Adaptive stratified sampling for structural reliability analysis

Song, Chenxiao; Kawai, Reiichiro

doi:10.1016/j.strusafe.2022.102292

Cited by 14 publications

(6 citation statements)

References 52 publications

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“…This can help preserve the data distribution because each stratum reflects a particular characteristic of the population. This is particularly useful in classification tasks, where the goal is to predict the class of a new instance based on its features [1,2]. If the sampling is not properly implemented, or if the subgroups are not well-defined or representative of the population, then stratified sampling can potentially lead to bias or altered distribution of data.…”

Section: Stratified Samplingmentioning

confidence: 99%

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Preserving Data Distribution in Sampling and Instance Selection with Renyi's Divergence

Sadoghi-Yazdi,

Ashkezari-Toussi,

Ramezanzadeh-Yazdi

2023

Preprint

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This paper presents a novel method for sampling based on a distribution function. By leveraging Renyi's divergence criterion, a recursive formulation is directly derived from the disparity between the original and estimated distributions. The Gradient descent algorithm is employed to achieve this recursive equation, and then new samples are derived. Since this method uses the distribution of the original data, it has the ability to preserve the data distribution in the sampled dataset. In instances where the original distribution is unknown, Kernel Density Estimation is employed for estimation. Experimental results demonstrate that the proposed method effectively preserves the data distribution and prevents any alteration in the data concept while maintaining the predictability of the model over selected instances. More precisely, this method has successfully reduced the dataset size by approximately $70\%$, while the accuracy of the learning algorithm has remained unaffected.

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Section: Stratified Samplingmentioning

confidence: 99%

“…Sampling-based techniques: These methods randomly sample a subset of instances from the original dataset. Examples include simple random sampling, stratified sampling [1,2], and systematic sampling [3].…”

Section: Introductionmentioning

confidence: 99%

Preserving Data Distribution in Sampling and Instance Selection with Renyi's Divergence

Sadoghi-Yazdi,

Ashkezari-Toussi,

Ramezanzadeh-Yazdi

2023

Preprint

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“…Quantities of smart sampling techniques have been proposed to reduce the number of samples needed to achieve a satisfactory level of accuracy, such as stratified sampling (a well-known type of stratified sampling is Latin hypercube sampling (McKay et al, 1979)), importance sampling (Tokdar and Kass, 2010), and subset simulation (Au and Beck, 2001). Song and Kawai (2023) proposed an adaptive stratified sampling method to conduct structural reliability analysis. Zuniga et al, (2021) integrated dimension reduction techniques into importance sampling approach to conduct structural reliability assessment.…”

Section: Introductionmentioning

confidence: 99%

Investigation on a novel reliability analysis approach integrating adaptive space division and direction sampling

Han

Frangopol

2023

Advances in Structural Engineering

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Multitudes of algorithms have been proposed to evaluate the failure probability of components and systems. Among all these algorithms, direction sampling is a promising one. However, a major computational effort involved in direction sampling is that for each direction sample a root-searching process needs to be conducted to obtain the distance between the origin and the failure surface, which can be computationally expensive. In addition, the failure probability along a direction is hard to obtain when the direction vector intersects the failure surface multiple times. This paper proposes a novel approach to obtain densely populated points locating on the failure surface and utilizing these points to conduct reliability analysis with direction sampling. The process of obtaining the population consists in dividing the initial hypercube space into multiple lattice grids, identifying the grids crossing the failure surface, and dividing these grids into smaller ones. The iterative division process stops when the grids cut across by the failure surface are small enough so that the centers of these grids can be considered located on the failure surface. Several numerical tests are performed to validate the applicability of the proposed approach. Through these tests, it can be concluded that for the situation where the intersection between the direction vector and the failure surface is unique, the proposed approach will lead, with high accuracy, to a failure probability. For the situation where the intersection is not unique, satisfactory estimation of failure probabilities can also be achieved using approximation methods. For high-dimensional reliability problems, clustering techniques can be utilized to reduce the computational cost.

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“…These strategies attract increasing attention in structural reliability analysis [10]. Addressing both, the incorporation of the proper general decomposition and adaptive importance sampling has shown promising results [11].…”

Section: Introductionmentioning

confidence: 99%

Model order reduction in subset simulations using the proper orthogonal decomposition

Thaler,

Shields,

Markert

et al. 2023

Proc Appl Math and Mech

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The crude Monte Carlo method is computationally expensive. Hence, incorporating model order reduction methods enabling reliability analysis for high‐dimensional problems is necessary. However, this strategy may result in an inaccurate estimation of the probability of failure for rare events for two reasons. First, the model order reduction, represented by the proper orthogonal decomposition (POD) here, requires response information in the form of snapshots a priori. To capture the essential nonlinear response behavior, we propose to update the proper orthogonal modes using extreme events. Second, the crude Monte Carlo simulation requires many samples to estimate low failure probabilities reliably. To this end, subset simulation found wide application in reliability analysis to reduce computational effort. Following this strategy, the proposed samples gradually move toward the failure region. Thus, incorporating updates of the modes is particularly promising in evaluating samples from the current subset region. This contribution shows the computational efficiency of POD within subset simulations. We then propose to leverage the estimation of the probability of failure by updating the modes within each subset.

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Adaptive stratified sampling for structural reliability analysis

Cited by 14 publications

References 52 publications

Preserving Data Distribution in Sampling and Instance Selection with Renyi's Divergence

Preserving Data Distribution in Sampling and Instance Selection with Renyi's Divergence

Investigation on a novel reliability analysis approach integrating adaptive space division and direction sampling

Model order reduction in subset simulations using the proper orthogonal decomposition

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