Predicting Thermal System Performance and Estimating Parameters for Systems Burdened With Uncertainties and Noise Using Hierarchical Bayesian Inference

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
A. F. Emery ◽  
D. Bardot
Keyword(s):  
Heat Transfer ◽  
System Performance ◽  
Taylor Series Expansion ◽  
Heat Losses ◽  
Thermal System ◽  
Computing Power ◽  
Bayesian Hierarchical ◽  
Hierarchical Bayesian Inference ◽  
Transfer Problems ◽  
The Bayesian Approach

The precision of estimates of system performance and of parameters that affect the performance is often based upon the standard deviation obtained from the usual equation for the propagation of variances derived from a Taylor series expansion. With ever increasing computing power it is now possible to utilize the Bayesian hierarchical approach to yield improved estimates of the precision. Although quite popular in the statistical community, the Bayesian approach has not been widely used in the heat transfer and fluid mechanics communities because of its complexity and subjectivity. The paper develops the necessary equations and applies them to two typical heat transfer problems, measurement of conductivity with heat losses and heat transfer from a fin. Because of the heat loss the probability distribution of the conductivity is far from Gaussian. Using this conductivity distribution for the fin gives a very long tailed distribution for the heat transfer from the fin.

Predicting System Performance and Estimating Parameters for Systems Burdened With Uncertainties and Noise Using Bayesian Inference

2008 ◽  
Author(s):  
A. F. Emery ◽  
D. Bardot
Keyword(s):  
Heat Transfer ◽  
Bayesian Inference ◽  
System Performance ◽  
Taylor Series Expansion ◽  
Substantial Effect ◽  
Simple Problem ◽  
Transfer Coefficients ◽  
Strong Function ◽  
Heat Transfer Coefficients ◽  
Transfer Problems

The precision of estimates of system performance and parameter estimation is often based upon the standard deviation obtained from the usual equation for the propagation of variances derived from a Taylor series expansion [1]. With increasing computing power, it is often suggested that the more complex Bayesian inference approach may yield improved estimates of the precision. The Bayesian approach has not been widely used in the heat transfer and fluid mechanics communities. The paper develops the necessary equations and applies them to two typical heat transfer problems. It is shown that, even for the simple problem of heat loss from a fin, that the predicted performance can be a strong function of relatively minor changes in the heat transfer coefficients or the thermal conductivity and as a consequence that the form of the parameter variability has a substantial effect.

Full-Scale Bounds Estimation for the Nonlinear Transient Heat Transfer Problems with Interval Uncertainties

2021 ◽  
pp. 2150026
Author(s):  
Ruifei Peng ◽  
Haitian Yang ◽  
Yanni Xue
Keyword(s):  
Heat Transfer ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Transient Heat Transfer ◽  
High Fidelity ◽  
Interval Scale ◽  
Nonlinear Transient ◽  
Transfer Problems ◽  
Derivatives Of

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

Approximation and Identification of Fractional Systems

2005 ◽  
Author(s):  
Amel Benchellal ◽  
Thierry Poinot ◽  
Jean-Claude Trigeassou
Keyword(s):  
Heat Transfer ◽  
Spectral Band ◽  
State Space Model ◽  
Thermal System ◽  
Fractional Systems ◽  
Space Model ◽  
Proposed Model ◽  
Fractional Integrator ◽  
Fractional System ◽  
Transfer Problems

Heat transfer problems obey to diffusion phenomenon. They can be modelled with the help of fractional systems. The simulation of these particular systems is based on a fractional integrator where the non integer behaviour acts only on a limited spectral band. Starting from frequential considerations, a more general approximation of the fractional system is proposed in this communication. It makes it possible to define a state-space model for simulation of transients, and to carry out an output-error technique in order to estimate the parameters of the model. A real application on a thermal system is presented to illustrate the advantages of the proposed model.

scholarly journals Application of RC delay time for estimation of thermal properties

2021 ◽  
Vol 2116 (1) ◽  
pp. 012111
Author(s):  
Priyanka Jena ◽  
Rajesh Gupta
Keyword(s):  
Heat Transfer ◽  
Stainless Steel ◽  
Thermal Properties ◽  
Delay Time ◽  
Thermal System ◽  
Inverse Heat Transfer ◽  
Conductivity Range ◽  
Rc Circuit ◽  
Transfer Problems ◽  
Rc Delay

Abstract The analogy between the electrical and thermal system has been extensively used to solve different kinds of direct heat transfer problems. However, this analogy has not been explored much to obtain solutions of inverse heat transfer problems like estimation of thermal properties. This paper presents an approach of estimation of thermal properties using the correspondence between the thermal and electrical domains by exploiting the concept of RC delay time in the resistance-capacitance (RC) circuit. Simulations and experiments have been performed on stainless steel and glass samples to show the applicability of the proposed approach for materials belonging to different conductivity range.

Approximate Solution of a Class of Radiative Heat Transfer Problems

2000 ◽  
Vol 122 (3) ◽  
pp. 606-612 ◽  
Author(s):  
H. Qiao ◽  
Y. Ren ◽  
B. Zhang
Keyword(s):  
Heat Transfer ◽  
Approximate Solution ◽  
Series Expansion ◽  
Taylor Series ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Transfer Problems ◽  
Series Expansion Method

An approximate solution is presented for a class of radiative heat transfer problems within enclosures having black or diffuse-gray surfaces based on a modified Taylor series expansion method; such radiative transfer problems are generally represented by integral equations. The approach avoids use of any boundary/initial conditions associated with the original Taylor series expansion method and leads to an approximate solution in a simple closed form to the radiant integral equations, which can be computed straightforwardly on a modern personal computer using symbolic computing codes such as Maple. The method can be effectively and efficiently applied to deal with enclosures involving more than one or two surfaces, for which direct numerical integration may be subject to instability, or require an excessive amount of computation. The computed numerical results for representative thermal problems are in excellent agreement with those obtained by other numerical approaches. [S0022-1481(00)00203-6]

THE MODAL IDENTIFICATION METHOD IN NONLINEAR HEAT TRANSFER PROBLEMS

Equipment ◽  
2006 ◽  
Author(s):  
O. Balima ◽  
D. Petit ◽  
J. B. Saulnier ◽  
M. Girault ◽  
Y. Favennec
Keyword(s):  
Heat Transfer ◽  
Modal Identification ◽  
Identification Method ◽  
Nonlinear Heat Transfer ◽  
Transfer Problems
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