Identification of linear systems: a practical guideline to accurate modeling
Identification of linear systems: a practical guideline to accurate modeling
Estimation Techniques for Distributed Parameter Systems
Estimation Techniques for Distributed Parameter Systems
Coefficient identification in elliptic partial differential equation
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
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The "inverse problem" of determining parameter distributions in linear elastic structures has been explored widely in the literature. In the present article we discuss this problem in the context of a particular formulation of linear elastic systems, dividing the associated inverse problems into two classes which we call Case 1 and Case 2. In the first case the elastic parameters can be obtained by solving a certain set of linear algebraic equations, typically poorly conditioned. In the second case the corresponding problem involves nonlinear equations which usually must be solved by approximation methods, including the Gauss-Newton method for overdetermined systems. Here we discuss the application of this method and a related, empirically more stable, method which we call the inverse Gauss-Newton method. Convergence theorems are established and computational results for sample problems are presented.