Christian Soize

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Verified

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• PhD
• Professor Emeritus at Gustave Eiffel University

We present a quantum computing formulation to address a challenging problem in the development of probabilistic learning on manifolds (PLoM). It involves solving the spectral problem of the high-dimensional Fokker-Planck (FKP) operator, which remains beyond the reach of classical computing. Our ultimate goal is to develop an efficient approach for...

We present a quantum computing formulation to address a challenging problem in the development of probabilistic learning on manifolds (PLoM). It involves solving the spectral problem of the high-dimensional Fokker-Planck (FKP) operator, which remains beyond the reach of classical computing. Our ultimate goal is to develop an efficient approach for...

This paper presents a probabilistic learning method on random manifolds for building and updating statistical surrogate models using small datasets. The approach accounts for various types of variables, including random, controlled, and latent, forming a random manifold that links quantities of interest to controlled variables. This paper consolida...

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a pro...

We present a probabilistic learning inference that assimilates data (tar-get set) into a parameterized large stochastic computational model resulting from discretizing a stochastic boundary value problem (BVP). A target is imposed on a vector-valued random quantity of interest (QoI), observed as the stochastic solution of the BVP. The probabilistic...

This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall t...

This paper presents a model to describe the nonlinear dynamics of a drillstring in horizontal con guration, which is intended to correctly predict the three-dimensional dynamics of this complex structure. This model uses a beam theory, with e ects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements tha...

The main novelty of this paper consists of presenting a statistical artificial neural network (ANN)-based model for a robust prediction of the frequency-dependent aeroacoustic liner impedance using an aeroacoustic computational model (ACM) dataset of small size. The model, focusing on percentage of open area (POA) and sound pressure level (SPL) at...

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an It\^o equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a p...

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a pro...

This article is the second part of a previous article devoted to the deterministic aspects. Here, we present a comprehensive study on the development and application of a novel stochastic second-gradient continuum model for particle-based materials. An application is presented concerning colloidal crystals. Since we are dealing with particle-based...

This paper introduces a methodology for updating the nonlinear stochastic dynamics of a nozzle with uncertain computational model. The approach focuses on a high-dimensional nonlinear computational model constrained by a small target dataset. Challenges include the large number of degrees-of-freedom, geometric nonlinearities, material uncertainties...

This paper discusses wave propagation in unbounded particle-based materials described by a second-gradient continuum model, recently introduced by the authors, to provide an identification technique. The term particle-based materials denotes materials modeled as assemblies of particles, disregarding typical granular material properties such as cont...

In the world of connected automated objects, increasingly rich and structured data are collected daily (positions, environmental variables, etc.). In this work, we are interested in the characterization of the variability of the trajectories of one of these objects (robot, drone, or delivery droid for example) along a particular path from irregular...

This paper proposes, for particle-based materials, a higher-order nonlocal elasticity continuum model that includes the Piola peridynamics and the Eringen nonlocal elasticity. When referring to particle-based materials, we denote systems that can be modeled as assemblies of material points (or particles). Note that this paper is not devoted to gran...

This work is concerned with the construction of statistical surrogates for concurrent multiscale modeling in structures comprising nonlinear random materials. The development of surrogates approximating a homogenization operator is a fairly classical topic that has been addressed through various methods, including polynomial- and deep-learning-base...

We consider a high-dimensional nonlinear computational model of a dynamical system, parameterized by a vector-valued control parameter, in the presence of uncertainties represented by an uncontrolled parameter modeled by a vector-valued random variable, and possibly with stochastic excitation. The objective is to construct a statistical sur-rogate...

A formulation and an algorithm are presented to construct a truncated polynomial chaos representation of a vector-valued random output. This representation depends on a vector-valued random input with a known probability measure and a vector-valued random latent variable with an unknown probability measure. The construction of this PCE representati...

The railway world is undergoing major changes. The advent of new technologies allows us to rethink the train system and face new challenges, but one must not forget all the ecological constraints that are now accentuated by the increase in energy costs. This paper focuses on the optimization of the driver commands to limit the energy consumption of...

An overview of the author works, many of which were carried out in collaboration, is presented. The first part concerns the quantification of uncertainties for complex engineering science systems for which analyzes are now carried out using large numerical simulation models. More recently, machine learning methods have appeared in this field to add...

