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Journal ArticleDOI

Inverse estimation of thermal properties using Bayesian inference and three different sampling techniques

02 Jan 2017-Inverse Problems in Science and Engineering (Taylor & Francis)-Vol. 25, Iss: 1, pp 73-88
TL;DR: In this paper, three different thermal properties such as thermal conductivity, heat transfer coefficient and emissivity are retrieved simultaneously using Bayesian inverse framework and two population-based sampling techniques such as Parallel Tempering (PT) and Evolutionary Monte-Carlo (EMC) are used along with MH-MCMC to sample through correlated PPDF to retrieve the above three thermal properties.
Abstract: In this article, three different thermal properties such as thermal conductivity, heat transfer coefficient and emissivity are retrieved simultaneously using Bayesian inverse framework. Metropolis–Hasting Markov Chain Monte-Carlo (MH-MCMC) sampling is more commonly used in the literature to sample through posterior probability distribution function (PPDF) to find the expectations such as mean, standard deviation. However, when the posterior is multi-model/correlated, sometimes MH-MCMC struck with one mode and fails to sample through other modes which have significant probability. Nevertheless, efficient sampling techniques are being developed during the last decade to overcome this problem. Therefore, in the present work two population-based sampling techniques such as Parallel Tempering (PT) and Evolutionary Monte-Carlo (EMC) are used along with MH-MCMC to sample through correlated PPDF to retrieve the above three thermal properties. The estimation is carried out at three levels of measurement errors. Th...
Citations
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Journal ArticleDOI
TL;DR: In this paper, the boundary geometry shape is identified by the finite element method (FEM) without iteration and mesh reconstruction for two-dimensional (2D) and threedimensional (3D) inverse heat conduction.
Abstract: The boundary geometry shape is identified by the finite element method (FEM) without iteration and mesh reconstruction for two-dimensional (2-D) and three-dimensional (3-D) inverse heat conduction ...

17 citations


Cites background from "Inverse estimation of thermal prope..."

  • ...In general, the research of IHCPs mainly includes identifying the boundary conditions [1, 2], material properties [3], heat sources [4, 5], and geometry configurations [6, 7]....

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Journal ArticleDOI
TL;DR: In this paper, the authors developed a digital twin based on an inversion procedure, integrating process monitoring with simulation of composites manufacturing to provide a real time probabilistic estimation of process outcomes.
Abstract: Funding information Cranfield University; EU Abstract This paper addresses the development of a digital twin, based on an inversion procedure, integrating process monitoring with simulation of composites manufacturing to provide a real time probabilistic estimation of process outcomes. A computationally efficient surrogate model was developed based on Kriging. The surrogate model reduces the computational time allowing inversion in real time. The tool was implemented in the filling stage of an resin transfer molding processing of a carbon fiber reinforced part resulting in the probabilistic prediction of unknown parameters. Flow monitoring data were acquired using dielectric sensors. The inverse scheme based on Markov Chain Monte Carlo uses input parameters, such as permeability and viscosity, as unknown stochastic variables. The scheme enhances the model by reducing model parameter uncertainty yielding an accurate on line estimation of process outcomes and critical events such as racetracking. The inverse scheme provides a prediction of filling duration with an error of about 5% using information obtained within the first 30% of the process.

12 citations

Journal ArticleDOI
01 Sep 2016
TL;DR: In this paper, the inverse heat conduction problem (IHCP) involving the simultaneous estimation of principal thermal conductivities (kxx,kyy,kzz ) and specific heat capacity of orthotropic materials is solved by using surrogate forward model.
Abstract: In this work, inverse heat conduction problem (IHCP) involving the simultaneous estimation of principal thermal conductivities (kxx,kyy,kzz ) and specific heat capacity of orthotropic materials is solved by using surrogate forward model. Uniformly distributed random samples for each unknown parameter is generated from the prior knowledge about these parameters and Finite Volume Method (FVM) is employed to solve the forward problem for temperature distribution with space and time. A supervised machine learning technique- Gaussian Process Regression (GPR) is used to construct the surrogate forward model with the available temperature solution and randomly generated unknown parameter data. The statistical and machine learning toolbox available in MATLAB R2015b is used for this purpose. The robustness of the surrogate model constructed using GPR is examined by carrying out the parameter estimation for 100 new randomly generated test samples at a measurement error of ±0.3K. The temperature measurement is obtained by adding random noise with the mean at zero and known standard deviation (σ = 0.1) to the FVM solution of the forward problem. The test results show that Mean Percentage Deviation (MPD) of all test samples for all parameters is < 10%.

