What about the relevance of the diffusion parameters identified in the case of incomplete Fickian and non-Fickian kinetics?

2018 ◽  
Vol 53 (11) ◽  
pp. 1555-1565
Author(s):  
Julie Cocaud ◽  
Amandine Célino ◽  
Sylvain Fréour ◽  
Frédéric Jacquemin
Keyword(s):  
Reference Values ◽  
Model Identification ◽  
Water Concentration ◽  
Least Square Method ◽  
Least Square ◽  
Data Sets ◽  
Data Set ◽  
Diffusion Parameters ◽  
Alternative Approach ◽  
Truncation Threshold

The aim of this work is to study the relevance of the diffusion parameters identified on kinetics whose saturation levels are unknown. Two types of diffusion kinetics have been considered: a Fickian and a non-Fickian kinetics. Numerical experiments, based on the generation of noisy data corresponding to reference values of diffusion parameters, have been carried out. The two models used in this study are Fick's model and the «Dual-Fick» model. Identification procedures were then applied on these data sets, truncated at different critical times. In the specific case of Dual Fick kinetics, the classical least square method was compared to an alternative approach based on the piecewise analysis of the shape of the diffusion curves. The identified parameters may deviate significantly from the expected reference values when the truncation threshold of the data set precedes the steady state. Also, these inaccurate parameters impact the predictions of global water uptake, water concentration profiles and stresses gradients through the thickness of the sample.

scholarly journals Data approximation using Lotka-Volterra models and a software minimization function

2019 ◽  
Vol 15 (2) ◽  
pp. 5-14
Author(s):  
M. Fečkan ◽  
J. Pačuta
Keyword(s):  
Mathematical Models ◽  
Historical Data ◽  
Least Square Method ◽  
Least Square ◽  
Data Set ◽  
Data Approximation ◽  
Standard Methods ◽  
Volterra Models ◽  
Coefficient Estimation

Abstract In recent years, a lot of effort has been put into finding suitable mathematical models that fit historical data set. Such models often include coefficients and the accuracy of data approximation depends on them. So the goal is to choose the unknown coefficients to achieve the best possible approximation of data by the corresponding solution of the model. One of the standard methods for coefficient estimation is the least square method. This can provide us data approximation but it can also serve as a starting method for further minimizations such as Matlab function fminsearch.

Interdiffusion of major elements at 1 atmosphere between natural shoshonitic and rhyolitic melts

2019 ◽  
Vol 104 (10) ◽  
pp. 1444-1454 ◽  
Author(s):  
Diego González-García ◽  
Francesco Vetere ◽  
Harald Behrens ◽  
Maurizio Petrelli ◽  
Daniele Morgavi ◽  
...  
Keyword(s):  
Water Concentration ◽  
Major Elements ◽  
Data Sets ◽  
Uphill Diffusion ◽  
Data Set ◽  
Strong Linear Correlation ◽  
Binary Diffusion Coefficients ◽  
Diffusive Fluxes ◽  
Couple Method ◽  
Compensation Law

Abstract The diffusive mass exchange of eight major elements (Si, Ti, Al, Fe, Mg, Ca, Na, and K) between natural, nominally dry shoshonitic and rhyolitic melts was studied at atmospheric pressure and temperatures between 1230 and 1413 °C using the diffusion couple method. For six elements, effective binary diffusion coefficients were calculated by means of a concentration-dependent method to obtain an internally consistent data set. Among these components, the range in diffusivities is restricted, pointing to a coupling of their diffusive fluxes. We find that the calculated diffusivities fit well into the Arrhenius relation, with activation energies (Ea) ranging from 258 to 399 kJ/mol in rhyolitic (70 wt% SiO2) melt and from 294 to 426 kJ/mol in the latitic melt (58 wt% SiO2). Ti shows the lowest Ea, while Si, Fe, Mg, Ca, and K have a similar value. A strong linear correlation is observed between logD0 and Ea, confirming the validity of the compensation law for this system. Uphill diffusion is observed in Al in the form of a concentration minimum in the rhyolitic side of the couple, (at ca. 69 wt% SiO2), and in Na indicated by a maximum in the shoshonitic side (ca. 59 wt% SiO2). Fe shows weak signs of uphill diffusion, possibly due to the contribution of ferric iron. The data presented here extend the database of previously published diffusivities in the shoshonite-rhyolite system (González-García et al. 2017) toward the water-free end and allows us to better constrain the water-dependence of major element diffusion at very low water concentrations. Combining both data sets, we find that logD is proportional to the square root of water concentration for a range between 0 and 2 wt% H2O. These results are of particular interest in the study of mass transfer phenomena in alkaline volcanic systems.

