Inverse Heat Transfer. Fundamentals and Applications

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Preface of the First Edition
Authors
PART I: Introduction and Parameter Estimation
	Chapter 1 Basic Concepts
		1.1 Inverse Heat Transfer Problem Concept
		1.2 Classification of IHTPs
		1.3 Difficulties in the Solution of Inverse Heat Transfer Problems
		1.4 An Overview of Solution Techniques for Inverse Heat Transfer Problems
		1.5 Basic Steps for the Solution of Inverse Heat Transfer Problems
		Problems
		Note 1: Statistical Concepts
			Random Variable
			Probability Distribution
			Expected Value of X
			Expected Value of a Function g(X)
			Variance of a Random Variable X
			Covariance of Two Random Variables X and Y
			Gaussian Distribution
			Uniform Distribution
			Rayleigh Distribution
			Gamma Distribution
			Beta Distribution
			Chi-Square Distribution
			Covariance Matrix
			Multivariate Gaussian Distribution
	Chapter 2 Parameter Estimation: Minimization of an Objective Function without Prior Information about the Unknown Parameters
		2.1 Objective Function
		2.2 Technique I: The Levenberg-Marquardt Method
			The Direct Problem
			The Inverse Problem
			The Iterative Procedure for Technique I
			The Stopping Criteria for Technique I
			The Computational Algorithm for Technique I
		2.3 Technique II: The Conjugate Gradient Method for Parameter Estimation
			The Direct Problem
			The Inverse Problem
			The Iterative Procedure for Technique II
			The Stopping Criterion for Technique II
			The Computational Algorithm for Technique II
		2.4 Sensitivity Coefficients
			Methods of Determining the Sensitivity Coefficients
				Direct Analytic Solution for Determining Sensitivity Coefficients
				The Boundary Value Problem Approach for Determining the Sensitivity Coefficients
				Finite Difference Approximation for Determining Sensitivity Coefficients
		2.5 Design of Optimum Experiments
		2.6 The Use of Multiple Sensors
		2.7 Statistical Analysis
		2.8 Estimation of Thermal Conductivity Components of an Orthotropic Heat Conducting Medium
			The Direct Problem
			The Inverse Problem
			Analysis of the Sensitivity Coefficients and Design of Optimum Experiments
			Parameter Estimation and Statistical Analysis
		2.9 Technique III: The Conjugate Gradient Method with Adjoint Problem for Parameter Estimation
			The Direct Problem
			The Inverse Problem
			The Sensitivity Problem
			The Adjoint Problem
			The Gradient Equation
			The Iterative Procedure for Technique III
			The Stopping Criterion for Technique III
			The Computational Algorithm for Technique III
			The Use of Multiple Sensors
		2.10 Estimation of a Heat Source Term in a Heat Conduction Problem
		Problems
		Note 1: Search Step-Size for Technique II
		Note 2: Search Step-Size for Technique III
	Chapter 3 Parameter Estimation: Minimization of an Objective Function with Prior Information about the Unknown Parameters
		3.1 Objective Function
			Maximum a Posteriori Objective Function with a Uniform Prior
			Maximum a Posteriori Objective Function with a Gaussian Prior
			Maximum a Posteriori Objective Function with a Truncated Gaussian Prior
		3.2 Minimization of the Objective Function
		3.3 Identification of the Thermophysical Properties of Semi-Transparent Materials
			The Direct Problem
			The Inverse Problem
			Analysis of the Sensitivity Coefficients and Design of Optimum Experiments
			Parameter Estimation and Statistical Analysis
		Problems
	Chapter 4 Parameter Estimation: Stochastic Simulation with Prior Information about the Unknown Parameters
		4.1 Markov Chains
		4.2 Technique IV: Markov Chain Monte Carlo (MCMC) Method
			Proposal Distribution
				Random Walk
				Independent Move
		4.3 MCMC Estimation of Thermal Conductivity Components of an Orthotropic Heat Conducting Medium
			The Direct Problem
			The Inverse Problem
