Prognostic modelling of crack growth in a tensioned steel band

The general problem of identifying the condition of a structure or machine, and in particular its vibration signature, as a means to optimize maintenance costs and reliability is currently of great interest. This work presents a method for predicting the state of damage in the future for prognostic maintenance, rather than just identifying the current state of damage for diagnostic maintenance. Prognostics carries great economic importance because it allows the assessment of the likelihood of failure as a function of future time in terms of past and current conditions. We present an experimental example using the modal response of a notched, tensioned, steel band undergoing broadband vibration excitation to propagate cracks across the notched area until failure. The natural modes of the band are monitored during fatigue and the modal frequency shifts are used as a prognostic observable. A Kalman filter is then used track these modal frequency shifts and predict the likelihood and time when the amount of frequency shift is indicative of imminent failure. As a practical approach for prognostics of the band failure, we examine whether the modal frequencies are converging towards a stable state (such as during the break-in period), or diverging away from a stable state. A new probability density function for the remaining useful life is derived from the kinematic model. This method of using the kinematic state of a damage observable for failure prognostics can be extended to any dynamical system with observable features which correlate with damage or fatigue state.