CANONICAL-DISSIPATIVE NONEQUILIBRIUM ENERGY DISTRIBUTIONS: PARAMETER ESTIMATION VIA IMPLICIT MOMENT METHOD, IMPLEMENTATION AND APPLICATION

2013 ◽  
Vol 27 (28) ◽  
pp. 1350156 ◽  
Author(s):  
T. D. FRANK ◽  
S. KIM ◽  
D. G. DOTOV
Keyword(s):  
Moment Method ◽  
Hand Movements ◽  
Systematic Change ◽  
Model Parameters ◽  
Energy Distributions ◽  
Normal Distributions ◽  
Distribution Parameters ◽  
Parameter Values ◽  
Energy Moments ◽  
Nonequilibrium Energy

Canonical-dissipative nonequilibrium energy distributions play an important role in the life sciences. In one of the most fundamental forms, such energy distributions correspond to two-parametric normal distributions truncated to the left. We present an implicit moment method involving the first and second energy moments to estimate the distribution parameters. It is shown that the method is consistent with Cohen's 1949 formula. The implementation of the algorithm is discussed and the range of admissible parameter values is identified. In addition, an application to an earlier study on human oscillatory hand movements is presented. In this earlier study, energy was conceptualized as the energy of a Hamiltonian oscillator model. The canonical-dissipative approach allows for studying the systematic change of the model parameters with oscillation frequency. It is shown that the results obtained with the implicit moment method are consistent with those derived in the earlier study by other means.

scholarly journals Normal approximation for mixtures of normal distributions and the evolution of phenotypic traits

2021 ◽  
Vol 53 (1) ◽  
pp. 162-188
Author(s):  
Krzysztof Bartoszek ◽  
Torkel Erhardsson
Keyword(s):  
Normal Distribution ◽  
Phenotypic Trait ◽  
Phenotypic Traits ◽  
Normal Distributions ◽  
Average Value ◽  
Conditional Moments ◽  
Mixture Of Normal Distributions ◽  
Explicit Bounds ◽  
Mixtures Of Normal Distributions ◽  
Parameter Values

AbstractExplicit bounds are given for the Kolmogorov and Wasserstein distances between a mixture of normal distributions, by which we mean that the conditional distribution given some $\sigma$ -algebra is normal, and a normal distribution with properly chosen parameter values. The bounds depend only on the first two moments of the first two conditional moments given the $\sigma$ -algebra. The proof is based on Stein’s method. As an application, we consider the Yule–Ornstein–Uhlenbeck model, used in the field of phylogenetic comparative methods. We obtain bounds for both distances between the distribution of the average value of a phenotypic trait over n related species, and a normal distribution. The bounds imply and extend earlier limit theorems by Bartoszek and Sagitov.

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 An enhanced set of displacement parameter restraints in CRYSTALS

2018 ◽  
Vol 51 (4) ◽  
pp. 1059-1068 ◽  
Author(s):  
Pascal Parois ◽  
James Arnold ◽  
Richard Cooper
Keyword(s):  
Structural Model ◽  
Rigid Bodies ◽  
Model Parameters ◽  
Coordinate Systems ◽  
Principal Axes ◽  
Anisotropic Displacement Parameters ◽  
Set Up ◽  
Meaningful Relationships ◽  
Parameter Values ◽  
Total Model

Crystallographic restraints are widely used during refinement of small-molecule and macromolecular crystal structures. They can be especially useful for introducing additional observations and information into structure refinements against low-quality or low-resolution data (e.g. data obtained at high pressure) or to retain physically meaningful parameter values in disordered or unstable refinements. However, despite the fact that the anisotropic displacement parameters (ADPs) often constitute more than half of the total model parameters determined in a structure analysis, there are relatively few useful restraints for them, examples being Hirshfeld rigid-bond restraints, direct equivalence of parameters and SHELXL RIGU-type restraints. Conversely, geometric parameters can be subject to a multitude of restraints (e.g. absolute or relative distance, angle, planarity, chiral volume, and geometric similarity). This article presents a series of new ADP restraints implemented in CRYSTALS [Parois, Cooper & Thompson (2015), Chem. Cent. J. 9, 30] to give more control over ADPs by restraining, in a variety of ways, the directions and magnitudes of the principal axes of the ellipsoids in locally defined coordinate systems. The use of these new ADPs results in more realistic models, as well as a better user experience, through restraints that are more efficient and faster to set up. The use of these restraints is recommended to preserve physically meaningful relationships between displacement parameters in a structural model for rigid bodies, rotationally disordered groups and low-completeness data.

