An optimization study of the ALAVR vibration-based damage detection method

Damage in an idealized structure is characterized by extracting a previously proposed feature, the average local attractor variance ratio (ALAVR), from the system's response to a specialized nonlinear input. The study focuses on the effects of dimensionality on the utility of the ALAVR feature as a structural damage indicator. The dimensionality of the time series responses can be varied from a minimal two dimensional (one time delay embedding) up to and beyond the theoretically recommended dimension from the Takens embedding theorem prescribed such that the dynamics of the original system is completely reconstructed in the delay coordinate system. The nonlinear driving input, generated from the output of a nonlinear oscillator, can effect the dimensionality of the system's response through a tuning process in the Lyapunov domain. By considering the effects of input and output dimensionality, this study attempts to suggest an optimized formulation of the ALAVR method.