Data-driven modeling of general damping systems by k-means clustering and two-stage regression

Damping is one of the most complicated phenomena in structural analysis and design. In principle, damping arises with energy dissipation in the vibration and therefore, friction, plasticity and viscosity etc are common sources of damping. Though various damping models have been proposed, they are only applicable to some certain damping phenomena and there is no unified way to model an arbitrary damping system. To the end, this paper presents a data-driven framework for modeling of general damping systems. There are three key ingredients in establishing this framework. At first, pre-defined dictionaries of basis functions are built to describe the hysteretic and viscous behaviors of a general damping model. Secondly, the k-means clustering technique is applied to separate the two datasets corresponding to respective hysteretic and viscous parts of the damping model from the measured data. Thirdly, a two-stage regression procedure is invoked where the viscous and hysteretic parts of the damping model are identified sequentially from the readily separated two datasets. Such identification proceeds by means of linear least-squares regression and sparse regularization. As a consequence, if a new damping system whose hysteretic and viscous behaviors are totally reflected in the dictionary, the underlying model equation can be directly and quickly recovered through the proposed data-driven approach. Numerical examples as well as an experimental test are studied to demonstrate the effectiveness and efficiency of the proposed data-driven modeling approach for general damping systems.