A generalized interval probability-based optimization method for training generalized hidden Markov model

Recently a generalized hidden Markov model (GHMM) was proposed for solving the information fusion problems under aleatory and epistemic uncertainties in engineering application. In GHMM, aleatory uncertainty is captured by the probability measure whereas epistemic uncertainty is modeled by generalized interval. In this paper, the problem of how to train the GHMM with a small amount of observation data is studied. An optimization method as a generalization of the Baum-Welch algorithm is proposed. With a generalized Baum-Welch's auxiliary function and the Jensen inequality based on generalized interval, the GHMM parameters are estimated and updated by the lower and upper bounds of observation sequences. A set of training and re-estimation formulas are developed. With a multiple observation expectation maximization (EM) algorithm, the training method guarantees the local maxima of the lower and the upper bounds. Two case studies of recognizing the tool wear and cutting states in manufacturing is described to demonstrate the proposed method. The results show that the optimized GHMM has a good recognition performance.

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