scholarly journals Technology of Balanced Identification for Selection of Pine Transpiration Mathematical Model

2019 ◽  
Vol 14 (2) ◽  
pp. 665-682
Author(s):  
A.V. Sokolov ◽  
V.K. Bolondinsky ◽  
V.V. Voloshinov
Keyword(s):  
Mathematical Model ◽  
Cross Validation ◽  
Quantitative Measure ◽  
Unknown Parameters ◽  
Current Implementation ◽  
Modeling Errors ◽  
Cross Validation Error ◽  
Data Source ◽  
Balanced Optimization ◽  
Selection Of

The application of numerical technology for evaluation the correspondence of a mathematical model and experimental data via the balanced (optimization) identification method is demonstrated with comparing various models of pine transpiration. A quantitative measure of the model evaluation is the cross-validation error. Current implementation of the technology allow the researcher to formulate the computing task in a text file, which contains: mathematical model formulas (including differential and/or integration equations); declarations of parameters and/or functions to be identified; data source (with experimental measurements) and additional settings of the numerical method. As a result, the software package returns unknown parameters, functions, and modeling errors. This technology is successfully used to various models in biology, medicine, physics, etc.

DIFFERENTIAL EQUATIONS FOR TRAIN STARTING WITH ELASTIC CONNECTIONS

2021 ◽  
Vol 2 ◽  
pp. 18-26
Author(s):  
I.P. POPOV
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Friction Force ◽  
Static Friction ◽  
Longitudinal Vibrations ◽  
Maximum Tension ◽  
Inert Mass ◽  
The Moment ◽  
Elastic Couplings ◽  
Selection Of

The starting mode for the train is the most difficult. An effective method of pulling is the selection of coupling clearances. In this case, the cars are set in motion sequentially and the inert mass, as well as the static friction force immediately at the moment of starting, are minimal. This method has two significant drawbacks - a small fixed value of the gaps in the couplings and the shock nature of the impulse transfer. These disadvantages can be avoided by using elastically deformable couplings. The aim of this work is to construct a mathematical model of "easy" starting of a train with elastic couplings. The softening of the train start-off mode is essentially due to the replacement of the simultaneous start-off of the sections with alternate ones. To exclude longitudinal vibrations of the composition, after reaching the maximum tension of the coupling, the possibility of its harmonic compression should be mechanically blocked.

scholarly journals Analysis of the Modified Construction of the Column Mechanism MacPherson

2018 ◽  
Vol 19 (11) ◽  
pp. 41-44
Author(s):  
Marek Kwietniewski ◽  
Tadeusz Bil
Keyword(s):  
Mathematical Model ◽  
Steering Wheel ◽  
Passenger Cars ◽  
Proper Selection ◽  
Front Suspension ◽  
Change Of Direction ◽  
Partial Elimination ◽  
Selection Of

The McPherson column name comes from the inventor of this Earle S. MacPherson solution, which was first manufactured at the Ford plant in 1949. This is one of the most commonly used types of front suspension in popular passenger cars. The advantage of this type of suspension is a compact construction, but the disadvantage is. The influence of the damping motion on the position of the steering wheel may result in an unintentional change of direction of travel. At the same time, there is a slight additional tilt of the wheels when the "spring" movement. In the proposed solution, partial elimination of this type of incorrectness is proposed by changing the type of connection of the steering rod end to the steering wheels of the vehicle. The introduced change consists in replacing one of the spherical joints in these joints into two rotary joints. Such a change introduces a mathematical model describing the behavior of the suspension under the influence of the depreciation of additional parameters. Proper selection of these parameters allows for significant reduction of unnecessary direction changes during driving. The described model of the structure of the mechanism allows to analyze the influence of all its dimensions on the selected parameters of the behavior of the wheels during the ride, resulting from the movement of the suspension and steering.

Bayesian Model Assessment and Comparison Using Cross-Validation Predictive Densities

2002 ◽  
Vol 14 (10) ◽  
pp. 2439-2468 ◽  
Author(s):  
Aki Vehtari ◽  
Jouko Lampinen
Keyword(s):  
Expected Utility ◽  
Cross Validation ◽  
Monte Carlo Sampling ◽  
Point Estimate ◽  
Model Assessment ◽  
Predictive Densities ◽  
Fold Cross Validation ◽  
Selection Of ◽  
Natural Way ◽  
Real World Problems

In this work, we discuss practical methods for the assessment, comparison, and selection of complex hierarchical Bayesian models. A natural way to assess the goodness of the model is to estimate its future predictive capability by estimating expected utilities. Instead of just making a point estimate, it is important to obtain the distribution of the expected utility estimate because it describes the uncertainty in the estimate. The distributions of the expected utility estimates can also be used to compare models, for example, by computing the probability of one model having a better expected utility than some other model. We propose an approach using cross-validation predictive densities to obtain expected utility estimates and Bayesian bootstrap to obtain samples from their distributions. We also discuss the probabilistic assumptions made and properties of two practical cross-validation methods, importance sampling and k-fold cross-validation. As illustrative examples, we use multilayer perceptron neural networks and gaussian processes with Markov chain Monte Carlo sampling in one toy problem and two challenging real-world problems.

