The paper introduces a technique that decomposes the dynamics of a nonlinear system about an equilibrium into low-order components, which then can be used to reconstruct the full dynamics. This is a nonlinear analogue of linear modal analysis. The dynamics is decomposed using Invariant Spectral Foliation (ISF), which is defined as the smoothest invariant foliation about an equilibrium and hence unique under general conditions. The conjugate dynamics of an ISF can be used as a reduced order model. An ISF can be fitted to vibration data without carrying out a model identification first. The theory is illustrated on a analytic example and on free-vibration data of a clamped-clamped beam.

本文介绍了一种技术，该技术将关于平衡的非线性系统的动力学分解为低阶分量，然后可以将其用于重构完整的动力学。这是线性模态分析的非线性模拟。动力学使用不变谱叶面（ISF）进行分解，该光谱被定义为关于平衡的最平滑不变叶面，因此在一般条件下是唯一的。ISF的共轭动力学可以用作降阶模型。ISF可以适合振动数据，而无需先执行模型识别。该理论在一个解析示例和一个夹钳梁的自由振动数据上得到了说明。