scholarly journals ESTIMATING VALUE-AT-RISK BASED ON NON-NORMAL DISTRIBUTIONS

2015 ◽  
Vol 3 ◽  
pp. 188-195 ◽  
Author(s):  
Mária Bohdalová ◽  
Michal Greguš
Keyword(s):  
At Risk ◽  
Risk Factor ◽  
Value At Risk ◽  
Likelihood Method ◽  
Normal Distributions ◽  
Confidence Levels ◽  
Portfolio Returns ◽  
Distribution Parameters ◽  
Financial Portfolios ◽  
Daily Changes

The article presents a comparative study of parametric linear value-at-risk (VaR) models used for estimating the risk of financial portfolios. We illustrate how to adjust VaR for auto-correlation in portfolio returns. The article presents static and dynamic methodology to compute VaR, based on the assumption that daily changes are independent and identically distributed (normal or non-normal) or auto-correlated in terms of the risk factor dynamics. We estimate the parametric linear VaR over a risk horizon of 1 day and 10 days at 99% and 95% confidence levels for the same data. We compare the parametric VaR and a VaR obtained using Monte Carlo simulations with historical simulations and use the maximum likelihood method to calibrate the distribution parameters of our risk factors. The study investigated whether the parametric linear VaR applies to contemporary risk factor analysis and pertained to selected foreign rates.

New Research of Transformer Windings Partial Discharge Based on Non-Even Distribution Parameters Model

2014 ◽  
Vol 521 ◽  
pp. 343-346
Author(s):  
Yu Sheng Quan ◽  
Pu Xin Shi ◽  
Shai Gen Han ◽  
Ning Chen
Keyword(s):  
Power System ◽  
Partial Discharge ◽  
Normal Operation ◽  
Model Parameters ◽  
Distribution Parameters ◽  
New Research ◽  
Discharge Detection

Transformer is the primary equipment of power system. The normal operation of transformers has great significance of the security and stability of a power system. Once partial discharge happened in the winds of a transformer, it will accelerate the aging of the insulation, and may damage the windings. This paper analyzes the effect of partial discharge to transformer windings, and founding a model of non-even distribution parameters. Separate the even distribution parameters model into three parts and partial discharge happens in the second one. The partial discharge leads to changing of the model parameters. And port voltage changes with it. Partial discharge detection achieved according to the changing of port voltage.

scholarly journals Robust Mixture Modeling Based on Two-Piece Scale Mixtures of Normal Family

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 38 ◽  
Author(s):  
Mohsen Maleki ◽  
Javier Contreras-Reyes ◽  
Mohammad Mahmoudi
Keyword(s):  
Real Data ◽  
Finite Mixture ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Normal Distributions ◽  
Scale Mixtures ◽  
Robust Model ◽  
Heavy Tailed Distributions ◽  
The Family ◽  
Heavy Tailed

In this paper, we examine the finite mixture (FM) model with a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family components. This family allows the development of a robust estimation of FM models. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and light/heavy tailed distributions. It represents an alternative family to the well-known scale mixtures of the skew normal (SMSN) family studied by Branco and Dey (2001). Also, the TP-SMN covers the SMN (normal, t, slash, and contaminated normal distributions) as the symmetric members and two-piece versions of them as asymmetric members. A key feature of this study is using a suitable hierarchical representation of the family to obtain maximum likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and real data, and then compared to other finite mixture of SMSN models.

scholarly journals Modelling temperature variations in polar snow using DAISY

1997 ◽  
Vol 43 (143) ◽  
pp. 180-191 ◽  
Author(s):  
Ε. M. Morris ◽  
H. -P. Bader ◽  
P. Weilenmann
Keyword(s):  
Field Experiments ◽  
A Priori ◽  
Model Parameters ◽  
Data Set ◽  
International Geophysical Year ◽  
Snow Model ◽  
Using Data ◽  
Polar Snow ◽  
Parameter Values ◽  
The Antarctic

AbstractA physics-based snow model has been calibrated using data collected at Halley Bay, Antarctica, during the International Geophysical Year. Variations in snow temperature and density are well-simulated using values for the model parameters within the range reported from other polar field experiments. The effect of uncertainty in the parameter values on the accuracy of the predictions is no greater than the effect of instrumental error in the input data. Thus, this model can be used with parameters determined a priori rather than by optimization. The model has been validated using an independent data set from Halley Bay and then used to estimate 10 m temperatures on the Antarctic Peninsula plateau over the last half-century.

