Identification and Experiment Design

Viscoelastic materials can today be found in a wide range of practical applications. In order to make efficient use of these materials in construction, it is of importance to know how they behave when subjected to dynamic load. Characterization of viscoelastic materials is therefore an important topic, that has received a lot of attention over the years. This thesis treats different methods for identifying the complex modulus of an viscoelastic material. The complex modulus is a frequency dependent material function, that describes the deformation of the material when subjected to stress. With knowledge of this and other material functions, it is possible to simulate and predict how the material behaves under different kinds of dynamic load. The complex modulus is often identified through wave propagation testing, where the vis-coelastic material is subjected to some kind of load and the response then measured. Models describing the wave propagation in the setups are then needed. In order for the identification to be accurate, it is important that these models can describe the wave propagation in an adequate way. A statistical test quantity is therefore derived and used to evaluate the wave propagation models in this thesis. Both nonparametric and parametric identification of the complex modulus is considered in this thesis. An important aspect of the identification is the accuracy of the estimates. Theoretical expressions for the variance of the estimates are therefore derived, both for the nonpara-metric and the parametric identification. In order for the identification to be as accurate as possible, it is also important that the experimental data contains as much valuable information as possible. Different experimental conditions, such as sensor locations and choice of excitation, can influence the amount of information in the data. The procedure of determining optimal values for such design parameters is known as optimal experiment design. In this thesis, both optimal sensor locations and optimal excitation are considered. Acknowledgments First of all, I would like to express my sincere gratitude to my supervisor Prof. Torsten Söderström for taking me on as a PhD student, for sharing his profound knowledge, and for guiding me during this time. It has been a true privilege working with you! I would also like to thank my co-workers at the division of Solid Mechanics, Uppsala University: Dr. Saed Mousavi for performing all the experiments needed for this thesis, Dr. Lars Hillström for letting me use his data, and Prof. Bengt …