1st Edition

Inverse Engineering Handbook

Edited By

Keith A. Woodbury




ISBN 9780849308611
Published September 25, 2002 by CRC Press
480 Pages 184 B/W Illustrations

USD $290.00

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Book Description

Inverse problems have been the focus of a growing number of research efforts over the last 40 years-and rightly so. The ability to determine a "cause" from an observed "effect" is a powerful one. Researchers now have at their disposal a variety of techniques for solving inverse problems, techniques that go well beyond those useful for relatively simple parameter estimation problems. The question is, where can one find a single, comprehensive resource that details these methods?

The answer is the Inverse Engineering Handbook. Leading experts in inverse problems have joined forces to produce the definitive reference that allows readers to understand, implement, and benefit from a variety of problem-solving techniques. Each chapter details a method developed or refined by its contributor, who provides clear explanations, examples, and in many cases, software algorithms. The presentation begins with methods for parameter estimation, which build a bridge to boundary function estimation problems. The techniques addressed include sequential function estimation, mollification, space marching techniques, and adjoint, Monte Carlo, and gradient-based methods. Discussions also cover important experimental aspects, including experiment design and the effects of uncertain parameters.

While many of the examples presented focus on heat transfer, the techniques discussed are applicable to a wide range of inverse problems. Anyone interested in inverse problems, regardless of their specialty, will find the Inverse Engineering Handbook to be a unique and invaluable compendium of up-to-date techniques.

Table of Contents

SEQUENTIAL METHODS IN PARAMETER ESTIMATION
James V. Beck, Professor Emeritus, Michigan State University, USA
Abstract
Introduction
Parameter vs. Function Estimation
Common Research Paradigms in Heat Transfer
Sequential Estimation over Experiments for Linear Problems
Ill-Posed Problems: Tikhonov Regularization
Matrix Form of Taylor Series Expansion
Gauss Method of Minimization for Nonlinear Estimation Problems
Confidence Regions
Optimal Experiments
Summary
References
SEQUENTIAL FUNCTION SPECIFICATION METHOD USING FUTURE TIMES FOR FUNCTION ESTIMATION
Keith A. Woodbury, The University of Alabama, USA
Abstract
Nomenclature
Introduction
Linear Problems
Nonlinear Problems
Summary
References
THE ADJOINT METHOD TO COMPUTE THE NUMERICAL SOLUTIONS OF INVERSE PROBLEMS
Yvon Jarny, Ecole Polytechnique de L'Université de Nantes, France
Introduction
Modelling Equations
Least Squares and Gradient Algorithms
Lagrange Multipliers
The Adjoint Method
The Adjoint Method to Minimize the LS-Criterion with Algebraic Modelling Equations
The Adjoint Method to Minimize the LS-Criterion with Integral Modelling Equation
Adjoint Method to Minimize LS-Criteria with Ordinary Differential Equations as Constraints
Adjoint Method to Minimize LS-Criteria with Partial Differential Equations as Constraints
Conclusion and Summary
References
MOLLIFICATION AND SPACE MARCHING
Diego A. Murio, University of Cincinnati, USA
Mollification In R1
Data Smoothing
Identification of Parameters in 1-D IHCP
Discrete Mollification in R2
References
INVERSE HEAT CONDUCTION USING MONTE CARLO METHOD
A. Haji-Sheikh, University of Texas at Arlington, USA
Introduction
Introduction to Monte Carlo Method
Random Walks in Direct Monte Carlo Simulation
Monte Carlo Method for Inverse Heat Conduction
Conclusion
Nomenclature
References
CORRELATED DATA AND STOCHASTIC PROCESSES
Ashley Emery, University of Washington, USA
Introduction
Correlation and Its Effect on Precision
Least Squares Estimation and Linearization
Determination of
Ergodic and Stationary Processes
Uncertain Parameters
Bayesian Probabilities, Prior Information, and Uncertain Parameters
Conclusions
OPTIMAL EXPERIMENT DESIGN
Aleksey V. Nenarokomov, Moscow State Aviation Institute, Russia
Introduction
Brief Historical Analysis of Background and Survey
Experiment Design Problem Statement
Iterative Method of Optimal Design of Thermosensors Installation and Time of Signals Readings
Experiment Design for Lumped Parameter Systems
Conclusions
References
BOUNDARY ELEMENT TECHNIQUES FOR INVERSE PROBLEMS
Thomas J. Martin, Pratt & Whitney Engine Company and George S. Dulikravich, University of Texas at Arlington, USA
Introduction
Inverse Heat Conduction
Ill-Posed Boundary Conditions in Fluid Flow
Ill-Posed Surface Tractions and Deformations in Elastostatics
Inverse Detection of Sources
Transient Problems
References

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Editor(s)

Biography

Woodbury\, Keith A.

Reviews

"…serves as a good introduction and tutorial for this important area of applied mathematics. Several of the articles provide extensive MATLAB codes for specific problems."
--James E. Epperson, Mathematical Reviews, 2004