Model Reduction of Linear Systems with Random Parameters

This paper is devoted to model reduction of linear time invariant (LTI) systems with random parameters. A novel framework is proposed to deal with this challenging problem. It consists in the combination of the generalized polynomial chaos (GPC) formalism and the truncated balanced realization (TBR) based method. The GPC formalism is known to be a powerful tool for the random uncertainty propagation and quantification while the TBR is efficient in model reduction of LTI systems. So, to couple these two methods helps to generate an efficient methodology to reduce linear models with random parameters. Two techniques exploiting this combination are proposed and tested on the model reduction of a mechanical system with random parameters. High efficiency is shown for both methods.