Modified hidden semi-Markov models for motor wear prognosis

Prognosis can greatly benefit system maintenance via prediction of the remaining-useful life (RUL). The hidden semi-Markov model (HSMM) has been proposed as a prognostic modelling in previous research (M Dong and D He, Hidden semi-Markov model-based methodology for multi-sensor equipment health diagnosis and prognosis. Eur. J. Oper. Res., 2007, 178(3), 858–878), as improvement to the conventional hidden Markov model. When using the existing HSMM algorithm, it has been found that the underflow issue may arise in the computation of the forward and backward variables at the forward–backward method for large data sequences. This note presents a revision for the existing HSMM algorithm, which aims to eliminate the possible underflow issue during computation. A modified forward–backward training algorithm and an expectation-modification method are used to estimate the model parameters, including the state transition probability matrix, initial state distribution, and observation probability matrix. The proposed method is validated with a simulation example of bearing wear prognostics for a linear actuator application. The proposed modification of the HSMM algorithm can lower the requirement for numerical accuracy of the computational platform, without the negative impact on the RUL prediction, and benefit the development of cost-effective on-board prognosis.