The hasofer-lind-rackwitz-fiessler (HLRF) algorithm of the first order reliability method may fail in the presence of nonlinear problems. As a simple and efficient meta-heuristic strategy, the teaching-learning-based ...
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The hasofer-lind-rackwitz-fiessler (HLRF) algorithm of the first order reliability method may fail in the presence of nonlinear problems. As a simple and efficient meta-heuristic strategy, the teaching-learning-based optimization (TLBO) algorithm accompanied with one of its variants, TLBO with triangular varying population sizes, is employed in reliability analysis to overcome the numerical difficulties that occurs in the HLRF algorithm or its modifications of the first order reliability method mainly falling into a state of instability such as periodic solutions and chaos. In the meantime, choice on the penalty coefficient in the equivalent unconstrained optimization problem of reliability analysis is discussed. A more appropriate scheme to adaptively select a sequence of the penalty coefficients in iterations is presented in terms of Karush-Kuhn-Tucker (KKT) conditions to ensure the equivalence of the original constrained optimization problem of the first order reliability method. Numerical experiments show that, compared with the manner of exponential growth might producing great errors in complex and nonlinear problems, the adaptive choice of penalty coefficients in light of KKT conditions results in a good efficiency with a satisfactory accuracy especially when TLBO with triangular varying population sizes is utilized to solve the equivalent optimization problem of reliability analysis.
作者：
Zhao, WeiChen, YangYangLiu, JikeJinan Univ
Sch Mech & Construct Engn MOE Key Lab Disaster Forecast & Control Engn Guangzhou 510632 Guangdong Peoples R China Guangzhou Univ
Earthquake Engn Res & Test Ctr Guangzhou 510405 Guangdong Peoples R China Sun Yat Sen Univ
Dept Mech Guangzhou 510275 Guangdong Peoples R China
In nonlinear problems, the hasofer-lind-rackwitz-fiessler algorithm of the first order reliability method sometimes is puzzled by its non-convergence. A new hasofer-lind-rackwitz-fiessler algorithm incorporating Barzi...
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In nonlinear problems, the hasofer-lind-rackwitz-fiessler algorithm of the first order reliability method sometimes is puzzled by its non-convergence. A new hasofer-lind-rackwitz-fiessler algorithm incorporating Barzilai-Borwein step is investigated in this paper to speed up the rate of convergence and performs in a stable manner. The algorithm is essentially established on the basis of the global Barzilai-Borwein gradient method, which is dealt with two stages. The first stage, implemented by the traditional steepest descent method with specific decayed step sizes, prepares a good initial point for the global Barzilai-Borwein gradient algorithm in the second stage, which takes the merit function as the objective to locate the most probable failure point. The efficiency and convergence of the proposed method and some other reliability analysis methods are presented and discussed in details by several numerical examples. It is found that the proposed method is stable and very efficient in the nonlinear problems except those super nonlinear ones, even more accurate than the descent direction method with step sizes following the fixed exponential decay strategy. (C) 2019 Elsevier Inc. All rights reserved.
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