A new effective approach for computation of reliability index in nonlinear problems of reliability analysis

Shayanfar, Mohsen Ali; Barkhordari, Mohammad Ali; Roudak, Mohammad Amin

doi:10.1016/j.cnsns.2018.01.016

Cited by 19 publications

(3 citation statements)

References 27 publications

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“…For this example, Gong and Yi 11 used the finitestep-length iterative algorithm to reach the answer, and they obtained the reliability indexes b = 2.2995 and 1.8455 when P = 1 and 10 under the properly selected step-length, respectively. In Shayanfar et al, 36 the reliability indexes b are 2.3050 and 1.8459, respectively. For the compared methods in our paper, as can be seen from Table 2, HLRF fails to converge for P = 1, 5, 10, whereas both iHLRF and our proposed method can converge to the MPP with almost the same reliability index, and their reliability results under P = 1 and 10 are well agreed with previous ones.…”

Section: Examplementioning

confidence: 97%

An improved first order reliability method based on modified Armijo rule and interpolation-based backtracking scheme

Zhou

Wang

Xiao

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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Hasofer-Lind and Rackwtiz-Fiessler (HLRF) method is an efficient iterative algorithm for locating the most probable failure point and calculating the first order reliability index in structural reliability analysis. However, this method may encounter numerical instability problems for high nonlinear limit state function (LSF). In this paper, an improved HLRF-based first order reliability method is developed based on a modified Armijo line search rule and an interpolation-based step size backtracking scheme to improve the robustness and efficiency of the original HLRF method. Compared with other improved HLRF-based methods, the proposed method can not only guarantee the global convergence but also adaptively estimate some sensitive algorithm parameters, such as initial step size, step-size reduction coefficient, using the current known iterative information. Ten selected examples with high nonlinear LSFs are used to compare the robustness and efficiency of the proposed method with the original HLRF method and the improved HLRF (iHLRF) method. Results indicate that the proposed method is not only more computationally efficient but also less sensitive to the remaining user-defined algorithm parameters than the iHLRF method.

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Section: Examplementioning

confidence: 97%

An improved first order reliability method based on modified Armijo rule and interpolation-based backtracking scheme

Zhou

Wang

Xiao

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part O:

View full text Add to dashboard Cite

show abstract

“…Compared to methods following the three afore-mentioned three clues, methods emphasize on searching algorithms seem more efficient and accurate, which are realized by regulating the sampling process strategically through some algorithms. The family of searching algorithms for structural reliability is board and varied, in which some of the heuristic ones are directional divisions [34][35][36][37], swarm algorithms [38,39], genetic algorithms [40][41][42], gradient or difference-based algorithms [43,44], etc. Yet, further improvements on searching algorithms with respect to the following aspects are always welcomed: 1, maximizing computational efficiency by minimizing the number of redundant samplings; 2, increasing robustness by adapting to a board type range of PFs; 3, stabilization of the convergence rate; 4, customization for different engineering cases according to the requirement of accuracy.…”

Section: Introductionmentioning

confidence: 99%

Breadth-First Search Multi-Dimensional Binary Search Tree based Algorithms for Structural

Xu¹

2022

Preprint

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This research proposes a set of novel algorithms for structural reliability estimation based on muti-dimensional binary search tree and breadth-first search, namely the reliability accuracy supervised searching algorithm, the limit-state surface resolution supervised searching algorithm and the reliability index precision supervised fast searching algorithm. The proposed algorithms have the following strengths: 1, all the proposed algorithms have satisfactory computational efficiency by reducing redundant samplings; 2, their computational costs are stable and computable; 3, performance functions of high non-linearity can be will handled; 4, the reliability accuracy supervised searching algorithm can adapt its computational cost according to a prescribed accuracy; 5, the limit-state surface resolution supervised searching algorithm is able to probe sharp changes on limit-state surfaces; 6, the reliability index precision supervised fast searching algorithm computes the reliability index with sufficient precision in a fast way.

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“…In a structure, uncertainty can be observed in materials, loads and geometry. Evaluation of the probability of failure in the presence of uncertainty is the main purpose in structural reliability analysis [4][5][6]. The following definite multi-dimensional integral gives the probability of failure…”

Section: Introductionmentioning

confidence: 99%

An Iterative Two-step Lagrangian-based Method for Evaluation of Structural Reliability Index

Roudak

Karamloo²,

Shayanfar³

2022

Period. Polytech. Civil Eng.

Self Cite

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In structural reliability analysis, Hasofer-Lind and Rackwitz-Fiessler (HL-RF) method is a widely used approximation method for evaluating the reliability index. However, by increasing the nonlinearity or complexity in the limit state function of a structure, HL-RF may get in trouble for convergence. This paper represents an iterative algorithm that tries to minimize the Lagrange function, associated with the reliability problem. In each iteration of this method, two steps are followed, to satisfy the minimization condition and the existing constraint. In the first step, a movement for minimization in a descent direction is followed. In the second step, another search direction contributes to approach limit state surface, and therefore the next iteration can start from the vicinity of the surface. Employing Lagrange reliability function and limit state function simultaneously in the proposed two-step Lagrangian-based method (TSLB) can help to control the numerical instability in highly nonlinear problems. The accuracy and robustness of the proposed algorithm are shown in illustrative examples of the literature.

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A new effective approach for computation of reliability index in nonlinear problems of reliability analysis

Cited by 19 publications

References 27 publications

An improved first order reliability method based on modified Armijo rule and interpolation-based backtracking scheme

An improved first order reliability method based on modified Armijo rule and interpolation-based backtracking scheme

Breadth-First Search Multi-Dimensional Binary Search Tree based Algorithms for Structural

An Iterative Two-step Lagrangian-based Method for Evaluation of Structural Reliability Index

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