1st Edition

Inverse Engineering Handbook

Edited By Keith A. Woodbury Copyright 2003
    480 Pages 184 B/W Illustrations
    by CRC Press

    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.

    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

    Biography

    Woodbury\, Keith A.

    "…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