Parameter estimation of fractional systems application to heat transfer

2001 ◽  
Author(s):  
J. Lin ◽  
T. Poinot ◽  
J.-C. Trigeassou ◽  
P. Coirault
Keyword(s):  
Heat Transfer ◽  
Parameter Estimation ◽  
Fractional Systems

scholarly journals Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5073
Author(s):  
Farzad Mohebbi ◽  
Mathieu Sellier
Keyword(s):  
Heat Transfer ◽  
Parameter Estimation ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Inverse Analysis ◽  
Functional Form ◽  
Transfer Problem ◽  
Function Estimation ◽  
Inverse Heat Transfer ◽  
Inverse Heat Transfer Problem

This paper presents a numerical method to address function estimation problems in inverse heat transfer problems using parameter estimation approach without prior information on the functional form of the variable to be estimated. Using an inverse analysis, the functional form of a time-dependent heat transfer coefficient is estimated efficiently and accurately. The functional form of the heat transfer coefficient is assumed unknown and the inverse heat transfer problem should be treated using a function estimation approach by solving sensitivity and adjoint problems during the minimization process. Based on proposing a new sensitivity matrix, however, the functional form can be estimated in an accurate and very efficient manner using a parameter estimation approach without the need for solving the sensitivity and adjoint problems and imposing extra computational cost, mathematical complexity, and implementation efforts. In the proposed sensitivity analysis scheme, all sensitivity coefficients can be computed in only one direct problem solution at each iteration. In this inverse heat transfer problem, the body shape is irregular and meshed using a body-fitted grid generation method. The direct heat conduction problem is solved using the finite-difference method. The steepest-descent method is used as a minimization algorithm to minimize the defined objective function and the termination of the minimization process is carried out based on the discrepancy principle. A test case with three different functional forms and two different measurement errors is considered to show the accuracy and efficiency of the used inverse analysis.

Parameter Estimation of Fractional Systems: Application to the Modeling of a Lead-Acid Battery

2000 ◽  
Vol 33 (15) ◽  
pp. 983-988 ◽  
Author(s):  
Jun Lin ◽  
Thierry Poinot ◽  
Jean-Claude Trigeassou ◽  
Régis Ouvrard
Keyword(s):  
Parameter Estimation ◽  
Lead Acid Battery ◽  
Fractional Systems ◽  
Lead Acid

Complementary Experiments for Parameter Estimation in Heat Transfer Model

2021 ◽  
Author(s):  
Halak N. Mehta ◽  
Patnarin Benyathiar ◽  
Dharmendra K. Mishra ◽  
Michael Varney
Keyword(s):  
Heat Transfer ◽  
Parameter Estimation ◽  
Heat Transfer Model ◽  
Transfer Model

Inverse Modeling Techniques for Parameter Estimation in Engineering Simulation Models

2006 ◽  
Author(s):  
Srikanth Akkaram ◽  
Don Beeson ◽  
Harish Agarwal ◽  
Gene Wiggs
Keyword(s):  
Heat Transfer ◽  
Parameter Estimation ◽  
Inverse Modeling ◽  
Simulation Models ◽  
Posteriori Probability ◽  
Design System ◽  
Model Parameters ◽  
Input And Output ◽  
Ill Posed ◽  
Well Posed

