Flexible Profile Compact Thermal Models for Practical Geometries

2007 ◽  
Vol 129 (3) ◽  
pp. 256-259 ◽  
Author(s):  
Mohamed-Nabil Sabry
Keyword(s):  
A Priori ◽  
A Priori Estimate ◽  
Operating Conditions ◽  
Heat Sources ◽  
Order Of Accuracy ◽  
New Approach ◽  
Thermal Models ◽  
Volumetric Heating ◽  
2D Structure ◽  
Node Size

Recent advances in compact thermal models have led to the emergence of a new concept allowing models to be created at any desired order of accuracy. Traditionally, increasing precision was attained by increasing the number of nodes. This strategy faces many problems; in particular, for the case of multiple heat sources (MCM) and∕or stacked dies, because different operating conditions will lead to different temperature and heat flux profiles that will require different node partitioning in order to be matched. In fact, classical approaches face a difficulty in selecting appropriate node size and position, as well as the inability to provide an a priori estimate of the number of nodes needed. The new concept is based on the use of a flexible profile to account for different possible uses of the model. In particular, it can deal with different patterns of heat generation encountered in MCM and stacked dies, and hence it is truly boundary conditions independent. Moreover, the new approach gives access to the tangential temperature gradient. This valuable information for designers in order to assess reliability cannot be predicted by classical compact model approaches. The concept was presented earlier for a simple rectangular 2D structure with surface heating (2004, 10th THERMINIC Conference, pp. 273–280). In this paper, the concept will be generalized to 3D parallelepiped boxes with both surface and∕or volumetric heating. The second achievement is the possibility to deal with geometries that can be decomposed into boxes.

High Precision Compact Thermal Models

2005 ◽  
Author(s):  
Mohamed-Nabil Sabry
Keyword(s):  
A Priori ◽  
A Priori Estimate ◽  
Compact Model ◽  
Heat Sources ◽  
New Approach ◽  
Thermal Models ◽  
Common Structure ◽  
Accuracy Level ◽  
Original Approach ◽  
Node Size

This paper is a step towards building a more complete theory of compact thermal models, in which their common structure is highlighted and hence the sources of errors inevitably present in any compact model clearly revealed. This approach is further extended in order to propose an original approach to attain any desired level of precision. Different methods already proposed by other authors can all benefit from the approach proposed here in order to raise accuracy level. Traditionally, increasing precision was attained by increasing the number of nodes. This strategy faces many problems, like the difficulty to select node size and position, as well as the inability to provide an a priori estimate of the number of nodes needed. In particular, this strategy fails in the case of multiple heat sources (MCM). The actual approach relies on a “flexible” pattern model that allows us to avoid such problems. Moreover, the new approach gives access to the tangential temperature gradient. This valuable information for designers in order to assess reliability can not be predicted by classical compact model approaches.

scholarly journals Virtual Sensor for Calibration of Thermal Models of Machine Tools

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Alexander Dementjev ◽  
Burkhard Hensel ◽  
Klaus Kabitzsch ◽  
Bernd Kauschinger ◽  
Steffen Schroeder
Keyword(s):  
Machine Tools ◽  
Model Calibration ◽  
Thermal Deformation ◽  
A Priori ◽  
High Dimensional ◽  
Effective Solution ◽  
Adequate Model ◽  
New Approach ◽  
Thermal Models ◽  
Industrial Manufacturing

Machine tools are important parts of high-complex industrial manufacturing. Thus, the end product quality strictly depends on the accuracy of these machines, but they are prone to deformation caused by their own heat. The deformation needs to be compensated in order to assure accurate production. So an adequate model of the high-dimensional thermal deformation process must be created and parameters of this model must be evaluated. Unfortunately, such parameters are often unknown and cannot be calculated a priori. Parameter identification during real experiments is not an option for these models because of its high engineering and machine time effort. The installation of additional sensors to measure these parameters directly is uneconomical. Instead, an effective calibration of thermal models can be reached by combining real and virtual measurements on a machine tool during its real operation, without additional sensors installation. In this paper, a new approach for thermal model calibration is presented. The expected results are very promising and can be recommended as an effective solution for this class of problems.

Compact Thermal Models: A Global Approach

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Mohamed-Nabil Sabry ◽  
Hossam Saleh Abdelmeguid
Keyword(s):  
Degrees Of Freedom ◽  
Quantitative Description ◽  
Operating Conditions ◽  
Electronic Systems ◽  
New Approach ◽  
Thermal Models ◽  
Cooling Devices ◽  
Precision Level ◽  
Access To Data ◽  
Level Of Analysis

The construction and usage of compact thermal models (CTMs), for the thermal analysis as well as the design of cooling devices for electronic systems, are reviewed. These models have many advantages over the so called detailed models based on 3D simulations, mainly being a convenient and simple quantitative description of the modeled object, when constructional details are either unavailable or too detailed to be of use at the desired level of analysis. However, CTMs have manifested some deficiencies in many cases, in particular, multiple chip modules (MCM) and stacked dies. The opposite approach, detailed modeling, is more reliable, although extremely heavy. A new approach is proposed that solves this dilemma by bridging the gap between compact and detailed models. While retaining all advantages of CTMs, i.e., having a limited number of degrees of freedom and not requiring detailed constructional features, it can attain any required precision level depending on the degree of complexity adopted. It gives reliable results covering all operating conditions including MCM and stacked dies. Moreover, it gives access to data on surface temperature gradients that were never obtained before by compact models and are highly important for reliability issues.

