  The root mean squared error is an important measure used in a variety of
applications such as structural dynamics and acoustics to model averaged
deviations from standard behavior. For large-scale systems, simulations of this
quantity quickly become computationally prohibitive. Classical model order
reduction techniques attempt to resolve this issue via the construction of
surrogate models that emulate the root mean squared error measure using an
intermediate linear system. However, this approach requires a potentially large
number of linear outputs, which can be 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. We test the proposed methods on a model for the
vibrational response of a plate with tuned vibration absorbers.