Nonlinear Model Identification From Multiple Data Sets Using an Orthogonal Forward Search Algorithm

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Ping Li ◽  
Hua-Liang Wei ◽  
Stephen A. Billings ◽  
Michael A. Balikhin ◽  
Richard Boynton
Keyword(s):  
Search Algorithm ◽  
Model Identification ◽  
Identification Problem ◽  
Data Sets ◽  
Nonlinear Dynamic Model ◽  
Data Set ◽  
Multiple Data ◽  
Orthogonal Search ◽  
Data Points ◽  
Multiple Data Sets

A basic assumption on the data used for nonlinear dynamic model identification is that the data points are continuously collected in chronological order. However, there are situations in practice where this assumption does not hold and we end up with an identification problem from multiple data sets. The problem is addressed in this paper and a new cross-validation-based orthogonal search algorithm for NARMAX model identification from multiple data sets is proposed. The algorithm aims at identifying a single model from multiple data sets so as to extend the applicability of the standard method in the cases, such as the data sets for identification are obtained from multiple tests or a series of experiments, or the data set is discontinuous because of missing data points. The proposed method can also be viewed as a way to improve the performance of the standard orthogonal search method for model identification by making full use of all the available data segments in hand. Simulated and real data are used in this paper to illustrate the operation and to demonstrate the effectiveness of the proposed method.

scholarly journals Fixed part of the model for breeding value estimation in pigs based on litter size

2007 ◽  
Vol 23 (5-6-1) ◽  
pp. 429-436
Author(s):  
D. Radojkovic ◽  
M. Petrovic ◽  
M. Mijatovic ◽  
C. Radovic
Keyword(s):  
Linear Regression ◽  
Fixed Effects ◽  
Statistical Significance ◽  
Least Square Method ◽  
Least Square ◽  
Breeding Value ◽  
Data Sets ◽  
Value Analysis ◽  
Applied Model ◽  
The Republic

The goal of this paper was to investigate the effect of various fixed effects on the number of born alive piglets in litter (NBA), based on results of Swedish Landrace sow fertility on three farms in Serbia, in order to determine the best adapted model for assessing genetic parameters and breeding value. Analysis of phenotipic variability of the NBA of Swedish Landrace sows was carried out based on fertility results on three swine farms (A, B and C) in the Republic of Serbia. Data sets encompassed reproduction indicators for 2803 (A), 1826 (B) and 2235 (C) sows, i.e. their 11014, 6757 and 8452 litters, respectively. For this analysis was used fix model of least square method which includes fixed effects of farrowing number, season of conception shown as combination of year and month, litter genotype, duration of previous period from weaning to conception, effect of sow age at farrowing like quadratic regression nested within farrowing number and linear regression influence of duration of previous lactation. The average NBA was within the interval from 9.13 (A) to 9.76 piglets (B and C). The monitored trait statistically highly significantly (p<0.001) varied under the effect of all systematic factors encompassed by the applied model, regardless of the source of analyzed data, Only the linear regression effect of duration of previous lactation for farm B was assessed as having lower statistical significance (p<0.05).

scholarly journals Estimation of Informal Sector of the Nigerian Construction Industry

2020 ◽  
pp. 203-208
Author(s):  
Ojo O. J. ◽  
Yusuf B. A. ◽  
Aremu J. A.
Keyword(s):  
Construction Industry ◽  
Informal Sector ◽  
Instrumental Variable ◽  
Value Added ◽  
Least Square Method ◽  
Cement Industry ◽  
Least Square ◽  
Pool Data ◽  
Time Series Regression ◽  
Data Set

The study estimated the output of informal sector of the Nigerian Cement Industry through the consumption of cement by the Nigerian Construction industry. The research was conducted using secondary data. The study adopted the statistical model of informal sector estimation, Nigeria construction industry being cement intensive, cement consumption approach was used for the estimation of the informal sector of the industry by using annual cement consumption as an independent variable against the annual construction output in a time series regression analysis, treating the informal sector output as an omitted variable in the ordinary least square method of estimation. Annual value added tax (VAT) pool data set was chosen as an instrumental variable. Using the instrumental variable method of estimation, the informal sector proportion of the Nigeria construction industry was therefore estimated. The study concluded that the informal sector of the Nigerian construction industry is 4.07 percent of the industry's output.