To be able to calculate a parameterized aeroacoustic liner impedance, a robust statistical metamodel is constructed as a function of the frequency and of the control parameters that are the percentage of open area and the sound pressure level. This construction is based on the use of simulated data generated with a computationally expensive aeroaco...

This paper presents a theoretical approach for identifying the dimensionless mean coefficient of participating fuzzy mass which is the main unknown parameter of the type I or II fuzzy law previously introduced by the author. This method is based on the use of the associated power flow equation, each power term being identified by using a global sta...

This chapter deals with the detuning optimization of a mistuned bladed disk in the presence of geometrical nonlinearities. A full data basis is constructed by using a finite element model of a bladed disk with cyclic order 12, which allows all the possible detuning configurations to be computed. It is then proposed to reformulate the combinatorial...

This work concerns the probabilistic analysis of particle-based materials. More precisely, this work is devoted to the stochastic modeling of the geometric and constitutive microscale parameters associated with particle-pair interactions of an existing model for particle-based materials. Such an issue is addressed with a probabilistic methodology t...

The paper presents an appropriate and efficient methodology for updating the control parameters of very large uncertain computational models, which are used for analyzing the linear vibrations in the frequency domain of highly complex structures for which there are an enormous number of intertwined local and global elastic structural modes in the b...

EDITORIAL: AI IN COMPUTATIONAL MECHANICS AND ENGINEERING SCIENCES. -------------------------------------------------------------------- Artificial Intelligence (AI) approaches have been widely used during the last two decades for different purposes and have remained a highly-researched topic, especially for complex real-world problems. On this basi...

The novel stochastic model to produce voiced sounds proposed in this paper uses the source-filter Fant theory to generate voice signals and, consequently, it does not consider the coupling between the vocal tract and the vocal folds. Two novelties are proposed in the paper. The first one is the new model obtained from the unification of two other d...

This paper deals with the taking into account a given target set of realizations as constraints in the Kullback–Leibler divergence minimum principle (KLDMP). We present a novel probabilistic learning algorithm that makes it possible to use the KLDMP when the constraints are not defined by a target set of statistical moments for the quantity of inte...

Guest editorial for special issue of Feb. 2023

One major industrial challenge is to consider the detuning as a technological means to reduce the dynamical amplifications induced by mistuning. Due to technological evolutions, the nonlinear geometrical effects induced by the large displacements cannot longer be neglected. Recently, methodologies for the robust analysis of detuned/mistuned bladed-...

The train is a complex nonlinear system, whose dynamic behavior is difficult to predict accurately because of its environmental sensitivity. Indeed, in spite of a relative fine modeling of the vehicle and its rolling environment (track and wind), the slightest uncontrolled disturbance can modify the dynamic comportment of the train. For this reason...

We address the problem of noise reduction in modern aircraft engines, targeting the low frequency tonal noises by means of tailored acoustic liners in the nacelle. Due to the prohibitive cost of high fidelity computational models for design optimisation, we use Probabilistic learning on Manifolds (PLoM) for constructing statistical meta-models (sur...

One major industrial challenge is to consider the detuning as a technological means to reduce the dy-namical amplifications induced by mistuning. A full analysis of the detuning optimization of mistuned bladed-disks with finite displacements is carried out on a 12 bladed-disk finite element model. The paper is based on a computational methodology p...

Controlling the energy consumed by our systems has turned to be an important stake in today's world and especially in the railway domain, since transports constitute one of the largest energy consumers. In the railway sector, the energy consumed by high-speed trains depends on many variables such as the vehicle characteristics, the rolling environm...

This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle, which is used as a probabilistic learning algorithm. This permits the effective integration of data into predictive models. We consider the probabilistic learning of a random vector that is made up of either a quantity...

This paper deals with a probabilistic learning inference that allows for integrating data (target set) into predictive models for which the target set is constituted of statistical moments of the quantity of interest (QoI) and for which the training set is constituted of a small number of points. In a first part, we present a mathematical analysis...

The paper deals with the nonlinear stochastic dynamics concerning the detuning optimization in presence of random mistuning of bladed-disks with geometrical nonlinearities. We present an efficient computational methodology for reducing the computational cost, an analysis of the detuning, and the detuning optimization, based on the use of a high-fid...

