Interpolatory model reduction of dynamical systems with root mean squared error

The root mean squared error is an important measure used in a variety of applications like structural dynamics and acoustics to model averaged deviations from standard behavior. For large-scale systems, simulations of this quantity quickly become computationally prohibitive. Model order reduction techniques resolve this issue via the construction of surrogate models that emulate the root mean squared error measure using an intermediate linear system. However, classical approaches require a large number of system outputs, which is disadvantageous in the design of reduced-order models. In this work, we consider directly the root mean squared error as the quantity of interest using the concept of quadratic-output models and propose several new model reduction techniques for the construction of appropriate surrogates. Numerical tests are performed on a model of a plate with tuned vibration absorbers.