scholarly journals Empirical Localization of Observation Impact in Ensemble Kalman Filters

2013 ◽  
Vol 141 (11) ◽  
pp. 4140-4153 ◽  
Author(s):  
Jeffrey Anderson ◽  
Lili Lei
Keyword(s):  
Kalman Filters ◽  
Horizontal Distance ◽  
State Variables ◽  
Sampling Errors ◽  
Ensemble Kalman Filters ◽  
Filter Performance ◽  
State Variable ◽  
The Impact ◽  
Mean Square Errors ◽  
Low Order

Abstract Localization is a method for reducing the impact of sampling errors in ensemble Kalman filters. Here, the regression coefficient, or gain, relating ensemble increments for observed quantity y to increments for state variable x is multiplied by a real number α defined as a localization. Localization of the impact of observations on model state variables is required for good performance when applying ensemble data assimilation to large atmospheric and oceanic problems. Localization also improves performance in idealized low-order ensemble assimilation applications. An algorithm that computes localization from the output of an ensemble observing system simulation experiment (OSSE) is described. The algorithm produces localizations for sets of pairs of observations and state variables: for instance, all state variables that are between 300- and 400-km horizontal distance from an observation. The algorithm is applied in a low-order model to produce localizations from the output of an OSSE and the computed localizations are then used in a new OSSE. Results are compared to assimilations using tuned localizations that are approximately Gaussian functions of the distance between an observation and a state variable. In most cases, the empirically computed localizations produce the lowest root-mean-square errors in subsequent OSSEs. Localizations derived from OSSE output can provide guidance for localization in real assimilation experiments. Applying the algorithm in large geophysical applications may help to tune localization for improved ensemble filter performance.

scholarly journals Analysis of the Impact of the Type of Sampling of Representative Properties on the Results of Mass Appraisal

2020 ◽  
Vol 20 (2) ◽  
pp. 152-167
Author(s):  
Sebastian Gnat
Keyword(s):  
Real Estate ◽  
Random Sampling ◽  
Simple Random Sampling ◽  
Multiple Regression Model ◽  
Stratified Sampling ◽  
Sampling Errors ◽  
Real Estate Valuation ◽  
Simple Sampling ◽  
The Impact ◽  
Mean Square Errors

Abstract Research background: Mass valuation is a process in which many properties are valued simultaneously with a uniform approach. An example of a procedure used for mass real estate valuation is the Szczecin Algorithm of Real Estate Mass Appraisal (SAREMA), which can be developed into a multiple regression model. The algorithm is based on a set of drawn representative properties. This set determines, inter alia, the quality of obtained valuations. Purpose: The objective of the study is to verify the hypothesis whether changing the method of sampling representative properties from the originally used simple random sampling to stratified sampling improves the results of the SAREMA econometric variant. Research methodology: The article presents a study that uses two methods of representative properties sampling – simple random sampling and stratified sampling. Errors of the models of valuation created taking into account both methods of sampling and different number of representative properties are compared. A key aspect of the survey is the choice of a better sampling method. Results: The study has shown that stratified sampling improves valuation results and, more specifically, allows for lower root mean square errors. Stratified sampling yielded better results in the initial phase of the study with more observations, but reducing the percentage of strata participating in the draws, despite the increase in RMSE, guaranteed lower errors than the corresponding results based on simple sampling in all variants of the study. Novelty: The article confirms the possibility of improving the results of mass property valuation by changing the scheme of representative properties sampling. The results allowed for the conclusion that stratified sampling is a better way of creating a set of representative properties.

scholarly journals On Serial Observation Processing in Localized Ensemble Kalman Filters

2015 ◽  
Vol 143 (5) ◽  
pp. 1554-1567 ◽  
Author(s):  
Lars Nerger
Keyword(s):  
Ensemble Kalman Filter ◽  
Kalman Filters ◽  
Large Scale ◽  
The State ◽  
Ensemble Kalman Filters ◽  
Filter Performance ◽  
Error Covariance ◽  
Analysis Process ◽  
Scale Models ◽  
Serial Observation

