Probability-interval hybrid uncertainty analysis for structures with both aleatory and epistemic uncertainties: a review

Jiang, Chao; Zheng, Jing; Han, Xu

doi:10.1007/s00158-017-1864-4

Cited by 138 publications

(60 citation statements)

References 132 publications

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“…Based on Equation (13), we can also easily obtain the sensitivities in (32). The optimality criteria (OC) method 66 is very efficient for optimization problems with a large number of design variables with a single constraint, which is a typical case in the continuous shape and topology optimization with a material usage constraint.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…The majority of current studies with respect to uncertainty focuses on either aleatory or epistemic uncertainty. However, it is noted that a number of engineering problems actually involve both types of uncertainties in the design . Hence, this paper investigates the design optimization problems of structures under the hybrid uncertainties.…”

Section: Introductionmentioning

confidence: 99%

“…However, it is noted that a number of engineering problems actually involve both types of uncertainties in the design. 32 Hence, this paper investigates the design optimization problems of structures under the hybrid uncertainties. For some uncertain parameters, we can obtain a sufficient number of high-quality samples to create their precise probability distributions, whereas for some other uncertain parameters, due to difficulties or high costs in testing, the interval bounds are relatively easier to be found.…”

Section: Introductionmentioning

confidence: 99%

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Robust topology optimization for cellular composites with hybrid uncertainties

Zheng

Luo

et al. 2018

Numerical Meth Engineering

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Summary This paper will develop a new robust topology optimization method for the concurrent design of cellular composites with an array of identical microstructures subject to random‐interval hybrid uncertainties. A concurrent topology optimization framework is formulated to optimize both the composite macrostructure and the material microstructure. The robust objective function is defined based on the interval mean and interval variance of the corresponding objective function. A new uncertain propagation approach, termed as a hybrid univariate dimension reduction method, is proposed to estimate the interval mean and variance. The sensitivity information of the robust objective function can be obtained after the uncertainty analysis. Several numerical examples are used to validate the effectiveness of the proposed robust topology optimization method.

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Section: Sensitivity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust topology optimization for cellular composites with hybrid uncertainties

Zheng

Luo

et al. 2018

Numerical Meth Engineering

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“…Zheng et al [53,54] developed two RTO approaches to find the robust hierarchical design of the structure with type Ⅱ hybrid uncertainties, in which the probability distribution and variation interval are respectively 4 employed to describe different parameters. It would be suitable for problems that partially have interval variational uncertain variable with unknown distribution type and parameter, but could not be efficient for imprecise probability [39]. Considering that the probability uncertainty which is difficult to be expressed by precise parameters in actual engineering, the CTO method considering uncertainty with imprecise probability is still to be developed.…”

Section: Introductionmentioning

confidence: 99%

Robust concurrent topology optimization of structure and its composite material considering uncertainty with imprecise probability

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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This paper studied a robust concurrent topology optimization (RCTO) approach to design the structure and its composite materials simultaneously. For the first time, the material uncertainty with imprecise probability is integrated into the multi-scale concurrent topology optimization (CTO) framework. To describe the imprecise probabilistic uncertainty efficiently, the type I hybrid interval random model is adopted. An improved hybrid perturbation analysis (IHPA) method is formulated to estimate the expectation and stand variance of the objective function in the worst case. Combined with the bi-directional evolutionary structural optimization (BESO) framework, the robust designs of the structure and its composite material are carried out. Several 2D and 3D numerical examples are presented to illustrate the effectiveness of the proposed method. The results show that the proposed method has high efficiency and low precision loss. In addition, the proposed RCTO approach remains efficient in both of linear static and dynamic structures, which shows its extensive adaptability.where J Y and J Y denote the lower and upper bounds of interval vector J Y . The symbol m J Y is the mean value of J Y , which can be calculated by averaging the lower and upper bounds value as shown in Eq. (16b). I J Y denotes the variation interval of J Y , which depends on the difference of the lower and upper bound values as shown in Eq. (16c). The deviation J Y  of the symmetrical interval can be acquired by averaging the upper and lower bounds of J Y as shown in Eq. (16d). In the combined form, the J-th hybrid interval random parameter( ) JJ X Y can be formulated as RCTO Volume fraction of solid: 95.6% Volume fraction of Phase 1: 70.3% DCTO Volume fraction of solid: 95.1% Volume fraction of phase 1: 70.7% 33 (b) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 93.0% Volume fraction of phase 1: 72.4% DCTO Volume fraction of solid: 92.7% Volume fraction of phase 1: 72.7% (c) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 90.4% Volume fraction of phase 1: 74.9% DCTO Volume fraction of solid: 88.9% Volume fraction of phase 1: 76.3%JJ J ee JJ J J J J e J J e J J JJ J e e J J J J J J J J e J J e 2 2 J J J J JK J e e J J J J J J J J J J J J J e J J JJ JJ e J J J J JJ J J e J J J J e JJ e J J J J 3m d I e J J J J x X X e J J e J J e J J e J J e J J e J J e e e e J J J J e J J J J e J J J J H T A a J J J J H a J J J J pT A J J J J A e J J J J A e J J J J J J J J a i A Y J J J J p a i A Y J J J J a i J J J J a i A Y J J J J p a i A Y J J J J Ne ia A i J J J J a i J J J J Ne ia A i J J J J

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“…However, both of them approximate the performance function in the whole design space and the approximation error is hard to be kept under control. A systematic and in‐depth review on HRA and other related theories was made in Reference .…”

Section: Introductionmentioning

confidence: 99%

Bounds approximation of limit‐state surface based on active learning Kriging model with truncated candidate region for random‐interval hybrid reliability analysis

Yuan

Wang

et al. 2019

Numerical Meth Engineering

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Summary This article reports a brand‐new methodology based on active learning Kriging model for hybrid reliability analysis (HRA) with both random and interval variables. Unlike probabilistic reliability analysis, the limit state surface (LSS) of HRA is projected into a banded region in the domain of random variables. Only approximating the bounds of the banded region is able to meet the accuracy requirement of HRA. In the proposed methodology, the HRA problem is innovatively transformed into a traditional system reliability analysis (SRA) problem with numerous failure modes. And then a basic idea from the field of SRA is borrowed into HRA, and the so‐called truncated candidate region (TCR) for HRA is proposed. In each iteration, the negligible region which probably does not influence the bounds estimation of failure probability is truncated from the original candidate region, and the optimal training point is chosen from the TCR. After several iterations, the TCR will converge to the true ideal candidate region, that is, the candidate region without the inner part of LSS, and the added training points will be driven to the region around the bounds of LSS. The performance of the proposed method is compared with relevant methods by five case studies.

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Probability-interval hybrid uncertainty analysis for structures with both aleatory and epistemic uncertainties: a review

Cited by 138 publications

References 132 publications

Robust topology optimization for cellular composites with hybrid uncertainties

Robust topology optimization for cellular composites with hybrid uncertainties

Robust concurrent topology optimization of structure and its composite material considering uncertainty with imprecise probability

Bounds approximation of limit‐state surface based on active learning Kriging model with truncated candidate region for random‐interval hybrid reliability analysis

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