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.

翻译：均方根误差是结构动力学和声学等多种应用中用于模拟与标准行为平均偏差的重要度量。对于大规模系统，该量的模拟计算很快会变得不可行。经典模型降阶技术试图通过构建代理模型来解决此问题，这些模型使用中间线性系统来模拟均方根误差度量。然而，这种方法需要可能大量的线性输出，这在降阶模型设计中可能不利。在本工作中，我们直接考虑均方根误差作为关注量，利用二次输出模型的概念，并提出了几种新的模型降阶技术来构建合适的代理模型。我们在一个带有调谐振动吸收器的平板振动响应模型上测试了所提出的方法。