Model-free data-driven identification algorithm enhanced by local manifold learning

Su, Tung-Huan; Jean, Jimmy Gaspard; Chen, Chuin-Shan

doi:10.1007/s00466-022-02255-x

Cited by 4 publications

(4 citation statements)

References 43 publications

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“…Subsequently, the corresponding uncertain mechanical stresses are obtained by extending Equation (10) to…”

Section: Extension To Uncertaintymentioning

confidence: 99%

“…Instead,

\mathbb {C}_e = \mathbb {C}=C\cdot \bm{I}\ \forall e

is set in this contribution with the identity tensor I , whereby different recommendations for the scaling factor C are given in literature. Depending on the focus on stresses or strains, these vary between 10 10 Pa [4], 10 7 Pa [10] and 10 5 Pa [1]. Minimizing the sum of local objective functions of all Gauss points e , weighted by the associated volumes

w_e

with compatibility constraint Equation () enforced by Lagrange multipliers leads to the stationary equation

\begin{equation} \delta {\left(\sum _{X=1}^{N_X}\sum _{e = 1}^{m}w_e \Vert (\bm{\varepsilon }_e^X-\hat{\bm{\varepsilon }}_{a(e,\,X)},\, \bm{\sigma }_e^X-\hat{\bm{\sigma }}_{a(e,\,X)})\Vert _{\mathbb {C}_e}- (w_e \bm{B}_e^T\bm{\sigma }_e^X - \bm{f}_X)\bm{\lambda }_X\right)}=0, \end{equation}

mapping associating mechanical states to material states, expressed as

a:(e,\,X)\mapsto i

.…”

Section: Data‐driven Identificationmentioning

confidence: 99%

“…[9] and an approach for integrating a local manifold learning technique is presented in ref. [10]. The consideration of a reduced domain is addressed in ref.…”

Section: Data-driven Identificationmentioning

confidence: 99%

See 2 more Smart Citations

Incorporating uncertainty in stress‐strain data acquisition: extended model‐free data‐driven identification

Zschocke,

Graf,

Kaliske

2023

Proc Appl Math and Mech

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Based on the increasing ability to collect and store large amounts of data and information, data‐driven methods have recently gained importance in the context of computational mechanics. Compared to the traditional approach of defining a suitable constitutive model and fit the parameters to experimental data, these methods aim to capture complex material behavior without the assumption of a certain material formulation. Distinguished are model‐based data‐driven methods, leading to an approximation of the constitutive material description for example, by neural networks, and model‐free data‐driven methods. The approach of data‐driven computational mechanics (DDCM), introduced by Kirchdoerfer and Ortiz (2016), enables to circumvent any material modeling step by directly incorporating material data into the structural analysis. A basic prerequisite for both types of data‐driven methods is a large amount of data representing the material behavior, in solid mechanics consisting of stresses and strains. Obtaining these databases numerically by multiscale approaches is computationally expensive and requires the definition of lower scale models. In case of an experimental characterization, constitutive descriptions are generally required to compute the stress states corresponding to displacement fields, for example, identified by full‐field measurement techniques, such as digital image correlation (DIC). The method of data‐driven identification (DDI), introduced in Leygue et al. (2018) based on the principles of DDCM, enables the determination of detailed information about the constitutive behavior based on displacement fields and applied boundary conditions without a specific material model. Stresses corresponding to given strains are identified by iteratively clustering and enforcing equilibrium. The algorithm has shown to be applicable to synthetic as well as real data taking linear and non‐linear material behavior into account. Generalized polymorphic uncertainty models, resulting as a combination of aleatoric and epistemic uncertainty models, are utilized to take variability, imprecision, inaccuracy and incompleteness of data into account. The consideration of uncertain material properties by data‐driven simulation approaches leads to the requirement of data sets representing uncertain material behavior. In this contribution, different sources of uncertainty occurring within DDI of stress‐strain relations are addressed and an efficient method for the identification of data sets representing uncertain material behavior based on the concept of DDI is proposed. In order to demonstrate the developed methods, numerical examples are carried out.

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“…Subsequently, the corresponding uncertain mechanical stresses are obtained by extending Equation (10) to…”

Section: Extension To Uncertaintymentioning

confidence: 99%

“…Instead,

\mathbb {C}_e = \mathbb {C}=C\cdot \bm{I}\ \forall e

w_e

with compatibility constraint Equation () enforced by Lagrange multipliers leads to the stationary equation

\begin{equation} \delta {\left(\sum _{X=1}^{N_X}\sum _{e = 1}^{m}w_e \Vert (\bm{\varepsilon }_e^X-\hat{\bm{\varepsilon }}_{a(e,\,X)},\, \bm{\sigma }_e^X-\hat{\bm{\sigma }}_{a(e,\,X)})\Vert _{\mathbb {C}_e}- (w_e \bm{B}_e^T\bm{\sigma }_e^X - \bm{f}_X)\bm{\lambda }_X\right)}=0, \end{equation}

mapping associating mechanical states to material states, expressed as

a:(e,\,X)\mapsto i

.…”

Section: Data‐driven Identificationmentioning

confidence: 99%

See 1 more Smart Citation

Incorporating uncertainty in stress‐strain data acquisition: extended model‐free data‐driven identification

Zschocke,

Graf,

Kaliske

2023

Proc Appl Math and Mech

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show abstract

“…To overcome this challenge, researchers explored several possibilities. Data-driven techniques [3][4][5] were proposed to bypass material modeling at the microscopic scale. Another novel and notable effort was to use neural networks to create FE-like shape functions, which results in a lot more accuracy than FEM with the same number of degrees of freedom [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Graph-enhanced deep material network: multiscale materials modeling with microstructural informatics

Jean,

Su,

Huang

et al. 2024

Comput Mech

Self Cite

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This study addresses the fundamental challenge of extending the deep material network (DMN) to accommodate multiple microstructures. DMN has gained significant attention due to its ability to be used for fast and accurate nonlinear multiscale modeling while being only trained on linear elastic data. Due to its limitation to a single microstructure, various works sought to generalize it based on the macroscopic description of microstructures. In this work, we utilize a mechanistic machine learning approach grounded instead in microstructural informatics, which can potentially be used for any family of microstructures. This is achieved by learning from the graph representation of microstructures through graph neural networks. Such an approach is a first in works related to DMN. We propose a mixed graph neural network (GNN)-DMN model that can single-handedly treat multiple microstructures and derive their DMN representations. Two examples are designed to demonstrate the validity and reliability of the approach, even when it comes to the prediction of nonlinear responses for microstructures unseen during training. Furthermore, the model trained on microstructures with complex topology accurately makes inferences on microstructures created under different and simpler assumptions. Our work opens the door for the possibility of unifying the multiscale modeling of many families of microstructures under a single model, as well as new possibilities in material design.

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Data-driven confidence bound for structural response using segmented least squares: a mixed-integer programming approach

Kanno

2024

Japan J. Indust. Appl. Math.

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As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.

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Model-free data-driven identification algorithm enhanced by local manifold learning

Cited by 4 publications

References 43 publications

Incorporating uncertainty in stress‐strain data acquisition: extended model‐free data‐driven identification

Incorporating uncertainty in stress‐strain data acquisition: extended model‐free data‐driven identification

Graph-enhanced deep material network: multiscale materials modeling with microstructural informatics

Data-driven confidence bound for structural response using segmented least squares: a mixed-integer programming approach

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