scholarly journals Spatial Flow-Field Approximation Using Few Thermodynamic Measurements—Part I: Formulation and Area Averaging

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Pranay Seshadri ◽  
Duncan Simpson ◽  
George Thorne ◽  
Andrew Duncan ◽  
Geoffrey Parks
Keyword(s):  
Field Approximation ◽  
Circumferential Direction ◽  
Temperature Measurements ◽  
Model Parameters ◽  
Spatial Average ◽  
Modeling Framework ◽  
Similar Temperature ◽  
Sparse Measurements ◽  
Flow Quantity ◽  
Selection Of

Abstract Our investigation raises an important question that is of relevance to the wider turbomachinery community: how do we estimate the spatial average of a flow quantity given finite (and sparse) measurements? This paper seeks to advance efforts to answer this question rigorously. In this paper, we develop a regularized multivariate linear regression framework for studying engine temperature measurements. As part of this investigation, we study the temperature measurements obtained from the same axial plane across five different engines yielding a total of 82 datasets. The five different engines have similar architectures and therefore similar temperature spatial harmonics are expected. Our problem is to estimate the spatial field in engine temperature given a few measurements obtained from thermocouples positioned on a set of rakes. Our motivation for doing so is to understand key engine temperature modes that cannot be captured in a rig or in computational simulations, as the cause of these modes may not be replicated in these simpler environments. To this end, we develop a multivariate linear least-squares model with Tikhonov regularization to estimate the 2D temperature spatial field. Our model uses a Fourier expansion in the circumferential direction and a quadratic polynomial expansion in the radial direction. One important component of our modeling framework is the selection of model parameters, i.e., the harmonics in the circumferential direction. A training-testing paradigm is proposed and applied to quantify the harmonics.

scholarly journals Inter-trial effects in priming of pop-out: Comparison of computational updating models

2021 ◽  
Vol 17 (9) ◽  
pp. e1009332
Author(s):  
Fredrik Allenmark ◽  
Ahu Gokce ◽  
Thomas Geyer ◽  
Artyom Zinchenko ◽  
Hermann J. Müller ◽  
...  
Keyword(s):  
Model Comparison ◽  
Response Times ◽  
Target Position ◽  
Preceding Trial ◽  
Target Color ◽  
Model Parameters ◽  
Target Feature ◽  
Modeling Framework ◽  
Trial Effect ◽  
Starting Point

In visual search tasks, repeating features or the position of the target results in faster response times. Such inter-trial ‘priming’ effects occur not just for repetitions from the immediately preceding trial but also from trials further back. A paradigm known to produce particularly long-lasting inter-trial effects–of the target-defining feature, target position, and response (feature)–is the ‘priming of pop-out’ (PoP) paradigm, which typically uses sparse search displays and random swapping across trials of target- and distractor-defining features. However, the mechanisms underlying these inter-trial effects are still not well understood. To address this, we applied a modeling framework combining an evidence accumulation (EA) model with different computational updating rules of the model parameters (i.e., the drift rate and starting point of EA) for different aspects of stimulus history, to data from a (previously published) PoP study that had revealed significant inter-trial effects from several trials back for repetitions of the target color, the target position, and (response-critical) target feature. By performing a systematic model comparison, we aimed to determine which EA model parameter and which updating rule for that parameter best accounts for each inter-trial effect and the associated n-back temporal profile. We found that, in general, our modeling framework could accurately predict the n-back temporal profiles. Further, target color- and position-based inter-trial effects were best understood as arising from redistribution of a limited-capacity weight resource which determines the EA rate. In contrast, response-based inter-trial effects were best explained by a bias of the starting point towards the response associated with a previous target; this bias appeared largely tied to the position of the target. These findings elucidate how our cognitive system continually tracks, and updates an internal predictive model of, a number of separable stimulus and response parameters in order to optimize task performance.

scholarly journals Особенности фазовой диаграммы полужестких бозонов на квадратной решетке

