Nonlinear system analysis with Karhunen-Loeve Transform

The Karhunen-Loeve Transform was established to find structures in random process data. Nonlinear dynamical systems often appear to have uncorrelated output in case of chaotic behavior. This analogy leads to the idea of analyzing nonlinear dynamical systems with methods developed for random processes. The Karhunen-Loeve Transform provides a basis for different approaches to the investigation of these systems. This paper gives an introduction to the mathematical concept and an overview of popular Karhunen-Loeve Transform applications. It focuses on approaches to state monitoring of nonlinear dynamical systems based on experimental data.