In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability model. The given targets are statistical moments for which the underlying realizations are not available. Under t...

This work is devoted to the vibroacoustics of complex systems over a broad-frequency band of analysis. The considered system is composed of a complex structure coupled with an internal acoustic cavity. On one hand, the global displacements are associated with the main stiff part and on the other hand, the local displacements are associated with the...

This article presents an approach for characterizing and estimating statistical dependence between a large number of observables in a composite material system. Conditional regression is carried out using the estimated joint density function, permitting a systematic exploration of interdependence between fine scale and coarse observables that can b...

The speed profile of a train plays an important role in energy consumption and resulting costs. The industrial objective of this work is thus to develop a method to reduce the energy consumed by a train over a journey by playing on the driver commands (traction and braking forces) while respecting punctuality constraints. First, a rigid body approa...

The probabilistic learning on manifolds (PLoM) introduced in 20161 has solved difficult supervised problems for the “small data” limit where the number N of points in the training set is small. Many extensions have since been proposed, making it possible to deal with increasingly complex cases. However, the performance limit has been observed and e...

This paper presents a construction and the analysis of a class of non-Gaussian positive-definite matrix-valued homogeneous random fields with uncertain spectral measure for stochastic elliptic operators. Then the stochastic elliptic boundary value problem in a bounded domain of the 3D-space is introduced and analyzed for stochastic homogenization.

This paper presents the computational stochastic homogenization of a heterogeneous 3D-linear anisotropic elastic microstructure that cannot be described in terms of constituents at microscale, as live tissues. The random apparent elasticity field at mesoscale is then modeled in a class of non-Gaussian positive-definite tensor-valued homogeneous ran...

The speed profile of a train plays an important role in energy consumption and resulting costs. The industrial objective of this work is thus to develop a method to reduce the energy consumed by a train over a journey by playing on the driver commands (traction and braking forces) while respecting punctuality constraints. First, a rigid body approa...

A novel extension of the Probabilistic Learning on Manifolds (PLoM) is presented. It makes it possible to synthesize solutions to a wide range of nonlinear stochastic boundary value problems described by partial differential equations (PDEs) for which a stochastic computational model (SCM) is available and which depend on a vector-valued random con...

A novel stochastic model to produce voiced sounds is proposed and, mainly, the corresponding identification of some model parameters using an Artificial Neural Network (ANN). The procedure described in this paper is about an intermediate step, which has as final objective to identify pathologies in the vocal folds through the voice of patients, tha...

This paper present a construction and the analysis of a class of non-Gaussian positive-definite matrix-valued homogeneous random fields with uncertain spectral measure for stochastic elliptic operators. Then the stochastic elliptic boundary value problem in a bounded domain of the 3D-space is introduced and analyzed for stochastic homogenization.

This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall t...

This paper is devoted to the robust optimization of nacelle liners (acoustic treatments). The full computational aeroacoustic model is based on the convected Helmholtz equation in presence of a nonhomogeneous flow velocity field, which is computed by solving the potential Euler equations. Uncertainties are taken into account in order to increase th...

The probabilistic learning on manifolds (PLoM) introduced in 2016 has solved difficult supervised problems for the ``small data'' limit where the number N of points in the training set is small. Many extensions have since been proposed, making it possible to deal with increasingly complex cases. However, the performance limit has been observed and...

Global sensitivity analysis provides insight into how sources of uncertainty contribute to uncertainty in predictions of computational models. Global sensitivity indices, also called variance-based sensitivity indices and Sobol indices, are most often computed with Monte Carlo methods. However, when the computational model is computationally expens...

This paper presents a machine learning approach for detecting structural stiffness changes of civil engineering structures considered as dynamical systems, using only an experimental database constituted of a small number of records related to the experimental first eigenfrequency of the structure and a set of measured temperatures. Since the numbe...

This paper is devoted to the robust optimization of nacelle liners (acoustic treatments). The full computational aeroacoustic model is based on the convected Helmholtz equation in presence of a nonhomogeneous flow velocity field, which is computed by solving the potential Euler equations. Uncertainties are taken into account in order to increase th...

