Fractional-Order System Identification of Viscoelastic Behavior: A Frequency Domain Based Experimental Study

Abstract

In this work, the fractional-order modeling of viscoelastic behavior is investigated based on measurement data in the frequency domain. For the results of two different test setups we apply existing parameter estimation algorithms designed for fractional-order transfer functions. These algorithms require a priori knowledge of the system structure including the commensurate order of differentiation. An iterative procedure is used to evaluate the influence of the unknown structure. The measured polymer samples show a viscoelastic stress response. We can show that integer-order models are not capable of capturing this behavior. For a set of predefined structures, the best obtained fractional-order models, however, show a significant variation of parameters. The chosen structure also depends on the used algorithm, therefore additional considerations have to be included in the identification process to generate reliable physical models.