Stochastic modeling for hysteretic bit–rock interaction of a drill string under torsional vibrations

© The Author(s) 2019. This paper aims at constructing a stochastic model for the hysteretic behavior of the nonlinear bit–rock interaction of a drill string under torsional vibrations. The proposed model takes into account the fluctuations of the stick–slip oscillations observed during the drilling process. These fluctuations are modeled by introducing a stochastic process associated with the variations of the torque on bit, which is a function of the bit speed. The parameters of the stochastic model are calibrated with field data. The response of the proposed stochastic model, considering the random bit–rock interaction, is analyzed, and statistics related to the stability of the drill string are estimated

A numerical study of ultrasonic response of random cortical bone plates

A probabilistic study on ultrasound wave reflection and transmission from cortical bone plates is proposed. The cortical bone is  modeled by an anisotropic and heterogeneous elastic plate sandwiched between two fluids and has randomly varied elastic properties in the thickness direction. A parametric stochastic model is proposed to describe the elastic heterogeneity in the plate. Reflection and transmission coefficients are computed via the semi-analytical finite element (SAFE) method. The effect of material heterogeneity on reflected and transmitted waves is investigated from a probabilistic point of view. The parametric study highlights effects of the uncertainty of material properties on the reflection and transmission coefficients by varying the frequency, angle of incidence and bone thickness

Hysteretic bit/rock interaction model to analyze the torsional dynamics of a drill string

The present paper proposes a novel hysteretic (non-reversible) bit/rock interaction model for the torsional dynamics of a drill string. Non-reversible means that the torque-on-bit depends not only on the bit speed, but also on the bit acceleration, producing a type of hysteretic cycle. The continuous drill string system is discretized by means of the finite element method and a reduced-order model is constructed using the normal modes of the associated conservative system. The parameters of the proposed hysteretic bit/rock interaction model is fitted with field data. The non-linear torsional vibration and the stability map of the drill string system are analyzed employing the proposed bit/rock interaction model and also a commonly used reversible model (without hysteresis). It turns out that the hysteretic model affects the stability region of the system

On the Solution of Statistical Inverse Problems using Machine Learning Methods based on Artificial Neural Networks

International audienceThis work adresses the solution of a statistical inverse problem in computational elastodynamics using machine learning based on artificial neural networks (ANNs). The stochastic computational model (SCM) corresponds to a simplified random elasto-acoustic multilayer model of a biological system that is representative of the axial transmission technique for the ultrasonic characterization of cortical bone properties from experimental velocity measurements. The three-layer biological system consists 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 [1]. Such SCM is 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 characterizing the spatial correlation structure of the random elasticity field. An innovative ANN-based identification methodology has been recently proposed in [2] and applied to multiscale computational mechanics. In this work, the proposed methodology is extended to linear elastodynamics for the statistical inverse identification of the four aforementioned hyperparameters from fourteen 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 consisting 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 kernel density estimation methods to improve the ANN performance, (iii) designing an efficient ANN trained using the processed database to identify the optimal hyperparameters corresponding to given expected quantities of interest, (iv) constructing a probabilistic model of the network input random vector to take into account the uncertainties on the input quantities of interest, and (v) designing another ANN trained using the initial and processed input data to identify the probabilistic model of the network input random vector from given observed quantities of interest.REFERENCES[1] C. Desceliers, C. Soize, S. Naili, 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, 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

Statistical inverse problem for the mesoscale model of apparent elasticity properties by training an artificial neural network

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. An efficient methodology has been recently proposed in [2,3] to address this statistical inverse problem, which consists in solving a multiscale and multi-objective optimization problem with limited experimental information at both macroscale and mesoscale. The multiobjective 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. In this work, we propose to train an artificial neural network in using in silico data generated by a multiscale computational model and a probabilistic mesoscopic model of the random material, for which the output layer corresponds to the values of the hyperparameters and the input layer corresponds to the values of the three experimentally measured indicators at mesoscale and the six algebraically independent components of the effective elasticity tensor at macroscale. Nevertheless, training an artificial neural network with such in silico data usually fails to solve the statistical inverse problem [4] and large discrepancies are observed between the values of the network targets and the outputs due to the stochastic nature of the mapping between the hyperparameters and the indicators. To circumvent this issue, the in silico data corresponding to the network input features are statistically processed by conditional probability using kernel smoothing techniques. Such a statistical processing of the network input data introduces uncertainties on the values that have to be presented at the input of the network since such processed input features are not directly observable by experimental measurements. A probabilistic model of the network inputs is then introduced to take into account such uncertainties. Consequently, for given experimental values obtained at both macroscale and mesoscale of the indicators, we finally propose to design an additional artificial neural network for which the outputs model the uncertainties on the optimal hyperparameters of the probabilistic mesoscopic model.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., Pled T., Desceliers C., Robust Multiscale Identification of Apparent Elastic Properties at Mesoscale for Random Heterogeneous Materials with Multiscale Field Measurements. Materials (2020), 13(12):2826[4] Pled F., Desceliers C., Zhang T., A robust solution of a statistical inverse problem in multiscalecomputational mechanics using an artificial neural network, Comput. Methods Appl. Mech.Engrg. 373 (2021):11354