Incremental modeling of a new high-order polynomial surrogate model

Wu, Jinglai; Luo, Zhen; Zheng, Jing; Jiang, Chao

doi:10.1016/j.apm.2015.12.002

Cited by 58 publications

(22 citation statements)

References 43 publications

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“…Under the circumstances that sufficient information is unavailable to define the distribution models of uncertainties, which is frequently encountered in engineering, the non-probabilistic methodologies can be applied alternatively [42][43][44][45][46][47]. The interval-based approaches [48][49][50], which require the bounds of the uncertain parameters only, are the typical ones among them. The orthogonal Chebyshev series based algorithms [42,48,49] are transparent, transplantable and non-intrusive.…”

Section: Introductionmentioning

confidence: 99%

“…The interval-based approaches [48][49][50], which require the bounds of the uncertain parameters only, are the typical ones among them. The orthogonal Chebyshev series based algorithms [42,48,49] are transparent, transplantable and non-intrusive. These methods transform the uncertain dynamic equations into a set of deterministic ones without breaking into the original solution process.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics analysis of a hollow-shaft rotor system with an open crack under model uncertainties

Yang

et al. 2020

Communications in Nonlinear Science and Numerical Simulation

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This paper focuses on the vibration behaviors of a hollow-shaft rotor in presence of an open crack under inherent uncertainties. Non-probabilistic interval variables are used to represent the uncertain parameters, which releases the high demands of probabilistic knowledge in traditional methods. In modeling the shaft, local stiffness matrix of the cracked element is derived by using the neutral axis method. The periodic response of the rotor system is solved by combination of the finite element method (FEM) and the harmonic balance method (HBM). A simple mathematical function, termed as the uncertain response surrogate function (URSF), is constructed to estimate the vibration response in various cases where different parametric uncertainties are taken into consideration. To verify the robustness and accuracy of the URSF, the bounds of estimated response are compared with those obtained from the classical methods. Results show that the surrogate function has good accuracy and robustness, providing an effective method and guidance for diagnosing crack in uncertain context.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics analysis of a hollow-shaft rotor system with an open crack under model uncertainties

Yang

et al. 2020

Communications in Nonlinear Science and Numerical Simulation

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“…Thus, the incremental sampling method is employed to balance the conflict between the accuracy and the efficiency. In the incremental sampling method, the truncated order n starts from 2, and then, it will gradually increase until the termination condition is satisfied . However, the incremental sampling method is usually applied for the complex problems with numerous variables and high order, but it is not suitable for the case that the calculation of the sample point is very time consuming …”

Section: Cpe‐based Methodsmentioning

confidence: 99%

“…As a result, the efficiency of the ICPE method reduces significantly. Wu et al proposed the order increment strategy based on the high‐order Chebyshev polynomial surrogate model for the interval uncertainty analysis. The proposed method overcomes the routines of the expensive numerical simulations in engineering.…”

Section: Introductionmentioning

confidence: 99%

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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“…The metamodelling accuracy and efficiency can be significantly improved using sequential sampling algorithms. These algorithms start with a small set of initial points and iteratively extend the dataset [22,23,24].…”

Section: Introductionmentioning

confidence: 99%

Sequential sensitivity analysis of expensive black-box simulators with metamodelling

Steenkiste

Herten

Couckuyt

et al. 2018

Applied Mathematical Modelling

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Simulators are an essential tool in the design and analysis of complex systems. For many tasks in engineering, highly accurate simulators are used instead of expensive real-life experiments. As accuracy increases, these simulators are becoming computationally more expensive to evaluate. Sensitivity analysis provides information on the importance of the inputs with regard to the outputs. This does not only provide critical information about the workings of the system but also allows to discard inputs with low impact on the outputs. However, sensitivity analysis is an expensive process in terms of number of evaluations. Hence, metamodelling techniques are used to reduce the computational burden. In this paper we present, discuss and evaluate a novel algorithm for sequential variance-based and derivative-based sensitivity analysis of expensive blackbox simulators using metamodelling. Two new stopping criteria are proposed on top of the traditional model error based stopping criteria. Extensive testing on benchmark problems and engineering use cases shows the sensitivity indices can be efficiently and accurately computed with a limited number of simulator evaluations.

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Incremental modeling of a new high-order polynomial surrogate model

Cited by 58 publications

References 43 publications

Dynamics analysis of a hollow-shaft rotor system with an open crack under model uncertainties

Dynamics analysis of a hollow-shaft rotor system with an open crack under model uncertainties

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

Sequential sensitivity analysis of expensive black-box simulators with metamodelling

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