Observability of modally reduced order models with unknown parameters

Abstract

Modally reduced order models are commonly adopted in system inversion. Their observability requires specific attention, since these models only accurately describe the dynamic behavior of the underlying system in a limited frequency range. This paper elaborates a methodology to investigate the observability of modally reduced order models with unknown parameters. The focus is on a particular type of model where the quasi-static contribution of the out-of-band modes is accounted for using so-called dummy modes. The observability test is performed by means of the commonly used Observability Rank Condition (ORC). The proposed methodology is illustrated by multiple examples from structural engineering. It is found that modally reduced order models serve as a valuable alternative for full order models when applied in system inversion. Not only are they computationally much less demanding, but due to their strong link with the underlying full order model, they also allow for the identification of physical parameters, such as mass or stiffness.