2021 ◽  
Vol 63 (9) ◽  
pp. 1361
Author(s):  
В.В. Конев ◽  
Ю.Д. Панов
Keyword(s):  
Mean Field ◽  
Hard Core ◽  
Field Approximation ◽  
Charge Ordering ◽  
Mean Field Approximation ◽  
New Order ◽  
Model Parameters ◽  
Local Correlation ◽  
The Mean ◽  
Limit Form

We investigated the phase diagrams of a system of charged semi-hardcore bosons in the mean-field approximation. It is shown that an increase in the local correlation parameter leads to the transformation of the phase diagram of the system from the form characteristic of hard-core bosons to the limit form with a parabolic dependence of the critical temperature of the charge ordering on the boson concentration. The evolution between these limiting cases depends on the ratio of the model parameters and is accompanied by various effects, including a change in the type of phase transition, the appearance of new order-order transitions, and the appearance of new critical points.

scholarly journals Selection of catchment descriptors for the physical similarity approach. Part II: Application

2013 ◽  
Vol 8 (No. 4) ◽  
pp. 186-194
Author(s):  
M. Heřmanovský ◽  
P. Pech
Keyword(s):  
Land Cover ◽  
A Priori ◽  
Model Parameters ◽  
Physical Similarity ◽  
Model Parameter ◽  
Soil Moisture Accounting ◽  
Estimated Parameters ◽  
Selection Of

This paper demonstrates an application of the previously published method for selection of optimal catchment descriptors, according to which similar catchments can be identified for the purpose of estimation of the Sacramento – Soil Moisture Accounting (SAC-SMA) model parameters for a set of tested catchments, based on the physical similarity approach. For the purpose of the analysis, the following data from the Model Parameter Estimation Experiment (MOPEX) project were taken: a priori model parameter sets used as reference values for comparison with the newly estimated parameters, and catchment descriptors of four categories (climatic descriptors, soil properties, land cover and catchment morphology). The inverse clustering method, with Andrews’ curves for a homogeneity check, was used for the catchment grouping process. The optimal catchment descriptors were selected on the basis of two criteria, one comparing different subsets of catchment descriptors of the same size (MIN), the other one evaluating the improvement after addition of another catchment descriptor (MAX). The results suggest that the proposed method and the two criteria used may lead to the selection of a subset of conditionally optimal catchment descriptors from a broader set of them. As expected, the quality of the resulting subset of optimal catchment descriptors is mainly dependent on the number and type of the descriptors in the broader set. In the presented case study, six to seven catchment descriptors (two climatic, two soil and at least two land-cover descriptors) were identified as optimal for regionalisation of the SAC-SMA model parameters for a set of MOPEX catchments.

scholarly journals The Bayesian Covariance Structure Model for Testlets

2020 ◽  
pp. 107699862094120
Author(s):  
Jean-Paul Fox ◽  
Jeremias Wenzel ◽  
Konrad Klotzke
Keyword(s):  
Random Effects ◽  
Random Effect ◽  
Covariance Structure ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Random Effects Model ◽  
Structure Model ◽  
Modeling Framework ◽  
Irt Models ◽  
Covariance Structure Model

Standard item response theory (IRT) models have been extended with testlet effects to account for the nesting of items; these are well known as (Bayesian) testlet models or random effect models for testlets. The testlet modeling framework has several disadvantages. A sufficient number of testlet items are needed to estimate testlet effects, and a sufficient number of individuals are needed to estimate testlet variance. The prior for the testlet variance parameter can only represent a positive association among testlet items. The inclusion of testlet parameters significantly increases the number of model parameters, which can lead to computational problems. To avoid these problems, a Bayesian covariance structure model (BCSM) for testlets is proposed, where standard IRT models are extended with a covariance structure model to account for dependences among testlet items. In the BCSM, the dependence among testlet items is modeled without using testlet effects. This approach does not imply any sample size restrictions and is very efficient in terms of the number of parameters needed to describe testlet dependences. The BCSM is compared to the well-known Bayesian random effects model for testlets using a simulation study. Specifically for testlets with a few items, a small number of test takers, or weak associations among testlet items, the BCSM shows more accurate estimation results than the random effects model.

