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On the Design of Artificial Neural Networks for solving Statistical Inverse Problems in Computational Biomechanics

Abstract : This work deals with the statistical inverse identification of geometrical and mechanical properties of a biological tissue (cortical bone) using artificial neural networks (ANNs). The stochastic computational model (SCM) corresponds to a random elasto-acoustic multilayer model [1] for the ultrasonic characterization of cortical bone properties with the axial transmission technique. It allows for simulating the propagation of ultrasonic waves through a three-layer biological system made up of two deterministic homogeneous acoustic fluid layers (soft tissues and marrow bone) surrounding a random heterogeneous elastic solid layer (weaken cortical bone). A probabilistic model of the random elasticity field is introduced to take into account the uncertainties induced by the experimental configuration. The input hyperparameters of the SCM are the thicknesses of healthy and weaken parts of cortical bone, a dispersion parameter controlling the statistical fluctuations of the random elasticity field, and a spatial correlation length along the thickness direction characterizing the spatial correlation structure of the random elasticity field. The output quantities of interest of the SCM are the scattered acoustic energies stored at 14 receivers located inside the soft tissues layer. The statistical inverse problem related to the identification of these hyperparameters from given quantities of interest may be solved using classical stochastic optimization algorithms that usually require many calls to the SCM, thus resulting in a high computational cost. Alternatively, an ANN-based identification method [2] is proposed here and applied to the identification of the hyperparameters from the quantities of interest of the SCM. An initial database is first generated by using forward simulations of the SCM and allows a dataset of hyperparameters and quantities of interest to be collected. A processed database is then constructed by conditioning the hyperparameters with respect to the quantities of interest using classical kernel density estimation methods for improving the ANN performance. A multilayer ANN is finally designed and trained from the processed database to learn the nonlinear mapping between the quantities of interest (ANN inputs) and the corresponding expected mean value of the hyperparameters (ANN outputs). Lastly, the trained ANN can be used to directly perform the identification of the hyperparameters from given quantities of interest. REFERENCES [1] C. Desceliers, C. Soize, S. Naili, and G. Haiat. Probabilistic model of the human cortical bone with mechanical alterations in ultrasonic range. Mechanical Systems and Signal Processing, 32:170–177, 2012. [2] F. Pled, C. Desceliers, and T. Zhang. A robust solution of a statistical inverse problem in multiscale computational mechanics using an artificial neural network. Computer Methods in Applied Mechanics and Engineering, 373:113540, 2021.
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Submitted on : Thursday, September 15, 2022 - 7:31:19 PM
Last modification on : Thursday, September 29, 2022 - 2:21:15 PM


  • HAL Id : hal-03763600, version 1



Florent Pled, Christophe Desceliers. On the Design of Artificial Neural Networks for solving Statistical Inverse Problems in Computational Biomechanics. 15th World Congress on Computational Mechanics (WCCM XV), Jul 2022, Yokohama (virtual), Japan. ⟨hal-03763600⟩



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