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

Multigrid sequential data assimilation for the large-eddy simulation of a massively separated bluff-body flow

The potential for data-driven applications to scale-resolving simulations of turbulent flows is assessed herein. Multigrid sequential data assimilation algorithms have been used to calibrate solvers for Large Eddy Simulation for the analysis of the high-Reynolds-number flow around a rectangular cylinder of aspect ratio 5:1. This test case has been chosen because of a number of physical complexities which elude accurate representation using reduced-order numerical simulation. The results for the statistical moments of the velocity and pressure flow field show that the data-driven techniques employed, which are based on the Ensemble Kalman Filter, are able to significantly improve the predictive features of the solver for reduced grid resolution. In addition, it was observed that, despite the sparse and asymmetric distribution of observation in the data-driven process, the data augmented results exhibit perfectly symmetric statistics and a significantly improved accuracy also far from the sensor location

Synchronization and optimization of Large Eddy Simulation using an online Ensemble Kalman Filter

An online Data Assimilation strategy based on the Ensemble Kalman Filter (EnKF) is used to improve the predictive capabilities of Large Eddy Simulation (LES) for the analysis of the turbulent flow in a plane channel, $Re_\tau \approx 550$. The algorithm sequentially combines the LES prediction with high-fidelity, sparse instantaneous data obtained from a Direct Numerical Simulation (DNS). It is shown that the procedure provides an augmented state which exhibits higher accuracy than the LES model and it synchronizes with the time evolution of the high-fidelity DNS data if the hyperparameters governing the EnKF are properly chosen. In addition, the data-driven algorithm is able to improve the accuracy of the subgrid-scale model included in the LES, the Smagorinsky model, via the optimization of a free coefficient. However, while the online EnKF strategy is able to reduce the global error of the LES prediction, a discrepancy with the reference DNS data is still observed because of structural flaws of the subgrid-scale model used

Estimation of a semi-physical GLBE model using dual EnKF learning algorithm coupled with a sensor network design strategy: application to air field monitoring

International audienceIn this paper, we present the fusion of two complementary approaches for modeling and monitoring the spatio-temporal behavior of a fluid flow system. We also propose a mobile sensor deployment strategy to produce the most accurate estimate of the true system state. For this purpose, deterministic and statistical information was used. We adopted a filtering method based on a semi-physical model which derives from a fluid flow numerical model known as lattice Boltzmann model (LBM). The a priori physical knowledge was introduced by the Navier-Stokes equations which were discretized by the lattice Boltzmann approach. Moreover, its multiple-relaxation-time (MRT) variant not only improved the stability, but also enabled the introduction of additional degrees of freedom to be estimated like the synaptic weights of a neural network. The statistical knowledge was then introduced into the model by performing a sequential learning of these parameters and an estimation of the speed field of the fluid flow starting from measurements. The low spatial density of measurements, the large amount of data inherent to environmental issues and the nonlinearity of the generalized lattice Boltzmann equations (GLBE) enjoined us to use the ensemble Kalman filter (EnKF) for the recursive estimation procedure. A dual state-parameter estimation which results in a significantly reduced computation time was used by combining two filters consecutively activated in the same iteration. Finally, we proposed to complete the lack of spatial information of the sparse-observation network by adding a mobile sensor, which was routed to the location where the cell-by-cell output estimation error was the highest. Experimental results in the context of the standard lid-driven cavity problem revealed the presence of few zones of interest, where fixed sensors can be deployed to increase performances in terms of convergence speed and estimation quality. Finally, the study showed the feasibility of introducing some additional parameters which act as degrees of freedom, to perform large-eddy simulation of turbulent flows without numerical instabilities

Combined state and parameter estimation in level-set methods

Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous learning algorithm for state and parameter estimation with level-set methods. A Bayesian approach based on data assimilation is introduced. Data assimilation is enabled by the ensemble Kalman filter and smoother, which are used in their probabilistic formulations. The level-set data assimilation framework is verified in onedimensional and two-dimensional test cases, where state estimation, parameter estimation and uncertainty quantification are performed. The statistical performance of the proposed ensemble Kalman filter and smoother is quantified by twin experiments. In the twin experiments, the combined state and parameter estimation fully recovers the reference solution, which validates the proposed algorithm. The level-set data assimilation framework is then applied to the prediction of the nonlinear dynamics of a forced premixed flame, which exhibits the formation of sharp cusps and intricate topological changes, such as pinch-off events. The proposed physics-informed statistical learning algorithm opens up new possibilities for making reduced-order models of interfaces quantitatively predictive, any time that reference data is available