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

• A generalized Jensen inequality and a generalized Baum–Welch′s auxiliary function are proposed.
• A generalized Baum–Welch algorithm is used for training generalized hidden Markov model.
• The performance of generalized Baum–Welch algorithm is validated by a case study of cutting processing.
• The tool wear and cutting states are recognized by 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.

The need to distinguish aleatory and epistemic uncertainty has been widely recognized in engineering applications. A generalized hidden Markov model (GHMM), as a generalization of HMM in the context of generalized interval probability theory, is proposed in this paper. In GHMM, aleatory uncertainty is represented as probability; interval is used to capture epistemic uncertainty. The optimization of GHMM parameters is a crucial problem for model calibration. A generalized interval probability-based optimization method is used for training generalized hidden Markov model. The proposed optimization method takes advantage of the good algebraic property using the generalized interval probability, which provides an efficient approach to train the GHMM. The experimental evaluation of the proposed GHMM method is provided by two cases of tool state and cutting state recognition in manufacturing processes.Figure optionsDownload as PowerPoint slide