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A probabilistic artificial neural network for a robust identification of the random apparent elasticity tensor field at mesoscale

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Abstract

For many materials, the microstructure is complex and highly heterogenous. An efficient approach for constructing the model of such materials consists in modeling their apparent elasticity properties at mesoscale by a tensor-valued random field [1]. Nevertheless, an important challenge is related to the identification of the hyperparameters of such a probabilistic mesoscopic model with limited experimental measurements. An efficient methodology has been recently proposed in [2,3] to address this statistical inverse problem, which consists in solving a multiscale and multi-objective optimization problem with limited experimental information at both macroscale and mesoscale. In this work, we propose to train an artificial neural network in using in silico data generated by a multiscale computational model and a probabilistic mesoscopic model of the random material, for which the output layer corresponds to the values of the hyperparameters and the input layer corresponds to the values of three scalars characterizing the spatial fluctuations of the strain tensor experimentally measured at mesoscale and the six algebraically independent components of the effective elasticity tensor at macroscale. Nevertheless, training an artificial neural network with such in silico data usually fails to solve the statistical inverse problem [4]. That is why a training dataset is constructed by processing the input data as the conditional mean values of the experimental features given the values of the hyperparameters to be identified. Then, a probabilistic model of such processed inputs is introduced given the experimental features. Consequently, for given experimental features obtained at both macroscale and mesoscales, we finally design a stochastic artificial neural network to quantify the uncertainties on the optimal values of the hyperparameters given experimental features. REFERENCES [1] Soize C., Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size. Probabilistic Engineering Mechanics (2008), 23(2):307-323. [2] Nguyen M-T., Desceliers C., Soize C., Allain J-M., Gharbi H., Multiscale identification of the random elasticity field at mesoscale of a heterogeneous microstructure using multiscale experimental observations. International Journal for Multiscale Computational Engineering (2015), 13(4):281-295. [3] Zhang T., Pled T., Desceliers C., Robust Multiscale Identification of Apparent Elastic Properties at Mesoscale for Random Heterogeneous Materials with Multiscale Field Measurements. Materials (2020),13 (12):2826. [4] Pled F., Desceliers C., Zhang T., A robust solution of a statistical inverse problem in multiscale computational mechanics using an artificial neural network, Comput. Methods Appl. Mech. Engrg. 373 (2021):113540.
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hal-03278148 , version 1 (05-07-2021)

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  • HAL Id : hal-03278148 , version 1

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Christophe Desceliers, Florent Pled. A probabilistic artificial neural network for a robust identification of the random apparent elasticity tensor field at mesoscale. 16th U.S. National Congress on Computational Mechanics (USNCCM16), Jul 2021, Chicago, Illinois (virtual), United States. ⟨hal-03278148⟩
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