**Karl-Hans Laermann**

**Inverse Problems in Experimental Structural Analysis**

Summary: An important eld of practical application of experimental mechanics methods is to be seen in structural health monitoring with special regard to existing structures. Such monitoring demands the identication of characteristic structural control parameters like stiness and compliance in order to justify the actual condition of the object under control. Experimental methods and measurement-systems on high technological level yield the basic information on the state of displacements of structures and their changes during the time of operation and enable the determination of the parameters. This leads inevitably to inverse problems, solution methods of which are presented in the script on hand.

After denition of inverse problems in Lecture I dierent solution methods are theoretically dealt with like matrix inversion methods, iterative algorithms, the methods of successive forward simulation and articial neural networks. The sensitivity matrix based method is described in greater detail.

In Lecture II the application of some solutions is explained more closely with simple examples and dierent formulation of questions, linear elastic response of material provided. With that diculties are considered to select an unequivocal solution among from a variety of results.

Because dierent solution methods as weil as even one and the same method can yield a variety of results, all of which solving the basic equations but do not necessarily meet the requirements of the considered problem.

With regard to visco-elastic material response solutions are dealt with in Lecture III to determine the time-depending functions of the decisive parameters like creep compliance and relaxation modulus. The application is demonstrated by some examples. Finally a method is proposed how to ascertain the parameters related to aged structures, if their whole previous history is unknown.

These Lecture Notes may be of interest for all those, who in practice have to get down on the task of health monitoring and who are not interested in extended studying the mathematical coherence of inverse problems.

Quelle: Zentralblatt MATH