A PCE-based multiscale framework for the characterization of uncertainties in complex systems

Mehrez, Loujaine; Fish, Jacob; Aitharaju, Venkat; Rodgers, Will; Ghanem, Roger

doi:10.1007/s00466-017-1502-4

Cited by 21 publications

(16 citation statements)

References 33 publications

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“…In this section, we study the ability of the thermo‐chemo‐mechanical multiscale approach to predict as manufactured part distortion and the effect of residual stress resulting from curing‐cooling stages of the manufacturing process on the loading capacity. In these studies we consider laminates based on noncrimp fabric carbon fiber embedded in epoxy resin for which experimental data exist . All laminates are quasiisotropic, 1.8 mm thick, and consisting of eight plies with various layups as described below.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In these studies we consider laminates based on noncrimp fabric carbon fiber embedded in epoxy resin for which experimental data exist. 18,25,26 All laminates are quasiisotropic, 1.8 mm thick, and consisting of eight plies with various layups as described below. The carbon fiber and resin are assumed to be transversely isotropic and isotropic, respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

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A coupled thermo‐chemo‐mechanical reduced‐order multiscale model for predicting process‐induced distortions, residual stresses, and strength

Yuan

Aitharaju

Fish

2019

Numerical Meth Engineering

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Summary We study residual stresses and part distortion induced by a manufacturing process of a polymer matrix composite and its effect on the component strength. Unlike most of the thermo‐chemo‐mechanical models in the literature where governing multiphysics equations are directly formulated on the macroscale, we present a multiscale‐multiphysics approach. To address the enormous computational complexity involved, a reduced‐order homogenization was originally developed for a single physics problem is employed. The proposed reduced‐order two‐scale thermo‐chemo‐mechanical model has been validated for predicting part distortion beam strength in three‐point bending test. It is shown that while macroscopic stresses are relatively low, and therefore often ignored in practice, stresses at the scale of microconstituents are significant and may have an effect on the overall composite component strength.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

A coupled thermo‐chemo‐mechanical reduced‐order multiscale model for predicting process‐induced distortions, residual stresses, and strength

Yuan

Aitharaju

Fish

2019

Numerical Meth Engineering

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“…A summary is then presented of the various numerical simulators used to approximate these observables as constrained by the physics. A polynomial-chaos based approach to this same problem is described elsewhere [16]. The objective of that work was to develop efficient multi-scale stochastic representations.…”

Section: Multiscale Interactions In Composite Systemsmentioning

confidence: 99%

“…Nonlinear interactions can be significant between features and behaviors and different scales. An upscaling methodology that takes into consideration these nonlinearities is used herein [18,16]. We specifically use the methodology as implemented in the software environment Multiscale Designer [17].…”

Section: Multiscale Interactions In Composite Systemsmentioning

confidence: 99%

Probabilistic learning and updating of a digital twin for composite material systems

Ghanem

Soize

Mehrez

et al. 2020

Numerical Meth Engineering

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This paper presents an approach for characterizing and estimating statistical dependence between a large number of observables in a composite material system. Conditional regression is carried out using the estimated joint density function, permitting a systematic exploration of interdependence between fine scale and coarse observables that can be used for both prognosis and design of complex material systems. An example demonstrates the integration of experimental data with a computational database. The statistical approach is based on the probabilistic learning on manifolds recently developed by the authors. This approach leverages intrinsic structure detected through diffusion on graphs with projected stochastic differential equations to generate samples constrained to that structure.

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“…More recent works attempt to quantify the information loss between scales and to model the cross scale dependencies within the model. For example a multiscale PCE method was proposed in Mehrez et al [28] to model the dependencies of the outputs at a particular level in a hierarchical structure of models on the inputs at finer scales. A generalized hidden Markov model (GHMM) is employed in Wang [29] for the same purpose.…”

Section: Introductionmentioning

confidence: 99%

Multiscale Uncertainty Quantification with Arbitrary Polynomial Chaos

Pepper

Montomoli

Sharma

2019

Computer Methods in Applied Mechanics and Engineering

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This work presents a framework for upscaling uncertainty in multiscale models. The problem is relevant to aerospace applications where it is necessary to estimate the reliability of a complete part such as an aeroplane wing from experimental data on coupons. A particular aspect relevant to aerospace is the scarcity of data available. The framework needs two main aspects: an upscaling equivalence in a probabilistic sense and an efficient (sparse) Non-Intrusive Polynomial Chaos formulation able to deal with scarce data. The upscaling equivalence is defined by a Probability Density Function (PDF) matching approach. By representing the inputs of a coarse-scale model with a generalized Polynomial Chaos Expansion (gPCE) the stochastic upscaling problem can be recast as an optimisation problem. In order to define a data driven framework able to deal with scarce data a Sparse Approximation for Moment Based Arbitrary Polynomial Chaos is used. Sparsity allows the solution of this optimisation problem to be made less computationally intensive than upscaling methods relying on Monte Carlo sampling. Moreover this makes the PDF matching method more viable for industrial applications where individual simulation runs may be computationally expensive. Arbitrary Polynomial Chaos is used to allow the framework to use directly experimental data. Finally, the difference between the distributions is quantified using the Kolmogorov-Smirnov (KS) distance and the method of moments in the case of a multi-objective optimisation. It is shown that filtering of dynamical information contained in the fine-scale by the coarse model may be avoided through the construction of a low-fidelity, high-order model.

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A PCE-based multiscale framework for the characterization of uncertainties in complex systems

Cited by 21 publications

References 33 publications

A coupled thermo‐chemo‐mechanical reduced‐order multiscale model for predicting process‐induced distortions, residual stresses, and strength

A coupled thermo‐chemo‐mechanical reduced‐order multiscale model for predicting process‐induced distortions, residual stresses, and strength

Probabilistic learning and updating of a digital twin for composite material systems

Multiscale Uncertainty Quantification with Arbitrary Polynomial Chaos

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