scholarly journals Efficient Characterization of Uncertain Model Parameters with a Reduced-Order Ensemble Kalman Filter

2014 ◽  
Vol 36 (2) ◽  
pp. B198-B224 ◽  
Author(s):  
Binghuai Lin ◽  
Dennis McLaughlin
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Model Parameters ◽  
Reduced Order ◽  
Uncertain Model

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.

scholarly journals Modeling the impact of drought on canopy carbon and water fluxes through parameter optimization using an ensemble Kalman filter

2009 ◽  
Vol 6 (4) ◽  
pp. 8279-8309 ◽  
Author(s):  
W. Ju ◽  
S. Wang ◽  
G. Yu ◽  
Y. Zhou ◽  
H. Wang
Keyword(s):  
Kalman Filter ◽  
Parameter Optimization ◽  
Ensemble Kalman Filter ◽  
Terrestrial Ecosystems ◽  
Model Parameters ◽  
Interannual Variations ◽  
Atmospheric Water ◽  
Model Parameterization ◽  
Coniferous Plantation ◽  
The Impact

Abstract. Soil and atmospheric water deficits have significant influences on CO2 and energy exchanges between the atmosphere and terrestrial ecosystems. Model parameterization significantly affects the ability of a model to simulate carbon, water, and energy fluxes. In this study, an ensemble Kalman filter (EnKF) and observations of gross primary productivity (GPP) and latent heat (LE) fluxes were used to optimize model parameters significantly affecting the calculation of these fluxes for a subtropical coniferous plantation in southeastern China. The optimized parameters include the maximum carboxylation rate (Vcmax), the Ball-Berry coefficient (m) and the coefficient determining the sensitivity of stomatal conductance to atmospheric water vapor deficit D0). Optimized Vcmax and m showed larger seasonal and interannual variations than D0. Seasonal variations of Vcmax and m are more pronounced than the interannual variations. Vcmax and m are associated with soil water content (SWC). During dry periods, SWC at the 20 cm depth can explain 61% and 64% of variations of Vcmax and m, respectively. EnKF parameter optimization improves the simulations of GPP, LE and sensible heat (SH), mainly during dry periods. After parameter optimization using EnKF, the variations of GPP, LE and SH explained by the model increased by 1% to 4% at half-hourly steps and by 3% to 5% at daily time steps. Efforts are needed to develop algorithms that can properly describe the variations of these parameters under different environmental conditions.

scholarly journals Identification of hydrological model parameter variation using ensemble Kalman filter

2016 ◽  
Vol 20 (12) ◽  
pp. 4949-4961 ◽  
Author(s):  
Chao Deng ◽  
Pan Liu ◽  
Shenglian Guo ◽  
Zejun Li ◽  
Dingbao Wang
Keyword(s):  
Kalman Filter ◽  
Temporal Variation ◽  
Ensemble Kalman Filter ◽  
Water Conservation ◽  
Hydrological Model ◽  
Anthropogenic Activities ◽  
Temporal Variations ◽  
Balance Model ◽  
Model Parameters ◽  
Water Storage Capacity

Abstract. Hydrological model parameters play an important role in the ability of model prediction. In a stationary context, parameters of hydrological models are treated as constants; however, model parameters may vary with time under climate change and anthropogenic activities. The technique of ensemble Kalman filter (EnKF) is proposed to identify the temporal variation of parameters for a two-parameter monthly water balance model (TWBM) by assimilating the runoff observations. Through a synthetic experiment, the proposed method is evaluated with time-invariant (i.e., constant) parameters and different types of parameter variations, including trend, abrupt change and periodicity. Various levels of observation uncertainty are designed to examine the performance of the EnKF. The results show that the EnKF can successfully capture the temporal variations of the model parameters. The application to the Wudinghe basin shows that the water storage capacity (SC) of the TWBM model has an apparent increasing trend during the period from 1958 to 2000. The identified temporal variation of SC is explained by land use and land cover changes due to soil and water conservation measures. In contrast, the application to the Tongtianhe basin shows that the estimated SC has no significant variation during the simulation period of 1982–2013, corresponding to the relatively stationary catchment properties. The evapotranspiration parameter (C) has temporal variations while no obvious change patterns exist. The proposed method provides an effective tool for quantifying the temporal variations of the model parameters, thereby improving the accuracy and reliability of model simulations and forecasts.

