Covariance Localization with the Diffusion-Based Correlation Models

2013 ◽  
Vol 141 (2) ◽  
pp. 848-860 ◽  
Author(s):  
Max Yaremchuk ◽  
Dmitry Nechaev
Keyword(s):  
Covariance Matrices ◽  
Polynomial Functions ◽  
State Variables ◽  
Ensemble Size ◽  
Diffusion Operator ◽  
Homogeneity Assumption ◽  
Correlation Models ◽  
Sample Covariance ◽  
The Impact ◽  
Decorrelation Scale

Abstract Improving the performance of ensemble filters applied to models with many state variables requires regularization of the covariance estimates by localizing the impact of observations on state variables. A covariance localization technique based on modeling of the sample covariance with polynomial functions of the diffusion operator (DL method) is presented. Performance of the technique is compared with the nonadaptive (NAL) and adaptive (AL) ensemble localization schemes in the framework of numerical experiments with synthetic covariance matrices in a realistically inhomogeneous setting. It is shown that the DL approach is comparable in accuracy with the AL method when the ensemble size is less than 100. With larger ensembles, the accuracy of the DL approach is limited by the local homogeneity assumption underlying the technique. Computationally, the DL method is comparable with the NAL technique if the ratio of the local decorrelation scale to the grid step is not too large.

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.

scholarly journals Parameters Estimation and Prediction of Water Movement and Solute Transport in Layered, Variably Saturated Soils Using the Ensemble Kalman Filter

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1520
Author(s):  
Zheng Jiang ◽  
Quanzhong Huang ◽  
Gendong Li ◽  
Guangyong Li
Keyword(s):  
Kalman Filter ◽  
Solute Transport ◽  
Ensemble Kalman Filter ◽  
Water Movement ◽  
Parameters Estimation ◽  
Saturated Soils ◽  
Hydrological Models ◽  
State Variables ◽  
Ensemble Size ◽  
Highly Nonlinear

The parameters of water movement and solute transport models are essential for the accurate simulation of soil moisture and salinity, particularly for layered soils in field conditions. Parameter estimation can be achieved using the inverse modeling method. However, this type of method cannot fully consider the uncertainties of measurements, boundary conditions, and parameters, resulting in inaccurate estimations of parameters and predictions of state variables. The ensemble Kalman filter (EnKF) is well-suited to data assimilation and parameter prediction in Situations with large numbers of variables and uncertainties. Thus, in this study, the EnKF was used to estimate the parameters of water movement and solute transport in layered, variably saturated soils. Our results indicate that when used in conjunction with the HYDRUS-1D software (University of California Riverside, California, CA, USA) the EnKF effectively estimates parameters and predicts state variables for layered, variably saturated soils. The assimilation of factors such as the initial perturbation and ensemble size significantly affected in the simulated results. A proposed ensemble size range of 50–100 was used when applying the EnKF to the highly nonlinear hydrological models of the present study. Although the simulation results for moisture did not exhibit substantial improvement with the assimilation, the simulation of the salinity was significantly improved through the assimilation of the salinity and relative solutetransport parameters. Reducing the uncertainties in measured data can improve the goodness-of-fit in the application of the EnKF method. Sparse field condition observation data also benefited from the accurate measurement of state variables in the case of EnKF assimilation. However, the application of the EnKF algorithm for layered, variably saturated soils with hydrological models requires further study, because it is a challenging and highly nonlinear problem.

scholarly journals On the principal components of sample covariance matrices

2015 ◽  
Vol 164 (1-2) ◽  
pp. 459-552 ◽  
Author(s):  
Alex Bloemendal ◽  
Antti Knowles ◽  
Horng-Tzer Yau ◽  
Jun Yin
Keyword(s):  
Principal Components ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance

Some strong convergence theorems for eigenvalues of general sample covariance matrices

2021 ◽  
Author(s):  
Yanqing Yin
Keyword(s):  
General Population ◽  
Strong Convergence ◽  
Spectral Properties ◽  
Closed Interval ◽  
Open Interval ◽  
Convergence Result ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Class Of Matrices

The aim of this paper is to investigate the spectral properties of sample covariance matrices under a more general population. We consider a class of matrices of the form [Formula: see text], where [Formula: see text] is a [Formula: see text] nonrandom matrix and [Formula: see text] is an [Formula: see text] matrix consisting of i.i.d standard complex entries. [Formula: see text] as [Formula: see text] while [Formula: see text] can be arbitrary but no smaller than [Formula: see text]. We first prove that under some mild assumptions, with probability 1, for all large [Formula: see text], there will be no eigenvalues in any closed interval contained in an open interval which is outside the supports of the limiting distributions for all sufficiently large [Formula: see text]. Then we get the strong convergence result for the extreme eigenvalues as an extension of Bai-Yin law.

Response Analysis of van der Pol Vibro-Impact System with Coulomb Friction Under Gaussian White Noise

2018 ◽  
Vol 28 (13) ◽  
pp. 1830043 ◽  
Author(s):  
Meng Su ◽  
Wei Xu ◽  
Guidong Yang
Keyword(s):  
White Noise ◽  
Coulomb Friction ◽  
Gaussian White Noise ◽  
Original System ◽  
Stochastic Averaging ◽  
Response Analysis ◽  
State Variables ◽  
Van Der Pol ◽  
Impact System ◽  
The Impact

In this paper, the stationary response of a van der Pol vibro-impact system with Coulomb friction excited by Gaussian white noise is studied. The Zhuravlev nonsmooth transformation of the state variables is utilized to transform the original system to a new system without the impact term. Then, the stochastic averaging method is applied to the equivalent system to obtain the stationary probability density functions (pdfs). The accuracy of the analytical results obtained from the proposed procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different damping coefficients, restitution coefficients, amplitudes of friction and noise intensities on the response are discussed. Additionally, stochastic P-bifurcations are explored.

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