Identification of Fractional-Order Models for Viscoelastic Behavior

Abstract

In this thesis, the fractional-order modeling of viscoelastic behavior based on measurement data obtained in the frequency domain is analyzed. Polymer samples as well as the transfer behavior of a hydraulic dashpot are investigated, whereby two different experimental setups are used for the former. Existing fractional-order transfer function estimation algorithms based on integer-order identification techniques are applied. These algorithms require a priori knowledge of the system structure including the commensurate order of differentiation. Hence an iterative procedure is used to evaluate the influence of the unknown structure. To avoid this, a global optimization is introduced, where the commensurate order is also part of the parameter set to be optimized. The measured polymer samples show a viscoelastic stress response. It can be shown that known model structures of low order for viscoelastic models can represent the measured transfer behavior very well. It is also proven that integer-order models do not reach the accuracy achieved with fractional-order approaches. For low-dimensional models, for which similar coefficients are estimated, the commensurate order is also in a limited range. However, as soon as there are only small deviations or the given model orders increase, it fluctuates enormously between 0 and 1. Additional considerations have to be included in the identification process to generate reliable physical models. The investigated dashpot is rather approximated by integer-order models.