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A Metric for Modal Truncation in Model Reduction Problems Part 2: Extension to Systems with High-Dimensional Input Space

机译：模型减少问题中模态截断的度量部分第2部分：扩展到具有高维输入空间的系统

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In the first part of this study, a theoretical investigation of an improved modal approach and a complete error analysis of the proposed modal dominancy metric were presented. In this part the problem of metric non-uniqueness for systems with multiple eigenvalues is described and a method to circumvent this problem based on spatial distribution of either the sensors or the actuators is proposed. This technique is implemented using QR factorization without solving Lyapunov equations. Moreover, the method is improved such that it is able to use the information extracted from spectral properties of the input. Also in order to make the method more effective, information extracted from the input internal structure is incorporated in the modal ranking process. It is shown that this improvement is particularly effective in problems with high-dimensional input and/or output space such as in distributed loading and moving load problems. Finally the performance of the method is validated for a high order system subjected to a high-dimensional input force. That originates from a railway track moving load problem.
机译：在本研究的第一部分，提出了改进的模态方法的理论研究和提出的模态主导度量的完整误差分析。在这部分中，描述了具有多个特征值的系统的度量非唯一性问题，并且提出了一种基于传感器或致动器的空间分布来绕过该问题的方法。使用QR分解来实现该技术，而无需解决Lyapunov方程。此外，改进了该方法，使得能够使用从输入的光谱特性提取的信息。而且为了使方法更有效地，从输入内部结构中提取的信息结合在模态排名过程中。结果表明，这种改进在高维输入和/或输出空间的问题中特别有效，例如分布式负载和移动负载问题。最后，验证了该方法的性能，用于经受高维输入力的高阶系统。这起源于铁路轨道移动负载问题。

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