Anas Batou

Generation of accelerograms compatible with design specifications using information theory

This paper deals with the generation of seismic accelerograms which are compatible with a given response spectrum and other design specifications. The time sampling of the stochastic accelerogram yields a time series represented by a random vector in high dimension. The probability density function of this random vector is constructed using the maximum entropy (MaxEnt) principle under constraints defined by the available information (design specifications). In this paper, an adapted algorithm is proposed to identify the Lagrange multipliers introduced in the MaxEnt principle to take into account the constraints. This algorithm is based on (1) the minimization of an appropriate convex functional and (2) the construction of the probability distribution defined as the invariant measure of an Itô stochastic differential equation in order to estimate the integrals in high dimension of the problem. The constraints related to a seismic accelerogram are developed explicitly. This methodology is validated through an application for which the available information is related to the variance of each component of the random vector representing the accelerogram, statistics on the response spectrum, on the peak ground acceleration, on the cumulative absolute velocity and on the end-values for the velocity and for the displacement.

Reduced-Order Computational Model for Low-Frequency Dynamics of Automobiles

A reduced-order model is constructed to predict, for the low-frequency range, the dynamical responses in the stiff parts of an automobile constituted of stiff and flexible parts. The vehicle has then many elastic modes in this range due to the presence of many flexible parts and equipment. A nonusual reduced-order model is introduced. The family of the elastic modes is not used and is replaced by an adapted vector basis of the admissible space of global displacements. Such a construction requires a decomposition of the domain of the structure in subdomains in order to control the spatial wave length of the global displacements. The fast marching method is used to carry out the subdomain decomposition. A probabilistic model of uncertainties is introduced. The parameters controlling the level of uncertainties are estimated solving a statistical inverse problem. The methodology is validated with a large computational model of an automobile.

Experimental identification of stochastic processes using an uncertain computational non-linear dynamical model

The problem presented deals with tubes bundles in Pressurized Water Reactors. The final objective is to identify a model of the external loads applied to theses tubes bundles through the knowledge of dynamical responses. In complex dynamical systems, such an identification is difficult due to the size of the computational model and due to the high number of parameters to be identified. As a consequence, a simplified computational model is constructed. The introduction of such a simplified model introduces model uncertainties. We are first interested in the implementation (modelling and identification) of a probabilistic approach of uncertainties in the mean computational model using the non-parametric probabilistic approach for parameter uncertainties and model uncertainties. In addition, a probabilistic model for the stochastic loads is constructed to take into account model uncertainties in the probabilistic model of the stochastic loads. Finally, the non-linear stochastic dynamical system submited to the uncertain stochastic loads is used to identify the probability model of its uncertainties. In a first part, the theory is presented. The second part is devoted to the validation of the theory in presenting an application.

Hysteretic (Non-reversible) Bit-Rock Interaction Model for Torsional Vibration Analysis of a Drillstring

This paper aims at constructing a novel hysteretic (non-reversible) bit-rock interaction model for the torsional dynamics of a drillstring. Non-reversible means that the torque on bit is not represented only in terms of the bit speed, but also of the bit acceleration, producing a hysteretic behavior. Here, the drillstring is considered as a continuous system which is discretized by means of the finite element method, where a reduced-order model is applied using the normal modes of the associated conservative system. The nonlinear torsional vibrations of the drillstring system are analyzed comparing the proposed bit-rock interaction model to a commonly used reversible model (without hysteresis). The parameters of the proposed hysteretic bit-rock interaction and of the commonly used reversible model are fitted to field data. Results show the system including a bit-rock interaction model with hysteresis effects reproduces a good approach of stick-slip cycle, and the simulated drillstring dynamics using the bit-rock interaction presents a similar behavior comparing to the field data.

Nonlinear Microstructured Material to Reduce Noise and Vibrations at Low Frequencies

