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Article: Local polynomial modeling and variable bandwidth selection for time-varying linear systems

TitleLocal polynomial modeling and variable bandwidth selection for time-varying linear systems
Authors
KeywordsBandwidth selection
least squares (LS)
local polynomial modeling (LPM)
maximum-likelihood estimation
system identification
time-varying linear systems (TVLSs)
Issue Date2011
PublisherIEEE.
Citation
Ieee Transactions On Instrumentation And Measurement, 2011, v. 60 n. 3, p. 1102-1117 How to Cite?
AbstractThis paper proposes a local polynomial modeling (LPM) approach and variable bandwidth selection (VBS) algorithm for identifying time-varying linear systems (TVLSs). The proposed method models the time-varying coefficients of a TVLS locally by polynomials, which can be estimated by least squares estimation with a kernel having a certain bandwidth. The asymptotic behavior of the proposed LPM estimator is studied, and the existence of an optimal local bandwidth which minimizes the local mean-square error is established. A new data-driven VBS algorithm is then proposed to estimate this optimal variable bandwidth adaptively and locally. An individual bandwidth is assigned for each coefficient instead of the whole coefficient vector so as to improve the accuracy in fast-varying systems encountered in fault detection and other applications. Important practical issues such as online implementation are also discussed. Simulation results show that the LPM-VBS method outperforms conventional TVLS identification methods, such as the recursive least squares algorithm and generalized random walk Kalman filter/smoother, in a wide variety of testing conditions, in particular, at moderate to high signal-to-noise ratio. Using local linearization, the LPM method is further extended to identify time-varying systems with mild nonlinearities. Simulation results show that the proposed LPM-VBS method can achieve a satisfactory performance for mildly nonlinear systems based on appropriate linearization. Finally, the proposed method is applied to a practical problem of voltage-flicker-tracking problem in power systems. The usefulness of the proposed approach is demonstrated by its improved performance over other conventional methods. © 2006 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/124681
ISSN
2015 Impact Factor: 1.808
2015 SCImago Journal Rankings: 1.022
ISI Accession Number ID
Funding AgencyGrant Number
Research Grants Council of Hong Kong
University of Hong Kong
Funding Information:

This work was supported in part by the Grant from the Research Grants Council of Hong Kong and in part by The University of Hong Kong CRCG Small Project Funding. The Associate Editor coordinating the review process for this paper was Dr. Tadeusz Dobrowiecki.

References

 

DC FieldValueLanguage
dc.contributor.authorChan, SCen_HK
dc.contributor.authorZhang, ZGen_HK
dc.date.accessioned2010-10-31T10:48:12Z-
dc.date.available2010-10-31T10:48:12Z-
dc.date.issued2011en_HK
dc.identifier.citationIeee Transactions On Instrumentation And Measurement, 2011, v. 60 n. 3, p. 1102-1117en_HK
dc.identifier.issn0018-9456en_HK
dc.identifier.urihttp://hdl.handle.net/10722/124681-
dc.description.abstractThis paper proposes a local polynomial modeling (LPM) approach and variable bandwidth selection (VBS) algorithm for identifying time-varying linear systems (TVLSs). The proposed method models the time-varying coefficients of a TVLS locally by polynomials, which can be estimated by least squares estimation with a kernel having a certain bandwidth. The asymptotic behavior of the proposed LPM estimator is studied, and the existence of an optimal local bandwidth which minimizes the local mean-square error is established. A new data-driven VBS algorithm is then proposed to estimate this optimal variable bandwidth adaptively and locally. An individual bandwidth is assigned for each coefficient instead of the whole coefficient vector so as to improve the accuracy in fast-varying systems encountered in fault detection and other applications. Important practical issues such as online implementation are also discussed. Simulation results show that the LPM-VBS method outperforms conventional TVLS identification methods, such as the recursive least squares algorithm and generalized random walk Kalman filter/smoother, in a wide variety of testing conditions, in particular, at moderate to high signal-to-noise ratio. Using local linearization, the LPM method is further extended to identify time-varying systems with mild nonlinearities. Simulation results show that the proposed LPM-VBS method can achieve a satisfactory performance for mildly nonlinear systems based on appropriate linearization. Finally, the proposed method is applied to a practical problem of voltage-flicker-tracking problem in power systems. The usefulness of the proposed approach is demonstrated by its improved performance over other conventional methods. © 2006 IEEE.en_HK
dc.languageengen_HK
dc.publisherIEEE.-
dc.relation.ispartofIEEE Transactions on Instrumentation and Measurementen_HK
dc.rightsIEEE Transactions on Instrumentation and Measurement. Copyright © IEEE.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rights©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.-
dc.subjectBandwidth selectionen_HK
dc.subjectleast squares (LS)en_HK
dc.subjectlocal polynomial modeling (LPM)en_HK
dc.subjectmaximum-likelihood estimationen_HK
dc.subjectsystem identificationen_HK
dc.subjecttime-varying linear systems (TVLSs)en_HK
dc.titleLocal polynomial modeling and variable bandwidth selection for time-varying linear systemsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0018-9456&volume=PP&issue=99&spage=1&epage=16&date=2010&atitle=Local+polynomial+modeling+and+variable+bandwidth+selection+for+time-varying+linear+systems-
dc.identifier.emailChan, SC:scchan@eee.hku.hken_HK
dc.identifier.authorityChan, SC=rp00094en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1109/TIM.2010.2064850en_HK
dc.identifier.scopuseid_2-s2.0-79951678089en_HK
dc.identifier.hkuros174336en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79951678089&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume60en_HK
dc.identifier.issue3en_HK
dc.identifier.spage1102en_HK
dc.identifier.epage1117en_HK
dc.identifier.isiWOS:000287085500046-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridChan, SC=13310287100en_HK
dc.identifier.scopusauthoridZhang, ZG=8407277900en_HK

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