We describe a statistical pattern-recognition approach to machine monitoring. The approach comprises a classification scheme using Gaussian mixture models (GMMs) that classifies features based on a time-frequency representation using the wavelet transform. The GMM trained with the EM algorithm has comparable flexibility with the multilayered perceptron in modeling nonstationary, multimodal machine signal characteristics, but has significantly fewer parameters to train. Also, using an example set of machine signals we show that the wavelet transform is particularly appropriate for capturing the time-frequency properties of transients of varying time constants and harmonic content. The benefits of both the GMM classifier and wavelet representation are manifested in superior classification performance and much lower computational complexity, as well as better robustness to finite-sample effects.>

An overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing. A natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image. In particular, it is shown how the wavelet transform directly suggests such a modeling paradigm. This perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time-like variable. The investigation of models on homogeneous trees is emphasized. The framework examined here allows for consideration, in a very natural way, of the fusion of data from sensors with differing resolutions. Also, thanks to the fact that wavelet transforms do an excellent job of 'compressing' large classes of covariance kernels, it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect.>

The authors introduce a class of multiscale stochastic processes which are Markov in scale and which are characterized by dynamic state models evolving in scale. The models for these processes are motivated by the theory of multiscale representations and the wavelet transform. The authors formulate an optimal estimation problem based on these models, which has potential applications to sensor fusion problems where there exist data from sensors of differing resolution, and provide an efficient algorithm based on the wavelet transform. They give examples applying these models to first-order Gauss-Markov processes.>