Abstract Ensemble square root filters can either assimilate all observations that are available at a given time at once, or assimilate the observations in batches or one at a time. For large-scale models, the filters are typically applied with a localized analysis step. This study demonstrates that the interaction of serial observation processing and localization can destabilize the analysis process, and it examines under which conditions the instability becomes significant. The instability results from a repeated inconsistent update of the state error covariance matrix that is caused by the localization. The inconsistency is present in all ensemble Kalman filters, except for the classical ensemble Kalman filter with perturbed observations. With serial observation processing, its effect is small in cases when the assimilation changes the ensemble of model states only slightly. However, when the assimilation has a strong effect on the state estimates, the interaction of localization and serial observation processing can significantly deteriorate the filter performance. In realistic large-scale applications, when the assimilation changes the states only slightly and when the distribution of the observations is irregular and changing over time, the instability is likely not significant.

scholarly journals Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering

2003 ◽  
Author(s):  
Dan Simon ◽  
Donald L. Simon
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Kalman Filters ◽  
Inequality Constraints ◽  
Computational Effort ◽  
Estimation Accuracy ◽  
State Variables ◽  
Turbofan Engine ◽  
State Variable ◽  
State Variable Constraints

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results obtained from application to a turbofan engine model. This model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.

scholarly journals A Probabilistic Approach to Adaptive Covariance Localization for Serial Ensemble Square Root Filters

2014 ◽  
Vol 142 (12) ◽  
pp. 4499-4518 ◽  
Author(s):  
Yicun Zhen ◽  
Fuqing Zhang
Keyword(s):  
Probabilistic Approach ◽  
Filter Method ◽  
Square Root ◽  
Ensemble Size ◽  
Sampling Errors ◽  
Jeffreys Prior ◽  
Ensemble Kalman Filters ◽  
Localization Radius ◽  
Lorenz 96 ◽  
The Impact

Abstract This study proposes a variational approach to adaptively determine the optimum radius of influence for ensemble covariance localization when uncorrelated observations are assimilated sequentially. The covariance localization is commonly used by various ensemble Kalman filters to limit the impact of covariance sampling errors when the ensemble size is small relative to the dimension of the state. The probabilistic approach is based on the premise of finding an optimum localization radius that minimizes the distance between the Kalman update using the localized sampling covariance versus using the true covariance, when the sequential ensemble Kalman square root filter method is used. The authors first examine the effectiveness of the proposed method for the cases when the true covariance is known or can be approximated by a sufficiently large ensemble size. Not surprisingly, it is found that the smaller the true covariance distance or the smaller the ensemble, the smaller the localization radius that is needed. The authors further generalize the method to the more usual scenario that the true covariance is unknown but can be represented or estimated probabilistically based on the ensemble sampling covariance. The mathematical formula for this probabilistic and adaptive approach with the use of the Jeffreys prior is derived. Promising results and limitations of this new method are discussed through experiments using the Lorenz-96 system.

scholarly journals Accounting for Model Error from Unresolved Scales in Ensemble Kalman Filters by Stochastic Parameterization

2017 ◽  
Vol 145 (9) ◽  
pp. 3709-3723 ◽  
Author(s):  
Fei Lu ◽  
Xuemin Tu ◽  
Alexandre J. Chorin
Keyword(s):  
Kalman Filters ◽  
Numerical Experiments ◽  
Sampling Error ◽  
Forecast Model ◽  
Model Error ◽  
Ensemble Size ◽  
Ensemble Kalman Filters ◽  
Filter Performance ◽  
Performance Results ◽  
Lorenz 96

The use of discrete-time stochastic parameterization to account for model error due to unresolved scales in ensemble Kalman filters is investigated by numerical experiments. The parameterization quantifies the model error and produces an improved non-Markovian forecast model, which generates high quality forecast ensembles and improves filter performance. Results are compared with the methods of dealing with model error through covariance inflation and localization (IL), using as an example the two-layer Lorenz-96 system. The numerical results show that when the ensemble size is sufficiently large, the parameterization is more effective in accounting for the model error than IL; if the ensemble size is small, IL is needed to reduce sampling error, but the parameterization further improves the performance of the filter. This suggests that in real applications where the ensemble size is relatively small, the filter can achieve better performance than pure IL if stochastic parameterization methods are combined with IL.

