Regularization of Parameter Problems for Dynamic Beam Models

Abstract: The field of inverse problems is an area in applied mathematics that is of great importance in several scientific and industrial applications. Since an inverse problem is typically founded on non-linear and ill-posed models it is a very difficult problem to solve. To find a regularized solution it is crucial to have a priori information about the solution. Therefore, general theories are not sufficient considering new applications.In this thesis we consider the inverse problem to determine the beam bending stiffness from measurements of the transverse dynamic displacement. Of special interest is to localize parts with reduced bending stiffness. Driven by requirements in the wood-industry it is not enough considering time-efficient algorithms, the models must also be adapted to manage extremely short calculation times.For the developing of efficient methods inverse problems based on the fourth order Euler-Bernoulli beam equation and the second order string equation are studied. Important results are the transformation of a nonlinear regularization problem to a linear one and a convex procedure for finding parts with reduced bending stiffness.

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