Entropy Indices for Estimation of the Remaining Useful Life

Accurate estimation of the remaining useful life (RUL) of a machine can have significant operational and financial benefits for the companies. The biggest challenge in the remaining useful life (RUL) estimation are features that exhibit monotonic behaviour correlated with the level of deterioration of the machine’s condition. This is particularly challenging under variable operating conditions. The proposed RUL estimation approach is based on characterising the energy distribution of vibration signals. The features hereupon quantify the departure from the initial healthy state by calculating the f-divergence measures. Then the divergence measure is modelled as the output of a hidden Markov process in state space. In the general case, the states of the nonlinear model are estimated by means of unscented Kalman filter. Future evolution of the states and the outputs can be evaluated by Monte Carlo simulations. Hereupon, one can evaluate the distribution of times at which the calculated output hits the limit value marking the end of operability. The approach was applied to the problem of monitoring the turbine of a milling machine. The experiment was designed as a run-to-failure test thus allowing the natural progression of the mechanical fault.