Diagnosis and Prognosis of Degradation Process via Hidden Semi-Markov Model

The intelligent estimation of degradation state and the prediction of remaining useful life (RUL) are important for the maintenance of industrial equipment. In this study, the degradation process of equipment is modeled as an improved hidden semi-Markov model (HSMM), in which the dependence of durations of adjacent degradation states is described and modeled in the HSMM. To avoid underflow problem in computing the forward and backward variables, a modified forward–backward algorithm is proposed in the HSMM. Based on the improved algorithm, online estimation of degradation state and the distribution of RUL can be obtained. Case studies on tool wearing diagnosis and prognosis have verified the effectiveness of this model.