Nonparametric Tracking of the Time-Varying Dynamics of Weakly Nonlinear Periodically Time-Varying Systems Using Periodic Inputs
In this paper, a nonparametric estimation procedure is presented in order to track the evolution of the dynamics of continuous (discrete)-time (non)-linear periodically time-varying (PTV) systems. Multisine excitations are applied to a PTV system since this kind of excitation signals allows us to di...
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Veröffentlicht in: | IEEE transactions on instrumentation and measurement 2012-05, Vol.61 (5), p.1384-1394 |
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description | In this paper, a nonparametric estimation procedure is presented in order to track the evolution of the dynamics of continuous (discrete)-time (non)-linear periodically time-varying (PTV) systems. Multisine excitations are applied to a PTV system since this kind of excitation signals allows us to discriminate between the noise and the nonlinear distortion from a single experiment. The key idea is that a linear PTV system can be decomposed into an (in)finite series of transfer functions, the so-called harmonic transfer functions (HTFs). Moreover, a systematic methodology to determine the number of significant branches is provided in this paper as well. Making use of the local polynomial approximation, a method that was recently developed for multivariable (non)-linear time invariant systems, the HTFs, together with their uncertainties embedded in an output-error framework, are then obtained from only one single experiment. From these nonparametric estimates, the evolution of the dynamics, described by the instantaneous transfer function (ITF), can then be achieved in a simple way. The effectiveness of the identification scheme will be first illustrated through simulations before a real system will be identified. Eventually, the methodology is applied to a weakly nonlinear PTV electronic circuit. |
doi_str_mv | 10.1109/TIM.2011.2175830 |
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Multisine excitations are applied to a PTV system since this kind of excitation signals allows us to discriminate between the noise and the nonlinear distortion from a single experiment. The key idea is that a linear PTV system can be decomposed into an (in)finite series of transfer functions, the so-called harmonic transfer functions (HTFs). Moreover, a systematic methodology to determine the number of significant branches is provided in this paper as well. Making use of the local polynomial approximation, a method that was recently developed for multivariable (non)-linear time invariant systems, the HTFs, together with their uncertainties embedded in an output-error framework, are then obtained from only one single experiment. From these nonparametric estimates, the evolution of the dynamics, described by the instantaneous transfer function (ITF), can then be achieved in a simple way. The effectiveness of the identification scheme will be first illustrated through simulations before a real system will be identified. Eventually, the methodology is applied to a weakly nonlinear PTV electronic circuit.</description><identifier>ISSN: 0018-9456</identifier><identifier>EISSN: 1557-9662</identifier><identifier>DOI: 10.1109/TIM.2011.2175830</identifier><identifier>CODEN: IEIMAO</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Dynamical systems ; Evolution ; Excitation ; Frequency domain analysis ; Instantaneous transfer function (ITF) ; Instrumentation ; Kernel ; Methodology ; multisine excitations ; Noise ; Nonlinear distortion ; nonlinear distortions ; Nonlinear dynamics ; Nonlinearity ; nonparametric modeling ; output error ; periodically time-varying (PTV) systems ; Polynomials ; Studies ; Time varying systems ; Transfer functions</subject><ispartof>IEEE transactions on instrumentation and measurement, 2012-05, Vol.61 (5), p.1384-1394</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) May 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c323t-1b852f50f69be48ef9e4ba23d0d5d721e45951e2d13e907d5d69fd87101b64363</citedby><cites>FETCH-LOGICAL-c323t-1b852f50f69be48ef9e4ba23d0d5d721e45951e2d13e907d5d69fd87101b64363</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6104144$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/6104144$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Louarroudi, E.</creatorcontrib><creatorcontrib>Pintelon, R.</creatorcontrib><creatorcontrib>Lataire, J.</creatorcontrib><title>Nonparametric Tracking of the Time-Varying Dynamics of Weakly Nonlinear Periodically Time-Varying Systems Using Periodic Inputs</title><title>IEEE transactions on instrumentation and measurement</title><addtitle>TIM</addtitle><description>In this paper, a nonparametric estimation procedure is presented in order to track the evolution of the dynamics of continuous (discrete)-time (non)-linear periodically time-varying (PTV) systems. Multisine excitations are applied to a PTV system since this kind of excitation signals allows us to discriminate between the noise and the nonlinear distortion from a single experiment. The key idea is that a linear PTV system can be decomposed into an (in)finite series of transfer functions, the so-called harmonic transfer functions (HTFs). Moreover, a systematic methodology to determine the number of significant branches is provided in this paper as well. Making use of the local polynomial approximation, a method that was recently developed for multivariable (non)-linear time invariant systems, the HTFs, together with their uncertainties embedded in an output-error framework, are then obtained from only one single experiment. From these nonparametric estimates, the evolution of the dynamics, described by the instantaneous transfer function (ITF), can then be achieved in a simple way. The effectiveness of the identification scheme will be first illustrated through simulations before a real system will be identified. Eventually, the methodology is applied to a weakly nonlinear PTV electronic circuit.