Quality-Relevant Monitoring of Batch Processes Based on Stochastic Programming with Multiple Output Modes

To implement the quality-relevant monitoring scheme for batch processes with multiple output modes, this paper presents a novel methodology based on stochastic programming. Bringing together tools from stochastic programming and ensemble learning, the developed methodology focuses on the robust monitoring of process quality-relevant variables by taking the stochastic nature of batch process parameters explicitly into consideration. To handle the problem of missing data and lack of historical batch data, a bagging approach is introduced to generate individual quality-relevant sub-datasets, which are used to construct the corresponding monitoring sub-models. For each model, stochastic programming is used to construct an optimal quality trajectory, which is regarded as the reference for online quality monitoring. Then, for each sub-model, a corresponding control limit is obtained by computing historical residuals between the actual output and the optimal trajectory. For online monitoring, the current sample is examined by all sub-models, and whether the monitoring statistic exceeds the control limits is recorded for further analysis. The final step is ensemble learning via Bayesian fusion strategy, which is under the probabilistic framework. The implementation and effectiveness of the developed methodology are demonstrated through two case studies, including a numerical example, and a simulated fed-batch penicillin fermentation process.