Soft Sensor Based on Causal Secondary Variable Selection for Multimode Batch Processes

Batch processes play an important role in manufacturing, and their precise quality prediction is essential. Data-driven soft sensors, which estimate hard-to-measure variables using easily measurable process variables, are used for key variables prediction in batch processes. However, variations in raw materials and operating conditions lead to distribution differences in data across batches. These differences in data distribution can significantly impact the predictive accuracy of data-driven soft sensor models. To address this issue, a novel soft sensor based on causal secondary variable selection for multimode batch processes is proposed. First, a method for calculating transfer entropy (TE), called fuzzy dispersion TE (FDTE), is proposed for causal inference between variables. It uses fuzzy dispersion to symbolize the original time series, which can reduce computational burden and improve causal inference accuracy. Second, the batch process is partitioned into multiple modes by the sequence-constrained fuzzy c-means (SCFCM), and then FDTE is calculated to determine causal relationships between variables and secondary variables for each mode are selected. Based on these, a relevance vector machine (RVM)-based soft sensor model is established for each mode. The effectiveness of the proposed soft sensor based on causal secondary variable selection is verified through numerical simulations, the penicillin fermentation process, and the chlortetracycline fermentation process.