{"id":{"repo_id":"must-thes","oai_identifier":"oai:scholarsmine.mst.edu:doctoral_dissertations-3783"},"canonical_url":"https://search.dev.ndltd.org/etd/must-thes/oai:scholarsmine.mst.edu:doctoral_dissertations-3783","repository":{"repo_id":"must-thes","name":"Missouri University of Science and Technology","base_url":"https://scholarsmine.mst.edu/do/oai/"},"display":{"title":"Time-dependent reliability methodologies with saddlepoint approximation","abstract":"\"Engineers always encounter time-dependent uncertainties that ubiquitously exist, such as the random deterioration of material properties and time-variant loads. Therefore the reliability of engineering systems becomes time-dependent. It is crucial to predict the time-dependent reliability in the design stage, given possible catastrophic consequences of a failure. Although extensive research has been conducted on reliability analysis, estimating the reliability accurately and efficiently is still challenging. The objective of this work is to develop accurate and efficient reliability methodologies for engineering design. The basic idea is the integration of traditional reliability methods with saddlepoint approximation (SPA), which can accurately approximate the tail distribution of a random variable. Four methods are proposed in this work. The first three methods deal with time-independent reliability while the last one estimates the time-dependent reliability. The first method combines SPA with first-order approximation and achieves higher accuracy over the traditional first-order reliability method when bimodal distributions are involved. The second method further improves the accuracy of reliability estimation by integrating SPA with the second-order approximation. The third method extends the second method into the reliability-based design for higher accuracy, and the high efficiency is maintained by an efficient algorithm for searching for an equivalent reliability index. The fourth method uses sequential efficient global optimization to convert a time-dependent problem into a time-independent counterpart. Then the second method is utilized to estimate the time-independent reliability after the conversion. The accuracy and effectiveness of the above methods are demonstrated by both numerical examples and engineering applications\"--Abstract, page iv.","abstract_html":""Engineers always encounter time-dependent uncertainties that ubiquitously exist, such as the random deterioration of material properties and time-variant loads. Therefore the reliability of engineering systems becomes time-dependent. It is crucial to predict the time-dependent reliability in the design stage, given possible catastrophic consequences of a failure. Although extensive research has been conducted on reliability analysis, estimating the reliability accurately and efficiently is still challenging. The objective of this work is to develop accurate and efficient reliability methodologies for engineering design. The basic idea is the integration of traditional reliability methods with saddlepoint approximation (SPA), which can accurately approximate the tail distribution of a random variable. Four methods are proposed in this work. The first three methods deal with time-independent reliability while the last one estimates the time-dependent reliability. The first method combines SPA with first-order approximation and achieves higher accuracy over the traditional first-order reliability method when bimodal distributions are involved. The second method further improves the accuracy of reliability estimation by integrating SPA with the second-order approximation. The third method extends the second method into the reliability-based design for higher accuracy, and the high efficiency is maintained by an efficient algorithm for searching for an equivalent reliability index. The fourth method uses sequential efficient global optimization to convert a time-dependent problem into a time-independent counterpart. Then the second method is utilized to estimate the time-independent reliability after the conversion. The accuracy and effectiveness of the above methods are demonstrated by both numerical examples and engineering applications"--Abstract, page iv.","abstract_has_math":false,"creators":["Hu, Zhangli"],"institution":"Missouri University of Science and Technology","degree_name":"Ph. D. in Mechanical Engineering","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T03:18:26Z","subjects":["Design under uncertainty","Optimization","Reliability","Simulation-based design","Uncertainty","Uncertainty quantification","Mechanical Engineering"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/2778","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Hu, Zhangli"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Mechanical Engineering"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Missouri University of Science and Technology"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Design under uncertainty","Optimization","Reliability","Simulation-based design","Uncertainty","Uncertainty quantification","Mechanical Engineering"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/2778"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"Engineers always encounter time-dependent uncertainties that ubiquitously exist, such as the random deterioration of material properties and time-variant loads. Therefore the reliability of engineering systems becomes time-dependent. It is crucial to predict the time-dependent reliability in the design stage, given possible catastrophic consequences of a failure. Although extensive research has been conducted on reliability analysis, estimating the reliability accurately and efficiently is still challenging. The objective of this work is to develop accurate and efficient reliability methodologies for engineering design. The basic idea is the integration of traditional reliability methods with saddlepoint approximation (SPA), which can accurately approximate the tail distribution of a random variable. Four methods are proposed in this work. The first three methods deal with time-independent reliability while the last one estimates the time-dependent reliability. The first method combines SPA with first-order approximation and achieves higher accuracy over the traditional first-order reliability method when bimodal distributions are involved. The second method further improves the accuracy of reliability estimation by integrating SPA with the second-order approximation. The third method extends the second method into the reliability-based design for higher accuracy, and the high efficiency is maintained by an efficient algorithm for searching for an equivalent reliability index. The fourth method uses sequential efficient global optimization to convert a time-dependent problem into a time-independent counterpart. Then the second method is utilized to estimate the time-independent reliability after the conversion. The accuracy and effectiveness of the above methods are demonstrated by both numerical examples and engineering applications\"--Abstract, page iv."]},{"key":"dc:title","label":"Title","values":["Time-dependent reliability methodologies with saddlepoint approximation"]}]}],"canonical_facts":{"dc:creator":["Hu, Zhangli"],"dc:description.abstract":["\"Engineers always encounter time-dependent uncertainties that ubiquitously exist, such as the random deterioration of material properties and time-variant loads. Therefore the reliability of engineering systems becomes time-dependent. It is crucial to predict the time-dependent reliability in the design stage, given possible catastrophic consequences of a failure. Although extensive research has been conducted on reliability analysis, estimating the reliability accurately and efficiently is still challenging. The objective of this work is to develop accurate and efficient reliability methodologies for engineering design. The basic idea is the integration of traditional reliability methods with saddlepoint approximation (SPA), which can accurately approximate the tail distribution of a random variable. Four methods are proposed in this work. The first three methods deal with time-independent reliability while the last one estimates the time-dependent reliability. The first method combines SPA with first-order approximation and achieves higher accuracy over the traditional first-order reliability method when bimodal distributions are involved. The second method further improves the accuracy of reliability estimation by integrating SPA with the second-order approximation. The third method extends the second method into the reliability-based design for higher accuracy, and the high efficiency is maintained by an efficient algorithm for searching for an equivalent reliability index. The fourth method uses sequential efficient global optimization to convert a time-dependent problem into a time-independent counterpart. Then the second method is utilized to estimate the time-independent reliability after the conversion. The accuracy and effectiveness of the above methods are demonstrated by both numerical examples and engineering applications\"--Abstract, page iv."],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/2778"],"dc:subject":["Design under uncertainty","Optimization","Reliability","Simulation-based design","Uncertainty","Uncertainty quantification","Mechanical Engineering"],"dc:title":["Time-dependent reliability methodologies with saddlepoint approximation"],"dc:type":["Dissertation - Open Access"],"thesis:degree_name":["Ph. D. in Mechanical Engineering"],"thesis:institution_name":["Missouri University of Science and Technology"]},"updated_at":"2026-07-24T03:18:26Z"}