A first order reliability method based on hybrid conjugate approach with adaptive Barzilai–Borwein steps
In the first order reliability method (FORM), the Hasofer–Lind and Rackwitz–Flessler (HL–RF) algorithm sometimes encounters numerical instability problems due to the highly nonlinear limit state function (LSF). In this paper, an improved HL–RF algorithm introducing the hybrid conjugate gradient meth...
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description | In the first order reliability method (FORM), the Hasofer–Lind and Rackwitz–Flessler (HL–RF) algorithm sometimes encounters numerical instability problems due to the highly nonlinear limit state function (LSF). In this paper, an improved HL–RF algorithm introducing the hybrid conjugate gradient method with adaptive Barzilai–Borwein step sizes is developed to enhance the robustness and efficiency of the original HL–RF method. The proposed algorithm is composed of two stages, the steepest descent method is performed in the first stage to move to the vicinity of the most probable failure point (MPFP) and provide a good initial location for the second stage. Along with the hybrid conjugate search direction defined by the descent direction of the non-differential merit function, the second stage quantizes the adaptive Barzilai–Borwein step sizes to accelerate the process of locating the final MPFP under the nonmonotone line search rule. Eight illustrative examples with nonlinear LSFs are analyzed in detail to validate the performance of the proposed algorithm compared with other first order reliability methods. The results indicate that the proposed algorithm is not only computationally efficient but also robust in terms of convergence, especially for those problems with super nonlinear LSFs and with nonlinear LSFs involving high-frequency noise terms.
•Non-differential merit function is chosen to monitor the iterations.•Novel hybrid conjugate search direction of the most probable point is defined.•Global Barzilai–Borwein steps accelerate the convergence speed.•Optimal initial step size is set to be 1 in the nonmonotone line search stage.•Problems with high nonlinearities and high-frequency noises are solved efficiently. |
doi_str_mv | 10.1016/j.cma.2022.115670 |
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•Non-differential merit function is chosen to monitor the iterations.•Novel hybrid conjugate search direction of the most probable point is defined.•Global Barzilai–Borwein steps accelerate the convergence speed.•Optimal initial step size is set to be 1 in the nonmonotone line search stage.•Problems with high nonlinearities and high-frequency noises are solved efficiently.</description><identifier>ISSN: 0045-7825</identifier><identifier>EISSN: 1879-2138</identifier><identifier>DOI: 10.1016/j.cma.2022.115670</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Algorithms ; Barzilai–Borwein step size ; Conjugate gradient method ; First order reliability method ; Limit states ; Most probable failure point ; Reliability ; Reliability index ; Robustness (mathematics) ; Steepest descent method</subject><ispartof>Computer methods in applied mechanics and engineering, 2022-11, Vol.401, p.115670, Article 115670</ispartof><rights>2022 Elsevier B.V.</rights><rights>Copyright Elsevier BV Nov 1, 2022</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-d73bf19f42892764201d5f8a62c82a6ca2f52137fadbd3d947396d8103f823193</citedby><cites>FETCH-LOGICAL-c325t-d73bf19f42892764201d5f8a62c82a6ca2f52137fadbd3d947396d8103f823193</cites><orcidid>0000-0003-1339-8145</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0045782522006259$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3536,27903,27904,65309</link.rule.ids></links><search><creatorcontrib>Wang, Xiaoping</creatorcontrib><creatorcontrib>Zhao, Wei</creatorcontrib><creatorcontrib>Chen, Yangyang</creatorcontrib><creatorcontrib>Li, Xueyan</creatorcontrib><title>A first order reliability method based on hybrid conjugate approach with adaptive Barzilai–Borwein steps</title><title>Computer methods in applied mechanics and engineering</title><description>In the first order reliability method (FORM), the Hasofer–Lind and Rackwitz–Flessler (HL–RF) algorithm sometimes encounters numerical instability problems due to the highly nonlinear limit state function (LSF). In this paper, an improved HL–RF algorithm introducing the hybrid conjugate gradient method with adaptive Barzilai–Borwein step sizes is developed to enhance the robustness and efficiency of the original HL–RF method. The proposed algorithm is composed of two stages, the steepest descent method is performed in the first stage to move to the vicinity of the most probable failure point (MPFP) and provide a good initial location for the second stage. Along with the hybrid conjugate search direction defined by the descent direction of the non-differential merit function, the second stage quantizes the adaptive Barzilai–Borwein step sizes to accelerate the process of locating the final MPFP under the nonmonotone line search rule. Eight illustrative examples with nonlinear LSFs are analyzed in detail to validate the performance of the proposed algorithm compared with other first order reliability methods. The results indicate that the proposed algorithm is not only computationally efficient but also robust in terms of convergence, especially for those problems with super nonlinear LSFs and with nonlinear LSFs involving high-frequency noise terms.
