Practical inverse analysis in engineering

TLDR: In this article, a computer program for the solution of the General Inverse Problem using Dynamic Programming and Generalized Cross Validation Index is presented, which is a generalization of the generalized cross validation index.

Abstract: 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