{"id":1554,"date":"2023-02-24T18:56:21","date_gmt":"2023-02-24T18:56:21","guid":{"rendered":"https:\/\/sbia.org.br\/lnlm\/?page_id=1554"},"modified":"2023-02-24T18:57:35","modified_gmt":"2023-02-24T18:57:35","slug":"vol21-no1-art1","status":"publish","type":"page","link":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/","title":{"rendered":"Estimation of Kautz Poles in Wiener-Volterra Models Using Levenberg-Marquardt Algorithm"},"content":{"rendered":"<p>Higor de Souza Serafin <a href=\"https:\/\/orcid.org\/0000-0001-8425-6940\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>, Elder Oroski <a href=\"https:\/\/orcid.org\/0000-0003-3169-7245\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a>&#038; Andr\u00e9 Eug\u00eanio Lazzaretti <a href=\"https:\/\/orcid.org\/0000-0003-1861-3369\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1167\" src=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" alt=\"orcid\" width=\"20\" height=\"20\" \/><\/a><\/p>\n<p><strong>Abstract:<\/strong> This work approaches the problem of estimating the Kautz optimal poles in kernel expansion in Wiener-Volterra models. The analytical solution for the suboptimal case is already established in the literature. However, the solution for the two parameters that compose the poles is still open. In this paper, an optimization strategy using the Levenberg-Marquardt is presented. This algorithm is used to find kernel expansion parameters, with the same base for all dimensions. The construction of bases using digital filter is considered. To validate the implemented algorithm, data collected from the excitation of an electrically coupled drive system was used to analyze the impact of the search space thresholds and the behavior of Levenberg-Marquardt\u2019s parameters. It was also analyzed the impact on the model accuracy, as the number of functions in the base is increased. As a<br \/>\nresult, the models determined have achieved better results than the works found in the literature.<\/p>\n<p><strong>Keywords:<\/strong> Wiener-Volterra, Levenberg-Marquardt, system identification, Kautz function.<\/p>\n<p><strong>DOI code:<\/strong> <a href=\"http:\/\/dx.doi.org\/10.21528\/lnlm-vol21-no1-art1\">10.21528\/lnlm-vol21-no1-art1<\/a><\/p>\n<p><strong>PDF file:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2023\/02\/vol21-no1-art1.pdf\">vol21-no1-art1.pdf<\/a><\/p>\n<p><strong>BibTex file:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2023\/02\/vol21-no1-art1.bib\">vol21-no1-art1.bib<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Higor de Souza Serafin , Elder Oroski &#038; Andr\u00e9 Eug\u00eanio Lazzaretti Abstract: This work approaches the problem of estimating the Kautz optimal poles in kernel expansion in Wiener-Volterra models. The analytical solution for the suboptimal case is already established in <a href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1546,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1554","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Estimation of Kautz Poles in Wiener-Volterra Models Using Levenberg-Marquardt Algorithm - Learning and NonLinear Models<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Estimation of Kautz Poles in Wiener-Volterra Models Using Levenberg-Marquardt Algorithm - Learning and NonLinear Models\" \/>\n<meta property=\"og:description\" content=\"Higor de Souza Serafin , Elder Oroski &#038; Andr\u00e9 Eug\u00eanio Lazzaretti Abstract: This work approaches the problem of estimating the Kautz optimal poles in kernel expansion in Wiener-Volterra models. The analytical solution for the suboptimal case is already established in Read More ...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/\" \/>\n<meta property=\"og:site_name\" content=\"Learning and NonLinear Models\" \/>\n<meta property=\"article:modified_time\" content=\"2023-02-24T18:57:35+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/\",\"name\":\"Estimation of Kautz Poles in Wiener-Volterra Models Using Levenberg-Marquardt Algorithm - Learning and NonLinear Models\",\"isPartOf\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\",\"datePublished\":\"2023-02-24T18:56:21+00:00\",\"dateModified\":\"2023-02-24T18:57:35+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/#primaryimage\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\",\"contentUrl\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Browse issues\",\"item\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Learning &#038; Nonlinear Models &#8211; L&#038;NLM &#8211; Volume 21 &#8211; N\u00famero 1\",\"item\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Estimation of Kautz Poles in Wiener-Volterra Models Using Levenberg-Marquardt Algorithm\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#website\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/\",\"name\":\"Learning and NonLinear Models\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/sbia.org.br\/lnlm\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#organization\",\"name\":\"Learning and NonLinear Models\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png\",\"contentUrl\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2021\/07\/logo-lnlm.png\",\"width\":398,\"height\":94,\"caption\":\"Learning and NonLinear Models\"},\"image\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#\/schema\/logo\/image\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Estimation of Kautz Poles in Wiener-Volterra Models Using Levenberg-Marquardt Algorithm - Learning and NonLinear Models","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol21-no1\/vol21-no1-art1\/","og_locale":"pt_BR","og_type":"article","og_title":"Estimation of Kautz Poles in Wiener-Volterra Models Using Levenberg-Marquardt Algorithm - Learning and NonLinear Models","og_description":"Higor de Souza Serafin , Elder Oroski &#038; Andr\u00e9 Eug\u00eanio Lazzaretti Abstract: This work approaches the problem of estimating the Kautz optimal poles in kernel expansion in Wiener-Volterra models. 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