scholarly journals Cubature Ensemble Kalman Filter for Highly Dimensional Strongly Nonlinear Systems

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 144892-144907
Author(s):  
Qingwen Meng ◽  
Harry Leib ◽  
Xuyou Li
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Ensemble Kalman Filter ◽  
Strongly Nonlinear

scholarly journals Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems

2012 ◽  
Vol 19 (3) ◽  
pp. 383-399 ◽  
Author(s):  
M. Bocquet ◽  
P. Sakov
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Ensemble Kalman Filter ◽  
Kalman Filters ◽  
Finite Size ◽  
Ensemble Kalman Filters ◽  
Strongly Nonlinear ◽  
Perfect Model ◽  
Model Condition ◽  
Better Than

Abstract. The finite-size ensemble Kalman filter (EnKF-N) is an ensemble Kalman filter (EnKF) which, in perfect model condition, does not require inflation because it partially accounts for the ensemble sampling errors. For the Lorenz '63 and '95 toy-models, it was so far shown to perform as well or better than the EnKF with an optimally tuned inflation. The iterative ensemble Kalman filter (IEnKF) is an EnKF which was shown to perform much better than the EnKF in strongly nonlinear conditions, such as with the Lorenz '63 and '95 models, at the cost of iteratively updating the trajectories of the ensemble members. This article aims at further exploring the two filters and at combining both into an EnKF that does not require inflation in perfect model condition, and which is as efficient as the IEnKF in very nonlinear conditions. In this study, EnKF-N is first introduced and a new implementation is developed. It decomposes EnKF-N into a cheap two-step algorithm that amounts to computing an optimal inflation factor. This offers a justification of the use of the inflation technique in the traditional EnKF and why it can often be efficient. Secondly, the IEnKF is introduced following a new implementation based on the Levenberg-Marquardt optimisation algorithm. Then, the two approaches are combined to obtain the finite-size iterative ensemble Kalman filter (IEnKF-N). Several numerical experiments are performed on IEnKF-N with the Lorenz '95 model. These experiments demonstrate its numerical efficiency as well as its performance that offer, at least, the best of both filters. We have also selected a demanding case based on the Lorenz '63 model that points to ways to improve the finite-size ensemble Kalman filters. Eventually, IEnKF-N could be seen as the first brick of an efficient ensemble Kalman smoother for strongly nonlinear systems.

Data Assimilation for Strongly Nonlinear Problems by Transformed Ensemble Kalman Filter

SPE Journal ◽  
2014 ◽  
Vol 20 (01) ◽  
pp. 202-221 ◽  
Author(s):  
Qinzhuo Liao ◽  
Dongxiao Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Homogeneous Medium ◽  
Forward Model ◽  
Dynamic State ◽  
Initial Time ◽  
Static State ◽  
Strongly Nonlinear

Summary The ensemble Kalman filter (EnKF) has been widely used for data assimilation. It is challenging, however, when the relation of state and observation is strongly nonlinear. For example, near the flooding front in an immiscible flow, directly updating the saturation by use of the EnKF may lead to nonphysical results. One possible solution, which may be referred to as the restarted EnKF (REnKF), is to update the static state (e.g., permeability and porosity) and rerun the forward model from the initial time to obtain the updated dynamic state (e.g., pressure and saturation). However, it may become time-consuming, especially when the number of assimilation steps is large. In this study, we develop a transformed EnKF (TEnKF), in which the state is represented by displacement as an alternative variable. The displacement is first transformed from the forecasted state, then updated, and finally transformed back to obtain the updated state. Because the relation between displacement and observation is relatively linear, this new method provides a physically meaningful updated state without resolving the forward model. The TEnKF is tested in the history matching of multiphase flow in a 1D homogeneous medium, a 2D heterogeneous reservoir, and a 3D PUNQ-S3 model. The case studies show that the TEnKF produces physical results without the oscillation problem that occurs in the traditional EnKF, whereas the computational effort is reduced compared with the REnKF.

scholarly journals Comments on “Sigma-Point Kalman Filter Data Assimilation Methods for Strongly Nonlinear Systems”

2009 ◽  
Vol 66 (11) ◽  
pp. 3498-3500 ◽  
Author(s):  
Thomas M. Hamill ◽  
Jeffrey S. Whitaker ◽  
Jeffrey L. Anderson ◽  
Chris Snyder
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Data Assimilation ◽  
Sigma Point ◽  
Strongly Nonlinear

scholarly journals An Iterative EnKF for Strongly Nonlinear Systems

2012 ◽  
Vol 140 (6) ◽  
pp. 1988-2004 ◽  
Author(s):  
Pavel Sakov ◽  
Dean S. Oliver ◽  
Laurent Bertino
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Extended Kalman Filter ◽  
Large Scale ◽  
Lorenz Model ◽  
Model Framework ◽  
Simple Modification ◽  
Strongly Nonlinear ◽  
Perfect Model ◽  
Scale Models

