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.
Table of Contents
Dynamic Programming System 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