It turns out to be a challenging task to perform structural analysis utilizing the Hasofer-Lind and RackwitzFlessler (hl-rf) algorithm of the first order reliability method (FORM) due to its nonconvergence originating...
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It turns out to be a challenging task to perform structural analysis utilizing the Hasofer-Lind and RackwitzFlessler (hl-rf) algorithm of the first order reliability method (FORM) due to its nonconvergence originating from structural response with high nonlinearity. This paper develops a novel improved method for nonlinear problems of reliability analysis to circumvent the inabilities of some subsistent algorithms of the FORM. First, a reference point close to the limit state surface is caught in a sufficiently fast manner by the classical steepest descent approach with exponentially declining step sizes, which serves as the initial most probable point for the subsequent conjugate strategy. Second, a stable three-term conjugate search direction is established by the descent direction of a non-differentiable merit function, where the non-differentiable merit function provides a convenient way to monitor the convergence of the sequence. Third, the Barzilai-Borwein step sizes under the observation of the non-monotone line search technique are formulated to accelerate the convergence speed in iterations. Compared with some existing algorithms of the FORM, investigations on five illustrative examples reveal that the proposed method is robust and efficient in practical application, especially for those problems with high nonlinearities.
In the "first-order reliability method" (FORM), the hl-rf iterative algorithm is a recommended and widely used one to locate the design point and calculate the reliability index. However it may fail to conve...
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In the "first-order reliability method" (FORM), the hl-rf iterative algorithm is a recommended and widely used one to locate the design point and calculate the reliability index. However it may fail to converge if the limit state surface at the design point is highly nonlinear. In this paper, an easy iterative algorithm, which introduces a "new" step length to control the convergence of the sequence and can be named as finite-step-length iterative algorithm, is present. It is proved that the hl-rf method is a special case of this proposed algorithm when the step length tends to infinity and the reason why the hl-rf diverges is illustrated. This proposed algorithm is much easier than other optimization schemes, especially than the modified hl-rf algorithm, because the process of line search for obtaining the step length is not needed. Numerical results indicate that the proposed algorithm is effective and as simple as the hl-rf but more robust.
This paper divides the time of railway container transport chain into the drayage time by road, the storage time at departure station, the railway transit time and the storage time at arrival station according to oper...
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