This article is devoted to the linear dynamics of liquid-structure interactions for an elastic structure filled with compressible liquid (acoustic liquid), with slosh-ing and with capillarity effects on the free surface in presence of a gravity field. The objective is to detail the formulation and to quantify the role played by the elasticity in th...

The paper deals with the nonlinear stochastic dynamics concerning the detuning optimization in presence of random mistuning of bladed-disks with geometrical nonlinearities. We present an efficient computational methodology for reducing the computational cost, an analysis of the detuning, and the detuning optimization, based on the use of a high-fid...

div class="section abstract"> This paper deals with the vibroacoustics of complex systems over a broad frequency band of analysis. The considered system is composed of a complex structure coupled with an internal acoustic cavity. The vibroacoustics model is represented by the usual global-displacements elastic modes associated with the main part, a...

A novel extension of the Probabilistic Learning on Manifolds (PLoM) is presented. It makes it possible to synthesize solutions to a wide range of nonlinear stochastic boundary value problems described by partial differential equations (PDEs) for which a stochastic computational model (SCM) is available and depends on a vector-valued random control...

A novel approximate representation of non-Gaussian random vectors is introduced and validated, which can be viewed as a Compressed Principal Component Analysis (CPCA). This representation relies on the eigenvectors of the covariance matrix obtained as in a Principal Component Analysis (PCA) but expresses the random vector as a linear combination of...

This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the following assumptions: (1) neither the prior model nor the likelihood function are Gaussian and neither can be appr...

This paper presents novel mathematical results in support of the probabilistic learning on manifolds (PLoM) recently introduced by the authors. An initial dataset, constituted of a small number of points given in an Euclidean space, is given. The points are independent realizations of a vector-valued random variable for which its non-Gaussian proba...

Usually, to estimate the fatigue life of structural details in existing bridges, fatigue damage assessed with monitoring data is extrapolated linearly in time. In this study, a methodology is proposed for predicting the numbers of fatigue cycles with the peaks-over-threshold approach. On the other side, this POT approach, which is based on extreme...

This paper is devoted to the uncertainty quantification for 3D acoustic performance model of nacelle liners (acoustic treatments). Uncertainties are taken into account in order to increase the robustness of the predictions. A full computational acoustic propagation model based on the convected Helmholtz equation in presence of a non-homogeneous flo...

The focus of the present investigation is on the introduction of uncertainty directly in reduced order models of the nonlinear geometric response of structures following maximum entropy concepts. While the approach was formulated and preliminary validated in an earlier paper, its broad application to a variety of structures based on their finite el...

In this paper, we propose an uncertainty quantification analysis, which is the continuation of a recent work performed in a deterministic framework. The fluid–structure system under consideration is the one experimentally studied in the sixties by Abramson, Kana, and Lindholm from the Southwest Research Institute under NASA contract. This coupled s...

This work is devoted to the robust analysis of the effects of geometric nonlinearities on the nonlinear dynamic behavior of rotating detuned (intentionally mistuned) bladed disks in presence of unintentional mistuning (simply called mistuning). Mistuning induces uncertainties in the computational model, which are taken into account by a probabilist...

This work considers the challenging problem of identifying the statistical properties of random fields from indirect observations. To this end, a Bayesian approach is introduced, whose key step is the nonparametric approximation of the likelihood function from limited information. When the likelihood function is based on the evaluation of an expens...

This paper presents mathematical results in support of the methodology of the probabilistic learning on manifolds (PLoM) recently introduced by the authors, which has been used with success for analyzing complex engineering systems. The PLoM considers a given initial dataset constituted of a small number of points given in an Euclidean space, which...

An extension of the probabilistic learning on manifolds (PLoM), recently introduced by the authors, is presented: in addition to the initial dataset given for performing the probabilistic learning, constraints are given, which correspond to statistics of experiments or of physical models. We consider a non‐Gaussian random vector whose unknown proba...

This paper is devoted to the linear dynamics of liquid‐structure interactions for an elastic structure filled with compressible liquid (acoustic liquid), with sloshing and with capillarity effects on the free surface in presence of a gravity field. The objective is to detail the formulation and to quantify the role played by the elasticity in the n...

