Remaining Useful Life Prediction of IIoT Equipment Using Hidden Semi-Markov Model With Hyper-Erlang Sojourn Time

The prediction of the remaining useful life (RUL) of equipment is a pivotal function in realizing industrial intelligence within the Industrial Internet of Things (IIoT). It enables the formulation of corresponding predictive maintenance strategies, enhancing the reliability, availability, and safety of IIoT equipment. Given the limitations in existing literature, where the sojourn time distribution in each hidden state of the hidden semi-Markov model (HSMM) lacks universality, a hyper-Erlang distribution is employed to describe the distribution of sojourn times, which more accurately reflects the actual degradation process. The degradation process of the system is modeled as a three-state HSMM. States 0 and 1 are unobservable, representing healthy and warning states, respectively. Only state 2 is observable, representing the failure state. The expectation-maximization (EM) algorithm is utilized to estimate the unknown state parameters and observation parameters of the model. The posterior probability that the system is in the warning state is updated in real-time using Bayesian theorem. An explicit expression for the distribution of the RUL is derived. Predictions are made using an accelerated life test dataset for the gear shaft under varying load. A comparison is performed with the prediction methods, including the hidden Markov model (HMM), the mixture of Gaussians hidden Markov model (MoG-HMM), and the HSMM based on the Erlang distribution. The results demonstrate that the hidden semi-Markov degradation modeling approach, when considering the hyper-Erlang distribution, not only effectively reflects the degradation state of the gear shaft, but also facilitates high-precision prediction of the RUL of IIoT equipment.