303 research outputs found
Fluid flow dynamics under location uncertainty
We present a derivation of a stochastic model of Navier Stokes equations that
relies on a decomposition of the velocity fields into a differentiable drift
component and a time uncorrelated uncertainty random term. This type of
decomposition is reminiscent in spirit to the classical Reynolds decomposition.
However, the random velocity fluctuations considered here are not
differentiable with respect to time, and they must be handled through
stochastic calculus. The dynamics associated with the differentiable drift
component is derived from a stochastic version of the Reynolds transport
theorem. It includes in its general form an uncertainty dependent "subgrid"
bulk formula that cannot be immediately related to the usual Boussinesq eddy
viscosity assumption constructed from thermal molecular agitation analogy. This
formulation, emerging from uncertainties on the fluid parcels location,
explains with another viewpoint some subgrid eddy diffusion models currently
used in computational fluid dynamics or in geophysical sciences and paves the
way for new large-scales flow modelling. We finally describe an applications of
our formalism to the derivation of stochastic versions of the Shallow water
equations or to the definition of reduced order dynamical systems
A stochastic filter for fluid motion tracking
In this paper we present a method for the tracking of fluid flows velocity fields. The technique we propose is formalized within sequential Bayesian filter framework. The filter we propose here combines an ItĂ´ diffusion process coming from a stochastic formulation of the vorticity-velocity form of Navier-Stokes equation and discrete measurements extracted from an image sequence. The resulting tracker provides robust and consistent estimations of instantaneous motion fields along the whole image sequence. In order to handle a state space of reasonable dimension for the s-tochastic filtering problem, we represent the motion field as a combination of adapted basis functions. The used basis functions ensue from a mollification of Biot-Savart integral and a discretization of the vorticity and divergence maps of the fluid vector field. The efficiency of the method is demonstrated on a long real world sequence showing a vortex launch at tip of airplane wing. 1
Stochastic uncertainty models for the luminance consistency assumption
International audienceIn this paper, a stochastic formulation of the brightness consistency used in many computer vision problems involving dynamic scenes (motion estimation or point tracking for instance) is proposed. Usually, this model which assumes that the luminance of a point is constant along its trajectory is expressed in a differential form through the total derivative of the luminance function. This differential equation links linearly the point velocity to the spatial and temporal gradients of the luminance function. However when dealing with images, the available informations only hold at discrete time and on a discrete grid. In this paper we formalize the image luminance as a continuous function transported by a flow known only up to some uncertainties related to such a discretization process. Relying on stochastic calculus, we define a formulation of the luminance function preservation in which these uncertainties are taken into account. From such a framework, it can be shown that the usual deterministic optical flow constraint equation corresponds to our stochastic evolution under some strong constraints. These constraints can be relaxed by imposing a weaker temporal assumption on the luminance function and also in introducing anisotropic intensity-based uncertainties. We in addition show that these uncertainties can be computed at each point of the image grid from the image data and provide hence meaningful information on the reliability of the motion estimates. To demonstrate the benefit of such a stochastic formulation of the brightness consistency assumption, we have considered a local least squares motion estimator relying on this new constraint. This new motion estimator improves significantly the quality of the results
A particle filter to reconstruct a free-surface flow from a depth camera
We investigate the combined use of a Kinect depth sensor and of a stochastic
data assimilation method to recover free-surface flows. More specifically, we
use a Weighted ensemble Kalman filter method to reconstruct the complete state
of free-surface flows from a sequence of depth images only. This particle
filter accounts for model and observations errors. This data assimilation
scheme is enhanced with the use of two observations instead of one classically.
