1st Edition
Revival: Practical Inverse Analysis in Engineering (1997)
Continuing advances in computer technology have made it possible for engineers and scientists to construct increasingly realistic models of physical processes. Practical Inverse Analysis in Engineering addresses an important area of engineering that will become even more significant to engineers and scientists - combining measurements with engineering models. This self-contained text presents applied mathematical tools for bridging the gap between real-world measurements and mathematical models.
The book demonstrates how to treat "ill-conditioned" inverse analysis problems - those problems where the solution is extremely sensitive to the data - with the powerful theory of dynamic programming. A second theory, generalized-cross-validation, is also discussed as a useful partner in handling real data. The material in the book, much of it published for the first time, presents theories in a general unified setting, so readers can apply the information to their models. A disk containing DYNAVAL programming software lets readers try the methods presented in the text.
Introduction
The Simplest Exchange
Bellman's Principle of Optimality
First-Order Dynamic System
General Multidimensional System
Optimal Control as a Multistage Decision Process
Matrices and Differential Equations
Introduction
Vector-Matrix Calculus
The Exponential Matrix
Approximations to the Exponential Matrix
Eigenvalue Reduction
The General Inverse Problem
Introduction
Generalized Cross Validation
Dynamic Programming and Generalized Cross Validation
Chandrasekhar Equations
The Inverse Heat Conduction Problem
Introduction
One-Dimensional Example
Two-Dimensional Example
Eigenvalue Reduction Technique
L-Curve Analysis
The Inverse Structural Dynamics Problem
Introduction
Single-Degree-of-Freedom
Cantilever Beam Problem
Two-Dimensional Plate Problem
Smoothing and Differentiating Noisy Data
Introduction
Polynomial Approximation
Filtering a 60 Hz Signal
Frequency Analysis
Two-Dimensional Smoothing
Nonlinear Systems
Introduction
Linearization Methods
Nonlinear Inverse Heat Conduction
Nonlinear Spring Example
Successive Approximation in Policy Space
Sequential Estimation and System Identification
Introduction
Sequential Estimation
Multidimensional Sequential Estimation
Extended Levenberg-Marquardt's Method
Bibliography
Appendix A. DYNAVAL: A Computer Program for the Solution of the General Inverse Problem Using Dynamic Programming and Generalized Cross-Validation
Index
Biography
David Trujillo, Henry Busby
"The authors have written an excellent book that presents mathematical tools to combine real world measurements and mathematical models to create improved models for engineering systems or other physical processes."
-Applied Mechanics Review, March 1999