			Stochastic Simulation
		4.4 MCMC Estimation of Thermal Conductivity and Volumetric Heat Capacity of Viscous Liquids with the Line Heat Source Probe
			The Direct Problem
			The Inverse Problem
			Analysis of the Sensitivity Coefficients and Design of Optimum Experiments
			Stochastic Simulation
		4.5 MCMC Estimation of Thermophysical Parameters of Thin Metal Films Heated by Fast Laser Pulses
			The Direct Problem
			The Inverse Problem
			Analysis of the Sensitivity Coefficients and Design of Optimum Experiments
			Stochastic Simulation
		4.6 Analysis of Markov Chains
			Statistics
			Convergence of the Markov Chain
			Proposal Distribution
		4.7 Reduction of the Computational Time for Solving Inverse Problems with Technique IV
			Delayed Acceptance Metropolis-Hastings (DAMH) Algorithm
			Approximation Error Model (AEM) Approach
		4.8 Approximation Error Model to Account for Convective Effects in the Line Heat Source Probe Method
		Problems
		Note 1: Metropolis-Hastings Algorithm with Sampling by Blocks of Parameters
PART II: Function Estimation
	Chapter 5 Function Estimation: Minimization of an Objective Functional without Prior Information about the Unknown Functions
		5.1 Technique V: The Conjugate Gradient Method with Adjoint Problem for Function Estimation
			The Direct Problem
			The Inverse Problem
			The Sensitivity Problem
			The Adjoint Problem
			The Gradient Equation
			The Iterative Procedure for Technique V
			The Stopping Criterion for Technique V
			The Computational Algorithm for Technique V
		5.2 Estimation of the Spacewise and Timewise Variations of the Wall Heat Flux in Laminar Flow
			Direct Problem
			Inverse Problem
			Sensitivity Problem
			Adjoint Problem
			Gradient Equation
			Iterative Procedure
			Results
		5.3 Simultaneous Estimation of Spatially Dependent Diffusion Coefficient and Source Term in a Diffusion Problem
			Direct Problem
			Inverse Problem
			Sensitivity Problems
			Adjoint Problem
			Gradient Equations
			Iterative Procedure
			Results
		5.4 Simultaneous Estimation of the Spacewise and Timewise Variations of Mass and Heat Transfer Coefficients in Drying
			Direct Problem
			Inverse Problem
			Sensitivity Problems
			Adjoint Problem
			Gradient Equations
			Iterative Procedure
			Results
		Problems
		Note 1: Hilbert Spaces
		Note 2: Conjugate Gradient Method of Function Estimation
		Note 3: Additional Measurement for Selecting the Stopping Criterion of the Conjugate Gradient Method
	Chapter 6 Function Estimation: Solution within the Bayesian Framework of Statistics with Prior Information about the Unknown Functions
		6.1 Prior Distributions
			Hierarchical Models
		6.2 Estimation of the Kidney Metabolic Heat Generation Rate
			Direct Problem
			Inverse Problem
			Results
		6.3 Temperature Estimation of Inflamed Bowel
			Direct Problem
			Inverse Problem
			Results
		6.4 Detection of Contact Failures by Using Integral Transformed Measurements
			Direct Problem
			Inverse Problem
			Results
		6.5 Accelerated Bayesian Inference for the Estimation of Spatially Varying Heat Flux
			Direct Problem
			Inverse Problem
			Results
		Problems
PART III: State Estimation
	Chapter 7 State Estimation: Kalman Filter
		7.1 State Estimation Problem
		7.2 Technique VI: The Kalman Filter
		7.3 Estimation of a Transient Boundary Heat Flux That Varies over the Surface
		7.4 The Steady-State Kalman Filter
		Problems
	Chapter 8 State Estimation: Particle Filter
		8.1 Technique VII: The Sampling Importance Resampling (SIR) Algorithm
		8.2 Technique VII: The Auxiliary Sampling Importance Resampling (ASIR) Algorithm
		8.3 Technique VII: The Algorithm of Liu and West
		8.4 Estimation of the Fire Front in Regional Scale Wildfire Spread
		8.5 A Comparison of Particle Filter Algorithms in Bioheat Transfer
		Problems
Appendix: Approximate Bayesian Computation
References
Index