•Non-differential merit function is chosen to monitor the iterations.•Novel hybrid conjugate search direction of the most probable point is defined.•Global Barzilai–Borwein steps accelerate the convergence speed.•Optimal initial step size is set to be 1 in the nonmonotone line search stage.•Problems with high nonlinearities and high-frequency noises are solved efficiently.</description><subject>Algorithms</subject><subject>Barzilai–Borwein step size</subject><subject>Conjugate gradient method</subject><subject>First order reliability method</subject><subject>Limit states</subject><subject>Most probable failure point</subject><subject>Reliability</subject><subject>Reliability index</subject><subject>Robustness (mathematics)</subject><subject>Steepest descent method</subject><issn>0045-7825</issn><issn>1879-2138</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kL1OwzAUhS0EEqXwAGyWmBNsJ04cMbUVf1IlFpgtxz_EURoH221VJt6BN-RJSBVm7nKXc-495wPgGqMUI1zctqnciJQgQlKMaVGiEzDDrKwSgjN2CmYI5TQpGaHn4CKEFo3DMJmBdgGN9SFC55X20OvOitp2Nh7gRsfGKViLoBV0PWwOtbcKSte323cRNRTD4J2QDdzb2EChxBDtTsOl8J-2E_bn63vp_F7bHoaoh3AJzozogr7623Pw9nD_unpK1i-Pz6vFOpEZoTFRZVYbXJmcsIqURU4QVtQwURDJiCikIIaOpUojVK0yVeVlVhWKYZQZRjJcZXNwM90d031sdYi8dVvfjy85KSmtEC0KNKrwpJLeheC14YO3G-EPHCN-RMpbPiLlR6R8Qjp67iaPHuPvrPY8SKt7qZX1WkaunP3H_Qt1Kn-w</recordid><startdate>20221101</startdate><enddate>20221101</enddate><creator>Wang, Xiaoping</creator><creator>Zhao, Wei</creator><creator>Chen, Yangyang</creator><creator>Li, Xueyan</creator><general>Elsevier B.V</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-1339-8145</orcidid></search><sort><creationdate>20221101</creationdate><title>A first order reliability method based on hybrid conjugate approach with adaptive Barzilai–Borwein steps</title><author>Wang, Xiaoping ; Zhao, Wei ; Chen, Yangyang ; Li, Xueyan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-d73bf19f42892764201d5f8a62c82a6ca2f52137fadbd3d947396d8103f823193</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algorithms</topic><topic>Barzilai–Borwein step size</topic><topic>Conjugate gradient method</topic><topic>First order reliability method</topic><topic>Limit states</topic><topic>Most probable failure point</topic><topic>Reliability</topic><topic>Reliability index</topic><topic>Robustness (mathematics)</topic><topic>Steepest descent method</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Xiaoping</creatorcontrib><creatorcontrib>Zhao, Wei</creatorcontrib><creatorcontrib>Chen, Yangyang</creatorcontrib><creatorcontrib>Li, Xueyan</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computer methods in applied mechanics and engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Xiaoping</au><au>Zhao, Wei</au><au>Chen, Yangyang</au><au>Li, Xueyan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A first order reliability method based on hybrid conjugate approach with adaptive Barzilai–Borwein steps</atitle><jtitle>Computer methods in applied mechanics and engineering</jtitle><date>2022-11-01</date><risdate>2022</risdate><volume>401</volume><spage>115670</spage><pages>115670-</pages><artnum>115670</artnum><issn>0045-7825</issn><eissn>1879-2138</eissn><abstract>In the first order reliability method (FORM), the Hasofer–Lind and Rackwitz–Flessler (HL–RF) algorithm sometimes encounters numerical instability problems due to the highly nonlinear limit state function (LSF). In this paper, an improved HL–RF algorithm introducing the hybrid conjugate gradient method with adaptive Barzilai–Borwein step sizes is developed to enhance the robustness and efficiency of the original HL–RF method. The proposed algorithm is composed of two stages, the steepest descent method is performed in the first stage to move to the vicinity of the most probable failure point (MPFP) and provide a good initial location for the second stage. Along with the hybrid conjugate search direction defined by the descent direction of the non-differential merit function, the second stage quantizes the adaptive Barzilai–Borwein step sizes to accelerate the process of locating the final MPFP under the nonmonotone line search rule. Eight illustrative examples with nonlinear LSFs are analyzed in detail to validate the performance of the proposed algorithm compared with other first order reliability methods. The results indicate that the proposed algorithm is not only computationally efficient but also robust in terms of convergence, especially for those problems with super nonlinear LSFs and with nonlinear LSFs involving high-frequency noise terms.
•Non-differential merit function is chosen to monitor the iterations.•Novel hybrid conjugate search direction of the most probable point is defined.•Global Barzilai–Borwein steps accelerate the convergence speed.•Optimal initial step size is set to be 1 in the nonmonotone line search stage.•Problems with high nonlinearities and high-frequency noises are solved efficiently.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cma.2022.115670</doi><orcidid>https://orcid.org/0000-0003-1339-8145</orcidid></addata></record> |
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subjects | Algorithms Barzilai–Borwein step size Conjugate gradient method First order reliability method Limit states Most probable failure point Reliability Reliability index Robustness (mathematics) Steepest descent method |
title | A first order reliability method based on hybrid conjugate approach with adaptive Barzilai–Borwein steps |
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