Process trend analysis via wavelet domain hidden Markov models

This dissertation establishes a framework for process data management that can include signal de-noising, data compression and trend analysis tasks. This work focuses only on the signal de-noising and the trend analysis. Wavelet transform is used as a tool to break the process data into different frequency components. In signal de-noising, wavelet coefficients are considered as the joint effect of the signal and the noise, and in process monitoring, each process event is assumed to have different frequency contributions to the process data. Through the data representation in the wavelet domain, data from different sources are localized at specific location on the time-frequency plane. Then a tree structure hidden Markov model is used to characterize the statistical relationships among coefficients. It successfully removes the noise from the signal and preserves the signal. For process trend analysis, it correctly distinguishes process trends among different process operating conditions based on a suitable number of measurements. A case study using simulation data from a pH neutralization process is used to demonstrate the trend analysis result for the single variable case and a case study using simulation data from a CSTR is used to show the trend analysis result based on multiple measurements.