Characterization of Phase Space Topology Using Density: Application to Fault Diagnostics

Abstract

Almost all engineered systems are nonlinear and show nonlinear phenomena that can only be predicted by nonlinear models. However, the application of model-based approaches for diagnostics has been constrained mostly to linearized or simplified models. This paper introduces a fundamental approach for characterization of nonlinear response of systems based on the topology of the phase space trajectory. The method uses the density distribution of the system states to quantify this topology and extracts features that can be used for system diagnostics. The proposed method has been employed to diagnose a multi degree of freedom system with various simultaneous defects.