• multiphase batch processes;
  • partial similarity;
  • subspace separation;
  • common patterns;
  • phase representability;
  • cumulative manner


Phase-based subpartial least squares (subPLS) modeling algorithm has been used for online quality prediction in multiphase batches. It strictly assumes that the XY correlations are identical within the same phase so that they can be defined by a uniform regression model. However, the accuracy of this precondition has not been theoretically checked when put into practical application. Actually it does not always agree well with the real case and may have to be rejected for some practical processes. In the present work, it corrects the “absolute similarity” of subPLS modeling by a more general recognition that only one part of the underlying correlations are time-wise common within the same phase while the other part are time-specific, which is referred to as “partial similarity” here. Correspondingly, a two-step phase division strategy is developed, which separates the original phase measurement space into two different parts, the common subspace and uncommon subspace. It is only in the common subspace where the underlying XY correlations are similar, a phase-unified regression model can be extracted for online quality prediction. Moreover, based on the subspace separation, offline quality analyses are conducted in both subspaces to explore their respective cumulative manner and contribution in quality prediction. The strength and efficiency of the proposed algorithm are verified on a typical multiphase batch process, injection molding. © 2010 American Institute of Chemical Engineers AIChE J, 2011