**Abstract** : This work adresses the solution of a statistical inverse problem in computational elastodynamics using machine learning based (ML) on artificial neural networks (ANNs). The forward computational model corresponds to a simplified random elasto-acoustic multilayer model of a biological system (cortical bone) that is representative of the ultrasound axial transmission (AT) technique [1] for the in vivo ultrasonic characterization of cortical bone properties from experimental velocity measurements. Such a stochastic computational model (SCM) allows for simulating the propagation of ultrasonic waves axially transmitted along the bone axis through a three-layer biological system made up of a random heterogeneous damaged/weaken elastic solid layer (cortical bone layer) sandwiched between two deterministic homogeneous acoustic fluid layers (soft tissues and marrow bone layers) and excited by an acoustic line source located in the soft tissues layer [2]. The random fluctuations observed on the ultrasound velocity measurements due to uncertainties induced by the experimental configuration are taken into account by considering an ad hoc probabilistic model of the random elasticity field [3] with a simple spatial gradient model (fluid-solid mixture) for the mean material properties along the thickness direction in the cortical bone layer [2]. The SCM is then parameterized by two geometrical parameters, corresponding to the thicknesses of the “healthy” and “damaged” elastic solid parts, a dispersion parameter controlling the level of 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 . An innovative ANN-based identification methodology has been recently proposed in [4] and applied within the context of multiscale computational mechanics. In the present work, the proposed methodology is extended to the statistical inverse identification of the four aforementioned hyperparameters from fourteen relavant quantities of interest of the SCM, corresponding to the scattered acoustic energy stored at fourteen receivers located in the soft tissues layer. It consists in (i) constructing of a synthetic database generated from the SCM and made up of network input data (quantities of interest) and target data (hyperparameters), (ii) postprocessing this initial database by conditioning the network input data with respect to the network target data using classical kernel density estimation methods to improve the ANN performance, and (iii) designing an efficient ANN trained using the processed database to find the optimal hyperparameters (network outputs) corresponding to given experimental quantities of interest (network inputs). A probabilistic model of the network input random vector is then proposed to take into account the uncertainties introduced by the data conditioning and improve the robustness of the identification method. Another efficient ANN is finally designed using the initial and processed input data and allows for identifying the probabilistic model of the network input random vector from given experimentally observed quantities of interest.
REFERENCES
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