Reliability-based design optimization under dependent random variables by a generalized polynomial chaos expansion

Lee, Dongjin; Rahman, Sharif

doi:10.1007/s00158-021-03123-7

Cited by 14 publications

(2 citation statements)

References 38 publications

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“…Therefore, metamodeling methods are used in practical engineering, and the basic idea is to construct approximate (surrogate) models, i.e., to establish approximate mapping relationships between input variables and output responses by DOE, which play a role in computationally efficient and predictable responses at unknown points. Commonly used surrogate models include the response surface model [8], polynomial chaos expansions (PCEs) [9], kriging [10,11], polynomial chaos-kriging (PCK) [12], machine learning [13,14], support vector machines [15,16] and radial-basis functions [17]. Once the surrogate model has been constructed, reliability methods can be used to calculate the failure probability.…”

Section: Introductionmentioning

confidence: 99%

Active-Learning Reliability Analysis of Automotive Structures Based on Multi-Software Interaction in the MATLAB Environment

Wang,

Chen,

Zhang

et al. 2024

Applied Sciences

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The reliability design of automotive structures is characterized by numerous variables and implicit responses. The traditional design of experiments for metamodel construction often requires manual adjustment of model parameters and extensive finite element analysis, resulting in inefficiency. To address these issues, active learning-based reliability methods are effective solutions. This study proposes an active-learning reliability analysis method based on multi-software interaction. Firstly, through secondary development of different software and MATLAB (version 2023a)’s batch processing function, a multi-software interactive reliability analysis method is developed, achieving automation in structural parametric design, finite element analysis and post-processing. This provides a more efficient and convenient platform for the implementation of active learning. Secondly, the polynomial chaos–kriging (PCK) active-learning method is introduced, combining the advantages of polynomial chaos expansion (PCE) and kriging. The PCK method captures the global behavior of the computational model using regression-based PCE and local variations using interpolation-based kriging. This metamodel is constructed with fewer training samples, effectively replacing the real multi-dimensional implicit response relations, thereby improving the efficiency of modeling and reliability analysis. Finally, the specific implementation scheme is detailed. The accuracy and efficiency of the proposed method are verified by a reliability engineering example of body-in-white bending and torsional stiffness.

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Section: Introductionmentioning

confidence: 99%

Active-Learning Reliability Analysis of Automotive Structures Based on Multi-Software Interaction in the MATLAB Environment

Wang,

Chen,

Zhang

et al. 2024

Applied Sciences

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“…While standard MCS is can handle dependent random variables directly, it requires high-fidelity solves and therefore can be too expensive computationally. A practical version of the GPCE was recently introduced to effectively solve UQ and design optimization problems under arbitrary, dependent input random variables [19,20,21]. This work makes it possible to obtain the multivariate orthonormal polynomial basis consistent with any non-product-type probability measure of input numerically, instead of an analytical expression by a Rodrigues-type formula used in the prequel [34].…”

Section: Introductionmentioning

confidence: 99%

Bi-fidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos expansion

Kramer¹

2022

Preprint

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Digital twin models allow us to continuously assess the possible risk of damage and failure of a complex system. Yet high-fidelity digital twin models can be computationally expensive, making quick-turnaround assessment challenging. Towards this goal, this article proposes a novel bi-fidelity method for estimating the conditional value-at-risk (CVaR) for nonlinear systems subject to dependent and high-dimensional inputs. For models that can be evaluated fast, a method that integrates the dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) approximation with a standard sampling-based CVaR estimation is proposed. For expensive-to-evaluate models, a new bi-fidelity method is proposed that couples the DD-GPCE with a Fourier-polynomial expansions of the mapping between the stochastic low-fidelity and high-fidelity output data to ensure computational efficiency. The method employs a measure-consistent orthonormal polynomial in the random variable of the low-fidelity output to approximate the high-fidelity output. Numerical results for a structural mechanics truss with 36-dimensional (dependent random variable) inputs indicate that the DD-GPCE method provides very accurate CVaR estimates that require much lower computational effort than standard GPCE approximations. A second example considers the realistic problem of estimating the risk of damage to a fiber-reinforced composite laminate. The high-fidelity model is a finite element simulation that is prohibitively expensive for risk analysis, such as CVaR computation. Here, the novel bi-fidelity method can accurately estimate CVaR as it includes low-fidelity models in the estimation procedure and uses only a few high-fidelity model evaluations to significantly increase accuracy.

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A novel data-driven sparse polynomial chaos expansion for high-dimensional problems based on active subspace and sparse Bayesian learning

Zhong

et al. 2023

Struct Multidisc Optim

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Reliability-based design optimization under dependent random variables by a generalized polynomial chaos expansion

Cited by 14 publications

References 38 publications

Active-Learning Reliability Analysis of Automotive Structures Based on Multi-Software Interaction in the MATLAB Environment

Active-Learning Reliability Analysis of Automotive Structures Based on Multi-Software Interaction in the MATLAB Environment

Bi-fidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos expansion

A novel data-driven sparse polynomial chaos expansion for high-dimensional problems based on active subspace and sparse Bayesian learning

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