A Novel Algorithm for Structural Reliability Analysis Based on Finite Step Length and Armijo Line Search

Huang, Peng; Huang, Hong‐Zhong; Huang, Tudi

doi:10.3390/app9122546

Cited by 14 publications

(8 citation statements)

References 39 publications

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“…For the step size σ k of the interval analysis, it is determined according to the Armijo rule 46 :

σ^{k} = \max_{s} \{τ^{s} |g ({bold-italicy}^{k} + τ^{t} {bold-italicd}_{bold-italicy}^{k}) - g (y^{k}) < 0\},

where τ ∈ (0, 1) and s is the smallest nonnegative integer satisfying the inequality.…”

Section: Proposed Methods With Both Random and Interval Variablesmentioning

confidence: 99%

An efficient and robust structural reliability analysis method with mixed variables based on hybrid conjugate gradient direction

Huang

et al. 2021

Numerical Meth Engineering

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Traditional reliability analysis is based on probability theory with precise distributions. However, determining the distribution of all variables precisely is impossible due to insufficient information. Therefore, random and interval variables may be encountered, and probabilistic reliability methods are hard to use. The existing interval variables make reliability analysis more difficult. In this article, an efficient and robust hybrid reliability analysis method is proposed for structures with both random and interval variables. Firstly, a single-loop procedure is proposed by performing probabilistic analysis and interval analysis simultaneously in each most probable point search process. Then an improved conjugate sensitivity factor method based on hybrid conjugate gradient direction and adaptive finite step length is developed for probabilistic analysis. Meanwhile, the hybrid conjugate gradient direction together with active set is introduced into the projected gradient method for interval analysis. Finally, a comparison analysis with six numerical examples is provided to validate the performance of the proposed method. The results demonstrate that the proposed method is better than the existing methods in terms of efficiency and robustness for hybrid reliability analysis with random and interval variables.

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“…For the step size σ k of the interval analysis, it is determined according to the Armijo rule 46 :

σ^{k} = \max_{s} \{τ^{s} |g ({bold-italicy}^{k} + τ^{t} {bold-italicd}_{bold-italicy}^{k}) - g (y^{k}) < 0\},

where τ ∈ (0, 1) and s is the smallest nonnegative integer satisfying the inequality.…”

Section: Proposed Methods With Both Random and Interval Variablesmentioning

confidence: 99%

An efficient and robust structural reliability analysis method with mixed variables based on hybrid conjugate gradient direction

Huang

et al. 2021

Numerical Meth Engineering

View full text Add to dashboard Cite

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“…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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“…Unlike the fault diagnosis method requiring the structure to be failed [6]- [8], reliability analysis is throughout any stage of a structure's life. Quantifying the failure probability (FP) is central to conduct the reliability assessment of a structure, which can be defined as [9]:…”

Section: Introductionmentioning

confidence: 99%

One-Class Support Vector Machine Based Schemes for Structural Reliability Assessment Under Imbalanced Sample Conditions

et al. 2020

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Structural reliability analysis is the key approach to assess uncertainties so that to increase the safety of engineering structures. Quantifying the failure probability (FP) is central to direct the result of the reliability assessment. In aerospace and military fields, normal samples collected from a structure are easily available, however, failure samples are extremely limited. Such imbalanced samples circumstance may lead to a large approximate bias of the failure probability. The critical problem in structural reliability analysis is how to use a smaller number of samples to get more precise failure probabilities. Although the Monte Carlo simulation (MCS) is the recognized benchmark, the high computational cost of calling limit state function has forced people to seek alternative ways. On the other hand, the surrogate model method, such as the adaptive Kriging model (abbreviated as AK-MCS), has been proposed to reduce the computational burden. To evaluate small failure probability, however, the number of the candidate points must be large for a convergent solution. To this end, this paper constructs a security domain identified model (SDIM) based on the one-class support vector machine (SVM) and imbalanced data. Different types of misjudged samples and approximate errors of the trained SDIM are analyzed. Two schemes are proposed accordingly to reduce the tested estimate error of the failure probability. Comparing with MCS and AK-MCS, the numerical and engineering examples demonstrate the accuracy and efficiency of the proposed method under different scenarios.

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A Novel Algorithm for Structural Reliability Analysis Based on Finite Step Length and Armijo Line Search

Cited by 14 publications

References 39 publications

An efficient and robust structural reliability analysis method with mixed variables based on hybrid conjugate gradient direction

An efficient and robust structural reliability analysis method with mixed variables based on hybrid conjugate gradient direction

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

One-Class Support Vector Machine Based Schemes for Structural Reliability Assessment Under Imbalanced Sample Conditions

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