{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/78728"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/78728","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Inverse uncertainty quantification of input model parameters for thermal-hydraulics simulations using expectation-maximization under non-Bayesian and Bayesian framework","abstract":"Uncertainty quantification of computer simulation response requires knowledge of input model parameter uncertainty. However, like most system codes, nuclear thermal-hydraulics code TRACE does not provide any information on statistical properties of input model parameters. Moreover, the input model parameters in TRACE code are built using correlations from experiments performed under steady-state low pressure low flow conditions. Hence, they might not be accurate for use in analyses of high pressure high flow transients in a reactor core. This further highlights the need for quantification of input model parameter uncertainty. A mathematical framework is developed where Expectation-Maximization (EM) algorithm is implemented to quantify input model parameter uncertainty using the Maximum Likelihood Estimate (MLE) and Maximum a Posteriori (MAP) estimate. The difference between experimental measurements and nominal code predictions, which are the observables, are considered scalar random variables. A dispersed normal prior is assumed on the mean and an inverse gamma prior is assumed on the variance of the observable to determine MAP estimate. A log-normal transformation is used to transform input model parameter probability distribution function to pseudo-parameter space. The theory is formulated such that the observables are expressed either as a linear or a quadratic combination of pseudo parameters for MLE. MAP estimate, on the other hand, uses a linear model. In addition, the pseudo parameters are assumed to be normally distributed. Experimental data is collected from reflooding facility that simulates post Loss of Coolant Accident (LOCA). Thermal-hydraulics system code TRACE is used for calibration purposes. Discussion of results obtained from the implementation of the developed methodology is presented. The comparisons show that calibrated code results obtained using MAP estimates show consistent improvement over those obtained from MLE. The mean and variance of the input parameters hence calculated can be used along with the underlying distribution to perform uncertainty quantification on output code responses. Moreover, MAP estimates of variance are consistently lower compared to MLE due to regularization in the form of prior knowledge, hence providing greater credibility to inverse estimation.","abstract_html":"Uncertainty quantification of computer simulation response requires knowledge of input model parameter uncertainty. However, like most system codes, nuclear thermal-hydraulics code TRACE does not provide any information on statistical properties of input model parameters. Moreover, the input model parameters in TRACE code are built using correlations from experiments performed under steady-state low pressure low flow conditions. Hence, they might not be accurate for use in analyses of high pressure high flow transients in a reactor core. This further highlights the need for quantification of input model parameter uncertainty. A mathematical framework is developed where Expectation-Maximization (EM) algorithm is implemented to quantify input model parameter uncertainty using the Maximum Likelihood Estimate (MLE) and Maximum a Posteriori (MAP) estimate. The difference between experimental measurements and nominal code predictions, which are the observables, are considered scalar random variables. A dispersed normal prior is assumed on the mean and an inverse gamma prior is assumed on the variance of the observable to determine MAP estimate. A log-normal transformation is used to transform input model parameter probability distribution function to pseudo-parameter space. The theory is formulated such that the observables are expressed either as a linear or a quadratic combination of pseudo parameters for MLE. MAP estimate, on the other hand, uses a linear model. In addition, the pseudo parameters are assumed to be normally distributed. Experimental data is collected from reflooding facility that simulates post Loss of Coolant Accident (LOCA). Thermal-hydraulics system code TRACE is used for calibration purposes. Discussion of results obtained from the implementation of the developed methodology is presented. The comparisons show that calibrated code results obtained using MAP estimates show consistent improvement over those obtained from MLE. The mean and variance of the input parameters hence calculated can be used along with the underlying distribution to perform uncertainty quantification on output code responses. Moreover, MAP estimates of variance are consistently lower compared to MLE due to regularization in the form of prior knowledge, hence providing greater credibility to inverse estimation.","abstract_has_math":false,"creators":["Shrestha, Rijan Prasad"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Nuclear, Plasma, Radiolgc Engr","degree_department":null,"school":null,"contributors":["Kozlowski, Tomasz","Jewett, Brian","Uddin, Rizwan","Stubbins, James F."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-07-22T22:45:13Z","date_published":"2015-07-22T22:45:13Z","updated_at":"2026-07-22T22:26:12Z","subjects":["inverse uncertainty","expectation-maximization","bayesian","maximum a posteriori","thermal hydraulics code parameters"],"languages":["en"],"rights":["Copyright 2015 Rijan Shrestha"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/78728","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kozlowski, Tomasz","Jewett, Brian","Uddin, Rizwan","Stubbins, James F."]},{"key":"dc:creator","label":"Author","values":["Shrestha, Rijan Prasad"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-07-22T22:45:13Z","2017-07-23T09:15:31Z","2015-05","2015-04-23","2015-5"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Nuclear, Plasma, Radiolgc Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["inverse uncertainty","expectation-maximization","bayesian","maximum a posteriori","thermal hydraulics code parameters"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 Rijan Shrestha"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/78728"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Uncertainty quantification of computer simulation response requires knowledge of input model parameter uncertainty. However, like most system codes, nuclear thermal-hydraulics code TRACE does not provide any information on statistical properties of input model parameters. Moreover, the input model parameters in TRACE code are built using correlations from experiments performed under steady-state low pressure low flow conditions. Hence, they might not be accurate for use in analyses of high pressure high flow transients