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

[1]  Les E. Atlas,et al.  Hidden Markov models for monitoring machining tool-wear , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[2]  Hervé Bourlard,et al.  Using multiple time scales in a multi-stream speech recognition system , 1997, EUROSPEECH.

[3]  A. Willsky.  Multiresolution Markov models for signal and image processing , 2002, Proc. IEEE.

[4]  Mari Ostendorf,et al.  Parameter reduction schemes for loosely coupled HMMs , 2003, Comput. Speech Lang..

[5]  K. C. Chou,et al.  Multiscale recursive estimation, data fusion, and regularization , 1994, IEEE Trans. Autom. Control..

[6]  W. Clem Karl,et al.  Multiscale representations of Markov random fields , 1993, IEEE Trans. Signal Process..

[7]  Stephen Cox,et al.  Some statistical issues in the comparison of speech recognition algorithms , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[8]  Biing-Hwang Juang,et al.  Discriminative learning for minimum error classification [pattern recognition] , 1992, IEEE Trans. Signal Process..

[9]  Stuart J. Russell,et al.  Dynamic bayesian networks: representation, inference and learning , 2002 .

[10]  Yoram Singer,et al.  The Hierarchical Hidden Markov Model: Analysis and Applications , 1998, Machine Learning.

[11]  Paul William Prickett,et al.  An overview of approaches to end milling tool monitoring , 1999 .

[12]  Wojciech Pieczynski,et al.  Pairwise Markov Chains , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Alex Pentland,et al.  Coupled hidden Markov models for complex action recognition , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[14]  Robert D. Nowak,et al.  Wavelet-based statistical signal processing using hidden Markov models , 1998, IEEE Trans. Signal Process..

[15]  Mari Ostendorf,et al.  Multi-rate hidden Markov models and their application to machining tool-wear classification , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[16]  W. Pieczynski.  On Triplet Markov Chains , 2005 .

[17]  Kenneth A. Loparo,et al.  Tool wear condition monitoring in drilling operations using hidden Markov models (HMMs) , 2001 .

[18]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[19]  Li Dan,et al.  Tool wear and failure monitoring techniques for turning—A review , 1990 .

[20]  Z. M. Wang,et al.  Titanium alloys and their machinability—a review , 1997 .

[21]  David Haussler,et al.  Exploiting Generative Models in Discriminative Classifiers , 1998, NIPS.

[22]  Hervé Bourlard,et al.  A mew ASR approach based on independent processing and recombination of partial frequency bands , 1996, Proceeding of Fourth International Conference on Spoken Language Processing. ICSLP '96.

[23]  Lane M. D. Owsley,et al.  Self-organizing feature maps and hidden Markov models for machine-tool monitoring , 1997, IEEE Trans. Signal Process..

[24]  Steve Young,et al.  The HTK book , 1995 .

[25]  Les E. Atlas,et al.  Joint use of dynamical classifiers and ambiguity plane features , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[26]  Michael I. Jordan.  Graphical Models , 2003 .

[27]  Erkki Jantunen,et al.  A summary of methods applied to tool condition monitoring in drilling , 2002 .

[28]  Bernhard Sick,et al.  ON-LINE AND INDIRECT TOOL WEAR MONITORING IN TURNING WITH ARTIFICIAL NEURAL NETWORKS: A REVIEW OF MORE THAN A DECADE OF RESEARCH , 2002 .

[29]  Wojciech Pieczynski,et al.  Multiresolution hidden Markov chain model and unsupervised image segmentation , 2000, 4th IEEE Southwest Symposium on Image Analysis and Interpretation.

[30]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[31]  Larry P. Heck,et al.  A multiscale stochastic modeling approach to the monitoring of mechanical systems , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[32]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[33]  Gary D. Bernard,et al.  Multi-rate Hidden Markov Models for Monitoring of Machining Tool Wear , 2003 .

[34]  Ross D. Shachter.  Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams) , 1998, UAI.

[35]  DAVID G. KENDALL,et al.  Introduction to Mathematical Statistics , 1947, Nature.

[36]  Juergen Luettin,et al.  Asynchronous stream modeling for large vocabulary audio-visual speech recognition , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[37]  Andrew McCallum,et al.  Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data , 2001, ICML.

[38]  Robert M. Gray,et al.  Multiresolution image classification by hierarchical modeling with two-dimensional hidden Markov models , 2000, IEEE Trans. Inf. Theory.

[39]  D. E. Dimla,et al.  Sensor signals for tool-wear monitoring in metal cutting operations—a review of methods , 2000 .

[40]  S. Lauritzen,et al.  The TM algorithm for maximising a conditional likelihood function , 2001 .

[41]  Michael I. Jordan,et al.  Mixed Memory Markov Models: Decomposing Complex Stochastic Processes as Mixtures of Simpler Ones , 1999, Machine Learning.

[42]  S. Katagiri,et al.  Discriminative Learning for Minimum Error Classification , 2009 .

[43]  Herbert Gish,et al.  Evaluation of word confidence for speech recognition systems , 1999, Comput. Speech Lang..

[44]  Randall K Fish.  Dynamic models of machining vibrations, designed for classification of tool wear , 2001 .

[45]  Neri Merhav,et al.  Hidden Markov processes , 2002, IEEE Trans. Inf. Theory.

[46]  Michael I. Jordan,et al.  Factorial Hidden Markov Models , 1995, Machine Learning.

[47]  David J. Spiegelhalter,et al.  Probabilistic Networks and Expert Systems , 1999, Information Science and Statistics.

[48]  Larry P. Heck,et al.  Mechanical system monitoring using hidden Markov models , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[49]  Gary D. Bernard,et al.  Multilevel Classification of Milling Tool Wear with Confidence Estimation , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[50]  Elijah Kannatey-Asibu,et al.  Hidden Markov model-based tool wear monitoring in turning , 2002 .

[51]  Michèle Basseville,et al.  Modeling and estimation of multiresolution stochastic processes , 1992, IEEE Trans. Inf. Theory.

[52]  Yoshua Bengio,et al.  Diffusion of Context and Credit Information in Markovian Models , 1995, J. Artif. Intell. Res..

[53]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .