Proper orthogonal decomposition for model reduction of a vibroimpact system

Ritto, T.G.; Buezas, Fernando Salvador; Sampaio, Rubens

doi:10.1590/s1678-58782012000300013

Cited by 15 publications

(5 citation statements)

References 17 publications

(14 reference statements)

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“…The stochastic field n is then expanded using the Karhunen-Lo eve expansion (developed by Karhunen [17] and Lo eve [18]; for some applications see [19,20]):…”

Section: Stochastic Modelmentioning

confidence: 99%

Drill-string horizontal dynamics with uncertainty on the frictional force

Ritto

Escalante

Sampaio

et al. 2013

Journal of Sound and Vibration

108

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“…The stochastic field n is then expanded using the Karhunen-Lo eve expansion (developed by Karhunen [17] and Lo eve [18]; for some applications see [19,20]):…”

Section: Stochastic Modelmentioning

confidence: 99%

Drill-string horizontal dynamics with uncertainty on the frictional force

Ritto

Escalante

Sampaio

et al. 2013

Journal of Sound and Vibration

108

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“…Thus, PCA has been successfully applied in a variety of problems, eg, aeroelastic problems, damage detection, dynamic characterization, and modal analysis. It was initially applied in solid mechanics and then later employed in structural nonlinear dynamics and to analyze vibro‐impact systems …”

Section: Literature Reviewmentioning

confidence: 99%

“…It was initially applied in solid mechanics 37 and then later employed in structural nonlinear dynamics 38 and to analyze vibro-impact systems. 39 In particular, in the work of Dulong et al, 38 PCA has been employed for real-time analysis of nonlinear mechanical behaviors. Interestingly for our work, the approach is divided into a training phase and a real-time phase.…”

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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“…It was initially applied in solid mechanics by [27], due to its capability of describing complex phenomena in a reduced dimension. Then, it has been applied in structural non-linear dynamics to analyze a vibro-impact system [25] and, more in general, to the real-time analysis of non-linear mechanical behavior [10]. In this latter paper, the method is divided into a training phase and a real-time phase.…”

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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Proper orthogonal decomposition for model reduction of a vibroimpact system

Abstract: The application that inspires this work is the percussion drilling. This problem has impacts

Cited by 15 publications

References 17 publications

Drill-string horizontal dynamics with uncertainty on the frictional force

Drill-string horizontal dynamics with uncertainty on the frictional force

Applying functional principal components to structural topology optimization

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

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