Multirate Coupled Hidden Markov Models and Their Application to Machining Tool-Wear Classification

This paper introduces multirate coupled hidden Markov models (multirate HMMs, in short) for multiscale modeling of nonstationary processes, extending traditional HMMs from single to multiple time scales with hierarchical representations of the process state and observations. Scales in the multirate HMMs are organized in a coarse-to-fine manner with Markov conditional independence assumptions within and across scales, allowing for a parsimonious representation of both short- and long-term context and temporal dynamics. Efficient inference and parameter estimation algorithms for the multirate HMMs are given, which are similar to the analogous algorithms for HMMs. The model is applied to the classification of tool wear in titanium milling, for which acoustic emissions exhibit multiscale dynamics and long-range dependence. Experimental results show that the multirate extension outperforms HMMs in terms of both wear prediction accuracy and confidence estimation