scholarly journals Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering

2005 ◽  
Vol 127 (2) ◽  
pp. 323-328 ◽  
Author(s):  
Dan Simon ◽  
Donald L. Simon
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Kalman Filters ◽  
Inequality Constraints ◽  
Computational Effort ◽  
Estimation Accuracy ◽  
State Variables ◽  
Turbofan Engine ◽  
State Variable ◽  
State Variable Constraints

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state-variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state-variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state-variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results obtained from application to a turbofan engine model. This model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.

Impacts of separate rejection water treatment on the overall plant performance

2003 ◽  
Vol 48 (4) ◽  
pp. 139-146 ◽  
Author(s):  
B. Wett ◽  
J. Alex
Keyword(s):  
Water Treatment ◽  
Treatment Plant ◽  
Operating Experience ◽  
Plant Performance ◽  
High Tech ◽  
State Variables ◽  
Total N ◽  
Unit Process ◽  
Innovative Tool ◽  
The Impact

A separate rejection water treatment appears as a high-tech unit process which might be recommendable only for specific cases of an upgrading of an existing wastewater treatment plant. It is not the issue of this paper to consider a specific separate treatment process itself but to investigate the influence of such a process on the overall plant performance. A plant-wide model has been applied as an innovative tool to evaluate effects of the implemented sidestream strategy on the mainstream treatment. The model has been developed in the SIMBA environment and combines acknowledged mathematical descriptions of the activated sludge process (ASM1) and the anaerobic mesophilic digestion (Siegrist model). The model's calibration and validation was based on data from 5 years of operating experience of a full-scale rejection water treatment. The impact on the total N-elimination efficiency is demonstrated by detailed nitrogen mass flow schemes including the interactions between the wastewater and the sludge lane. Additionally limiting conditions due to dynamic N-return loads are displayed by the model's state variables.

scholarly journals A Rational Numerical Method for Simulation of Drop-Impact Dynamics of Oleo-Pneumatic Landing Gear

2021 ◽  
Vol 11 (9) ◽  
pp. 4136
Author(s):  
Rosario Pecora
Keyword(s):  
Numerical Method ◽  
Initial Conditions ◽  
Impact Load ◽  
Numerical Models ◽  
Landing Gear ◽  
Design Stage ◽  
Impact Dynamics ◽  
State Variables ◽  
Adopted Model ◽  
The Impact

Oleo-pneumatic landing gear is a complex mechanical system conceived to efficiently absorb and dissipate an aircraft’s kinetic energy at touchdown, thus reducing the impact load and acceleration transmitted to the airframe. Due to its significant influence on ground loads, this system is generally designed in parallel with the main structural components of the aircraft, such as the fuselage and wings. Robust numerical models for simulating landing gear impact dynamics are essential from the preliminary design stage in order to properly assess aircraft configuration and structural arrangements. Finite element (FE) analysis is a viable solution for supporting the design. However, regarding the oleo-pneumatic struts, FE-based simulation may become unpractical, since detailed models are required to obtain reliable results. Moreover, FE models could not be very versatile for accommodating the many design updates that usually occur at the beginning of the landing gear project or during the layout optimization process. In this work, a numerical method for simulating oleo-pneumatic landing gear drop dynamics is presented. To effectively support both the preliminary and advanced design of landing gear units, the proposed simulation approach rationally balances the level of sophistication of the adopted model with the need for accurate results. Although based on a formulation assuming only four state variables for the description of landing gear dynamics, the approach successfully accounts for all the relevant forces that arise during the drop and their influence on landing gear motion. A set of intercommunicating routines was implemented in MATLAB® environment to integrate the dynamic impact equations, starting from user-defined initial conditions and general parameters related to the geometric and structural configuration of the landing gear. The tool was then used to simulate a drop test of a reference landing gear, and the obtained results were successfully validated against available experimental data.

