Much has been written about theory and practice in the law, and the tension between practitioners and theorists. Judges do not cite theoretical articles often; they rarely "apply" theories to particular cases. These arguments are not revisited. Instead the Essay explores the working and interaction of theory and practice, practitioners and theorists. The Essay starts with a story about solving a legal issue using our intellectual tools - theory, practice, and their progenies: experience and "gut." Next the Essay elaborates on the nature of theory, practice, experience and "gut." The third part of the Essay discusses theories that are helpful to practitioners and those that are less helpful. The Essay concludes that practitioners theorize, and theorists practice. They use these intellectual tools differently because the goals and orientations of theorists and practitioners, and the constraints under which they act, differ. Theory, practice, experience and "gut" help us think, remember, decide and create. They complement each other like the two sides of the same coin: distinct but inseparable.

Of Theory and Practice

https://hal-upec-upem.archives-ouvertes.fr/hal-00743699/document

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Three-dimensional convolutional neural network (3D-CNN) for heterogeneous material homogenization

Christian Soize presents the main concepts, formulations, and recent advances in the use of a mathematical-mechanical modeling process to predict the responses of a real structural system in its environment.

Stochastic Models of Uncertainties in Computational Mechanics

A new generalized probabilistic approach of uncertainties is proposed for computational model in structural linear dynamics and can be extended without difficulty to computational linear vibroacoustics and Computational non-linear structural dynamics. This method allows the prior probability model of each type of uncertainties (model-parameter uncertainties and modeling errors) to be separately constructed and identified. The modeling errors are not taken into account with the usual output-prediction-error method but with the nonparametric probabilistic approach of modeling errors recently introduced and based on the use of the random matrix theory. The theory an identification procedure and a numerical validation are presented. Then a chaos decomposition with random coefficients is proposed to represent the prior probabilistic model of, random responses. The random germ is related to the prior probability model of model-parameter uncertainties. The random coefficients arc related to the prior probability model of modeling errors and then depends on the random matrices introduced by the nonparametric probabilistic approach of modeling errors. A validation is presented. Finally. a future perspective is introduced when experimental data are available. The prior probability model of the random coefficients can be improved in constructing a posterior probability model Using the Bayesian approach.

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Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions

https://hal-upec-upem.archives-ouvertes.fr/hal-00686153/document

Probabilistic approach for model and data uncertainties and its experimental identification in structural dynamics: Case of composite sandwich panels

This paper concerns uncertainties in structural dynamics for composite sandwich panels constituted of two thin carbon-resin skins and one high stiffness closed-cell foam core. Each skin is constituted of two unidirectional plies [60/-60]. Such light composite sandwich panels, manufactured with a same process, generally present a significant dispersion for their Frequency Response Functions (FRF) in the Low-Frequency (LF) and Medium-Frequency (MF) ranges. The objectives of this paper are (1) to study the dispersion due to the process by using experiments (2) to develop a predictive mean mechanical model based on the use of the laminated composite thin plate theory in dynamics and (3) to use a nonparametric probabilistic approach for data and model uncertainties to improve the predictability of the mean model in the MF dynamics.

https://hal-upec-upem.archives-ouvertes.fr/hal-00686190/document

Uncertainties in structural dynamics for composite sandwich panels

We present a probabilistic model allowing uncertainties induced by modeling errors and system-parameter uncertainties to be taken into account for a multi-layer composite sandwich panel. The sensitivity of the internal noise inside a bounded cavity coupled with the panel is analyzed with respect to uncertainties. Eight composite panels have been constructed by using the same manufacturing process. Experimental measurements of the vibration and acoustic responses have been performed in the low- and medium- frequency ranges. These measurements allow the probabilistic model of uncertainties to be identified.We present the probabilistic numerical model and its comparison with the experiments for validation.

https://hal-upec-upem.archives-ouvertes.fr/hal-00773337/document

Identification et validation expérimentale d'un modèle stochastique des incertitudes en vibroacoustique d'un panneau composite.

The paper deals with the robustness of uncertain computational elastoacoustic models in low- and medium-frequency ranges. The elastoacoustic system is made up of a heterogeneous viscoelastic structure coupled with an internal acoustic cavity filled with a dissipative acoustic fluid. A reduced mean elastoacoustic model is deduced from the mean finite element model by using the modal approach with the structural modes of the structure and the acoustic modes of the acoustic cavity. Data uncertainties and model uncertainties are taken into account by using a nonparametric probabilistic approach for the structure, for the acoustic cavity and for the vibroacoustic coupling interface. The main objectives of this paper are (1) to present experimental validation of the nonparametric probabilistic approach of model uncertainties and to propose methods to perform the experimental identification of the probabilistic model parameters, (2) to analyze the robustness of computational elastoacoustic models with respect to model and data uncertainties, (3) to study uncertainty propagation through complex elastoacoustic systems. Two experimental configurations are analyzed with the stochastic computational elastoacoustic model. The first experimental configuration is made up of a composite sandwich panel coupled with an acoustic cavity constituted of a simple rigid box. Experimental measurements have been performed for 8 manufactured composite panels. The second experimental configuration is a car made up of a complex heterogeneous structure coupled with a complex acoustic cavity. Experimental measurements have been performed for 22 manufactured cars of the same type with optional extra.

https://hal-upec-upem.archives-ouvertes.fr/hal-00684640/document

C. Chen

Papers

Probabilistic approach for model and data uncertainties and its experimental identification in structural dynamics: Case of composite sandwich panels

Uncertainties in structural dynamics for composite sandwich panels

Identification et validation expérimentale d'un modèle stochastique des incertitudes en vibroacoustique d'un panneau composite.

Computational elastoacoustics of uncertain complex systems and experimental validation