Toward Intelligent Fault Detection in Turbine Blades: Variational Vibration Models of Damaged Pinned-Pinned Beams

Inaccuracies in the modeling assumptions about the distributional characteristics of the monitored signatures have been shown to cause frequent false positives in vehicle monitoring systems for high-risk aerospace applications. To enable the development of robust fault detection methods, this work explores the deterministic as well as variational characteristics of failure signatures. Specifically, we explore the combined impact of crack damage and manufacturing variation on the vibrational characteristics of turbine blades modeled as pinned-pinned beams. The changes in the transverse vibration and associated eigenfrequencies of the beams are considered. Specifically, a complete variational beam vibration model is developed and presented that allows variations in geometry and material properties to be considered, with and without crack damage. To simplify variational simulation, separation of variables is used for fast simulations. This formulation is presented in detail. To establish a baseline of the effect of geometric variations on the system vibrational response, a complete numerical example is presented that includes damaged beams of ideal geometry and damaged beams with geometric variation. It is shown that changes in fault detection monitoring signals caused by geometric variation are small with those caused by damage and impending failure. Also, when combined, the impact of geometric variation and damage appear to be independent.