Development of Soft Sensor Based on Sequential Kernel Fuzzy Partitioning and Just-in-Time Relevance Vector Machine for Multiphase Batch Processes

Batch processes are important manufacturing approaches widely used in modern industry. During the manufacturing process, quality prediction is essential. Data-driven-based soft sensors have widely used for quality prediction because of the advantages of simple application and high flexibility. However, they do not perform well due to the characteristics of dynamic, nonlinear, and multiphases in batch processes. To address these issues, a soft sensor based on sequential kernel fuzzy partitioning (SKFP) and just-in-time relevance vector machine (JRVM), named SKFP-JRVM, is proposed in this work. First, an SKFP algorithm is proposed to divide batches into phases. In the SKFP algorithm, the inner and the sequential membership are constructed and compared to obtain highly accurate phase partitioning results. Meanwhile, a partitioning evaluation index is applied to automatically determine the optimal number of phases. Moreover, a soft sensor model based on the JRVM is built for each phase. The JRVM model not only considers the modeling samples of adjacent phases but also effectively addresses the problem of soft sensor modeling of process data with highly nonlinear and dynamic characteristics. The effectiveness of the SKFP-JRVM method is demonstrated on a numerical simulation and a penicillin fermentation process.