Robust identification of geometrical and mechanical properties using artificial neural networks for cortical bone damage prediction

International audienceThe present work deals with the statistical inverse identification of the geometrical and material hyperparameters of a stochastic computational mechanical model. This latter corresponds to a simplified random elasto-acoustic multilayer model of a biological system (cortical bone) that is representative of a quantitative ultrasound evaluation technique (axial transmission technique) for the ultrasonic characterization of cortical bone properties. The biomechanical system is composed 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 [1]. An ad hoc probabilistic model of the random elasticity field in the cortical bone layer is considered to take into account the random fluctuations of the experimental measurements. The hyperparameters of the stochastic computational model are 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). Identifying such hyperparameters from relevant quantities of interest by classical inverse identification methods requires a high-dimensional statistical inverse problem to be solved, which may be computationally expensive and hardly tractable in practice, and whose results would be arguably questionable when only limited experimental data are available. Alternatively, we propose to design and train a multilayer artificial neural network [2] for solving such a challenging statistical inverse problem and using a numerical database generated with the stochastic computational model in a preliminary (potentially computationally expensive) offline learning phase. The trained artificial neural network can then be used as an efficient random generator for drawing independent realizations and estimating a posterior probability density function of the random hyperparameters given some observed output quantities of interest in a (computationally cheap) online computing phase.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. Uncertainties in Structural Dynamics.[2] Martin T. Hagan, Howard B. Demuth, and Mark H. Beale. Neural Network Design. PWS Publishing Co., Boston, MA, USA, 1996