A Polynomial Chaos Expansion Based Reliability Method for Linear Random Structures

Yu, Huaqing; Gillot, F; Ichchou, Mohamed

doi:10.1260/1369-4332.15.12.2097

Cited by 6 publications

(3 citation statements)

References 36 publications

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“…Finally, there exist other well-established methods in the literature, based on alternative expansions, which involve a basis of known random functions with deterministic coefficients, namely, polynomial chaos expansion. The latest methodological developments of polynomial chaos expansion can be found in the works of Panayirci and Schuëller 29 and Yu et al, 30 whereas recent applications can be found in different fields, eg, hydrology, 31 piezoelectric materials, 32 and dosimetry to study human exposure to magnetic fields. 33 Resuming PCA, it is widely used in statistics to look at the covariance structure of multivariate and complex data.…”

Section: Dimensionality Reduction In Feamentioning

confidence: 99%

Applying functional principal components to structural topology optimization

Alaimo

Auricchio

Bianchini

et al. 2018

Numerical Meth Engineering

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Summary Structural topology optimization aims to enhance the mechanical performance of a structure while satisfying some functional constraints. Nearly all approaches proposed in the literature are iterative, and the optimal solution is found by repeatedly solving a finite element analysis (FEA). It is thus clear that the bottleneck is the high computational effort, as these approaches require solving the FEA a large number of times. In this work, we address the need for reducing the computational time by proposing a reduced basis method that relies on functional principal component analysis (FPCA). The methodology has been validated considering a simulated annealing approach for compliance minimization in 2 classical variable thickness problems. Results show the capability of FPCA to provide good results while reducing the computational times, ie, the computational time for an FEA is about one order of magnitude lower in the reduced FPCA space.

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Section: Dimensionality Reduction In Feamentioning

confidence: 99%

Applying functional principal components to structural topology optimization

Alaimo

Auricchio

Bianchini

et al. 2018

Numerical Meth Engineering

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“…For latest methodological developments on PCE, see for instance [22,34]. Recently, PCE has been applied in different areas, ranging from hydrology [28], properties of piezoelectric materials [31], and the study of stochastic dosimetry to assess the variability of human exposure to magnetic fields [19].…”

Section: Literature Reviewmentioning

confidence: 99%

Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

et al. 2015

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The great influence of uncertainties on the behavior of physical systems has always drawn attention to the importance of a stochastic approach to engineering problems. Accordingly, in this paper, we address the problem of solving a Finite Element analysis in the presence of uncertain parameters. We consider an approach in which several solutions of the problem are obtained in correspondence of parameters samples, and propose a novel non-intrusive method, which exploits the functional principal component analysis, to get acceptable computational efforts. Indeed, the proposed approach allows constructing an optimal basis of the solutions space and projecting the full Finite Element problem into a smaller space spanned by this basis. Even if solving the problem in this reduced space is computationally convenient, very good approximations are obtained by upper bounding the error between the full Finite Element solution and the reduced one. Finally, we assess the applicability of the proposed approach through different test cases, obtaining satisfactory results

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“…The metaheuristic algorithms are used for the optimization process and the Monte Carlo simulation method is used for reliability assessment. [31][32][33][34][35] The reliability-based robust design optimization (RBRDO) is investigated in three truss structures to assess the performance and efficiency of the suggested method.…”

Section: Introductionmentioning

confidence: 99%

A multi-step approach for reliability-based robust design optimization of truss structures

Mehanpour

Vaez

Fathali

2023

Proceedings of the Institution of Mechanical Engineers, Part O:

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There are two general methods of robust design optimization (RDO) and reliability-based robust design optimization (RBRDO) for the optimal design of structures with non-deterministic variables. In the problem-solving process of both RDO and RBRDO, assessing the probabilistic constraints of the problem and the standard deviation of the structural responses is time-consuming and costly. In this study, by presenting a multi-step approach, for a probable optimal solution, the deterministic constraints are first investigated. Then the limit state functions related to probabilistic constraints are computed based on the mean value of random variables (in the RBRDO problem) and in the step of uncertainties effects simulation on the response of the structure, probabilistic constraints are evaluated (in the RBRDO problem). Designs that not meeting the deterministic constraints or in the unsafe area for the mean values of the random variables are not included in calculating the first and second terms of the objective function and reliability assessment. This leads to reduce the volume of calculations. The Monte Carlo simulation method is used to assess the probabilistic constraints, and the EVPS metaheuristic algorithm is used for the optimization process. Three benchmark trusses of 10, 25, and 72 bars were studied to assess the efficiency of the proposed approach. The first objective function in these problems was the mean weight of trusses and the second objective function was the standard deviation of the displacement of a specific node in a certain direction.

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A Polynomial Chaos Expansion Based Reliability Method for Linear Random Structures

Cited by 6 publications

References 36 publications

Applying functional principal components to structural topology optimization

Applying functional principal components to structural topology optimization

Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

A multi-step approach for reliability-based robust design optimization of truss structures

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