Applying wavelet-based hidden Markov tree to enhancing performance of process monitoring

In this paper, wavelet-based hidden Markov tree (HMT) models is proposed to enhance the conventional time-scale only statistical process model (SPC) for process monitoring. HMT in the wavelet domain cannot only analyze the measurements at multiple scales in time and frequency but also capture the statistical behavior of real world measurements in these different scales. The former can provide better noise reduction and less signal distortion than conventional filtering methods; the latter can extract the statistical characteristics of the unmeasured disturbances, like the clustering and persistence of the practical data which are not considered in SPC. Based on HMT, a univariate and a multivariate SPC are respectively developed. Initially, the SPC model is trained in the wavelet domain using the data obtained from the normal operation regions. The model parameters are trained by the expectation maximization algorithm. After extracting the past operating information, the proposed method, like the philosophy of the traditional SPC, can generate simple monitoring charts, easily tracking and monitoring the occurrence of observable upsets. The comparisons of the existing SPC methods that explain the advantages of the properties of the newly proposed method are shown. They indicate that the proposed method can lead to more accurate results. Data from the monitoring practice in the industrial problems are presented to help readers delve into the matter.

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