Vibration-based damage assessment utilizing state space geometry changes: local attractor variance ratio

A novel feature extracted from a nonlinear time series is presented within the context of vibration-based damage detection in a system. An eight-degree-of-freedom spring-mass-damper 'structure' is considered with damage incurred by a stiffness degradation in one spring. The system is excited with a chaotic input, and by tuning the Lyapunov exponents of the chaotic excitation to the dominant eigenvalue of the structure the dimensionality of the entire system is effectively controlled. Both the input and output are viewed in state space as geometric objects, and the effect of the damage is shown to alter the geometric properties of the corresponding attractors at a local level, which may be captured in construction of the feature. The utility of the feature is compared with that of a number of modal-based features and shown to be superior in resolving capability and in robustness.