Trajectory shaping guidance law design using constraint-combining multiplier

2021 ◽  
pp. 095441002098637
Author(s):  
Min-Guk Seo ◽  
Chang-Hun Lee ◽  
Tae-Hun Kim
Keyword(s):  
Design Method ◽  
Impact Angle ◽  
State Variables ◽  
Flight Trajectory ◽  
Potential Significance ◽  
Guidance Law ◽  
Terminal Constraints ◽  
The Impact ◽  
Guidance Laws ◽  
Impact Angle Constraint

A new design method for trajectory shaping guidance laws with the impact angle constraint is proposed in this study. The basic idea is that the multiplier introduced to combine the equations for the terminal constraints is used to shape a flight trajectory as desired. To this end, the general form of impact angle control guidance (IACG) is first derived as a function of an arbitrary constraint-combining multiplier using the optimal control. We reveal that the constraint-combining multiplier satisfying the kinematics can be expressed as a function of state variables. From this result, the constraint-combining multiplier to achieve a desired trajectory can be obtained. Accordingly, when the desired trajectory is designed to satisfy the terminal constraints, the proposed method directly can provide a closed form of IACG laws that can achieve the desired trajectory. The potential significance of the proposed result is that various trajectory shaping IACG laws that can cope with various guidance goals can be readily determined compared to existing approaches. In this study, several examples are shown to validate the proposed method. The results also indicate that previous IACG laws belong to the subset of the proposed result. Finally, the characteristics of the proposed guidance laws are analyzed through numerical simulations.

scholarly journals Extreme Meteorological Events in a Coastal Lagoon Ecosystem: The Ria de Aveiro Lagoon (Portugal) Case Study

2021 ◽  
Vol 9 (7) ◽  
pp. 727
Author(s):  
José Fortes Lopes ◽  
Carina Lurdes Lopes ◽  
João Miguel Dias
Keyword(s):  
Water Temperature ◽  
Coastal Lagoon ◽  
Early Summer ◽  
Extreme Weather Events ◽  
Climate Change Scenarios ◽  
State Variables ◽  
Ria De Aveiro ◽  
Physical Conditions ◽  
Weather Events ◽  
The Impact

Extreme weather events (EWEs) represent meteorological hazards for coastal lagoon hydrodynamics, of which intensity and frequency are increasing over the last decades as a consequence of climate changes. The imbalances they generated should affect primarily vulnerable low-lying areas while potentially disturbing the physical balances (salt and water temperature) and, therefore, the ecosystem equilibrium. This study arises from the need to assess the impact of EWEs on the Ria de Aveiro, a lagoon situated in the Portuguese coastal area. Furthermore, it was considered that those events occur under the frame of a future sea-level rise, as predicted by several climate change scenarios. Two EWEs scenarios, a dry and an extremely wet early summer reflecting past situations and likely to occur in the future, were considered to assess the departure from the system baseline functioning. It was used as a biogeochemistry model that simulates the hydrodynamics, as well as the baseline physical and biogeochemistry state variables. The dry summer scenario, corresponding to a significant reduction in the river’s inflow, evidences a shift of the system to a situation under oceanic dominance characterized by colder and saltier water (~18 °C; 34 PSU) than the baseline while lowering the concentration of the nutrients and reducing the phytoplankton population to a low-level limit. Under a wet summer scenario, the lagoon shifted to a brackish and warmer situation (~21 °C, <15 PSU) in a time scale of some tidal periods, driven by the combining effect of the tidal transport and the river’s inflow. Phytoplankton patterns respond to variability on local and short-term scales that reflect physical conditions within the lagoon, inducing nutrient-supported growth. Overall, the results indicate that EWEs generate local and transient changes in physical conditions (namely salinity and water temperature) in response to the characteristic variability of the lagoon’s hydrodynamics associated with a tidal-dominated system. Therefore, in addition to the potential impact of changing physical conditions on the ecosystem, saline intrusion along the lagoon or the transfer of brackish water to the mouth of the system are the main consequences of EWEs, while the main biogeochemistry changes tend to remain moderate.

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