A new method is developed to obtain guaranteed error bounds on pointwise quantities of interest for linear transient viscodynamics problems. The calculation of strict error bounds is based on the concept of "constitutive relation error" (CRE) and the solution of an adjoint problem. The central and original point of this work is the treatment of the singularity in space and time introduced by the loading of the adjoint problem. Hence, the adjoint solution is decomposed into two parts: (i) an analytical part determined from Green's functions; (ii) a residual part approximated with classical numerical tools (finite element method, Newmark integration scheme). The capabilities and the limits of the proposed approach are analyzed on a 2D example.

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International audienceThe article aims at detecting and quantifying early structural damages usingdeterministic and probabilistic model updating techniques. To achieve this purpose,local information in a form of optical strain measurement is employed. Thestrategy consists in updating physical parameters associated to damages, suchas Young’s modulus, in order to minimize the gap between the numerical strainobtained from finite element solves and the strain sensor outputs. Generally,the damage estimation is an ill-posed inverse problem, and hence requires regularization.Herein, three model updating techniques are considered involvingdifferent type of regularization: classical Tikhonov regularization, ConstitutiveRelation Error based updating method and Bayesian approach.An illustration of these three approaches is proposed for localizing and quantifyingan early damage in a real 8 meter post-tensioned concrete beam. Numericalresults show that all the methods properly localize the damaged areaand give similar estimation of the damage leve

The paper deals with the results of an experimental campaign carried out on a post tensioned concrete beam with the aim of investigating the possibility to detect early warning signs of deterioration based on static and/or dynamic tests. The beam was tested in several configurations aimed to reproduce 5 different phases of the ‘life’ of the beam: in the original undamaged state, under increasing loss of tension in the post tensioning cables, during and after the formation of cracks at mid span, after a strengthening intervention carried out by means of a second tension cable, during and after the formation of further cracks on the strengthened beam. Responses of the beam were measured by an extensive set of instruments consisting of accelerometers, inclinometers, displacement transducers, strain gauges and optical fibers. In this paper data from accelerometers and displacement transducers have been exploited. The paper presents the test program and the dynamic characterization of the beam in the different damage scenarios in terms of the first modal frequency, identified from dynamic tests and of the bending stiffness monitored during static tests

We address the reconstruction of relevant two-dimensional (2D) flows in drinking water networks, especially in key elements such as pipe junctions, in view of representative water quality simulations. From the optimal control theory, a specific inverse technique using few sensors and computational fluid dynamics (CFD) models has been developed. First, we determine the boundary velocities, i.e., the control parameters, by minimizing a data misfit functional. Then, knowing the boundary velocities, a direct solve of the flow model is performed to get the space–time cartography of the water flow. To reduce the number of control parameters to be determined and thus restrict the number of sensors, the spatial shape of the boundary velocities is considered as an a priori information given by the water pipes engineering literature. Thus, only the time evolution of the boundary velocities has to be determined. The whole numerical procedure proposed in this paper easily fits in a general purpose finite element software, featuring user's friendliness for a wide engineering audience. Two ways are investigated to reduce the computation time associated to the flow reconstruction. The adjoint framework is used in the minimization process. The reconstruction of the flow using coarse discretizations and simple flow models, instead of 2D Navier–Stokes equations, is studied. The influence of the flow modeling and of the dicretization on the quality of the reconstructed velocity is studied on two examples: a water pipe junction and a 200 m subsection from a French water network. In the water pipe junction, we show that at a Reynolds number of 200 a hybrid approach combining an unsteady Stokes reconstruction and a single direct Navier–Stokes simulation outperforms the algorithms based on a single model. In the network subsection, we obtain an L2 error less than 1% between the reference velocity based on Navier–Stokes equations (Reynolds number of 200) and the velocity reconstructed from Stokes equation. In this case, the reconstruction lasts less than 1 min. Stokes based reconstruction of a Navier–Stokes flow in junctions at Reynolds number up to 100 yields the same accuracy and proves fast.