At the design stage of bridges, all possible actions and their combinations are to be considered. In certain cases, the influence of the environment must be taken into account in addition to design values of traffic loads. In order to assess the current state of an existing bridge, actual applied actions must be considered: updated traffic situatio...

This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the following assumptions: 1) neither the prior model nor the likelihood function are Gaussian and neither can be appro...

Recently, a novel probabilistic method for modeling and quantifying model-form uncertainties in a deterministic high-dimensional computational model was proposed and demonstrated for numerous applications in linear vibrations and nonlinear structural dynamics. The method relies on a stochastic projection-based reduced-order model (SPROM) grounded i...

We demonstrate, on a scramjet combustion problem, a constrained probabilistic learning approach that augments physics-based datasets with realizations that adhere to underlying constraints and scatter. The constraints are captured and delineated through diffusion maps, while the scatter is captured and sampled through a projected stochastic differe...

The present research concerns the dynamical analysis of mistuned rotating bladed-disks for which nonlinear geometrical effects exist. The present methodology requires the construction of an adapted reduced-order basis from which a nonlinear reduced-order model is constructed. The mistuning phenomenon is taken into account by considering a nonparame...

This work concerns the nonlinear numerical analysis of mistuned blades for a rotating detuned bladed-disk structure with geometrical nonlinearities. The detuning phenomenon is taken into account through a deterministic approach by modifying material properties of some blades. A nonlinear reduced-order model is obtained by setting up a basis using a...

Improvement of vibroacoustic models prediction capabilities requires an adapted indicator to compare experimental measurements with the results of the computational model. When dealing with highly uncertain objects such as series production cars, a probabilistic approach is mandatory to be able to describe the dispersion of experimental results. Mo...

This paper presents a Bayesian calibration method for a simulation-based model with stochastic functional input and output. The originality of the method lies in an adaptation involving the representation of the likelihood function by a Gaussian process surrogate model, to cope with the high computational cost of the simulation, while avoiding the...

Dans cette recherche, nous présentons une méthodologie pour l'analyse dynamique des effets non linéaires géométriques [1, 2] pour une structure de roue aubagée, constituée d'aubes désaccordées involontairement et intentionnellement. Le désaccordage intentionnel est mis en place de manière déterministe en considérant plusieurs types d'aubes de propr...

In this paper, we investigate the construction and identification of a new random field model for representing the constitutive behavior of laminated composites. Here, the material is modeled as a random hyperelastic medium characterized by a spatially dependent, stochastic and anisotropic strain energy function. The latter is parametrized by a set...

This paper presents a novel method for the state health monitoring of high-speed train suspensions from in-line acceleration measurements by embedded sensors, for maintenance purposes. We propose a model-based method relying on a multibody simulation code. It performs the simultaneous identification of several suspension mechanical parameters. It i...

We propose a probabilistic methodology for data-driven updating of non-Gaussian high-dimensional symmetric positive-definite matrices involved in computational models. We cast the data-driven updating as a Bayesian identification of the symmetric positive-definite matrices. The posterior thus obtained exhibits several hyperparameters that control t...

Using an advanced nonlinear fluid–structure reduced-order computational model, this work revisits and explains a resonance of the free surface of water contained in a thin elastic cylindrical tank, which was experimentally exhibited by Lindholm, 1962 and Abramson, 1966. The proposed simulation model allows the experimental setup to be reproduced. T...

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization from a non-Gaussian random vector. The manifold structure is learned using diffusion manifolds and the statisti...

Because of their large wavelength, the noise and the vibrations at low frequencies cannot easily be reduced in the structures by using dissipative materials contrarily to the waves at middle and high frequencies. A possible technique for obtaining an attenuation is to randomly distribute absorbers in a matrix to attenuate acoustic waves and vibrati...

Recently, a novel, nonparametric, probabilistic method for modeling and quantifying model‐form uncertainties in nonlinear computational mechanics was proposed. Its potential was demonstrated through several uncertainty quantification (UQ) applications in vibration analysis and nonlinear computational structural dynamics. This method, which relies o...

The computational burden of a large-eddy simulation for reactive flows is exacerbated in the presence of uncertainty in flow conditions or kinetic variables. A comprehensive statistical analysis, with a sufficiently large number of samples, remains elusive. Statistical learning is an approach that allows for extracting more information using fewer...