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Machine learning based on neural networks for the inverse identification of probability distributions - Application to the axial transmission technique for the ultrasonic characterization of damaged cortical bone properties

Abstract : This work is concerned with the inverse identification of probability distributions of geometrical and material hyperparameters of a stochastic computational model using machine learning based on neural networks [1]. The stochastic computational model corresponds to a simplified three-dimensional random elasto-acoustic multilayer model [2] that is representative of the experimental axial transmission (AT) technique [3] for the in vivo ultrasonic characterization of human cortical bone properties. The three-layer biological system is composed of two homogeneous acoustic fluid layers (modeling soft tissues and marrow bone) surrounding a heterogeneous (porous) elastic solid layer (modeling damaged/weaken cortical bone). The hyperparameters of the stochastic computational model are the thicknesses of healthy and damaged/weaken parts of cortical bone layer and the dispersion parameter controlling the statistical fluctuations of the random elasticity field within the healthy part of cortical bone. The output quantities of interest of the stochastic computational model are the scattered acoustic energies stored at 14 receivers located inside the soft tissues layer. The statistical inverse problem is formulated as a function fitting (or function approximation) problem and solved by using a neural network with random inputs and outputs. A multilayer shallow neural network is first designed to learn the nonlinear stochastic mapping between the input hyperparameters and the output quantities of interest of the stochastic computational model using the stochastic germs of the random elasticity field as inputs of the neural network. The (best) trained neural network can then be used as a random generator of independent realizations of the random hyperparameters. Thereafter, the conditional probability density function (pdf) of each random hyperparameter given the random vector of quantities of interest equals to an observed vector of quantities of interest can be constructed by using the kernel density estimation method that is one of the most efficient and popular kernel smoothing techniques in nonparametric statistics [4]. Finally, the proposed innovative strategy based on neural networks allows for constructing a random generator of independent realizations and estimating a posterior pdf of the random (geometrical and mechanical) hyperparameters of a stochastic computational model with a very low computational cost compared to classical statistical inverse identification procedures. References [1] Martin T. Hagan, Howard B. Demuth, and Mark H. Beale. Neural Network Design. PWS Publishing Co., Boston, MA, USA, 1996. [2] 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. [3] E. Bossy, M. Talmant, M. Defontaine, F. Patat, and P. Laugier. Bidirectional axial transmission can improve accuracy and precision of ultrasonic velocity measurement in cortical bone: a validation on test materials. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 51(1):71–79, 2004. [4] A. W. Bowman and A. Azzalini. Applied Smoothing Techniques for Data Analysis. Oxford University Press, Oxford, 1997.
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Submitted on : Thursday, April 21, 2022 - 3:10:55 PM
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  • HAL Id : hal-03638124, version 1

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Florent Pled, Christophe Desceliers, Amir H. Gandomi. Machine learning based on neural networks for the inverse identification of probability distributions - Application to the axial transmission technique for the ultrasonic characterization of damaged cortical bone properties. XI International Conference on Structural Dynamics (EURODYN 2020), Nov 2020, Athens, Greece. ⟨hal-03638124⟩

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