scholarly journals Local magnitude scale in Slovenia

2013 ◽  
Vol 34 ◽  
pp. 23-28 ◽  
Author(s):  
J. Bajc ◽  
Ž. Zaplotnik ◽  
M. Živčić ◽  
M. Čarman
Keyword(s):  
Vertical Component ◽  
Large Data ◽  
Least Square Method ◽  
Least Square ◽  
Magnitude Scale ◽  
Local Magnitude ◽  
Data Set ◽  
Seismic Stations ◽  
Short Period ◽  
Environment Agency

Abstract. In the paper a calibration study of the local magnitude scale in Slovenia is presented. The Seismology and Geology Office of the Slovenian Environment Agency routinely reports the magnitudes MLV of the earthquakes recorded by the Slovenian seismic stations. The magnitudes are computed from the maximum vertical component of the ground velocity with the magnitude equation that was derived some thirty years ago by regression analysis of the magnitudes recorded by a Wood-Anderson seismograph in Trieste and a short period seismograph in Ljubljana. In the study the present single magnitude MLV equation is replaced by a general form of the Richter local magnitude MWA equation. The attenuation function and station-component corrections that compensate the local effects near seismic stations are determined from the synthetic Wood-Anderson seismograms of a large data set by iterative least-square method. The data set used consists of approximately 18 000 earthquakes during a period of 14 yr, each digitally recorded on up to 29 stations. The derived magnitude equation is used to make the final comparison between the new MWA magnitudes and the routinely calculated MLV magnitudes. The results show good overall accordance between both magnitude equations. The main advantage of the introduction of station-component corrections is the reduced uncertainty of the local magnitude that is assigned to a certain earthquake.

Automatic/interactive bead alignment in electron tomographic image processing

1994 ◽  
Vol 52 ◽  
pp. 932-933
Author(s):  
Weiping Liu ◽  
Jennifer Fung ◽  
Craig Abbey ◽  
John W. Sedat ◽  
David A. Agard
Keyword(s):  
Least Square ◽  
Data Sets ◽  
Alignment Method ◽  
Coordinate Systems ◽  
Data Set ◽  
Reconstruction Process ◽  
Least Square Fitting ◽  
Set Up ◽  
Digital Projection ◽  
The Relationship

In the electron tomographic (EM) reconstruction process the mutual alignment between projections of different view angles is a crucial step. The routinely used alignment method is based on fiducial markers': a single-axis tilt projection series is collected with gold particles distributed on the specimen, the positions of high density gold beads on the projections are found, and the relationship between the specimen and the digital projection coordinate systems is determined from least-square fitting these found bead positions. There are four alignment parameters for each projection: two in shifts, one in in-plane rotation, and one in magnification. In the threedimensional studies of subcellular biological structures, we routinely collect data sets of more than 100 projections in the tilt range of ±75 ° with our automated EM set-up. Normally around 10 bead positions are used on each projection to achieve the alignment. Bead alignment used to be a laborious task since approximately 1000 bead positions need to be hand-picked for each data set.

scholarly journals Least Squares Consensus for Matching Local Features

Information ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 275
Author(s):  
Qingming Zhang ◽  
Buhai Shi ◽  
Haibo Xu
Keyword(s):  
Least Squares ◽  
Order Statistics ◽  
Random Sampling ◽  
Sampling Methods ◽  
Least Square Method ◽  
Least Square ◽  
Nearest Neighbour ◽  
Data Set ◽  
Alternative Scheme ◽  
New Approach

This paper presents a new approach to estimate the consensus in a data set. Under the framework of RANSAC, the perturbation on data has not been considered sufficiently. We analysis the computation of homography in RANSAC and find that the variance of its estimation monotonically decreases when the size of sample increases. From this result, we carry out an approach which can suppress the perturbation and estimate the consensus set simultaneously. Different from other consensus estimators based on random sampling methods, our approach builds on the least square method and the order statistics and therefore is an alternative scheme for consensus estimation. Combined with the nearest neighbour-based method, our approach reaches higher matching precision than the plain RANSAC and MSAC, which is shown in our simulations.

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