</description><subject>Dynamical systems</subject><subject>Evolution</subject><subject>Excitation</subject><subject>Frequency domain analysis</subject><subject>Instantaneous transfer function (ITF)</subject><subject>Instrumentation</subject><subject>Kernel</subject><subject>Methodology</subject><subject>multisine excitations</subject><subject>Noise</subject><subject>Nonlinear distortion</subject><subject>nonlinear distortions</subject><subject>Nonlinear dynamics</subject><subject>Nonlinearity</subject><subject>nonparametric modeling</subject><subject>output error</subject><subject>periodically time-varying (PTV) systems</subject><subject>Polynomials</subject><subject>Studies</subject><subject>Time varying systems</subject><subject>Transfer functions</subject><issn>0018-9456</issn><issn>1557-9662</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkc1P20AQxVcIJALljtSLxakXpzP76T1WUGiktCAR4Ght7HG74I901znk1H-9awWQ2tNo3vzeaEaPsXOEOSLYz6vF9zkHxDlHowoBB2yGSpncas0P2QwAi9xKpY_ZSYzPAGC0NDP258fQb1xwHY3BV9kquOrF9z-zocnGX5StfEf5owu7Sbva9a7zVZyGT-Re2l2W3K3vyYXsjoIfal-5Nsn_2O53caQuZg9x6t64bNFvtmP8wI4a10Y6e62n7OH66-ryW768vVlcflnmleBizHFdKN4oaLRdkyyosSTXjosaalUbjiSVVUi8RkEWTBK1berCIOBaS6HFKfu037sJw-8txbHsfKyobV1PwzaWCJwXhQRdJPTiP_R52IY-XVdaK8BYayYI9lAVhhgDNeUm-C59nDaVUyBlCqScAilfA0mWj3uLJ6J3XCNIlFL8BY4zh6o</recordid><startdate>201205</startdate><enddate>201205</enddate><creator>Louarroudi, E.</creator><creator>Pintelon, R.</creator><creator>Lataire, J.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>L7M</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>201205</creationdate><title>Nonparametric Tracking of the Time-Varying Dynamics of Weakly Nonlinear Periodically Time-Varying Systems Using Periodic Inputs</title><author>Louarroudi, E. ; Pintelon, R. ; Lataire, J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c323t-1b852f50f69be48ef9e4ba23d0d5d721e45951e2d13e907d5d69fd87101b64363</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Dynamical systems</topic><topic>Evolution</topic><topic>Excitation</topic><topic>Frequency domain analysis</topic><topic>Instantaneous transfer function (ITF)</topic><topic>Instrumentation</topic><topic>Kernel</topic><topic>Methodology</topic><topic>multisine excitations</topic><topic>Noise</topic><topic>Nonlinear distortion</topic><topic>nonlinear distortions</topic><topic>Nonlinear dynamics</topic><topic>Nonlinearity</topic><topic>nonparametric modeling</topic><topic>output error</topic><topic>periodically time-varying (PTV) systems</topic><topic>Polynomials</topic><topic>Studies</topic><topic>Time varying systems</topic><topic>Transfer functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Louarroudi, E.</creatorcontrib><creatorcontrib>Pintelon, R.</creatorcontrib><creatorcontrib>Lataire, J.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005–Present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on instrumentation and measurement</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Louarroudi, E.</au><au>Pintelon, R.</au><au>Lataire, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonparametric Tracking of the Time-Varying Dynamics of Weakly Nonlinear Periodically Time-Varying Systems Using Periodic Inputs</atitle><jtitle>IEEE transactions on instrumentation and measurement</jtitle><stitle>TIM</stitle><date>2012-05</date><risdate>2012</risdate><volume>61</volume><issue>5</issue><spage>1384</spage><epage>1394</epage><pages>1384-1394</pages><issn>0018-9456</issn><eissn>1557-9662</eissn><coden>IEIMAO</coden><abstract>In this paper, a nonparametric estimation procedure is presented in order to track the evolution of the dynamics of continuous (discrete)-time (non)-linear periodically time-varying (PTV) systems. Multisine excitations are applied to a PTV system since this kind of excitation signals allows us to discriminate between the noise and the nonlinear distortion from a single experiment. The key idea is that a linear PTV system can be decomposed into an (in)finite series of transfer functions, the so-called harmonic transfer functions (HTFs). Moreover, a systematic methodology to determine the number of significant branches is provided in this paper as well. Making use of the local polynomial approximation, a method that was recently developed for multivariable (non)-linear time invariant systems, the HTFs, together with their uncertainties embedded in an output-error framework, are then obtained from only one single experiment. From these nonparametric estimates, the evolution of the dynamics, described by the instantaneous transfer function (ITF), can then be achieved in a simple way. 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subjects | Dynamical systems Evolution Excitation Frequency domain analysis Instantaneous transfer function (ITF) Instrumentation Kernel Methodology multisine excitations Noise Nonlinear distortion nonlinear distortions Nonlinear dynamics Nonlinearity nonparametric modeling output error periodically time-varying (PTV) systems Polynomials Studies Time varying systems Transfer functions |
title | Nonparametric Tracking of the Time-Varying Dynamics of Weakly Nonlinear Periodically Time-Varying Systems Using Periodic Inputs |
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