At low frequencies, for which the wavelengths are wide, the acoustic waves and the mechanical vibrations cannot easily be reduced in the structures at macroscale by using dissipative materials, contrarily to the middle- and high-frequency ranges. The final objective of this work is to reduce the vibrations and the induced noise on a broad low-frequency band by using a microstructured material by inclusions that are randomly arranged in the material matrix. The dynamical regimes of the inclusions will be imposed in the nonlinear domain in order that the energy be effectively pumped over a broad frequency band around the resonance frequency, due to the nonlinearity. The first step of this work is to design and to analyze the efficiency of an inclusion, which is made up of a hollow frame including a point mass centered on a beam. This inclusion is designed in order to exhibit nonlinear geometric effects in the low-frequency band that is observed. For this first step, the objective is to develop the simplest mechanical model that has the capability to roughly predict the experimental results that are measured. The second step, which is not presented in the paper, will consist in developing a more sophisticated nonlinear dynamical model of the inclusion. In this paper, devoted to the first step, it is proved that the nonlinearity induces an attenuation on a broad frequency band around the resonance, contrarily to its linear behavior for which the attenuation is only active in a narrow frequency band around the resonance. We will present the design in terms of geometry, dimension and materials for the inclusion, the experimental manufacturing of this system realized with a 3D printing system, and the experimental measures that have been performed. We compare the prevision given by the stochastic computational model with the measurements. The results obtained exhibit the physical attenuation over a broad low-frequency band, which were expected.

MULTILEVEL STOCHASTIC REDUCED-ORDER MODEL IN LINEAR STRUCTURAL DYNAMICS FOR COMPLEX STRUCTURES

We present the construction of a multilevel stochastic reduced-order model devoted to the robust prediction of frequency response functions of complex linear dy-namical systems that are characterized by the presence of several structural scales in which there are local displacements in addition to the usual global displacements, and which are associated with the distinct low-, medium-, and high-frequency bands. As the levels of uncertainties are different in the three frequency bands, a multilevel stochastic reduced-order model using several orthogonal subspaces associated with the several types of displacements is developed. The objective of the paper is to demonstrate the capability of the multilevel stochastic reduced-order model to adapt the stochastic modeling of uncertainties to each one of the three frequency bands.

Generation of synthetic accelerograms compatible with a set of design specifications

The research addressed here concerns the generation of seismic accelerograms compatible with a given response spectrum and with other design specifications. The time sampling of the stochastic accelerogram yields a time series represented by a random vector in high dimension. The probability density function (pdf) of this random vector is constructed using the Maximum Entropy (MaxEnt) principle under constraints defined by the available information. In this paper, a new algorithm, adapted to the high stochastic dimension, is proposed to identify the Lagrange multipliers introduced in the MaxEnt principle to take into account the constraints. This novel algorithm is based on (1) the minimization of an appropriate convex functional and (2) the construction of the probability distribution defined as the invariant measure of an Ito Stochastic Differential Equation in order to estimate the integrals in high dimension of the problem.

GENERATION OF RESPONSE SPECTRUM COMPATIBLE ACCELEROGRAMS USING THE MAXIMUM ENTROPY PRINCIPLE

The research addressed here concerns the generation of seis mic accelerograms compatible with a given response spectrum and other associa ted properties. The time sampling of the stochastic accelerogram yields a time series represe nted by a random vector in high dimension. The probability density function (pdf) of this r andom vector is constructed using the Maximum Entropy (MaxEnt) principle under constraints d efined by the available informa- tion. In this paper, a new algorithm, adapted to the high stoc hastic dimension, is proposed to identify the Lagrange multipliers introduced in the MaxEntprinciple to take into account the constraints. This novel algorithm is based on (1) the minimi zation of an appropriate convex functional and (2) the construction of the probability dist ribution defined as the invariant mea- sure of an It Stochastic Differential Equation in order to es timate the integrals in high dimension of the problem.

Random Dynamical Response of a Multibody System with Uncertain Rigid Bodies

This paper is devoted to the construction of the random dynamical response of a multibody system with uncertain rigid bodies. We first construct a stochastic model of an uncertain rigid body by replacing the mass, the center of mass and the tensor of inertia by random variables. The prior probability distributions of the stochastic model are constructed using the maximum entropy principle under the constraints defined by the available information. The generator of independent realizations corresponding to the prior probability distribution of these random quantities are developed. Then, several uncertain rigid bodies can be linked each others in order to calculate the random response of a multibody dynamical system. An application is proposed to illustrate the theoretical development.

Identification of Stochastic Loads Applied to a Nonlinear Dynamical System Using an Uncertain Computational Model

This paper deals with the identification of stochastic loads applied to a nonlinear dynamical system for which a few experimental responses are available using an uncertain computational model. Uncertainties are induced by the use of a simplified computational model to predict the responses of the real system. A nonparametric probabilistic approach of both parameter uncertainties and model uncertainties is implemented in the simplified computational model in order to take into account uncertainties. The level of uncertainties is identified using the maximum likelihood method. The identified stochastic simplified computational model which is obtained is then used to perform the identification of the stochastic loads applied to the real nonlinear dynamical system. A numerical validation of the complete methodology is presented.