Artificial neural network for a robust identification of apparent elasticity properties at mesoscale with limited experimental measurements

International audienceFor many materials, as for instance the biological 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. Some recent works [2, 3] addressed this problem and an efficient methodology has been proposed which consists in solving a multiscale and multi-objective optimization problem with limited experimental information at both macroscale and mesoscale. The multi-objective cost functions that are used rely on four experimentally measured indicators that are sensitive to the values of the hyperparameters even with a very low number of experimental specimens: good results are obtained with only one specimen. The calculation of the optimal hyperparameters is carried out in using dedicated algorithms but they cannot quantify the probability level of the solution. In order to improve the robust identification of the hyperparameters, we propose to train an artificial neural network with a multiscale computational model and a probabilistic mesoscopic model of the material, for which the output layer corresponds to the values of the hyperparameters and the input layer corresponds to the values of the experimentally measured indicators, the effective elasticity tensor at macroscale and the values of a random vector involved in the probabilistic mesoscopic model. Consequently, for given values of the indicators and the effective elasticity properties, this artificial neural network can be used to propagate the uncertainties on the vector-valued stochastic germ to the optimal hyperparameters and then, the posterior probability density function of the random hyperparameters given the experimental values of the indicators.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., Desceliers C., Pled F., Experimental identification of mesoscopic elasticity tensor field for heterogeneous materials with complex microstructure using multiscale experimental imaging measurements. 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019), Jun 2019, Hersonissos, Crete Island, Greece