scholarly journals Initial value selection of the model parameters in the curve fitting phase of the dynamic SPECT imaging

2018 ◽  
Vol 51 (27) ◽  
pp. 241-246
Author(s):  
Zsófia Barna ◽  
Ákos Szlávecz ◽  
Gábor Hesz ◽  
Péter Somogyi ◽  
Katalin Kovács ◽  
...  
Keyword(s):  
Curve Fitting ◽  
Spect Imaging ◽  
Model Parameters ◽  
Dynamic Spect ◽  
Initial Value ◽  
Selection Of

A Mathematical Model of Evaporation and Dissolution From Oil Spills on Ice, Land, Water and Under Ice

1975 ◽  
Vol 10 (1) ◽  
pp. 132-141 ◽  
Author(s):  
P.J. Leinonen ◽  
D. Mackay
Keyword(s):  
Mass Transfer ◽  
Crude Oil ◽  
Transfer Coefficient ◽  
Mass Transfer Coefficient ◽  
Oil Spills ◽  
Aquatic Toxicity ◽  
Eddy Diffusivity ◽  
Model Parameters ◽  
Evaporation Flux ◽  
Selection Of

Abstract Mathematical models are presented which quantify the processes of evaporation and dissolution of components of crude oil in three situations: a spill on water, a spill on ice, and a spill under ice cover in which the oil lies between the water and ice phases. Constant spill area is assumed. The evaporation flux is calculated using a mass transfer coefficient based on windspeed and spill dimensions. The dissolution flux can be calculated from two models, a mass transfer coefficient approach and an eddy diffusivity approach involving the integration of a set of partial differential equations in depth and time. The selection of model parameters is discussed. For the three physical situations, using a synthetic crude oil, results are presented giving the relative rates of evaporation and dissolution and the aqueous phase concentration of selected hydrocarbons. The implications of the results for clean-up technology and aquatic toxicity are discussed, particularly with regard to spills under ice.

Automatic selection of arterial input function in DSC-MRI measurements for calculation of brain perfusion parameters using parametric modelling

2018 ◽  
Vol 13 (6) ◽  
pp. 58
Author(s):  
Seweryn Lipiński ◽  
Renata Kalicka
Keyword(s):  
Arterial Input Function ◽  
Regression Function ◽  
Input Function ◽  
Model Parameters ◽  
Parametric Modelling ◽  
Automatic Selection ◽  
Dsc Mri ◽  
Mri Measurements ◽  
Selection Of

A novel method and algorithm of automatic selection of arterial input function (AIF) is presented and its efficiency is proved using exemplary DSC-MRI measurements. The method chooses AIF devoted to a particular purpose, which is calculation of perfusion parameters with the use of parametric modelling of DSC-MRI data. The quality of medical diagnosis made on the basis of perfusion parameters depends on the quality of these parameters, which in turn is determined by the quality of the AIF signal. The proposed algorithm combines physiological requirements for AIF with mathematical criteria. The choice of parametric approach, instead of black-box modelling, allows better understanding of the investigated system functioning, as model parameters may be credited with physical interpretation. Furthermore, using multi-compartmental model of the DSC-MRI data with AIF regression function in an exponential form, gives direct, analytic results concerning the basic descriptors of AIF. The method chooses candidates for AIF on the basis of the descriptors quality. This step allows rejecting measurements which do not fulfil fundamental requirements concerning AIF from the physiological point of view. As these requirements are met, the next criterion can be adopted, that is the quality of fitting the regression function to measurements. The final step is choosing the AIF for calculating perfusion parameters with the best accuracy, which is attainable thanks to implementing the AIF devoted particularly to parametric modelling.

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