

{"id":684,"date":"2022-11-03T23:36:26","date_gmt":"2022-11-04T03:36:26","guid":{"rendered":"https:\/\/sites.temple.edu\/dslab\/?p=684"},"modified":"2024-02-12T04:42:05","modified_gmt":"2024-02-12T09:42:05","slug":"data-driven-discovery-of-governing-equations-of-li-ion-batteries-pertaining-state-of-charge","status":"publish","type":"post","link":"https:\/\/sites.temple.edu\/dslab\/?p=684","title":{"rendered":"Data-driven Discovery of Governing Equations of Li-ion Batteries Pertaining State of Charge"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"684\" class=\"elementor elementor-684\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-62a4fde5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"62a4fde5\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f67866f\" data-id=\"f67866f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6559696d elementor-widget elementor-widget-text-editor\" data-id=\"6559696d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><\/p>\n<p style=\"text-align: justify\">The complex electrochemical behavior of batteries results in nonlinear and high-dimensional dynamics. Accurate SOC prediction is paramount for increased performance, improved operational safety, and extended longevity of LiBs. The battery&#8217;s internal parameters are cell-dependent and change with operating conditions and battery health variations. We present a data-driven solution to discover governing equations pertaining to SOC dynamics from battery operando measurements.\u00a0<\/p>\n<p style=\"text-align: justify\"><img fetchpriority=\"high\" decoding=\"async\" class=\" wp-image-984 aligncenter\" src=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic_DataCollection-300x286.png\" alt=\"\" width=\"231\" height=\"220\" srcset=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic_DataCollection-300x286.png 300w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic_DataCollection.png 719w\" sizes=\"(max-width: 231px) 100vw, 231px\" \/><\/p>\n<figure>\n<p style=\"text-align: center\">Schematic of Data Collection Process<\/p>\n<p><img decoding=\"async\" class=\" wp-image-988 aligncenter\" style=\"text-align: start\" src=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic-of-Experimental-Setup-300x168.png\" alt=\"\" width=\"260\" height=\"146\" srcset=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic-of-Experimental-Setup-300x168.png 300w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic-of-Experimental-Setup-768x429.png 768w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic-of-Experimental-Setup.png 1015w\" sizes=\"(max-width: 260px) 100vw, 260px\" \/><\/p>\n<p style=\"text-align: center\">Schematic of Experimental Setup<\/p>\n<\/figure>\n<p><\/p>\n<p><\/p>\n<p style=\"text-align: justify\">Our approach relaxes the need for detailed knowledge of the battery\u2019s composition while maintaining prediction fidelity. The predictor consists of a library of candidate terms and a set of coefficients found via a sparsity-promoting algorithm. The library was enhanced with explicit physics-inspired terms to improve the predictor&#8217;s interpretability and generalizability. Further, we developed a Monte Carlo search of additional nonlinear terms to efficiently explore the high-dimensional search space and improve the characterization of highly nonlinear behaviors. Also, we developed a hyperparameter autotuning approach for identifying optimal coefficients that balance accuracy and complexity.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-1000 \" src=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic-of-MCLS.jpg\" alt=\"\" width=\"443\" height=\"160\" srcset=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic-of-MCLS.jpg 1370w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic-of-MCLS-300x108.jpg 300w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic-of-MCLS-768x277.jpg 768w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p style=\"text-align: center\">Schematic of Monte Carlo Library Search (MCLS)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-991 aligncenter\" src=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic-of-Autotunner-300x226.png\" alt=\"\" width=\"251\" height=\"189\" srcset=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic-of-Autotunner-300x226.png 300w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/Schematic-of-Autotunner.png 734w\" sizes=\"(max-width: 251px) 100vw, 251px\" \/><\/p>\n<p style=\"text-align: center\">Schematic of Hyperparameter Autotuner<\/p>\n<p style=\"text-align: justify\">We tuned the model&#8217;s performance and sparsity by exploring different combinations of candidate terms (basis functions) and data sampling rates. The resulting SOC predictor achieved high predictive performance scores (RMSE) of 2.2e-6 and 4.8e-4, respectively, for training and validation on experimental results corresponding to a stochastic drive cycle.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-997 \" src=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/TrainVal_SOCerror_RWBD_Stochastic_25C_withECM_v2.png\" alt=\"\" width=\"438\" height=\"259\" srcset=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/TrainVal_SOCerror_RWBD_Stochastic_25C_withECM_v2.png 1904w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/TrainVal_SOCerror_RWBD_Stochastic_25C_withECM_v2-300x177.png 300w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/TrainVal_SOCerror_RWBD_Stochastic_25C_withECM_v2-768x454.png 768w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/TrainVal_SOCerror_RWBD_Stochastic_25C_withECM_v2-1536x908.png 1536w\" sizes=\"(max-width: 438px) 100vw, 438px\" \/><\/p>\n<p style=\"text-align: center\">Training Results and Model-Validation to predict SOC from current, voltage, and initial SOC (Experimental Data)<\/p>\n<p style=\"text-align: justify\">The predictor achieved a generalizability RMSE of 8.5e-4 on unseen battery measurements corresponding to the standard US06 drive cycle, further showcasing the adaptability of the predictor and the enhanced modeling approach to new conditions.