{"id":1678,"date":"2024-03-10T00:31:45","date_gmt":"2024-03-10T00:31:45","guid":{"rendered":"https:\/\/sbia.org.br\/lnlm\/?page_id=1678"},"modified":"2024-05-29T18:08:11","modified_gmt":"2024-05-29T18:08:11","slug":"vol22-no1-art1","status":"publish","type":"page","link":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol22-no1\/vol22-no1-art1\/","title":{"rendered":"Inference of the Parameters of a Bioreactor via Approximate Bayesian Evidence"},"content":{"rendered":"<p>Filipe P. de Farias <a href=\"https:\/\/orcid.org\/0000-0003-1585-3682\"><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>, Davi de Lima Cruz <a href=\"https:\/\/orcid.org\/0009-0002-2293-4421\"><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; Michela Mulas <a href=\"https:\/\/orcid.org\/0000-0001-9120-2465\"><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> In the context of the recent water crisis, the development and improvement of technologies for efficiently treating wastewater becomes increasingly necessary. Aligned with this, the activated sludge process is widely used in biological wastewater treatment plants to remove carbon and nutrients from wastewater. Although significant advancements have been achieved in recent years in modelling these processes to improve their performance and energy efficiency, the models are still complex and difficult to calibrate using data from real plants. In this work, we use Bayesian inference frameworks to estimate the parameters of the activated sludge process. We employ Gaussian processes to estimate the solution to the differential equations of the activated sludge process model and we fit this estimation to manufactured data of the observations of the wastewater. We find that the use of the Bayesian inference framework outperforms the classical approach in scenarios where measurements are more strongly affected by noise.<\/p>\n<p><strong>Keywords:<\/strong> Activated sludge process, Wastewater treatment plants, Process modeling, Bayesian inference, Fenrir, Probabilistic Numerics.<\/p>\n<p><strong>DOI code:<\/strong> <a href=\"http:\/\/dx.doi.org\/10.21528\/lnlm-vol22-no1-art1\">10.21528\/lnlm-vol22-no1-art1<\/a><\/p>\n<p><strong>PDF file:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2024\/12\/vol22-no1-art1.pdf\">vol22-no1-art1.pdf<\/a><\/p>\n<p><strong>BibTex file:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/2024\/12\/vol22-no1-art1.bib\">vol22-no1-art1.bib<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Filipe P. de Farias , Davi de Lima Cruz &#038; Michela Mulas Abstract: In the context of the recent water crisis, the development and improvement of technologies for efficiently treating wastewater becomes increasingly necessary. Aligned with this, the activated sludge <a href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol22-no1\/vol22-no1-art1\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1675,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1678","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>Inference of the Parameters of a Bioreactor via Approximate Bayesian Evidence - 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\/vol22-no1\/vol22-no1-art1\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Inference of the Parameters of a Bioreactor via Approximate Bayesian Evidence - Learning and NonLinear Models\" \/>\n<meta property=\"og:description\" content=\"Filipe P. de Farias , Davi de Lima Cruz &#038; Michela Mulas Abstract: In the context of the recent water crisis, the development and improvement of technologies for efficiently treating wastewater becomes increasingly necessary. Aligned with this, the activated sludge Read More ...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol22-no1\/vol22-no1-art1\/\" \/>\n<meta property=\"og:site_name\" content=\"Learning and NonLinear Models\" \/>\n<meta property=\"article:modified_time\" content=\"2024-05-29T18:08:11+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=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol22-no1\/vol22-no1-art1\/\",\"url\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol22-no1\/vol22-no1-art1\/\",\"name\":\"Inference of the Parameters of a Bioreactor via Approximate Bayesian Evidence - Learning and NonLinear Models\",\"isPartOf\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol22-no1\/vol22-no1-art1\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol22-no1\/vol22-no1-art1\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2020\/09\/orcid.jpg\",\"datePublished\":\"2024-03-10T00:31:45+00:00\",\"dateModified\":\"2024-05-29T18:08:11+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol22-no1\/vol22-no1-art1\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol22-no1\/vol22-no1-art1\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol22-no1\/vol22-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\/vol22-no1\/vol22-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 22 &#8211; N\u00famero 1\",\"item\":\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol22-no1\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Inference of the Parameters of a Bioreactor via Approximate Bayesian Evidence\"}]},{\"@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":"Inference of the Parameters of a Bioreactor via Approximate Bayesian Evidence - 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\/vol22-no1\/vol22-no1-art1\/","og_locale":"pt_BR","og_type":"article","og_title":"Inference of the Parameters of a Bioreactor via Approximate Bayesian Evidence - Learning and NonLinear Models","og_description":"Filipe P. de Farias , Davi de Lima Cruz &#038; Michela Mulas Abstract: In the context of the recent water crisis, the development and improvement of technologies for efficiently treating wastewater becomes increasingly necessary. 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