Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

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  • Poster

    Multiscale Modeling of Wear Degradation

    (2015-01-07) Moraes, Alvaro; Ruggeri, Fabrizio; Tempone, Raul; Vilanova, Pedro; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Istituto di Matematica Applicata e Tecnologie Informatiche

    Cylinder liners of diesel engines used for marine propulsion are naturally subjected to a wear process, and may fail when their wear exceeds a specified limit. Since failures often represent high economical costs, it is utterly important to predict and avoid them. In this work [4], we model the wear process using a pure jump process. Therefore, the inference goal here is to estimate: the number of possible jumps, its sizes, the coefficients and the shapes of the jump intensities. We propose a multiscale approach for the inference problem that can be seen as an indirect inference scheme. We found that using a Gaussian approximation based on moment expansions, it is possible to accurately estimate the jump intensities and the jump amplitudes. We obtained results equivalent to the state of the art but using a simpler and less expensive approach.

  • Poster

    An Efficient Simulation Method for Rare Events

    (2015-01-07) Rached, Nadhir B.; Benkhelifa, Fatma; Kammoun, Abla; Alouini, Mohamed-Slim; Tempone, Raul; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering Program

    Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. Closed-form expressions for the sum distribution do not generally exist, which has led to an increasing interest in simulation approaches. A crude Monte Carlo (MC) simulation is the standard technique for the estimation of this type of probability. However, this approach is computationally expensive, especially when dealing with rare events. Variance reduction techniques are alternative approaches that can improve the computational efficiency of naive MC simulations. We propose an Importance Sampling (IS) simulation technique based on the well-known hazard rate twisting approach, that presents the advantage of being asymptotically optimal for any arbitrary RVs. The wide scope of applicability of the proposed method is mainly due to our particular way of selecting the twisting parameter. It is worth observing that this interesting feature is rarely satisfied by variance reduction algorithms whose performances were only proven under some restrictive assumptions. It comes along with a good efficiency, illustrated by some selected simulation results comparing the performance of our method with that of an algorithm based on a conditional MC technique.

  • Poster

    Flow, transport and diffusion in random geometries II: applications

    (2015-01-07) Asinari, Pietro; Ceglia, Diego; Icardi, Matteo; Prudhomme, Serge; Tempone, Raul; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Politecnico di Torino; Ecole Polytechnique de Montréal

    Multilevel Monte Carlo (MLMC) is an efficient and flexible solution for the propagation of uncertainties in complex models, where an explicit parametrization of the input randomness is not available or too expensive. We present several applications of our MLMC algorithm for flow, transport and diffusion in random heterogeneous materials. The absolute permeability and effective diffusivity (or formation factor) of micro-scale porous media samples are computed and the uncertainty related to the sampling procedures is studied. The algorithm is then extended to the transport problems and multiphase flows for the estimation of dispersion and relative permeability curves. The impact of water drops on random stuctured surfaces, with microfluidics applications to self-cleaning materials, is also studied and simulated. Finally the estimation of new drag correlation laws for poly-dispersed dilute and dense suspensions is presented.

  • Poster

    Goal-Oriented Compression of Random Fields

    (2015-01-07) Busch, Ingolf; Ernst, Oliver; Sprungk, Björn; Tempone, Raul; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; TU Chemnitz
  • Poster

    Secret-Sharing over Multiple-Antenna Channels with Transmit Correlation

    (2015-01-07) Zorgui, Marwen; Rezki, Zouheir; Alomair, Basel; Alouini, Mohamed-Slim; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering Program; The National Center for Cybersecurity Technology

    We consider secret-key agreement with public discussion over Rayleigh fastfading channels with transmit correlation. The legitimate receiver and the eavesdropper are assumed to have perfect channel knowledge while the transmitter has only knowledge of the transmit correlation matrix. First, We derive the expression of the key capacity under the considered setup. Then, we show that the optimal transmit strategy achieving the key capacity consists in transmitting Gaussian signals along the eingenvectors of the channel covariance matrix. The powers allocated to each channel mode are determined as the solution of a numerical optimization problem that we derive. We also provide a waterfilling interpretation of the optimal power allocation. Finally, we develop a necessary and sufficient condition for beamforming to be optimal, i.e., transmitting along the strongest channel mode only is key capacity-achieving.