Nonparametric identification of viscoelastic materials

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 nonparametric 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 uniaxial stress. With knowledge about this and other material functions, it is possible to simulate and predict how the material behaves under different kinds of dynamic loads. The complex modulus is often identified through wave propagation testing. An important aspect of identification is the accuracy of the estimates. For the identification to be as accurate as possible, it is important that the experimental data contains as much valuable information as possible. Different experimental condition, such as sensor locations and choice of excitation, can influence the amount of valuable information in the data. The procedure of determining optimal values for such design parameters is known as optimal experiment design. The first two papers of the thesis treats optimal experiment design for nonparametric identification of the complex modulus, based on wave propagation tests on large homogenous specimens. Optimal sensor locations is treated in the first paper, and optimal excitation in the second. In the third paper, a technique for estimating the complex modulus for a small pelletsized specimen is presented. Three different procedures are considered, and an analysis of the accuracy of the estimates is carried out. List of Publications This thesis is based on the following publications: [I] A. Rensfelt, S. Mousavi, M. Mossberg and T. Söderström. Optimal sensor locations for nonparametric identification of viscoelastic materials. Preliminary accepted for publication in Automatica, 2006. Short versions are also published as: A. Runqvist, M. Mossberg and T. Söderström. Optimal sensor locations for nonparametric identification of viscoelastic materials. 16th IFAC World Congress, July 4-8, 2005, Prague, Czech Republic. A. Runqvist, M. Mossberg and T. Söderström. On optimal sensor locations for nonparametric identification of viscoelastic materials. Technical Report 2005-006. Department of Information Technology, Uppsala University. [II] A. Rensfelt and T. Söderström. Optimal excitation for nonparametric identification of viscoelastic materials. Submitted, 2006. A version can be found in: A. Rensfelt and T. Söderström. Optimal excitation for nonparametric identification of viscoelastic materials. Technical Report 2006-034. Department of Information Technology, Uppsala University. [III] A. Runqvist, S. Mousavi and T. Söderström. Nonparametric identification of complex modulus using a non-equilibrium SHPB procedure. 14th IFAC Symposium on System Identification, March 29-31, 2006, Newcastle, Australia.