We evaluate the developed approach on two numerical test cases: a collapse of a
water column as a toy-example and a flow in an suddenly expanding flume as a
more realistic flow. The robustness of the method to depth data errors and also
to initial and inflow conditions is considered. We illustrate the interest of
using two observations instead of one observation into the correction step,
especially for unknown inflow boundary conditions. Then, the performance of the
Kinect sensor to capture temporal sequences of depth observations is
investigated. Finally, the efficiency of the algorithm is qualified for a wave
in a real rectangular flat bottom tank. It is shown that for basic initial
conditions, the particle filter rapidly and remarkably reconstructs velocity
and height of the free surface flow based on noisy measurements of the
elevation alone
Hybrid tracking approach using optical flow and pose estimation
International audienceThis paper proposes an hybrid approach to estimate the 3D pose of an object. The integration of texture information based on image intensities in a more classical non-linear edge-based pose estimation computation has proven to highly increase the reliability of the tracker. We propose in this work to exploit the data provided by an optical flow algorithm for a similar purpose. The advantage of using the optical flow is that it does not require any a priori knowledge on the object appearance. The registration of 2D and 3D cues for monocular tracking is performed by a non linear minimization. Results obtained show that using optical flow enables to perform robust 3D hybrid tracking even without any texture mode
Fluid flow estimation with multiscale ensemble filters based on motion measurements under location uncertainty
International audienceThis paper proposes a novel multi-scale fluid flow data assimilation approach, which integrates and complements the advantages of a Bayesian sequential assimilation technique, the Weighted Ensemble Kalman filter (WEnKF). The data assimilation proposed in this work incorporates measurement brought by an efficient multiscale stochastic formulation of the well-known Lucas-Kanade (LK) estimator. This estimator has the great advantage to provide uncertainties associated to the motion measurements at different scales. The proposed assimilation scheme benefits from this multiscale uncertainty information and enables to enforce a physically plausible dynamical consistency of the estimated motion fields along the image sequence. Experimental evaluations are presented on synthetic and real fluid flow sequences
Three-Dimensional Motion Estimation of Atmospheric Layers From Image Sequences
International audienceIn this paper, we address the problem of estimating three-dimensional motions of a stratified atmosphere from satellite image sequences. The analysis of three-dimensional atmospheric fluid flows associated with incomplete observation of atmospheric layers due to the sparsity of cloud systems is very difficult. This makes the estimation of dense atmospheric motion field from satellite images sequences very difficult. The recovery of the vertical component of fluid motion from a monocular sequence of image observations is a very challenging problem for which no solution exists in the literature. Based on a physically sound vertical decomposition of the atmosphere into cloud layers of different altitudes, we propose here a dense motion estimator dedicated to the extraction of three-dimensional wind fields characterizing the dynamics of a layered atmosphere. Wind estimation is performed over the complete three-dimensional space using a multi-layer model describing a stack of dynamic horizontal layers of evolving thickness, interacting at their boundaries via vertical winds. The efficiency of our approach is demonstrated on synthetic and real sequences
Pseudo-stochastic simulation of turbulent channel flows with near-wall modelling
The pseudo-stochastic model recently proposed by MĂ©min (2014) is investigated and compared with the large-eddy simulation methodology. The theoretical analysis shows that this model is a generalisation of the eddy-viscosity model, which does not undergo the same restrictive physical assumptions and describes physical phenomena usually not considered (turbophoresis and turbulent com-pressibility). Numerical simulations of turbulent channel flows are performed. In order to better reproduce the turbulence anisotropy, a near-wall damping function is derived and successfully validated: the damping is imposed only on wall-normal direction (minimal constraint) and it requires to set a single parameter (reduced empirical content). Simulations show the accuracy of the new model, especially when the computational grid becomes coarse. A weak turbophoresis phenomenon is detected near the wall, while turbulent compress-ibility effects appear to be possibly related to the streaks structures
High-resolution data assimilation through stochastic subgrid tensor and parameter estimation from 4DEnVar
International audienceIn this paper we explore a dynamical formulation allowing to assimilate high resolution data in a large-scale fluid flow model. This large-scale formulation relies on a random modeling of the small-scale velocity component and allows to take into account the scale discrepancy between the dynamics and the observations. It introduces a subgrid stress tensor that naturally emerges from a modified Reynolds transport theorem adapted to this stochastic representation of the flow. This principle is used within a stochastic shallow water model coupled with an 4DEnVar assimilation technique to estimate both the flow initial conditions and the inhomogeneous time-varying subgrid parameters. The performance of this modeling has been assessed numerically with both synthetic and real world data. Our strategy has shown to be very effective in providing a more relevant prior/posterior ensemble in terms of the dispersion compared to other tests using the standard shallow water equations with no subgrid parameterization or with simple eddy viscosity models. We also compared two localization techniques. The results indicate the localized covariance approach is more suitable to deal with the scale discrepancy related errors
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