11 citations

Journal ArticleDOI
TL;DR: In this paper, the authors reported the estimation of the unknown boundary heat flux from a fin using the Bayesian inference method, where the authors used the Markov Chain Monte Carlo (MCMC) powered by Metropolis-Hastings sampling algorithm along with the bayesian framework to explore the estimation space.
Abstract: This paper reports the estimation of the unknown boundary heat flux from a fin using the Bayesian inference method. The setup consists of a rectangular mild steel fin of dimensions 250×150×6 mm3 and an aluminium base plate of dimensions 250×150×8 mm3. The fin is subjected to constant heat flux at the base and the fin setup is modelled using ANSYS14.5. The problem considered is a conjugate heat transfer from the fin, and the Navier–Stokes equation is solved to obtain the flow parameters. Grid independence study is carried out to fix the number of grids for the study considered. To reduce the computational cost, computational fluid dynamics (CFD) is replaced with artificial neural network (ANN) as the forward model. The Markov Chain Monte Carlo (MCMC) powered by Metropolis–Hastings sampling algorithm along with the Bayesian framework is used to explore the estimation space. The sensitivity analysis of the estimated temperature with respect to the unknown parameter is discussed to know the dependency of the temperature with the parameter. This paper signifies the effect of a prior model on the execution of the inverse algorithm at different noise levels. The unknown heat flux is estimated for the surrogated temperature and the estimates are reported as mean, Maximum a Posteriori (MAP) and standard deviation. The effect of a-priori information on the estimated parameter is also addressed. The standard deviation in the estimation process is referred to as the uncertainty associated with the estimated parameters.

8 citations


Cites methods from "Inverse estimation of thermal prope..."

  • ...Somasundharam and Reddy [15] used MH-MCMC sampling algorithm in Bayesian inverse framework and estimated thermal conductivity, heat transfer coefficient and emissivity....

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  • ...Konda Reddy et al [9] carried out transient experiments on a rectangular fin and obtained temperature data using the transient Liquid Crystal Thermography (LCT) technique....

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Journal ArticleDOI
TL;DR: In this article, an ANN-driven forward model is combined with Bayesian framework and genetic algorithm to simultaneously estimate the unknown constants present in the interfacial heat transfer coefficient correlation, and Gaussian noise is added to the temperature distribution obtained using the forward approach to represent real-time experiments.
Abstract: The present methodology focuses on model reduction in which the prevalent one-dimensional transient heat conduction equation for a horizontal solidification of Sn–5wt%Pb alloy is replaced with Artificial Neural Network (ANN) in order to estimate the unknown constants present in the interfacial heat transfer coefficient correlation. As a novel approach, ANN-driven forward model is synergistically combined with Bayesian framework and Genetic algorithm to simultaneously estimate the unknown parameters and modelling error. Gaussian noise is then added to the temperature distribution obtained using the forward approach to represent real-time experiments. The hallmark of the present work is to reduce the computational time of both the forward and the inverse methods and to simultaneously estimate the unknown parameters using a-priori engineering knowledge. The results of the present methodology prove that the simultaneous estimation of unknown parameters can be effectively obtained only with the use of Bayesian framework.

5 citations

References
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Book
26 Jun 1995
TL;DR: The Finite Element Method as mentioned in this paper is a method for linear analysis in solid and structural mechanics, and it has been used in many applications, such as heat transfer, field problems, and Incompressible Fluid Flows.
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TL;DR: Montgomery and Runger's Engineering Statistics text as discussed by the authors provides a practical approach oriented to engineering as well as chemical and physical sciences by providing unique problem sets that reflect realistic situations, students learn how the material will be relevant in their careers.
Abstract: Montgomery and Runger's bestselling engineering statistics text provides a practical approach oriented to engineering as well as chemical and physical sciences. By providing unique problem sets that reflect realistic situations, students learn how the material will be relevant in their careers. With a focus on how statistical tools are integrated into the engineering problem-solving process, all major aspects of engineering statistics are covered. Developed with sponsorship from the National Science Foundation, this text incorporates many insights from the authors' teaching experience along with feedback from numerous adopters of previous editions.

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Journal ArticleDOI
TL;DR: Next, the authors discuss an additive model obtained by replacing the timevarying regression coefŽ cients by constants, and a brief summary of multivariate survival analysis, including measures of association and frailty models.
Abstract: (2004). Applied Statistics and Probability for Engineers. Technometrics: Vol. 46, No. 1, pp. 112-113.

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"Inverse estimation of thermal prope..." refers methods in this paper

  • ...After calculating x̄ and s, the 95% Bayesian confidence interval is calculated as [22] x̄ − 1....

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Book
01 Dec 2004
TL;DR: Inverse Problems and Interpretation of Measurements: Inverse problems and interpretation of measurements as mentioned in this paper, classical regularization methods, Statistical Inversion Theory, Nonstationary Inverse Problems, Classical Methods Revisited, Model Problems.
Abstract: Inverse Problems and Interpretation of Measurements.- Classical Regularization Methods.- Statistical Inversion Theory.- Nonstationary Inverse Problems.- Classical Methods Revisited.- Model Problems.- Case Studies.

1,825 citations

Book
01 Jan 1975
TL;DR: The Finite Element Method as discussed by the authors is a method to meet the Finite Elements Method of Linear Elasticity Theory (LETI) and is used in many of the problems of mesh generation.
Abstract: PART I. Meet the Finite Element Method. The Direct Approach: A Physical Interpretation. The Mathematical Approach: A Variational Interpretation. The Mathematical Approach: A Generalized Interpretation. Elements and Interpolation Functions. PART II. Elasticity Problems. General Field Problems. Heat Transfer Problems. Fluid Mechanics Problems. Boundary Conditions, Mesh Generation, and Other Practical Considerations. Appendix A: Matrices. Appendix B: Variational Calculus. Appendix C: Basic Equations from Linear Elasticity Theory. Appendix D: Basic Equations from Fluid Mechanics. Appendix E: Basic Equations from Heat Transfer. References. Index.

1,497 citations