First-Order Uncertain Hidden Semi-Markov Process for Failure Prognostics with Scarce Data

Failure prognostics aims at predicting the object equipment's future degradation trend and derives the remaining useful life with a predefined failure threshold. Hidden semi-Markov process (HSMP) is widely adopted for failure prognostics of degradation process with discrete states. The effective estimation of the holding time distribution on each degradation state is of critical importance for the prediction performance of a HSMP model. The distributions are generally estimated with frequencies-based probabilities given a large amount of degradation data. In practical engineering applications, it is difficult to collect enough data and the data can even be scarce. In such situations, the estimated distributions are no longer reliable. First-order uncertain hidden semi-Markov process (1-UHSMP) based on uncertain statistics is defined in this work. The holding time distributions in 1-UHSMP are described with uncertainty theory and are adaptively updated with conditional uncertainty distributions given observations related to the true degradation states. Analytical expressions are derived for the expected remaining useful life for 1-UHSMP with regular uncertainty distributions, i.e. normal and linear uncertainty distribution. The proposed method can build a degradation model from scarce data and derive adaptively the remaining useful life with associated uncertainty interval. A case study concerning centrifugal pumps in a nuclear power plant is considered to verify the effectiveness of 1-UHSMP.