The Design of a Robust Weighted Measurement Fusion Steady-State Kalman Filter

2014 ◽  
Vol 701-702 ◽  
pp. 624-629
Author(s):  
Wen Qiang Liu ◽  
Xue Mei Wang ◽  
Zi Li Deng
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Lyapunov Equation ◽  
Model Parameters ◽  
Invariant System ◽  
Parameter Uncertainties ◽  
Worst Case ◽  
Uncertain Model ◽  
Time Invariant ◽  
Time Invariant System

For the linear discrete-time multisensor time-invariant system with uncertain model parameters and measurement noise variances, by introducing fictitious noise to compensate the parameter uncertainties, using the minimax robust estimation principle, based on the worst-case conservative multisensor system with conservative upper bounds of measurement and fictitious noises variances, a robust weighted measurement fusion steady-state Kalman filter is presented. By the Lyapunov equation approach, it is proved that when the region of the parameter uncertainties is sufficient small, the corresponding actual fused filtering error variances are guaranteed to have a less-conservative upper bound. Simulation results show the effectiveness and correctness of the proposed results.

Data Assimilation of Coupled Fluid Flow and Geomechanics Using the Ensemble Kalman Filter

SPE Journal ◽  
2010 ◽  
Vol 15 (02) ◽  
pp. 382-394 ◽  
Author(s):  
Haibin Chang ◽  
Yan Chen ◽  
Dongxiao Zhang
Keyword(s):  
Fluid Flow ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Material Properties ◽  
Ensemble Kalman Filter ◽  
Oil Field ◽  
Reservoir Rock ◽  
Model Parameters ◽  
Stress Strain ◽  
Reservoir Flow

Summary In reservoir history matching or data assimilation, dynamic data, such as production rates and pressures, are used to constrain reservoir models and to update model parameters. As such, even if under certain conceptualization the model parameters do not vary with time, the estimate of such parameters may change with the available observations and, thus, with time. In reality, the production process may lead to changes in both the flow and geomechanics fields, which are dynamically coupled. For example, the variations in the stress/strain field lead to changes in porosity and permeability of the reservoir and, hence, in the flow field. In weak formations, such as the Lost Hills oil field, fluid extraction may cause a large compaction to the reservoir rock and a significant subsidence at the land surface, resulting in huge economic losses and detrimental environmental consequences. The strong nonlinear coupling between reservoir flow and geomechanics poses a challenge to constructing a reliable model for predicting oil recovery in such reservoirs. On the other hand, the subsidence and other geomechanics observations can provide additional insight into the nature of the reservoir rock and help constrain the reservoir model if used wisely. In this study, the ensemble-Kalman-filter (EnKF) approach is used to estimate reservoir flow and material properties by jointly assimilating dynamic flow and geomechanics observations. The resulting model can be used for managing and optimizing production operations and for mitigating the land subsidence. The use of surface displacement observations improves the match to both production and displacement data. Localization is used to facilitate the assimilation of a large amount of data and to mitigate the effect of spurious correlations resulting from small ensembles. Because the stress, strain, and displacement fields are updated together with the material properties in the EnKF, the issue of consistency at the analysis step of the EnKF is investigated. A 3D problem with reservoir fluid-flow and mechanical parameters close to those of the Lost Hills oil field is used to test the applicability.

Robust Centralized Fusion Steady-State Kalman Filter with Uncertain Parameters and Measurement Noise Variances

2014 ◽  
Vol 701-702 ◽  
pp. 532-537 ◽  
Author(s):  
Xue Mei Wang ◽  
Wen Qiang Liu ◽  
Zi Li Deng
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Lyapunov Equation ◽  
Small Region ◽  
Measurement Noise ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
New Approach ◽  
Uncertain Model ◽  
Robust Kalman Filter

For the linear discrete time multisensor system with uncertain model parameters and measurement noise variances, the centralized fusion robust steady-state Kalman filter is presented by a new approach of compensating the parameter uncertainties by a fictitious noise. Based on the Lyapunov equation, it is proved that for given fictitious noise variance, the variances of the actual filtering errors have a less-conservative upper bound when the uncertainty of parameters is limited in a sufficiently small region which is called as robust region of the parameter uncertainties. Further, a simulation example demonstrates how to search the robust region. It is also proved that the robust accuracy of the centralized fusion robust steady-state Kalman filter is higher than that of each local robust Kalman filter. A simulation example shows its effectiveness.

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