A generalized hidden Markov model and its applications in recognition of cutting states

Abstract

In the traditional hidden Markov model (HMM) for statistical learning and classification, aleatory uncertainty because of randomness and epistemic uncertainty that is due to the lack of knowledge are not differentiated. In this paper, a generalized hidden Markov model (GHMM) in the context of generalized interval probability theory is proposed. The parameters of GHMM are in the form of generalized interval probability, which provides a concise representation for the two kinds of uncertainty simultaneously. The generalized versions of the forward-backward, Viterbi, and Baum-Welch algorithms in GHMM are developed. The proposed algorithms take advantage of the algebraic property in the generalized interval probability. These algorithms provide an efficient approach to train the GHMM. The trained GHMM is used for state recognition with the criterion of maximum log-likelihood. A case study on recognizing the cutting states in manufacturing processes is provided to demonstrate the application of GHMM. The interval forms of the cutting signal are considered as the inputting of GHMM. The cutting states are recognized based on the learning algorithm of GHMM. With the two uncertainty components quantified, the reliability of GHMM in state recognition is superior to that of HMM.