A Self-Growing Hidden Markov Tree for Batch Process Monitoring

A growing wavelet-based hidden Markov tree (gHMT) for batch process monitoring is proposed. It starts with a small size wavelet-based hidden Markov tree (HMT) and successively increments the size of the wavelet tree until the desirable size is reached. This modeling scheme in the wavelet domain can not only analyze the measurements at multiple scales in time and frequency but also capture the statistical behavior of the real-world measurements at different scales. Unlike HMT with the structure covering the whole frequency ranges, gHMT has the ability to explicitly control over the complexity of the HMT architecture, retaining the smallest possible size and the accuracy of the model without introducing additional computational load. After the gHMT model extracts the past operating information, it can be used to generate simple monitoring charts, easily tracking and monitoring the occurrence of observable upsets for operating batch processes.