The envelope method in the problem of choosing a rational composition of measuring instruments

2021 ◽  
pp. 68-72
Author(s):  
Il'ya A. Meshchikhin ◽  
Sergej S. Gavryushin
Keyword(s):  
Mathematical Model ◽  
Monitoring Systems ◽  
Measuring Instruments ◽  
Key Points ◽  
Envelope Method ◽  
Loaded State ◽  
The Mathematical Model ◽  
Selection Of ◽  
Rational Composition

As part of the development of monitoring systems for the operation of technical objects, the problem of improving the quality of monitoring systems for the loaded state is considered. Based on the analysis of the mathematical model of the structure and its loading, a methodology for the selection of measuring instruments was developed. The urgency of the problem of calculating substantiation of the choice of key points of the structure is shown, at which it is possible to measure deformations for the subsequent restoration of the existing loads with maximum accuracy. An approach based on the envelope method for determining the rational composition of measuring instruments for restoring the loads acting on the structure is stated.

Аpplication of the mathematical model of human torso for modeling abbreval influence in wound ballistics

2020 ◽  
Vol 22 (3) ◽  
pp. 132-139
Author(s):  
A. V. Denisov ◽  
M. D. Stepanov ◽  
N. A. Haraldin ◽  
A. V. Stepanov ◽  
A. I. Borovkov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Element Model ◽  
Mechanical Action ◽  
Calculation Model ◽  
Calculation Results ◽  
Automated Processing ◽  
Original Calculation ◽  
Using Data ◽  
The Mathematical Model ◽  
Selection Of

Abstract. In the work, a review of scientific articles on the behavior of tissues and organs of the human body under local mechanical effects on it, as well as a description of the physico-mechanical properties of biological materials. The selection of mechanical behavior for each biological material as part of a mathematical model of the human torso was carried out, its finite element model was created, validation experiments were modeled using data presented in the literature. An original calculation model of a human torso with a tuned interaction of organs with each other was developed. Contact interaction parameters are determined. The developed computational model of a human torso was verified based on data from open sources for an experiment with mechanical action by a cylindrical impactor. An algorithm for processing pressure and acceleration graphs has been implemented in order to obtain tolerance curves. A specialized modular program has been created for the automated processing of calculation results and the output of the main results. 42 numerical tests were carried out simulating the entry of a steel ball into each of 21 zones for power engineers of 40 and 80 J. According to the results of the tests for each organ, pressure and acceleration tolerance curves were obtained, animations of the behavior of organs under shock were created, visualization of the pressure field propagation in organs was obtained torso.

scholarly journals Understanding the suffering of a patient with an illness: signs, context and strategies

2012 ◽  
Vol 20 (3) ◽  
pp. 619-628 ◽  
Author(s):  
César Hueso Montoro ◽  
José Siles González ◽  
Manuel Amezcua ◽  
Candela Bonill de las Nieves ◽  
Sonia Pastor Montero ◽  
...  
Keyword(s):  
Social Network ◽  
Research Method ◽  
Primary Data ◽  
Secondary Research ◽  
Primary Data Source ◽  
Data Source ◽  
Multidimensional Process ◽  
Selection Of

The aim of this study is to understand the suffering of a patient with an illness, by using a secondary research method, that is, a qualitative meta-study. The primary data source of the meta-study includes "biographical reports". This project is based on a case study, in which the first-hand experiences of a patient with an illness were collected. The findings of the reports were compiled using the Archivos de la Memoria collection of the Index Foundation (Granada, Spain) and journals specialized in editing these materials. A selection of 20 biographical reports was targeted. The results of the meta-study show that suffering is a multidimensional process within a framework of ambiguous feelings. The suffering involves family and social network participation. Patients develop a range of strategies to overcome the illness. One of the effects is the fear of illness relapse or worsening.

The Existence of A Priori Distinctions Between Learning Algorithms

1996 ◽  
Vol 8 (7) ◽  
pp. 1391-1420 ◽  
Author(s):  
David H. Wolpert
Keyword(s):  
Cross Validation ◽  
Learning Algorithm ◽  
A Priori ◽  
Learning Algorithms ◽  
Loss Functions ◽  
Average Error ◽  
Quadratic Loss ◽  
Training Set ◽  
Natural Restriction ◽  
Cross Validation Error

This is the second of two papers that use off-training set (OTS) error to investigate the assumption-free relationship between learning algorithms. The first paper discusses a particular set of ways to compare learning algorithms, according to which there are no distinctions between learning algorithms. This second paper concentrates on different ways of comparing learning algorithms from those used in the first paper. In particular this second paper discusses the associated a priori distinctions that do exist between learning algorithms. In this second paper it is shown, loosely speaking, that for loss functions other than zero-one (e.g., quadratic loss), there are a priori distinctions between algorithms. However, even for such loss functions, it is shown here that any algorithm is equivalent on average to its “randomized” version, and in this still has no first principles justification in terms of average error. Nonetheless, as this paper discusses, it may be that (for example) cross-validation has better head-to-head minimax properties than “anti-cross-validation” (choose the learning algorithm with the largest cross-validation error). This may be true even for zero-one loss, a loss function for which the notion of “randomization” would not be relevant. This paper also analyzes averages over hypotheses rather than targets. Such analyses hold for all possible priors over targets. Accordingly they prove, as a particular example, that cross-validation cannot be justified as a Bayesian procedure. In fact, for a very natural restriction of the class of learning algorithms, one should use anti-cross-validation rather than cross-validation (!).

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