Failure prognosis using nonlinear short-time prediction and multi-time scale recursive estimation

In this paper we describe a new, general purpose machinery diagnostic/prognostic algorithm for tracking and predicting evolving damage using only available "macroscopic" observable quantities. The damage is viewed as occurring in a hierarchical dynamical system consisting of a directly observable, "fast" subsystem coupled with a hidden, "slow" subsystem describing damage evolution. This method provides damage diagnostics and failure prognostics requiring only the measurements from the fast subsystem and a model of the slow subsystem. Damage tracking is accomplished by a two-time-scale modeling strategy based on phase space reconstruction using the measured fast-time data. Short-time predictive models are constructed using the reconstructed phase space of the reference (undamaged) fast sub-system. Later, fast-time data for the damaged system is collected and used to estimate the short-time reference model prediction error, or a tracking function. An average value of the tracking function over a given data record is used as a tracking metric, or measure of the current damage state. Recursive, nonlinear filtering is used to estimate the actual damage state based on the tracking metric input. Estimates of remaining useful life are obtained recursively using a linear Kalman filter. This method is applied to an experimental nonlinear oscillator containing a beam with a crack which propagates to complete failure. We demonstrate the ability to track the evolving damage state of the beam using only strain time series data. We also give accurate predictions of remaining useful life, in real time, beginning well in advance of the final complete fracture at the end of experiment.