Robust identification of elastic properties using the Modified Constitutive Relation Error

Azzouna, Mouldi Ben; Feissel, Pierre; Villon, Pierre

doi:10.1016/j.cma.2015.04.004

Cited by 28 publications

(37 citation statements)

References 21 publications

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“…We refer interested readers to the literatures for more details of parameter identification [44][45][46].…”

Section: Distance-minimizing Data-driven Problemmentioning

confidence: 99%

“…that are axiomatic or epistemic, while the second one consists of empirical models (e.g., material constitutive laws) based on experimental observation. But the empirical models inevitably involve incomplete experimental information [41,42], and the process of material parameter identification [44][45][46] remains numerically intractable. In DMDD, the constitutive law is replaced by the minimization of the distance between the computed state solution (strain and stress hereof) and a set of experimental data using a proper energy norm while enforcing the physical laws.…”

Section: Introductionmentioning

confidence: 99%

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A physics-constrained data-driven approach based on locally convex reconstruction for noisy database

Chen

2020

Computer Methods in Applied Mechanics and Engineering

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Physics-constrained data-driven computing is a hybrid approach that integrates universal physical laws with data-based models of experimental data to enhance the scientific computing. A new data-driven simulation approach enriched with a locally convex reconstruction, termed the local convexity data-driven (LCDD) computing, is proposed to enhance accuracy and robustness against noise and outliers in data sets in the data-driven computing. In this approach, for a given state obtained by the physical simulation, the corresponding optimum experimental solution is sought by projecting the state onto the associated local convex manifold reconstructed based on the nearest experimental data. This learning process of local data structure is less sensitivity to noisy data and consequently yields better accuracy. A penalty relaxation is also introduced to recast the local learning solver in the context of non-negative least squares that can be solved effectively. The reproducing kernel approximation with stabilized nodal integration are employed for the solution of the physical manifold to allow reduced stress-strain data at the discrete points for enhanced effectiveness in the LCDD learning solver. Due to the inherent manifold learning properties, LCDD performs well for high-dimensional data sets that are relatively sparse in real-world engineering applications. Numerical tests demonstrated that LCDD enhances nearly one order of accuracy compared to the standard distance-minimization data-driven scheme when dealing with noisy database, and a linear exactness is achieved when local stress-strain relation is linear.

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“…We refer interested readers to the literatures for more details of parameter identification [44][45][46].…”

Section: Distance-minimizing Data-driven Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A physics-constrained data-driven approach based on locally convex reconstruction for noisy database

Chen

2020

Computer Methods in Applied Mechanics and Engineering

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“…There has also been extensive previous work concerned with the use of empirical data for parameter identification in prespecified material models, or for automating the calibration of the models. For instance, the Errorin-Constitutive-Equations (ECE) method is an inverse method for the identification of material parameters such as the Youngs modulus of an elastic material [13,6,12,7,21,35,5,24,20,23]. While such approaches are efficient and reliable for their intended application, namely, the identification of material parameters, they differ from Data Driven Computing in that, while material identification schemes aim to determine the parameters of a prespecified material law from experimental data, Data Driven Computing dispenses with material models altogether and uses fundamental material data directly in the formulation of initial-boundary-value problems and attendant calculations thereof.…”

Section: Materials Identificationmentioning

confidence: 99%

Data Driven Computing with noisy material data sets

Kirchdoerfer

Ortiz

2017

Computer Methods in Applied Mechanics and Engineering

179

181

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We formulate a Data Driven Computing paradigm, termed maxent Data Driven Computing, that generalizes distance-minimizing Data Driven Computing and is robust with respect to outliers. Robustness is achieved by means of clustering analysis. Specifically, we assign data points a variable relevance depending on distance to the solution and on maximum-entropy estimation. The resulting scheme consists of the minimization of a suitably-defined free energy over phase space subject to compatibility and equilibrium constraints. Distanceminimizing Data Driven schemes are recovered in the limit of zero temperature. We present selected numerical tests that establish the convergence properties of the max-ent Data Driven solvers and solutions.

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“…Let us note that the Modied Constitutive Law Error, (M-CLE), was introduced as the sum of CLE and FEMU-type cost functions, T (CLE) + αT (FEMU) [19,20,50,51]. The weighting parameter α gives an additional handle to optimize the identication procedure.…”

Section: Constitutive Law Error (Cle)mentioning

confidence: 99%

Optimal procedure for the identification of constitutive parameters from experimentally measured displacement fields

Roux

Hild

2020

International Journal of Solids and Structures

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Measured displacement elds constitute a rich database for the identication of mechanical behavior. A variety of methods are available today to address this problem. A formalism is proposed showing that they all revert to the minimization of a quadratic norm (or semi-norm) between measured and computed displacement elds. However, they dier in the chosen metric.Transporting image noise through Digital Image Correlation and identication procedures, the uncertainty in the measured displacement elds (i.e., their full covariance) and the resulting uncertainty in the estimated constitutive parameters is assessed. Consequently, an optimal choice of metric (with respect to image noise) is proposed so that the resulting identication uncertainty is minimized.

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Robust identification of elastic properties using the Modified Constitutive Relation Error

Cited by 28 publications

References 21 publications

A physics-constrained data-driven approach based on locally convex reconstruction for noisy database

A physics-constrained data-driven approach based on locally convex reconstruction for noisy database

Data Driven Computing with noisy material data sets

Optimal procedure for the identification of constitutive parameters from experimentally measured displacement fields

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