Process trends analysis via wavelet-domain hidden Markov models

Wavelet-domain hidden Markov models (HMM) is a powerful tool for statistical modeling and processing of wavelet coefficients. It captures the dependence of the wavelet coefficients and the scale coefficients of a measured process variable respectively. A novel method using the model for on-line detection of process trend is introduced in this paper where all scale coefficients and several selected wavelet coefficients are taken into account. This paper presents the way to select the wavelet coefficients and to build HMMs with the selected wavelet coefficients and scale coefficients. For the selected wavelet coefficients, the method can reduce the ambiguities and the delay of classification with a little computational effort. We focus on the classification and detection of the process with multiple measured variables. A simulation study illustrates the improvement on the method that only uses the scale coefficients.