An Inverse Method for Simultaneous Estimation of Thermal Properties of Orthotropic Materials using Gaussian Process Regression
01 Sep 2016-Vol. 745, Iss: 3, pp 032090
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%.
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TL;DR: In this article, the Gaussian process regression model was used to find statistical correlations between thermal conductivity enhancement and physical parameters among various types of nanofluids, such as particle thermal conductivities, particle size, particle volume fraction, and temperature.
80 citations
TL;DR: In this article, a riveting process was developed to fasten carbon fiber/epoxy composite laminates, which poses a threat to the integrity of the structure's epoxy matrix.
14 citations
TL;DR: A data-driven deep learning model is built to predict the heterogeneous distribution of circle-shaped fillers in two-dimensional thermal composites using the temperature field in the composite as an input.
Abstract: Inverse problems involving transport phenomena are ubiquitous in engineering practice, but their solution is often challenging. In this work, we build a data-driven deep learning model to predict the heterogeneous distribution of circle-shaped fillers in two-dimensional thermal composites using the temperature field in the composite as an input. The deep learning model is based on convolutional neural networks with a U-shape architecture and encoding–decoding processes. The temperature field is cast into images of 128 × 128 pixels. When the true temperature at each pixel is given, the trained model can predict the distribution of fillers with an average accuracy of over 0.979. When the true temperature is only available at 0.88% of the pixels inside the composite, the model can predict the distribution of fillers with an average accuracy of 0.94, if the temperature at the unknown pixels is obtained through the Laplace interpolation. Even if the true temperature is only available at pixels on the boundary of the composite, the average prediction accuracy of the deep learning model can still reach 0.80; the prediction accuracy of the model can be improved by incorporating true temperature in regions where the model has low prediction confidence.
13 citations
Dissertation•
21 May 2020
8 citations
TL;DR: In this article, a nonparametric Bayesian approach for developing structure-property models for grain boundaries (GBs) with built-in uncertainty quantification (UQ) is presented.
4 citations
References
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Book•
01 Jan 2000TL;DR: Inverse heat transfer: Fundamentals and Applications, Second Edition as mentioned in this paper includes techniques within the Bayesian framework of statistics for the solution of inverse problems and their applications for solving problems in convective, conductive, radiative, and multi-physics problems.
Abstract: This book introduces the fundamental concepts of inverse heat transfer solutions and their applications for solving problems in convective, conductive, radiative, and multi-physics problems. Inverse Heat Transfer: Fundamentals and Applications, Second Edition includes techniques within the Bayesian framework of statistics for the solution of inverse problems. By modernizing the classic work of the late Professor M. Necati Ozisik and adding new examples and problems, this new edition provides a powerful tool for instructors, researchers, and graduate students studying thermal-fluid systems and heat transfer.
FEATURES
Introduces the fundamental concepts of inverse heat transfer
Presents in systematic fashion the basic steps of powerful inverse solution techniques
Develops inverse techniques of parameter estimation, function estimation, and state estimation
Applies these inverse techniques to the solution of practical inverse heat transfer problems
Shows inverse techniques for conduction, convection, radiation, and multi-physics phenomena
M. Necati Ozisik (1923–2008) retired in 1998 as Professor Emeritus of North Carolina State University’s Mechanical and Aerospace Engineering Department.
Helcio R. B. Orlande is a Professor of Mechanical Engineering at the Federal University of Rio de Janeiro (UFRJ), where he was the Department Head from 2006 to 2007.
933 citations
Book•
01 Jul 2011
TL;DR: This chapter discusses Gaussian Process Regression models, and some examples of Covariance Function and Model Selection, as well as some of the models used in this research.
Abstract: Introduction Functional Regression Models Gaussian Process Regression Some Data Sets and Associated Statistical Problems Bayesian Nonlinear Regression with Gaussian Process Priors Gaussian Process Prior and Posterior Posterior Consistency Asymptotic Properties of the Gaussian Process Regression Models Inference and Computation for Gaussian Process Regression Model Empirical Bayes Estimates Bayesian Inference and MCMC Numerical Computation Covariance Function and Model Selection Examples of Covariance Functions Selection of Covariance Functions Variable Selection Functional Regression Analysis Linear Functional Regression Model Gaussian Process Functional Regression Model GPFR Model with a Linear Functional Mean Model Mixed-Effects GPFR Models GPFR ANOVA Model Mixture Models and Curve Clustering Mixture GPR Models Mixtures of GPFR Models Curve Clustering Generalized Gaussian Process Regression for Non-Gaussian Functional Data Gaussian Process Binary Regression Model Generalized Gaussian Process Regression Generalized GPFR Model for Batch Data Mixture Models for Multinomial Batch Data Some Other Related Models Multivariate Gaussian Process Regression Model Gaussian Process Latent Variable Models Optimal Dynamic Control Using GPR Model RKHS and Gaussian Process Regression Appendices Bibliography Index Further Reading and Notes appear at the end of each chapter.
267 citations
TL;DR: In this paper, an inverse analysis is used to estimate linearly temperature dependent thermal conductivity components k x (T ), k y (T ) and specific heat capacity C ( T ) per unit volume for an orthotropic solid.
120 citations
TL;DR: In this paper, an inverse conduction-radiation problem for simultaneous estimation of the conduction radiation parameter, the optical thickness and the boundary emissivity from a knowledge of the measured temperature profile for combined conduction and radiation in a plane parallel participating medium is presented.
62 citations
TL;DR: In this article, a function estimation approach is applied to the inverse problem of determining the temperature dependence of either the volumetric heat capacity or the thermal conductivity, and the minimization is performed in an infinite dimensional space of functions.
Abstract: The estimation of the temperature dependence of thermophysical properties has been generally treated as a parameter estimation problem in the literature. In this paper, we apply a function estimation approach to the inverse problem of determining the temperature dependence of either the volumetric heat capacity or the thermal conductivity. No information regarding the functional form of the unknown property is required in the present approach, and the minimization is performed in an infinite dimensional space of functions. The Conjugate Gradient Method with Adjoint Equation is used in the inverse analysis. Results obtained by using simulated temperature measurements of a single sensor, slow that the present approach is capable of recovering functions containing discontinuities, which are the most difficult to be recovered by an inverse analysis. The effects of sensor location on the inverse problem solution are also addressed on the paper.
34 citations