An adjoined multi-model approach for monitoring batch and transient operations

Most process monitoring techniques are suitable for steady-state operation but inadequate for these multiphase transient operations with complex dynamics. Specifically, statistical approaches do not function adequately since the basic assumptions that the statistics are developed upon – normal distribution, stationarity – are violated. Consequently, they become prone to false positives and false negatives. Multi-model approaches overcome this by using several local models; however these perform inadequately in the interregnum between models. In this paper, we propose a method, called adjoined principal component analysis that overcomes this. The key characteristic of AdPCA is that the different models are not disjoint; rather they overlap at the edges of their regime and thus ensure smooth evolution of the monitoring. A fuzzy c-means algorithm is used to identify suitable regimes for the constituent models. The applications of the proposed methodology to a distillation unit startup and a fed-batch penicillin cultivation process illustrate the method's efficacy.