FINITE-DIFFERENCE METHODS FOR PROBLEM OF CONJUGATION OF HYPERBOLIC AND PARABOLIC EQUATIONS

2000 ◽  
Vol 10 (03) ◽  
pp. 361-377 ◽  
Author(s):  
ALEXANDER A. SAMARSKII ◽  
VICTOR I. KORZYUK ◽  
SERGEY V. LEMESHEVSKY ◽  
PETR P. MATUS
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
A Priori ◽  
Finite Difference Methods ◽  
A Priori Estimate ◽  
Stability And Convergence ◽  
Priori Estimate ◽  
Order Of Accuracy ◽  
Spatial Operator ◽  
The Given

A problem of conjugation of hyperbolic and parabolic equations in domain with moving boundaries is considered. Existence and uniqueness of a strong solution of the given problem are proved. A priori estimate for operator-difference scheme with non-self-adjoint spatial operator is obtain. Homogeneous difference scheme with constant weights for the conjugation problem is constructed. Moreover, consistency conditions are approximated with the second-order of accuracy with respect to spatial variables. Stability and convergence of the suggested scheme are investigated.

scholarly journals New solvability condition of 2-d nonlocal boundary value problem for Poisson’s operator on rectangle

2021 ◽  
Vol 2021 (1) ◽  
pp. 12-28
Author(s):  
Dovlet M. Dovletov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
A Priori Estimate ◽  
Rectangular Domain ◽  
Nonlocal Boundary Value Problem ◽  
Order Of Accuracy ◽  
Solvability Conditions ◽  
Accuracy Difference

Abstract Differential and difference interpretations of a nonlocal boundary value problem for Poisson’s equation in open rectangular domain are studied. New solvability conditions are obtained in respect of existence, uniqueness and a priori estimate of the classical solution. Second order of accuracy difference scheme is presented.

Mathematical Knowledge and the Interplay of Practices

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Philosophy Of Mathematics ◽  
Advanced Mathematics ◽  
New Approach ◽  
Agent Based ◽  
Epistemology Of Mathematics ◽  
Actual Experience ◽  
Elementary Math ◽  
Mathematical Tradition

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, the book uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, the book shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. It argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. It demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, the book challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Survey Data Quality in Analyzing Harmonized Indicators of Protest Behavior: A Survey Data Recycling Approach

2021 ◽  
pp. 000276422110216
Author(s):  
Kazimierz M. Slomczynski ◽  
Irina Tomescu-Dubrow ◽  
Ilona Wysmulek
Keyword(s):  
Data Processing ◽  
Data Quality ◽  
Survey Data ◽  
A Priori ◽  
Data Sets ◽  
New Approach ◽  
Survey Quality ◽  
Survey Error ◽  
Ex Post ◽  
The Impact

This article proposes a new approach to analyze protest participation measured in surveys of uneven quality. Because single international survey projects cover only a fraction of the world’s nations in specific periods, researchers increasingly turn to ex-post harmonization of different survey data sets not a priori designed as comparable. However, very few scholars systematically examine the impact of the survey data quality on substantive results. We argue that the variation in source data, especially deviations from standards of survey documentation, data processing, and computer files—proposed by methodologists of Total Survey Error, Survey Quality Monitoring, and Fitness for Intended Use—is important for analyzing protest behavior. In particular, we apply the Survey Data Recycling framework to investigate the extent to which indicators of attending demonstrations and signing petitions in 1,184 national survey projects are associated with measures of data quality, controlling for variability in the questionnaire items. We demonstrate that the null hypothesis of no impact of measures of survey quality on indicators of protest participation must be rejected. Measures of survey documentation, data processing, and computer records, taken together, explain over 5% of the intersurvey variance in the proportions of the populations attending demonstrations or signing petitions.

Instrumental Means for Managing the Rational Behavior of Self-Organizing Autonomous Intelligent Agents

2021 ◽  
Vol 22 (4) ◽  
pp. 171-180
Author(s):  
V. B. Melekhin ◽  
M. V. Khachumov
Keyword(s):  
Intelligent Agents ◽  
Environmental Changes ◽  
A Priori ◽  
Operating Conditions ◽  
Basic Principles ◽  
Purposeful Behavior ◽  
Problem Solvers ◽  
Boundary Estimates ◽  
Self Learning ◽  
Self Organizing

We formulate the basic principles of constructing a sign-signal control for the expedient behavior of autonomous intelligent agents in a priori undescribed conditions of a problematic environment. We clarify the concept of a self-organizing autonomous intelligent agent as a system capable of automatic goal-setting when a certain type of conditional and unconditional signal — signs appears in a problem environment. The procedures for planning the expedient behavior of autonomous intelligent agents have been developed, that imitate trial actions under uncertainty in the process of studying the regularities of transforming situations in a problem environment, which allows avoiding environmental changes in the process of self-learning that are not related to the achievement of a given goal. Boundary estimates of the proposed procedures complexity for planning expedient behavior are determined, confirming the possibility of their effective implementation on the on-board computer of the automatic control system for the expedient activity of autonomous intelligent agents. We carry out an imitation on a personal computer of the proposed procedures for planning purposeful behavior, confirming the effectiveness of their use to build intelligent problem solvers for autonomous intelligent agents in order to endow them with the ability to adapt to a priori undescribed operating conditions. The main types of connections between various conditional and unconditional signal — signs of a problem environment are structured, which allows autonomous intelligent agents to adapt to complex a priori undescribed and unstable conditions of functioning.

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