in a reactor core. This further highlights the need for quantification of input model parameter uncertainty. A mathematical framework is developed where Expectation-Maximization (EM) algorithm is implemented to quantify input model parameter uncertainty using the Maximum Likelihood Estimate (MLE) and Maximum a Posteriori (MAP) estimate. The difference between experimental measurements and nominal code predictions, which are the observables, are considered scalar random variables. A dispersed normal prior is assumed on the mean and an inverse gamma prior is assumed on the variance of the observable to determine MAP estimate. A log-normal transformation is used to transform input model parameter probability distribution function to pseudo-parameter space. The theory is formulated such that the observables are expressed either as a linear or a quadratic combination of pseudo parameters for MLE. MAP estimate, on the other hand, uses a linear model. In addition, the pseudo parameters are assumed to be normally distributed. Experimental data is collected from reflooding facility that simulates post Loss of Coolant Accident (LOCA). Thermal-hydraulics system code TRACE is used for calibration purposes. Discussion of results obtained from the implementation of the developed methodology is presented. The comparisons show that calibrated code results obtained using MAP estimates show consistent improvement over those obtained from MLE. The mean and variance of the input parameters hence calculated can be used along with the underlying distribution to perform uncertainty quantification on output code responses. Moreover, MAP estimates of variance are consistently lower compared to MLE due to regularization in the form of prior knowledge, hence providing greater credibility to inverse estimation.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2017-05-01","The student, Rijan Shrestha, accepted the attached license on 2015-04-17 at 10:21.","The student, Rijan Shrestha, submitted this Dissertation for approval on 2015-04-17 at 10:23.","This Dissertation was approved for publication on 2015-04-23 at 14:26.","DSpace SAF Submission Ingestion Package generated from Vireo submission #7817 on 2015-07-22 at 14:24:21","Made available in DSpace on 2015-07-22T22:45:13Z (GMT). No. of bitstreams: 2 SHRESTHA-DISSERTATION-2015.pdf: 5366106 bytes, checksum: 1180930b9249b9284512a61130bd46da (MD5) LICENSE.txt: 4211 bytes, checksum: 4e82103c44e1b09b5fe79bf7900de135 (MD5) Previous issue date: 2015-04-23","Embargo set by: Seth Robbins for item 79969 Lift date: 2017-07-22T22:46:21Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited Restriction Lifted for Item 79969 on 2017-07-23T09:15:31Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Inverse uncertainty quantification of input model parameters for thermal-hydraulics simulations using expectation-maximization under non-Bayesian and Bayesian framework"]}]}],"canonical_facts":{"dc:contributor":["Kozlowski, Tomasz","Jewett, Brian","Uddin, Rizwan","Stubbins, James F."],"dc:creator":["Shrestha, Rijan Prasad"],"dc:date":["2015-07-22T22:45:13Z","2017-07-23T09:15:31Z","2015-05","2015-04-23","2015-5"],"dc:description":["Uncertainty quantification of computer simulation response requires knowledge of input model parameter uncertainty. However, like most system codes, nuclear thermal-hydraulics code TRACE does not provide any information on statistical properties of input model parameters. Moreover, the input model parameters in TRACE code are built using correlations from experiments performed under steady-state low pressure low flow conditions. Hence, they might not be accurate for use in analyses of high pressure high flow transients in a reactor core. This further highlights the need for quantification of input model parameter uncertainty. A mathematical framework is developed where Expectation-Maximization (EM) algorithm is implemented to quantify input model parameter uncertainty using the Maximum Likelihood Estimate (MLE) and Maximum a Posteriori (MAP) estimate. The difference between experimental measurements and nominal code predictions, which are the observables, are considered scalar random variables. A dispersed normal prior is assumed on the mean and an inverse gamma prior is assumed on the variance of the observable to determine MAP estimate. A log-normal transformation is used to transform input model parameter probability distribution function to pseudo-parameter space. The theory is formulated such that the observables are expressed either as a linear or a quadratic combination of pseudo parameters for MLE. MAP estimate, on the other hand, uses a linear model. In addition, the pseudo parameters are assumed to be normally distributed. Experimental data is collected from reflooding facility that simulates post Loss of Coolant Accident (LOCA). Thermal-hydraulics system code TRACE is used for calibration purposes. Discussion of results obtained from the implementation of the developed methodology is presented. The comparisons show that calibrated code results obtained using MAP estimates show consistent improvement over those obtained from MLE. The mean and variance of the input parameters hence calculated can be used along with the underlying distribution to perform uncertainty quantification on output code responses. Moreover, MAP estimates of variance are consistently lower compared to MLE due to regularization in the form of prior knowledge, hence providing greater credibility to inverse estimation.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2017-05-01","The student, Rijan Shrestha, accepted the attached license on 2015-04-17 at 10:21.","The student, Rijan Shrestha, submitted this Dissertation for approval on 2015-04-17 at 10:23.","This Dissertation was approved for publication on 2015-04-23 at 14:26.","DSpace SAF Submission Ingestion Package generated from Vireo submission #7817 on 2015-07-22 at 14:24:21","Made available in DSpace on 2015-07-22T22:45:13Z (GMT). No. of bitstreams: 2 SHRESTHA-DISSERTATION-2015.pdf: 5366106 bytes, checksum: 1180930b9249b9284512a61130bd46da (MD5) LICENSE.txt: 4211 bytes, checksum: 4e82103c44e1b09b5fe79bf7900de135 (MD5) Previous issue date: 2015-04-23","Embargo set by: Seth Robbins for item 79969 Lift date: 2017-07-22T22:46:21Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited Restriction Lifted for Item 79969 on 2017-07-23T09:15:31Z."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/78728"],"dc:language":["en"],"dc:rights":["Copyright 2015 Rijan Shrestha"],"dc:subject":["inverse uncertainty","expectation-maximization","bayesian","maximum a posteriori","thermal hydraulics code parameters"],"dc:title":["Inverse uncertainty quantification of input model parameters for thermal-hydraulics simulations using expectation-maximization under non-Bayesian and Bayesian framework"],"dc:type":["text"],"thesis:degree_discipline":["Nuclear, Plasma, Radiolgc Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:12Z"}