Torsional damping of a back-to-back gearbox rig: Experimental measurements and frequency domain modelling

2002 ◽  
Vol 216 (2) ◽  
pp. 157-168 ◽  
Author(s):  
S J Drew ◽  
B J Stone
Keyword(s):  
Frequency Domain ◽  
Natural Frequencies ◽  
Model Parameters ◽  
Modal Damping ◽  
Torsional Damping ◽  
Analysis Of Results ◽  
Torsional Frequency ◽  
Signal Processing Methods ◽  
Parameter Values ◽  
Future Work

This paper is concerned with the experimental measurement and modelling of the torsional damping levels of a back-to-back gearbox rig. The aims of the investigation were to experimentally measure and analyse modal damping levels for the first nine torsional natural frequencies; to optimize damping parameters for modelling and to assess any limitations of the models for future work. Standard signal processing methods were used to determine modal damping levels from measured torsional frequency responses, with good confidence in the results. A damping sensitivity analysis for the two frequency domain receptance (FDR) models was used to determine optimum damping parameter values. Damping levels for six of nine natural frequencies were well matched with the experimental data. Discrepancies at other frequencies were attributed mainly to torsional-transverse coupling, present in the rig but not the model. Analysis of results for the ninth natural frequency determined a very low level of damping for the gearbox. It was also concluded that the model parameters may be used with confidence in a time domain receptance model for future investigations related to the test gearbox damping.

scholarly journals Spatial and Temporal Transferability of a Distributed Energy-Balance Glacier Melt Model

2011 ◽  
Vol 24 (5) ◽  
pp. 1480-1498 ◽  
Author(s):  
Andrew H. MacDougall ◽  
Gwenn E. Flowers
Keyword(s):  
Energy Balance ◽  
Yukon Territory ◽  
Model Parameters ◽  
Distributed Energy ◽  
Meteorological Forcing ◽  
Model Parameter ◽  
Model Transferability ◽  
Space And Time ◽  
Surface Ablation ◽  
Parameter Values

Abstract Modeling melt from glaciers is crucial to assessing regional hydrology and eustatic sea level rise. The transferability of such models in space and time has been widely assumed but rarely tested. To investigate melt model transferability, a distributed energy-balance melt model (DEBM) is applied to two small glaciers of opposing aspects that are 10 km apart in the Donjek Range of the St. Elias Mountains, Yukon Territory, Canada. An analysis is conducted in four stages to assess the transferability of the DEBM in space and time: 1) locally derived model parameter values and meteorological forcing variables are used to assess model skill; 2) model parameter values are transferred between glacier sites and between years of study; 3) measured meteorological forcing variables are transferred between glaciers using locally derived parameter values; 4) both model parameter values and measured meteorological forcing variables are transferred from one glacier site to the other, treating the second glacier site as an extension of the first. The model parameters are transferable in time to within a <10% uncertainty in the calculated surface ablation over most or all of a melt season. Transferring model parameters or meteorological forcing variables in space creates large errors in modeled ablation. If select quantities (ice albedo, initial snow depth, and summer snowfall) are retained at their locally measured values, model transferability can be improved to achieve ≤15% uncertainty in the calculated surface ablation.

scholarly journals Analysis of the spatial variation in the parameters of the SWAT model with application in Flanders, Northern Belgium

2004 ◽  
Vol 8 (5) ◽  
pp. 931-939 ◽  
Author(s):  
G. Heuvelmans ◽  
B. Muys ◽  
J. Feyen
Keyword(s):  
Stream Flow ◽  
Hydrological Model ◽  
Swat Model ◽  
Single Parameter ◽  
Model Parameters ◽  
Study Region ◽  
Entire Study ◽  
Time Periods ◽  
Parameter Values ◽  
Parameter Approach

Abstract. Operational applications of a hydrological model often require the prediction of stream flow in (future) time periods without stream flow observations or in ungauged catchments. Data for a case-specific optimisation of model parameters are not available for such applications, so parameters have to be derived from other catchments or time periods. It has been demonstrated that for applications of the SWAT in Northern Belgium, temporal transfers of the parameters have less influence than spatial transfers on the performance of the model. This study examines the spatial variation in parameter optima in more detail. The aim was to delineate zones wherein model parameters can be transferred without a significant loss of model performance. SWAT was calibrated for 25 catchments that are part of eight larger sub-basins of the Scheldt river basin. Two approaches are discussed for grouping these units in zones with a uniform set of parameters: a single parameter approach considering each parameter separately and a parameter set approach evaluating the parameterisation as a whole. For every catchment, the SWAT model was run with the local parameter optima, with the average parameter values for the entire study region (Flanders), with the zones delineated with the single parameter approach and with the zones obtained by the parameter set approach. Comparison of the model performances of these four parameterisation strategies indicates that both the single parameter and the parameter set zones lead to stream flow predictions that are more accurate than if the entire study region were treated as one single zone. On the other hand, the use of zonal average parameter values results in a considerably worse model fit compared to local parameter optima. Clustering of parameter sets gives a more accurate result than the single parameter approach and is, therefore, the preferred technique for use in the parameterisation of ungauged sub-catchments as part of the simulation of a large river basin. Keywords: hydrological model, regionalisation, parameterisation, spatial variability

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