Parametric model-order reduction for viscoelastic finite element models: an application to material parameter identification

In many engineering applications, viscoelastic treatments are used to suppress vibrations of lightly damped structures. Computational methods provide powerful tools for the design and analysis of these structures. The most commonly used method to model the dynamics of complex structures is the finite element method. Its use, however, often results in very large and computationally demanding models, especially when viscoelastic material behaviour has to be taken into account. To alleviate this problem, model-order reduction (MOR) techniques have been developed to reduce the size of the finite element model while still maintaining an accurate description of the most important system dynamics. In order to apply these MOR schemes, the parameter values of the full-order model have to be fixed. As a consequence, the resulting reduced-order model is only valid for one specific set of viscoelastic material properties. Recently though, parametric model-order reduction (pMOR) techniques have been introduced. These methods allow the parameter dependency to be retained in the reduced-order models. This makes them a valuable tool for use in optimization procedures, where the system model has to be evaluated time and again for varying parameter values. This paper presents a Krylov subspace technique for reduced-order modelling, embedded in a recent pMOR framework, to create reduced-order models of viscoelastic finite element models in which the dependency on the viscoelastic material parameters is retained. The viscoelastic material properties are modelled using the Golla-Hughes-McTavish formulation. This procedure is then applied to a finite element model of a cantilever beam with viscoelastic treatment. The resulting reduced-order model is used to identify viscoelastic material properties from experiments through an inverse optimization procedure, demonstrating both the efficiency and accuracy of the obtained reduced-order model.