Computational simulation models are extensively used in the development, design and analysis of an aircraft engine and its components to represent the physics of an underlying phenomenon. The use of such a model-based simulation in engineering often necessitates the need to estimate model parameters based on physical experiments or field data. This class of problems, referred to as inverse problems [1] in the literature can be classified as well-posed or ill-posed dependent on the quality (uncertainty) and quantity (amount) of data that is available to the engineer. The development of a generic inverse modeling solver in a probabilistic design system [2] requires the ability to handle diverse characteristics in various models. These characteristics include (a) varying fidelity in model accuracy with simulation times from a couple of seconds to many hours (b) models being black-box with the engineer having access to only the input and output (c) non-linearity in the model (d) time-dependent model input and output. The paper demonstrates methods that have been implemented to handle these features with emphasis on applications in heat transfer and applied mechanics. A practical issue faced in the application of inverse modeling for parameter estimation is ill-posedness that is characterized by instability and non-uniqueness in the solution. Generic methods to deal with ill-posedness include (a) model development, (b) optimal experimental design and (c) regularization methods. The purpose of this paper is to communicate the development and implementation of an inverse method that provides a solution for both well-posed as well as ill-posed problems using regularization based on the prior values of the parameters. In the case of an ill-posed problem, the method provides two solution schemes — a most probable solution closest to the prior, based on the singular value decomposition (SVD) and a maximum a-posteriori probability solution (MAP). The inverse problem is solved as a finite dimensional non-linear optimization problem using the SVD and/or MAP techniques tailored to the specifics of the application. The paper concludes with numerical examples and applications demonstrating the scope as well as validating the developed method. Engineering applications include heat transfer coefficient estimation for disk quenching in process modeling, material model parameter estimation, sparse clearance data modeling, steady state and transient engine high-pressure compressor heat transfer estimation.

scholarly journals Evaluation of the reliability of building energy performance models for parameter estimation

2019 ◽  
Author(s):  
  Жулиан Берже ◽  
  Денис Дутых
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Capacity ◽  
Parameter Estimation ◽  
Heat Transfer Coefficient ◽  
Diffusion Equation ◽  
Heat Diffusion ◽  
Unknown Parameters ◽  
Heat Diffusion Equation ◽  
The Heat Transfer Coefficient

The fidelity of a model relies both on its accuracy to predict the physical phenomena and its capability to estimate unknown parameters using observations. This article focuses on this second aspect by analyzing the reliability of two mathematical models proposed in the literature for the simulation of heat losses through building walls. The first one, named DF, is the classical heat diffusion equation combined with the DuFort-Frankel numerical scheme. The second is the so-called RC lumped approach, based on a simple ordinary differential equation to compute the temperature within the wall. The reliability is evaluated following a two stages method. First, samples of observations are generated using a pseudo-spectral numerical model for the heat diffusion equation with known input parameters. The results are then modified by adding a noise to simulate experimental measurements. Then, for each sample of observation, the parameter estimation problem is solved using one of the two mathematical models. The reliability is assessed based on the accuracy of the approach to recover the unknown parameter. Three case studies are considered for the estimation of ( i ) the heat capacity, ( ii ) the thermal conductivity or ( iii ) the heat transfer coefficient at the interface between the wall and the ambient air. For all cases, the DF mathematical model has a very satisfactory reliability to estimate the unknown parameters without any bias. However, the RC model lacks of fidelity and reliability. The error on the estimated parameter can reach 40% for the heat capacity, 80% for the thermal conductivity and 450% for the heat transfer coefficient.

scholarly journals Bayesian Parameter Estimation of Convective Heat Transfer Coefficients of a Roof-Mounted Radiant Barrier System

2005 ◽  
Vol 128 (2) ◽  
pp. 213-225 ◽  
Author(s):  
Philippe Lauret ◽  
Frédéric Miranville ◽  
Harry Boyer ◽  
François Garde ◽  
Laetitia Adelard
Keyword(s):  
Heat Transfer ◽  
Parameter Estimation ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Bayesian Methods ◽  
Thermal Model ◽  
Estimation Method ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Convective Heat Transfer Coefficients

This paper deals with the application of Bayesian methods to the estimation of two convective heat-transfer coefficients of a roof-mounted radiant barrier system. As part of an empirical validation of the thermal model of the roofing complex, a parametric sensitivity analysis highlighted the importance of convective coefficients in the thermal behavior of a roofing complex. A parameter estimation method is then used in order to find the values of the coefficients that lead to an improvement of the thermal model. However, instead of using a classical parameter estimation method, we used a Bayesian inference approach to parameter estimation. The aim of the paper is to introduce the basic concepts of this powerful method in this simple two-parameter case. We show that Bayesian methods introduce an explicit treatment of uncertainty in modeling and a corresponding measure of reliability for the conclusions reached.

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