Abstract The study considers an iterative formulation of the ensemble Kalman filter (EnKF) for strongly nonlinear systems in the perfect-model framework. In the first part, a scheme is introduced that is similar to the ensemble randomized maximal likelihood (EnRML) filter by Gu and Oliver. The two new elements in the scheme are the use of the ensemble square root filter instead of the traditional (perturbed observations) EnKF and rescaling of the ensemble anomalies with the ensemble transform matrix from the previous iteration instead of estimating sensitivities between the ensemble observations and ensemble anomalies at the start of the assimilation cycle by linear regression. A simple modification turns the scheme into an ensemble formulation of the iterative extended Kalman filter. The two versions of the algorithm are referred to as the iterative EnKF (IEnKF) and the iterative extended Kalman filter (IEKF). In the second part, the performance of the IEnKF and IEKF is tested in five numerical experiments: two with the 3-element Lorenz model and three with the 40-element Lorenz model. Both the IEnKF and IEKF show a considerable advantage over the EnKF in strongly nonlinear systems when the quality or density of observations are sufficient to constrain the model to the regime of mainly linear propagation of the ensemble anomalies as well as constraining the fast-growing modes, with a much smaller advantage otherwise. The IEnKF and IEKF can potentially be used with large-scale models, and can represent a robust and scalable alternative to particle filter (PF) and hybrid PF–EnKF schemes in strongly nonlinear systems.

Ensemble Kalman Filter for Out of Sequence Measurement Tracking

2012 ◽  
Vol 132 (10) ◽  
pp. 1617-1625
Author(s):  
Sirichai Pornsarayouth ◽  
Masaki Yamakita
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter

Data assimilation with the weighted ensemble Kalman filter

2010 ◽  
Author(s):  
Nicolas Papadakis ◽  
Etienne Mémin ◽  
Anne Cuzol ◽  
Nicolas Gengembre
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter

scholarly journals Assimilation of D-InSAR snow depth data by an ensemble Kalman filter

2021 ◽  
Vol 14 (6) ◽  
Author(s):  
Jinming Yang ◽  
Chengzhi Li
Keyword(s):  
Remote Sensing ◽  
Kalman Filter ◽  
Water Resource ◽  
Ensemble Kalman Filter ◽  
Snow Depth ◽  
Resource Assessment ◽  
Measured Data ◽  
Hydrological Process ◽  
Depth Data ◽  
Water Resource Assessment

AbstractSnow depth mirrors regional climate change and is a vital parameter for medium- and long-term numerical climate prediction, numerical simulation of land-surface hydrological process, and water resource assessment. However, the quality of the available snow depth products retrieved from remote sensing is inevitably affected by cloud and mountain shadow, and the spatiotemporal resolution of the snow depth data cannot meet the need of hydrological research and decision-making assistance. Therefore, a method to enhance the accuracy of snow depth data is urgently required. In the present study, three kinds of snow depth data which included the D-InSAR data retrieved from the remote sensing images of Sentinel-1 synthetic aperture radar, the automatically measured data using ultrasonic snow depth detectors, and the manually measured data were assimilated based on ensemble Kalman filter. The assimilated snow depth data were spatiotemporally consecutive and integrated. Under the constraint of the measured data, the accuracy of the assimilated snow depth data was higher and met the need of subsequent research. The development of ultrasonic snow depth detector and the application of D-InSAR technology in snow depth inversion had greatly alleviated the insufficiency of snow depth data in types and quantity. At the same time, the assimilation of multi-source snow depth data by ensemble Kalman filter also provides high-precision data to support remote sensing hydrological research, water resource assessment, and snow disaster prevention and control program.

scholarly journals Assimilation of Dynamic Combined Finite Discrete Element Methods Using the Ensemble Kalman Filter

2021 ◽  
Vol 11 (7) ◽  
pp. 2898
Author(s):  
Humberto C. Godinez ◽  
Esteban Rougier
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Failure Modes ◽  
Split Hopkinson Pressure Bar ◽  
Peak Stress ◽  
Discrete Element ◽  
Material Behavior ◽  
Model Parameters ◽  
Hopkinson Pressure Bar ◽  
Parameter Values

Simulation of fracture initiation, propagation, and arrest is a problem of interest for many applications in the scientific community. There are a number of numerical methods used for this purpose, and among the most widely accepted is the combined finite-discrete element method (FDEM). To model fracture with FDEM, material behavior is described by specifying a combination of elastic properties, strengths (in the normal and tangential directions), and energy dissipated in failure modes I and II, which are modeled by incorporating a parameterized softening curve defining a post-peak stress-displacement relationship unique to each material. In this work, we implement a data assimilation method to estimate key model parameter values with the objective of improving the calibration processes for FDEM fracture simulations. Specifically, we implement the ensemble Kalman filter assimilation method to the Hybrid Optimization Software Suite (HOSS), a FDEM-based code which was developed for the simulation of fracture and fragmentation behavior. We present a set of assimilation experiments to match the numerical results obtained for a Split Hopkinson Pressure Bar (SHPB) model with experimental observations for granite. We achieved this by calibrating a subset of model parameters. The results show a steady convergence of the assimilated parameter values towards observed time/stress curves from the SHPB observations. In particular, both tensile and shear strengths seem to be converging faster than the other parameters considered.

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