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To address this issue, this study proposes a novel active learning surrogate model method for reliability analysis. The approach integrates the radial basis function (RBF) with a newly designed learning function\n                    <jats:italic>E<\/jats:italic>\n                    , forming the RBF+E algorithm to reduce the number of performance function evaluations. RBF+E is constructed to ensure effective sampling by concentrating design samples within high\u2010probability\u2010density regions, guided by the Euclidean norm of design samples. Furthermore, during modeling procedure, a pseudo\u2010design point\u2010based samples reduction (PDPSR) strategy is introduced to further reduce the computational cost by reducing the size of the candidate sample set required for evaluating new design samples and estimating failure probability. Two numerical examples and two complex practical engineering applications are utilized to demonstrate the advantages of the proposed method. Results confirm that the RBF+E algorithm, combined with the PDPSR strategy, significantly reduces computational cost while maintaining precision. The efforts made in this study provide an effective strategy for reliability analysis of large and complex structures.\n                  <\/jats:p>","DOI":"10.1002\/qre.70029","type":"journal-article","created":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T06:00:23Z","timestamp":1753768823000},"page":"3506-3525","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Efficient Reliability Analysis via Active Learning: An Integrated Approach Using the RBF+E Algorithm and a Pseudo\u2010Design Point\u2010Based Samples Reduction Strategy"],"prefix":"10.1002","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9293-3649","authenticated-orcid":false,"given":"Yan\u2010Xu","family":"Wei","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering Taiyuan University of Technology  Taiyuan China"},{"name":"Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment Ministry of Education Taiyuan University of Technology  Taiyuan China"},{"name":"National Key Laboratory of Metal Forming Technology and Heavy Equipment Taiyuan University of Technology  Taiyuan China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shi\u2010Long","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering Taiyuan University of Technology  Taiyuan China"},{"name":"Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment Ministry of Education Taiyuan University of Technology  Taiyuan China"},{"name":"National Key Laboratory of Metal Forming Technology and Heavy Equipment Taiyuan University of Technology  Taiyuan China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo\u2010Wei","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering Beihang University  Beijing China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Reliability and Systems Engineering Beihang University  Beijing China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan\u2010Jie","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering Taiyuan University of Technology  Taiyuan China"},{"name":"Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment Ministry of Education Taiyuan University of Technology  Taiyuan China"},{"name":"National Key Laboratory of Metal Forming Technology and Heavy Equipment Taiyuan University of Technology  Taiyuan China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,7,28]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1680\/jmaen.2019.27"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2020.113027"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.3403"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.3493"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.3390\/ma13143239"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2018.11.002"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.3747"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2019.09.045"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.3534"},{"key":"e_1_2_9_11_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2018\/8794160","article-title":"Reliability Analysis on Structures Based on a Modified Iterative Response Surface Method","volume":"2018","author":"Wei Y. 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