Subspace decomposition and critical phase selection based cumulative quality analysis for multiphase batch processes

- Sequential and definite quality-relevant phases are obtained.
- The type of quality index is prejudged to determine whether it is of cumulative type.
- Subspace of variation is decomposed to explain cumulative quality effect.
- Critical phases are identified for inter-phase cumulative quality analysis.

Quality analysis and prediction have been of great significance to ensure consistent and high product quality for chemical engineering processes. However, previous methods have rarely analyzed the cumulative quality effect which is of typical nature for batch processes. That is, with time development, the process variation will determine the final product quality in a cumulative manner. Besides, they cannot get an early sense of the quality nature. In this paper, a quantitative index is defined which can check ahead of time whether the product quality result from accumulation or the addition of successive process variations and cumulative quality effect will be addressed for quality analysis and prediction of batch processes. Several crucial issues will be solved to explore the cumulative quality effect. First, a quality-relevant sequential phase partition method is proposed to separate multiple phases from batch processes by using fast search and find of density peaks clustering (FSFDP) algorithm. Second, after phase partition, a phase-wise cumulative quality analysis method is proposed based on subspace decomposition which can explore the non-repetitive quality-relevant information (NRQRI) from the process variation at each time within each phase. NRQRI refers to the quality-relevant process variations at each time that are orthogonal to those of previous time and thus represents complementary quality information which is the key index to cumulatively explain quality variations time-wise. Third, process-wise cumulative quality analysis is conducted where a critical phase selection strategy is developed to identify critical-to-cumulative-quality phases and quality predictions from critical phases are integrated to exclude influences of uncritical phases. By the two-level cumulative quality analysis (i.e., phase-wise and process-wise), it is feasible to judge whether the quality has the cumulative effect in advance and thus proper quality prediction model can be developed by identifying critical-to-cumulative-quality phases. The feasibility and performance of the proposed algorithm are illustrated by a typical chemical engineering process, injection molding.