{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/80892"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/80892","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"Application of Uncertainty Quantification in Control and Sensitivity Analysis: A Case Study on Type 1 Diabetes","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Nandi, Souransu; 0000-0002-3688-0500"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Singh, Tarunraj","Mechanical and Aerospace Engineering"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-10-29T16:47:55Z","date_published":"2019-10-29T16:47:55Z","updated_at":"2026-07-27T19:05:25Z","subjects":["mechanical engineering"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/80892","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Singh, Tarunraj","Mechanical and Aerospace Engineering"]},{"key":"dc:creator","label":"Author","values":["Nandi, Souransu; 0000-0002-3688-0500"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-10-29T16:47:55Z","2019","2019-08-05 16:18:01"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["mechanical engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/80892"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","Characterizing the uncertainty in mathematical models is an integral part of robust control and optimization: since a proper knowledge of the output uncertainties allow one to make better decisions. In this dissertation, we look at the applications of quantifying the uncertainty in mathematical models and how the information embedded in the quantified uncertainty can be used to design better control algorithms and assess underlying model dimensionality using global sensitivity analysis. Uncertainty quantification tools such as polynomial chaos and sampling are explored. The tools allow us to focus on what can be done after the uncertainty has been characterized. With that context, the thesis has been largely divided into three parts. The first part looks at robust control theory, where algorithms are developed to optimize performance for all possible uncertain realizations of a model as well as algorithms which concentrate on the most probable realizations. Here the idea of a trade off between robustness vs performance is noted and presented. The second part of the thesis looks at significant dimensions of uncertainty in mathematical models. Variance based as well as non-moment based metrics can be derived to quantify the contribution of particular uncertain input parameters to the uncertainty in the outputs. This information allows one to determine whether all the uncertain parameters are important or not. If the important parameters are not important, the non-important ones do not need to be considered to be uncertain and could be fixed with mean values during robust control or robust optimization problems thereby reducing the computational complexity of obtaining desired solutions. Here, in the dissertation not only are efficient algorithms to derive those metrics presented but also new metrics which better capture uncertainty contribution are proposed. The final part of the thesis comprises a case study on which the developed algorithms and measures are tested. The case study is on mathematical models of Type 1 Diabetes. Type 1 Diabetes is an extremely hot topic of research in the robust control and optimization community since the disease impacts millions of people. In this work, we derive control algorithms which help design insulin input profiles to keep blood glucose concentration levels within acceptable ranges and also present sensitivity analysis studies which determine important uncertainties in the type 1 diabetes models."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Application of Uncertainty Quantification in Control and Sensitivity Analysis: A Case Study on Type 1 Diabetes"]}]}],"canonical_facts":{"dc:contributor":["Singh, Tarunraj","Mechanical and Aerospace Engineering"],"dc:creator":["Nandi, Souransu; 0000-0002-3688-0500"],"dc:date":["2019-10-29T16:47:55Z","2019","2019-08-05 16:18:01"],"dc:description":["Ph.D.","Characterizing the uncertainty in mathematical models is an integral part of robust control and optimization: since a proper knowledge of the output uncertainties allow one to make better decisions. In this dissertation, we look at the applications of quantifying the uncertainty in mathematical models and how the information embedded in the quantified uncertainty can be used to design better control algorithms and assess underlying model dimensionality using global sensitivity analysis. Uncertainty quantification tools such as polynomial chaos and sampling are explored. The tools allow us to focus on what can be done after the uncertainty has been characterized. With that context, the thesis has been largely divided into three parts. The first part looks at robust control theory, where algorithms are developed to optimize performance for all possible uncertain realizations of a model as well as algorithms which concentrate on the most probable realizations. Here the idea of a trade off between robustness vs performance is noted and presented. The second part of the thesis looks at significant dimensions of uncertainty in mathematical models. Variance based as well as non-moment based metrics can be derived to quantify the contribution of particular uncertain input parameters to the uncertainty in the outputs. This information allows one to determine whether all the uncertain parameters are important or not. If the important parameters are not important, the non-important ones do not need to be considered to be uncertain and could be fixed with mean values during robust control or robust optimization problems thereby reducing the computational complexity of obtaining desired solutions. Here, in the dissertation not only are efficient algorithms to derive those metrics presented but also new metrics which better capture uncertainty contribution are proposed. The final part of the thesis comprises a case study on which the developed algorithms and measures are tested. The case study is on mathematical models of Type 1 Diabetes. Type 1 Diabetes is an extremely hot topic of research in the robust control and optimization community since the disease impacts millions of people. In this work, we derive control algorithms which help design insulin input profiles to keep blood glucose concentration levels within acceptable ranges and also present sensitivity analysis studies which determine important uncertainties in the type 1 diabetes models."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/80892"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["mechanical engineering"],"dc:title":["Application of Uncertainty Quantification in Control and Sensitivity Analysis: A Case Study on Type 1 Diabetes"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:25Z"}