.05.012

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title = "Nonparametric frequency response function estimates for switching piecewise linear systems",

abstract = "This paper proposes two algorithms (ATIRMM and ALPM) for estimating the time-varying behavior of single input single output (SISO) switching piecewise linear systems. Walsh basis functions are used to capture the non-smooth fast varying dynamics. The piecewise time-varying frequency response function (TV-FRF) is approximated by the sum of a series of LTI FRFs multiplied with a set of Walsh functions. The best linear time invariant approximation (BLTIA) of the TV-FRF is estimated with small uncertainty. Besides the BLTIA, the two methods are capable of estimating the noise power spectrum and the TV-FRF. The error analysis shows that ATIRMM delivers more accurate TV-FRF and BLTIA estimations, while ALPM has better performance in noise power spectrum estimation. The conclusions are illustrated by simulations.",

keywords = "Estimation uncertainty, Frequency response function, Nonparametric identification, Switching piecewise time-varying system",

author = "Tao Song and Fubiao Zhang and Defu Lin",

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T1 - Nonparametric frequency response function estimates for switching piecewise linear systems

AU - Song, Tao

AU - Zhang, Fubiao

AU - Lin, Defu

PY - 2016/12/1

Y1 - 2016/12/1

N2 - This paper proposes two algorithms (ATIRMM and ALPM) for estimating the time-varying behavior of single input single output (SISO) switching piecewise linear systems. Walsh basis functions are used to capture the non-smooth fast varying dynamics. The piecewise time-varying frequency response function (TV-FRF) is approximated by the sum of a series of LTI FRFs multiplied with a set of Walsh functions. The best linear time invariant approximation (BLTIA) of the TV-FRF is estimated with small uncertainty. Besides the BLTIA, the two methods are capable of estimating the noise power spectrum and the TV-FRF. The error analysis shows that ATIRMM delivers more accurate TV-FRF and BLTIA estimations, while ALPM has better performance in noise power spectrum estimation. The conclusions are illustrated by simulations.

AB - This paper proposes two algorithms (ATIRMM and ALPM) for estimating the time-varying behavior of single input single output (SISO) switching piecewise linear systems. Walsh basis functions are used to capture the non-smooth fast varying dynamics. The piecewise time-varying frequency response function (TV-FRF) is approximated by the sum of a series of LTI FRFs multiplied with a set of Walsh functions. The best linear time invariant approximation (BLTIA) of the TV-FRF is estimated with small uncertainty. Besides the BLTIA, the two methods are capable of estimating the noise power spectrum and the TV-FRF. The error analysis shows that ATIRMM delivers more accurate TV-FRF and BLTIA estimations, while ALPM has better performance in noise power spectrum estimation. The conclusions are illustrated by simulations.

KW - Estimation uncertainty

KW - Frequency response function

KW - Nonparametric identification

KW - Switching piecewise time-varying system

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U2 - 10.1016/j.sigpro.2016.05.012

DO - 10.1016/j.sigpro.2016.05.012

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SN - 0165-1684

VL - 129

SP - 150

EP - 165

JO - Signal Processing

JF - Signal Processing

ER -

Nonparametric frequency response function estimates for switching piecewise linear systems

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Keywords

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