An effective Kriging-based approximation for structural reliability analysis with random and interval variables

Zhang, Xufang; Wu, Zhenguang; Ma, Hui; Pandey, Mahesh D.

doi:10.1007/s00158-020-02825-8

Cited by 19 publications

(4 citation statements)

References 39 publications

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“…For 2-dimensional examples, i.e., examples 1 to 5, the LSFs have been drawn to reflect the characteristics of the functions schematically (Figs. [7][8][9][10][11].…”

Section: Resultsmentioning

confidence: 99%

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

Roudak

Karamloo²,

Shayanfar³

2022

Period. Polytech. Civil Eng.

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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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“…For 2-dimensional examples, i.e., examples 1 to 5, the LSFs have been drawn to reflect the characteristics of the functions schematically (Figs. [7][8][9][10][11].…”

Section: Resultsmentioning

confidence: 99%

“…(1) will be extremely challenging if the problem is complex. Simulation methods such as Monte Carlo simulation (MCS) [7][8][9], or approximation methods [10][11][12] are brought up as the alternatives. The exact solution is accessible in MCS, but at the cost of generating too many samples.…”

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.

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“…However, in practice we would encounter a more general random and interval hybrid uncertain problem with the increasing complexity of practical engineering analysis problems. 42 A series of fruitful achievements for hybrid uncertainty analysis have been achieved in this area based on the Taylor expansions, 43,44 orthogonal polynomial expansions, 45,46 dimension reduction methods, 47 Kriging surrogate models, 48 and so on. The existing hybrid uncertainty analysis methods are generally based on nested schemes, in which the random and interval uncertainties are considered sequentially.…”

Section: Introductionmentioning

confidence: 99%

Concurrent topology optimization for thermoelastic structures with random and interval hybrid uncertainties

Zheng

Ding

Jiang

et al. 2021

Numerical Meth Engineering

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A concurrent topology optimization for thermoelastic structures with random and interval hybrid uncertainties is discussed in this work. A robust topology optimization method is proposed for structures composed of periodic microstructures under thermal and mechanical coupled loads. The robust objective function is defined as a linear combination of the mean and standard variance under the worst case for the robust optimization model. An efficient hybrid orthogonal polynomial expansion (HOPE) method is developed to evaluate the robust objective function. The sensitivities for the robust topology optimization are then calculated based on the uncertainty analysis. Three numerical examples are provided to verify the effectiveness of the proposed method, and the Monte Carlo scanning test is used to validate the numerical accuracy of our proposed method. For comparison purpose, the topology optimizations under deterministic assumptions are also provided for these examples to show the importance of considering hybrid uncertainties.

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“…An approach named projection-outline-based active learning (POAL) 11,12 has been proposed to sequentially select training points; however, POAL lacks robustness. Zhang 13 used a Karush-Kuhn-Tucker-based criterion to identify the paired qualified samples that reflect both interval and random variables. An adaptive boundary utilizing FORM and the Kriging model has been proposed to recognize the simulation domain.…”

Section: Introductionmentioning

confidence: 99%

An efficient hybrid reliability analysis method based on active learning Kriging model and multimodal‐optimization‐based importance sampling

Wang

Yuan

Cai-ying

2021

Numerical Meth Engineering

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A novel method is proposed, which aims to solve rare‐event hybrid reliability problems with random and interval variables, where the performance function has various failure zones. It combines the active learning Kriging (ALK) model with importance sampling (IS) and evolutionary multimodal‐based multiobjective optimization (EMO‐MMO). The surrogate limit state surfaces (LSS) for the upper and lower failure probability bounds are respectively defined considering the Kriging variance. Failure candidate solutions located in different failure regions are generated by the EMO‐MMO method. Subsequently, all the most probable failure points (MPPs) are identified from those candidate solutions. The IS samples are simulated around the MPPs using the MPP‐based IS method. The IS samples located in unimportant regions are removed in order to improve the efficiency of approximating the surrogate LSSs. The optimal training points are selected from the truncated IS samples to update the Kriging model. After several training iterations, the surrogate LSSs are convergent. Ultimately, a reliable and unbiased estimation of the upper and lower failure probability bounds is provided. The performance of the ALK‐EMO‐IS‐HRA approach is verified through five application examples.

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An effective Kriging-based approximation for structural reliability analysis with random and interval variables

Cited by 19 publications

References 39 publications

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

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

Concurrent topology optimization for thermoelastic structures with random and interval hybrid uncertainties

An efficient hybrid reliability analysis method based on active learning Kriging model and multimodal‐optimization‐based importance sampling

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