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Cournon-d'Auvergne, France

Venkovic N.,Laval University | Sorelli L.,Laval University | Sudret B.,ETH Zurich | Yalamas T.,Center dAffaires du Zenith | Gagne R.,Universite de Sherbrooke
Probabilistic Engineering Mechanics | Year: 2013

The durability of concrete materials with regard to early-age volume changes and cracking phenomena depends on the evolution of the poroelastic properties of cement paste. The ability of engineers to control the uncertainty of the percolation threshold and the evolution of the elastic modulus, the Biot-Willis parameter and the skeleton Biot modulus is key for minimizing the vulnerability of concrete structures at early-age. This work presents original results on the uncertainty propagation and the sensitivity analysis of a multiscale poromechanics-hydration model applied to cement pastes of water-to-cement ratio of 0.40, 0.50 and 0.60. Notably, the proposed approach provides poroelastic properties required to model the behavior of partially saturated aging cement pastes (e.g. autogenous shrinkage) and it predicts the percolation threshold and undrained elastic modulus in good agreement with experimental data. The development of a stochastic metamodel using polynomial chaos expansions allows to propagate the uncertainties of kinetic parameters of hydration, cement phase composition, elastic moduli and morphological parameters of the microstructure. The presented results show that the propagation does not magnify the uncertainty of the single poroelastic properties although, their correlation may amplify the variability of the estimates obtained from poroelastic state equations. In order to reduce the uncertainty of the percolation threshold and that of the poroelastic properties at early-age, engineers need to assess more accurately the apparent activation energy of calcium aluminate and, later on, of the elastic modulus of low density calcium-silicate-hydrate. © 2012 Elsevier Ltd. Source

Blatman G.,French Institute for Advanced Mechanics | Blatman G.,Electricite de France | Sudret B.,French Institute for Advanced Mechanics | Sudret B.,Center dAffaires du Zenith
Journal of Computational Physics | Year: 2011

Polynomial chaos (PC) expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable (so-called polynomial chaos) basis. The number of terms to be computed grows dramatically with the size of the input random vector, which makes the computational cost of classical solution schemes (may it be intrusive (i.e. of Galerkin type) or non intrusive) unaffordable when the deterministic finite element model is expensive to evaluate.To address such problems, the paper describes a non intrusive method that builds a sparse PC expansion. First, an original strategy for truncating the PC expansions, based on hyperbolic index sets, is proposed. Then an adaptive algorithm based on least angle regression (LAR) is devised for automatically detecting the significant coefficients of the PC expansion. Beside the sparsity of the basis, the experimental design used at each step of the algorithm is systematically complemented in order to avoid the overfitting phenomenon. The accuracy of the PC metamodel is checked using an estimate inspired by statistical learning theory, namely the corrected leave-one-out error. As a consequence, a rather small number of PC terms are eventually retained (sparse representation), which may be obtained at a reduced computational cost compared to the classical " full" PC approximation. The convergence of the algorithm is shown on an analytical function. Then the method is illustrated on three stochastic finite element problems. The first model features 10 input random variables, whereas the two others involve an input random field, which is discretized into 38 and 30 - 500 random variables, respectively. © 2010 Elsevier Inc. Source

Pou J.-M.,Center dAffaires du Zenith | Leblond L.,PSA Peugeot Citroen
International Journal of Metrology and Quality Engineering | Year: 2015

Beyond their evaluations, measurement uncertainties raise many questions about their use in the context of the declaration of conformity of "products and services". If different approaches have been developed over the past years, including the "capability approach", 2012 has seen the JCGM document #106 being published. This paper just published, was taken as an international standard ISO/IEC Guide 98-4 by ISO in the very same year and has just been taken (2013) in the collection of French standards (NF ISO/IEC Guide 98-4). This approach is singularly different from traditional approaches in that it introduces Bayesian concepts in the world of Metrology that was hitherto relatively impermeable to it. With this new approach, metrologists discover that measure is not a science of discovery, but a science of confirmation (or denial) of an "a priori". © 2015 EDP Sciences. Source

Blatman G.,Electricite de France | Sudret B.,French Institute for Advanced Mechanics | Sudret B.,Center dAffaires du Zenith
Applications of Statistics and Probability in Civil Engineering -Proceedings of the 11th International Conference on Applications of Statistics and Probability in Civil Engineering | Year: 2011

Polynomial chaos (PC) expansions allow an explicit representation of the random response of a mechanical system whose input parameters are modelled by random variables. Recently, an iterative procedure based on Least Angle Regression has been devised in order to build up sparse PC approximations (i.e. PC representations containing a small number of significant coefficients) by means of a low number of model evaluations. This approach was dedicated to scalar model responses though. In contrast, a vector-valued response is considered in this paper. A two-step strategyis proposed in order to approximate all the response components by means of few PC representations. First, a principal component analysis (PCA) of the vector random response is carried out, making it possible to capture the main stochastic features of the response by means of a small number of (non physical) variables compared to the original number of output components. Then the LAR procedure is applied to each non physical variable. The method is finally applied to the study of the displacement field of a truss structure involving 10 random variables. © 2011 Taylor & Francis Group, London. Source

Caniou Y.,French Institute for Advanced Mechanics | Sudret B.,Center dAffaires du Zenith
Applications of Statistics and Probability in Civil Engineering -Proceedings of the 11th International Conference on Applications of Statistics and Probability in Civil Engineering | Year: 2011

Modern engineering based on virtual testing platforms involves multiple models with dependent parameters. In this work, a methodology to address global sensitivity analysis for this kind of problems is introduced. A moment-independent sensitivity index that suits problems with dependent parameters is reviewed. A metamodeling technique, namely the generalized polynomial chaos expansion is used to process massive simulations at low cost. The copula theory is briefly presented. It allows one to describe the dependence structure of parameters more precisely than a traditional correlation coefficient. The methodology is applied to the sensitivity analysis of a mechanical example, namely a composite beam under dead weight. © 2011 Taylor & Francis Group, London. Source

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