A new interval uncertain optimization method for structures using Chebyshev surrogate models

Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing

doi:10.1016/j.compstruc.2014.09.006

Cited by 92 publications

(38 citation statements)

References 46 publications

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“…Based on previous research works,(–) the band structures of PnCs can be approximated by the n‐ order truncated CPE with q‐ dimension. Thus, we have

f (() x, k) = \sum_{0 \leq i_{1}, i_{2}, ⋯, i_{q} \leq n} f_{i_{1}, i_{2}, ⋯, i_{q}} ((), k) C_{i_{1}, i_{2}, ⋯, i_{q}} ((), x), and i_{1}, i_{2}, ⋯, i_{q} = 0, 1, ⋯, n,

where x is the set of interval variables

x_{i}^{l} \in ([] - 1, 1)

.…”

Section: Cpe‐based Methodsmentioning

confidence: 99%

“…Based on previous research works, [36][37][38][39] the band structures of PnCs can be approximated by the n-order truncated CPE with q-dimension. Thus, we have…”

Section: Chebyshev Polynomial Expansionmentioning

confidence: 99%

“…Meanwhile, the Chebyshev surrogate model–based interval uncertain methodology was used for structure and vehicle suspension optimization. () Recently, the free vibration analysis of a carbon nanoscroll shell model was investigated by Taraghi et al in which the Chebyshev polynomial was used to evaluate the natural frequencies and the corresponding mode shapes of carbon nanoscroll in different boundary conditions. However, with the increase of the number of interval variables, the high‐order ICPE method with many sample data has to be used to achieve a satisfied accuracy.…”

Section: Introductionmentioning

confidence: 99%

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A polynomial‐based method for topology optimization of phononic crystals with unknown‐but‐bounded parameters

Xie

Liu

Huang

et al. 2018

Numerical Meth Engineering

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Summary The design and analysis of phononic crystals (PnCs) are generally based on the deterministic models without considering the effects of uncertainties. However, uncertainties that existed in PnCs may have a nontrivial impact on their band structure characteristics. In this paper, a sparse point sampling–based Chebyshev polynomial expansion (SPSCPE) method is proposed to estimate the extreme bounds of the band structures of PnCs. In the SPSCPE, the interval model is introduced to handle the unknown‐but‐bounded parameters. Then, the sparse point sampling scheme and the finite element method are used to calculate the coefficients of the Chebyshev polynomial expansion. After that, the SPSCPE method is applied for the band structure analysis of PnCs. Meanwhile, the checkerboard and hinge phenomena are eliminated by the hybrid discretization model. In the end, the genetic algorithm is introduced for the topology optimization of PnCs with unknown‐but‐bounded parameters. The specific frequency constraint is considered. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

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“…Based on previous research works,(–) the band structures of PnCs can be approximated by the n‐ order truncated CPE with q‐ dimension. Thus, we have

f (() x, k) = \sum_{0 \leq i_{1}, i_{2}, ⋯, i_{q} \leq n} f_{i_{1}, i_{2}, ⋯, i_{q}} ((), k) C_{i_{1}, i_{2}, ⋯, i_{q}} ((), x), and i_{1}, i_{2}, ⋯, i_{q} = 0, 1, ⋯, n,

where x is the set of interval variables

x_{i}^{l} \in ([] - 1, 1)

.…”

Section: Cpe‐based Methodsmentioning

confidence: 99%

“…Based on previous research works, [36][37][38][39] the band structures of PnCs can be approximated by the n-order truncated CPE with q-dimension. Thus, we have…”

Section: Chebyshev Polynomial Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A polynomial‐based method for topology optimization of phononic crystals with unknown‐but‐bounded parameters

Xie

Liu

Huang

et al. 2018

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…The interval objective and constraint functions were transformed into deterministic ones by prescribing their acceptable possibility levels, and the resulting deterministic model was further transformed into an unconstrained singleobjective one by weighting and penalty function methods, which was then solved by deterministic algorithms. Wu et al (2013;2015a) proposed the high-order Taylor inclusion function to compress overestimation in interval arithmetic and utilized the Chebyshev surrogate model to approximate the highorder coefficients of the Taylor inclusion function. They further integrated the Chebyshev inclusion function and an interval bisection algorithm to avoid the inner layer optimization.…”

Section: Introductionmentioning

confidence: 99%

Direct reliability-based design optimization of uncertain structures with interval parameters

Cheng

Tang

Liu

et al. 2016

J. Zhejiang Univ. Sci. A

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Abstract:In order to enhance the reliability of an uncertain structure with interval parameters and reduce its chance of function failure under potentially critical conditions, an interval reliability-based design optimization model is constructed. With the introduction of a unified formula for efficiently computing interval reliability, a new concept of the degree of interval reliability violation (DIRV) and the DIRV-based preferential guidelines are put forward for the direct ranking of various design vectors. A direct interval optimization algorithm integrating a nested genetic algorithm (GA) and the Kriging technique is proposed for solving the interval reliability-based design model, which avoids the complicated model transformation process in indirect ones and yields an interval solution that provides more insights into the optimization problem. The effectiveness of the proposed algorithm is demonstrated by a numeric example. Finally, the proposed direct reliability-based design optimization method is applied to the optimization of a press upper beam with interval uncertain parameters, the results of which demonstrate its feasibility and effectiveness in engineering.

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“…Surrogate models such as the Kriging predictor were used to improve the efficiency of gradient computation and thus to facilitate the convergence [36,37]. On the other hand, an interval inverse problem could be formulated as a nested double loop procedure where the Taylor inclusion function was introduced to compress the interval overestimation [38]. For practical applications, an interval inverse procedure has been developed to evaluate the load under which a reinforced concrete beam changed from its elastic behavior to a nonlinear one [30].…”

Section: Introductionmentioning

confidence: 99%

An interval model updating strategy using interval response surface models

Fang

Zhang

Ren

2015

Mechanical Systems and Signal Processing

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A new interval uncertain optimization method for structures using Chebyshev surrogate models

Cited by 92 publications

References 46 publications

A polynomial‐based method for topology optimization of phononic crystals with unknown‐but‐bounded parameters

A polynomial‐based method for topology optimization of phononic crystals with unknown‐but‐bounded parameters

Direct reliability-based design optimization of uncertain structures with interval parameters

An interval model updating strategy using interval response surface models

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