École Polytechnique Fédérale de Lausanne
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Uncertainty Quantification for Reduced Basis Approximations: "Natural Norm" A Posteriori Error Estimators
No full textWe present a technique for the rapid and reliable prediction of linear-functional outputs of coercive and non-coercive linear elliptic partial differential equations with affine parameter dependence. The essential components are: (i) rapidly convergent global reduced basis approximations – (Galerkin) projection onto a space WN spanned by solutions of the governing partial differential equation at N judiciously selected points in parameter space; (ii) a posteriori error estimation – relaxations of the error-residual equation that provide inexpensive yet sharp bounds for the error in the outputs of interest; and (iii) offline/online computational procedures – methods which decouple the generation and projection stages of the approximation process. The operation count for the online stage – in which, given a new parameter value, we calculate the output of interest and associated error bound – depends only on N (typically very small) and the parametric complexity of the problem. In this paper we propose a new “natural norm” formulation for our reduced basis error estimation framework that: (a) greatly simplifies and improves our inf–sup lower bound construction (offline) and evaluation (online) – a critical ingredient of our a posteriori error estimators; and (b) much better controls – significantly sharpens – our output error bounds, in particular (through deflation) for parameter values corresponding to nearly singular solution behavior. We apply the method to two illustrative problems: a coercive Laplacian heat conduction problem – which becomes singular as the heat transfer coefficient tends to zero; and a non-coercive Helmholtz acoustics problem – which becomes singular as we approach resonance. In both cases, we observe very economical and sharp construction of the requisite natural-norm inf–sup lower bound; rapid convergence of the reduced basis approximation; reasonable effectivities (even for near-singular behavior) for our deflated output error estimators; and significant – several order of magnitude – (online) computational savings relative to standard finite element procedures.CMCSSCI-SB-S
User Perception Model for Wearable Supervision Systems
No full textWearable supervision systems ease the deployment of advanced mobile solutions for the control of industrial plants. These systems are used to provide operators with the adequate information to perform the required manual operations on industrial plants. This paper presents the adaptation strategy developed to ensure that the operator perceives accurately the plant state relayed by a distant server despite the varying network conditions. The information provided to the user is mainly in the form of Augmented Reality video rendered in a Head Mounted Display. Using experimental subjective testing, the user video Quality of Perception is modeled to determine continuously the best encoding parameters values resulting from the compromise between the fluidity and the level of detail for real-time interaction with the plant. This model is then used by an adaptation scheme to reject output bitrate disturbances due to the variations of the spatial and temporal video content. The proposed approach adapts in real-time the parameters values of the video encoder to track a given reference bitrate.LASCI-STI-DGPrj_QoP_Adapt, Prj_6thSens
Entre savoirs experts et savoirs ordinaires : traduire les pratiques sociales dans le projet urbain
No full textLC
L'archéologue et le projet urbain dans la Genève de l’entre-deux-guerres
No full textLCCEjemplar dedicado a: La ville et l'expertis