A surrogate‐based iterative importance sampling method for structural reliability analysis

Tang, Zhangchun; Xia, Yanjun

doi:10.1002/qre.2352

Cited by 4 publications

(4 citation statements)

References 56 publications

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“…The aim of the structural reliability analysis is to obtain failure probabilities while taking into account the randomness of input variables 1–3 . The first‐order and second‐order reliability methods (FORM, SORM) have wide applications in reliability analysis 4,5 .…”

Section: Introductionmentioning

confidence: 99%

The adaptive weight learning function for reliability analysis and its application to multiple active learning methods

Liu

Zhou

et al. 2022

Quality & Reliability Eng

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In engineering, evaluating the failure probability of structures with complex performance functions is a challenging task. Some active learning methods based on the Kriging model gain considerable attention for structural reliability analysis. The existing learning functions offer new learning criterions to select sample points, but the probability density function (PDF) of sample points is ignored in some learning functions. To decrease selecting sample points in low PDF regions, this study presents a new adaptive weight learning function (WLF). The learning function WLF constituted by the adaptive orient function and the joint PDF can be applicable to multiple learning functions. Depending on the importance degree of candidate sample points, the sample points can be assigned different weight by learning function WLF. When the leaning function WLF is applicated to the existing active learning methods, the sample point with a higher PDF in neighborhood of the limit state function (LSF) can be given a larger weight to preferentially select into design of experiments (DoE). Therefore, the learning function WLF can help the multiple learning functions to select informative sample points with high PDF, which can further improve the efficiency of these learning functions. Four examples are used to illustrate the accuracy and efficiency as well as the suitability of the learning function WLF.

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Section: Introductionmentioning

confidence: 99%

The adaptive weight learning function for reliability analysis and its application to multiple active learning methods

Liu

Zhou

et al. 2022

Quality & Reliability Eng

View full text Add to dashboard Cite

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“…proposed the directional simulation method (DSM), which reduces the dimension limit state probability by identifying a set of directions for integration, integrating either in closed‐form or by approximation in those directions, finally weighted average of those direction is computed as failure probability 25 . Active learning methods are now state‐of‐the‐art, in which surrogate model is established by utilizing the learning function and criteria for iteration termination 26 . Reliability based design optimization based on reliability algorithm is a promising design method at present.…”

Section: Introductionmentioning

confidence: 99%

“…25 Active learning methods are now state-of-the-art, in which surrogate model is established by utilizing the learning function and criteria for iteration termination. 26 Reliability based design optimization based on reliability algorithm is a promising design method at present. Through a lot of research and comparison, Meng et al 27 pointed out that the traditional algorithm based on gradient iteration is less than meta heuristic algorithm in computing resource occupation, but the meta heuristic algorithm has better global convergence and robustness.…”

Section: Introductionmentioning

confidence: 99%

An improved reliability index based on regional equivalent conversion

Wang

Liu

Zhao

et al. 2022

Quality & Reliability Eng

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Aiming at the accuracy and efficiency of traditional reliability method for solving highly nonlinear problem, this paper proposes the regional equivalent conversion index (RECI) to compute reliability under arbitrary boundary and number of subdomains of limit state function. Firstly, we establish the model of RECI and the corresponding sampling method. Furthermore, the RECI of a series of parallel linear performance functions are computed by the proposed method. Besides the advanced first order and second moment method (AFOSM) are used to compute the reliability. Finally, the mapping relationship between RECI and reliability is established. Influence of sampling parameters on relative error is studied and optimal value is given. The parameters are optimized by analyzing the influence of the parameters on the precision. This method is also suitable for multiple failure modes without changing any process. Numerical examples are employed to demonstrate the feasibility of the proposed method for solving highly nonlinear problem in dimension 1–4.

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“…However, the accuracies of the FORM and SORM cannot be guaranteed when the performance function contains disjoint failure regions and exhibits high nonlinearity. To reduce the total calls to the performance function and computational burden, many advanced sampling techniques were proposed, for example, subset simulation (SS), 11 importance sampling (IS), 12,13 and line sampling (LS). 14 SS computes the failure probability as a product of a series of conditional probabilities that are estimated by the Markov chain Monte Carlo (MCMC) simulation.…”

Section: Introductionmentioning

confidence: 99%

AK-PDF: An active learning method combining kriging and probability density function for efficient reliability analysis

Zhou

Xiao

Zuo

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part O:

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An important challenge in structural reliability is to reduce the number of calls to evaluate the performance function, especially the complex implicit performance functions. To reduce the computational burden and improve the reliability analysis efficiency, a new active learning method is developed to consider the probability density function of samples based on the learning function U in an active learning reliability method that combines the kriging and Monte Carlo simulation. In the proposed method, the proposed active learning function contains two parts: part A is based on function U, and part B is based on the probability density function and function U. By changing the weights of parts A and B, the sample points close the limit-state function, and those in the region with a higher probability density function have more weight to be selected compared to the others. Subsequently, the kriging model can be constructed more effectively. The proposed method avoids a large number of time-consuming function evaluations, and the recommended weight is also reported. The performance of the proposed method is evaluated through three numerical examples and one engineering example. The results demonstrate the efficiency and accuracy of the proposed method.

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A surrogate‐based iterative importance sampling method for structural reliability analysis

Cited by 4 publications

References 56 publications

The adaptive weight learning function for reliability analysis and its application to multiple active learning methods

The adaptive weight learning function for reliability analysis and its application to multiple active learning methods

An improved reliability index based on regional equivalent conversion

AK-PDF: An active learning method combining kriging and probability density function for efficient reliability analysis

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