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-999 \" src=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/CV_SOCerror_RWBD_Stochastic_25C_withECM_v2.png\" alt=\"\" width=\"415\" height=\"246\" srcset=\"https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/CV_SOCerror_RWBD_Stochastic_25C_withECM_v2.png 1900w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/CV_SOCerror_RWBD_Stochastic_25C_withECM_v2-300x178.png 300w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/CV_SOCerror_RWBD_Stochastic_25C_withECM_v2-768x455.png 768w, https:\/\/sites.temple.edu\/dslab\/files\/2024\/02\/CV_SOCerror_RWBD_Stochastic_25C_withECM_v2-1536x909.png 1536w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><\/p>\n<p><\/p>\n<p><\/p>\n<p><\/p>\n<p><\/p>\n<p><\/p>\n<p style=\"text-align: justify\">The modeling technique includes explicit physics-inspired terms, which allows for interpretable and generalizable models.\u00a0Furthermore, the procedures and methods developed in this research are generic and can guide machine learning modeling of other dynamical systems.<\/p>\n<p><\/p>\n<p><\/p>\n<h3><u><b>Publications<\/b><\/u><\/h3>\n<p><\/p>\n<p><\/p>\n<ul>\n<li><a href=\"https:\/\/sites.temple.edu\/dslab\/?p=715\">Rodriguez, R.<\/a>., Ahmadzadeh, O., Wang, Y., &amp; Soudbakhsh, D. (2023). Data-driven Discovery of Lithium-Ion Battery State of Charge Dynamics. Journal of Dynamic Systems, Measurement, and Control, 1-13, <a href=\"https:\/\/doi.org\/10.1115\/1.4064026\">https:\/\/doi.org\/10.1115\/1.4064026<\/a>.<\/li>\n<li><a href=\"https:\/\/sites.temple.edu\/dslab\/?p=715\">Rodriguez, R.<\/a>,\u00a0Ahmadzadeh, O., Wang, Y., &amp; Soudbakhsh, D. (2023, May). Discovering governing equations of li-ion batteries pertaining state of charge using input-output data. In 2023 American Control Conference (ACC) (pp. 3081-3086), IEEE, <a href=\"https:\/\/doi.org\/10.23919\/ACC55779.2023.10156114\">https:\/\/doi.org\/10.23919\/ACC55779.2023.10156114<\/a>.<\/li>\n<li>Ahmadzadeh, O., <a href=\"https:\/\/sites.temple.edu\/dslab\/?p=715\">Rodriguez, R.<\/a>, Wang, Y., &amp; Soudbakhsh, D. (2023, May). A physics-inspired machine learning nonlinear model of li-ion batteries. In 2023 American Control Conference (ACC) (pp. 3087-3092). IEEE, <a href=\"https:\/\/doi.org\/10.23919\/ACC55779.2023.10156368\">https:\/\/doi.org\/10.23919\/ACC55779.2023.10156368<\/a>.<\/li>\n<li>Ahmadzadeh, O., <a href=\"https:\/\/sites.temple.edu\/dslab\/?p=715\">Rodriguez, R.<\/a>, and\u00a0Soudbakhsh, D. \u201cModelling of Li-ion Batteries for\u00a0Real-Time Analysis: A Data-Driven Approach\u201d, American Control Conference, 2022, <a href=\"https:\/\/doi.org\/10.23919\/ACC53348.2022.9867616\">https:\/\/doi.org\/10.23919\/ACC53348.2022.9867616<\/a><\/li>\n<\/ul>\n<p><\/p>\n<p><\/p>\n<p><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The complex electrochemical behavior of batteries results in nonlinear and high-dimensional dynamics. Accurate SOC prediction is paramount for increased performance, improved operational safety, and extended longevity of LiBs. The battery&#8217;s internal parameters are cell-dependent and change with operating conditions and battery health variations. We present a data-driven solution to discover governing equations pertaining to SOC &hellip; <a href=\"https:\/\/sites.temple.edu\/dslab\/?p=684\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Data-driven Discovery of Governing Equations of Li-ion Batteries Pertaining State of Charge<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":18183,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[10],"tags":[],"class_list":["post-684","post","type-post","status-publish","format-standard","hentry","category-research"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.temple.edu\/dslab\/index.php?rest_route=\/wp\/v2\/posts\/684","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.temple.edu\/dslab\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.temple.edu\/dslab\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.temple.edu\/dslab\/index.php?rest_route=\/wp\/v2\/users\/18183"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.temple.edu\/dslab\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=684"}],"version-history":[{"count":15,"href":"https:\/\/sites.temple.edu\/dslab\/index.php?rest_route=\/wp\/v2\/posts\/684\/revisions"}],"predecessor-version":[{"id":1009,"href":"https:\/\/sites.temple.edu\/dslab\/index.php?rest_route=\/wp\/v2\/posts\/684\/revisions\/1009"}],"wp:attachment":[{"href":"https:\/\/sites.temple.edu\/dslab\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=684"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.temple.edu\/dslab\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=684"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.temple.edu\/dslab\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=684"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}