2,303 research outputs found
Postprocessing of Non-Conservative Flux for Compatibility with Transport in Heterogeneous Media
A conservative flux postprocessing algorithm is presented for both
steady-state and dynamic flow models. The postprocessed flux is shown to have
the same convergence order as the original flux. An arbitrary flux
approximation is projected into a conservative subspace by adding a piecewise
constant correction that is minimized in a weighted norm. The application
of a weighted norm appears to yield better results for heterogeneous media than
the standard norm which has been considered in earlier works. We also
study the effect of different flux calculations on the domain boundary. In
particular we consider the continuous Galerkin finite element method for
solving Darcy flow and couple it with a discontinuous Galerkin finite element
method for an advective transport problem.Comment: 34 pages, 17 figures, 11 table
A Bayesian fusion model for space-time reconstruction of finely resolved velocities in turbulent flows from low resolution measurements
The study of turbulent flows calls for measurements with high resolution both
in space and in time. We propose a new approach to reconstruct
High-Temporal-High-Spatial resolution velocity fields by combining two sources
of information that are well-resolved either in space or in time, the
Low-Temporal-High-Spatial (LTHS) and the High-Temporal-Low-Spatial (HTLS)
resolution measurements. In the framework of co-conception between sensing and
data post-processing, this work extensively investigates a Bayesian
reconstruction approach using a simulated database. A Bayesian fusion model is
developed to solve the inverse problem of data reconstruction. The model uses a
Maximum A Posteriori estimate, which yields the most probable field knowing the
measurements. The DNS of a wall-bounded turbulent flow at moderate Reynolds
number is used to validate and assess the performances of the present approach.
Low resolution measurements are subsampled in time and space from the fully
resolved data. Reconstructed velocities are compared to the reference DNS to
estimate the reconstruction errors. The model is compared to other conventional
methods such as Linear Stochastic Estimation and cubic spline interpolation.
Results show the superior accuracy of the proposed method in all
configurations. Further investigations of model performances on various range
of scales demonstrate its robustness. Numerical experiments also permit to
estimate the expected maximum information level corresponding to limitations of
experimental instruments.Comment: 15 pages, 6 figure
AlphaPilot: Autonomous Drone Racing
This paper presents a novel system for autonomous, vision-based drone racing
combining learned data abstraction, nonlinear filtering, and time-optimal
trajectory planning. The system has successfully been deployed at the first
autonomous drone racing world championship: the 2019 AlphaPilot Challenge.
Contrary to traditional drone racing systems, which only detect the next gate,
our approach makes use of any visible gate and takes advantage of multiple,
simultaneous gate detections to compensate for drift in the state estimate and
build a global map of the gates. The global map and drift-compensated state
estimate allow the drone to navigate through the race course even when the
gates are not immediately visible and further enable to plan a near
time-optimal path through the race course in real time based on approximate
drone dynamics. The proposed system has been demonstrated to successfully guide
the drone through tight race courses reaching speeds up to 8m/s and ranked
second at the 2019 AlphaPilot Challenge.Comment: Accepted at Robotics: Science and Systems 2020, associated video at
https://youtu.be/DGjwm5PZQT
Adaptive mesh strategies for the spectral element method
An adaptive spectral method was developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the 1-D viscous Burger equation and the 2-D Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities, and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility, and general capabilities for high order spectral methods
Probabilistic ToF and Stereo Data Fusion Based on Mixed Pixel Measurement Models
This paper proposes a method for fusing data acquired by a ToF camera and a stereo pair based on a model for depth measurement by ToF cameras which accounts also for depth discontinuity artifacts due to the mixed pixel effect. Such model is exploited within both a ML and a MAP-MRF frameworks for ToF and stereo data fusion. The proposed MAP-MRF framework is characterized by site-dependent range values, a rather important feature since it can be used both to improve the accuracy and to decrease the computational complexity of standard MAP-MRF approaches. This paper, in order to optimize the site dependent global cost function characteristic of the proposed MAP-MRF approach, also introduces an extension to Loopy Belief Propagation which can be used in other contexts. Experimental data validate the proposed ToF measurements model and the effectiveness of the proposed fusion techniques
Parameter estimation for macroscopic pedestrian dynamics models from microscopic data
In this paper we develop a framework for parameter estimation in macroscopic
pedestrian models using individual trajectories -- microscopic data. We
consider a unidirectional flow of pedestrians in a corridor and assume that the
velocity decreases with the average density according to the fundamental
diagram. Our model is formed from a coupling between a density dependent
stochastic differential equation and a nonlinear partial differential equation
for the density, and is hence of McKean--Vlasov type. We discuss
identifiability of the parameters appearing in the fundamental diagram from
trajectories of individuals, and we introduce optimization and Bayesian methods
to perform the identification. We analyze the performance of the developed
methodologies in various situations, such as for different in- and outflow
conditions, for varying numbers of individual trajectories and for differing
channel geometries
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